[SYSTEMDS-3948] Row-wise Sparsity Estimator

src/main/java/org/apache/sysds/hops/estim/EstimatorRowWise.java

@@ -0,0 +1,325 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you 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 org.apache.sysds.hops.estim;
+
+import org.apache.commons.lang3.ArrayUtils;
+import org.apache.commons.lang3.NotImplementedException;
+import org.apache.sysds.hops.OptimizerUtils;
+import org.apache.sysds.runtime.data.SparseRow;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+import org.apache.sysds.runtime.meta.DataCharacteristics;
+import org.apache.sysds.runtime.meta.MatrixCharacteristics;
+
+import java.util.stream.DoubleStream;
+import java.util.stream.IntStream;
+
+/**
+ * This estimator implements an approach based on row-wise sparsity estimation,
+ * introduced in
+ * Lin, Chunxu, Wensheng Luo, Yixiang Fang, Chenhao Ma, Xilin Liu and Yuchi Ma:
+ * On Efficient Large Sparse Matrix Chain Multiplication.
+ * Proceedings of the ACM on Management of Data 2 (2024): 1 - 27.
+ */
+public class EstimatorRowWise extends SparsityEstimator {
+	@Override
+	public DataCharacteristics estim(MMNode root) {
+		estimInternChain(root);
+		double sparsity = DoubleStream.of((double[])root.getSynopsis()).average().orElse(0);
+
+		DataCharacteristics outputCharacteristics = deriveOutputCharacteristics(root, sparsity);
+		return root.setDataCharacteristics(outputCharacteristics);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, MatrixBlock m2) {
+		return estim(m1, m2, OpCode.MM);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, MatrixBlock m2, OpCode op) {
+		if( isExactMetadataOp(op, m1.getNumColumns()) ) {
+			return estimExactMetaData(m1.getDataCharacteristics(),
+				m2.getDataCharacteristics(), op).getSparsity();
+		}
+
+		double[] rsOut = estimIntern(m1, m2, op);
+		return DoubleStream.of(rsOut).average().orElse(0);
+	}
+
+	@Override
+	public double estim(MatrixBlock m1, OpCode op) {
+		if( isExactMetadataOp(op, m1.getNumColumns()) )
+			return estimExactMetaData(m1.getDataCharacteristics(), null, op).getSparsity();
+
+		double[] rsOut = estimIntern(m1, op);
+		return DoubleStream.of(rsOut).average().orElse(0);
+	}
+
+	private void estimInternChain(MMNode node) {
+		estimInternChain(node, null, null);
+	}
+
+	private void estimInternChain(MMNode node, double[] rsRightNeighbor, OpCode opRightNeighbor) {
+		double[] rsOut;
+		if(node.isLeaf()) {
+			MatrixBlock mb = node.getData();
+			if(rsRightNeighbor != null)
+				rsOut = estimIntern(mb, rsRightNeighbor, opRightNeighbor);
+			else
+				rsOut = getRowWiseSparsityVector(mb);
+		}
+		else {
+			switch(node.getOp()) {
+				case MM:
+					estimInternChain(node.getRight(), rsRightNeighbor, opRightNeighbor);
+					estimInternChain(node.getLeft(), (double[])(node.getRight().getSynopsis()), node.getOp());
+					rsOut = (double[])node.getLeft().getSynopsis();
+					break;
+				case CBIND:
+					/** NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into a cbind operation when having only row sparsity vectors
+					 */
+					estimInternChain(node.getLeft());
+					estimInternChain(node.getRight());
+					double[] rsCBind = estimInternCBind((double[])(node.getLeft().getSynopsis()), (double[])(node.getRight().getSynopsis()));
+					if(rsRightNeighbor != null) {
+						rsOut = (double[])estimInternMMFallback(rsCBind, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = (double[])rsCBind;
+					break;
+				case RBIND:
+					/** NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an rbind operation when having only row sparsity vectors
+					 */
+					estimInternChain(node.getLeft());
+					estimInternChain(node.getRight());
+					double[] rsRBind = estimInternRBind((double[])(node.getLeft().getSynopsis()), (double[])(node.getRight().getSynopsis()));
+					if(rsRightNeighbor != null) {
+						rsOut = (double[])estimInternMMFallback(rsRBind, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = (double[])rsRBind;
+					break;
+				case PLUS:
+					/** NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an element-wise operation when having only row sparsity vectors
+					 */
+					estimInternChain(node.getLeft());
+					estimInternChain(node.getRight());
+					double[] rsPlus = estimInternPlus((double[])(node.getLeft().getSynopsis()), (double[])(node.getRight().getSynopsis()));
+					if(rsRightNeighbor != null) {
+						rsOut = (double[])estimInternMMFallback(rsPlus, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = (double[])rsPlus;
+					break;
+				case MULT:
+					/** NOTE: considering the current node as new DAG for estimation (cut), since the row sparsity of
+					 * the right neighbor cannot be aggregated into an element-wise operation when having only row sparsity vectors
+					 */
+					estimInternChain(node.getLeft());
+					estimInternChain(node.getRight());
+					double[] rsMult = estimInternMult((double[])(node.getLeft().getSynopsis()), (double[])(node.getRight().getSynopsis()));
+					if(rsRightNeighbor != null) {
+						rsOut = (double[])estimInternMMFallback(rsMult, rsRightNeighbor);
+						if(opRightNeighbor != OpCode.MM)
+							throw new NotImplementedException("Fallback sparsity estimation has only been " +
+								"considered for MM operation w/ right neighbor yet.");
+					}
+					else
+						rsOut = (double[])rsMult;
+					break;
+				default:
+					throw new NotImplementedException("Chain estimation for operator " + node.getOp().toString() +
+					" is not supported yet.");
+			}
+		}
+		node.setSynopsis(rsOut);
+		node.setDataCharacteristics(deriveOutputCharacteristics(node, DoubleStream.of(rsOut).average().orElse(0)));
+		return;
+	}
+
+	private double[] estimIntern(MatrixBlock m1, MatrixBlock m2, OpCode op) {
+		double[] rsM2 = getRowWiseSparsityVector(m2);
+		return estimIntern(m1, rsM2, op);
+	}
+
+	private double[] estimIntern(MatrixBlock m1, double[] rsM2, OpCode op) {
+		switch(op) {
+			case MM:
+				return estimInternMM(m1, rsM2);
+			case CBIND:
+				return estimInternCBind(getRowWiseSparsityVector(m1), rsM2);
+			case RBIND:
+				return estimInternRBind(getRowWiseSparsityVector(m1), rsM2);
+			case PLUS:
+				return estimInternPlus(getRowWiseSparsityVector(m1), rsM2);
+			case MULT:
+				return estimInternMult(getRowWiseSparsityVector(m1), rsM2);
+			default:
+				throw new NotImplementedException("Sparsity estimation for operation " + op.toString() + " not supported yet.");
+		}
+	}
+
+	private double[] estimIntern(MatrixBlock mb, OpCode op) {
+		switch(op) {
+			case DIAG:
+				return estimInternDiag(mb);
+			default:
+				throw new NotImplementedException("Sparsity estimation for operation " + op.toString() + " not supported yet.");
+		}
+	}
+
+	// Corresponds to Algorithm 1 in the publication
+	private double[] estimInternMM(MatrixBlock m1, double[] rsM2) {
+		double[] rsOut = IntStream.range(0, m1.getNumRows()).mapToDouble(
+			r -> (double) 1 - IntStream.of(getNonZeroColumnIndices(m1, r)).mapToDouble(
+					c -> (double) 1 - rsM2[c]
+				).reduce((double) 1, (currentVal, val) -> currentVal * val))
+			.toArray();
+		return rsOut;
+	}
+
+	// NOTE: this is the best estimation possible when we only have the two row sparsity vectors
+	private double[] estimInternMMFallback(double[] rsM1, double[] rsM2) {
+		// NOTE: Considering the average would probably not be far off while saving computing time
+		// double avgRsM2 = DoubleStream.of(rsM2).average().orElse(0);
+		// double[] rsOut = DoubleStream.of(rsM1).map(
+		// 	rsM1I -> (double) 1 - Math.pow((double) 1 - (rsM1I * avgRsM2), rsM2.length)).toArray();
+		double[] rsOut = DoubleStream.of(rsM1).map(
+			rsM1I -> (double) 1 - DoubleStream.of(rsM2).reduce((double) 1,
+				(currentVal, rsM2J) -> currentVal * ((double) 1 - (rsM1I * rsM2J)))).toArray();
+		return rsOut;
+	}
+
+	private double[] estimInternCBind(double[] rsM1, double[] rsM2) {
+		// FIXME: this assumes that the number of columns is equivalent for both inputs
+		return IntStream.range(0, rsM1.length).mapToDouble(
+			idx -> (rsM1[idx] + rsM2[idx]) / (double) 2).toArray();
+	}
+
+	private double[] estimInternRBind(double[] rsM1, double[] rsM2) {
+		return ArrayUtils.addAll(rsM1, rsM2);
+	}
+
+	private double[] estimInternPlus(double[] rsM1, double[] rsM2) {
+		// row-wise average case estimates
+		// rsM1 + rsM2 - (rsM1 * rsM2)
+		return IntStream.range(0, rsM1.length).mapToDouble(
+			idx -> rsM1[idx] + rsM2[idx] - (rsM1[idx] * rsM2[idx])).toArray();
+	}
+
+	private double[] estimInternMult(double[] rsM1, double[] rsM2) {
+		// row-wise average case estimates
+		// rsM1 * rsM2
+		return IntStream.range(0, rsM1.length).mapToDouble(
+			idx -> rsM1[idx] * rsM2[idx]).toArray();
+	}
+
+	private double[] estimInternDiag(MatrixBlock mb) {
+		double[] rsOut = IntStream.range(0, mb.getNumRows()).mapToDouble(
+				rIdx -> (mb.get(rIdx, rIdx) == 0) ? 0d : 1d)
+			.toArray();
+		return rsOut;
+	}
+
+	private double[] getRowWiseSparsityVector(MatrixBlock mb) {
+		int numRows = mb.getNumRows();
+		if(mb.isInSparseFormat()) {
+			double[] rsArray = new double[numRows];
+			for(int counter = 0; counter < numRows; counter++) {
+				SparseRow sparseRow = mb.getSparseBlock().get(counter);
+				rsArray[counter] = (sparseRow == null) ? 0 : (double) sparseRow.size() / mb.getNumColumns();
+			}
+			return rsArray;
+		}
+		else {
+			return IntStream.range(0, numRows).mapToDouble(
+					rIdx -> (double) mb.getDenseBlock().countNonZeros(rIdx) / mb.getNumColumns())
+				.toArray();
+		}
+	}
+
+	private int[] getNonZeroColumnIndices(MatrixBlock mb, final int rIdx) {
+		int[] nonZeroCols;
+		if(mb.isInSparseFormat()) {
+			SparseRow sparseRow = mb.getSparseBlock().get(rIdx);
+			nonZeroCols = (sparseRow == null) ? new int[0] : sparseRow.indexes();
+		}
+		else {
+			nonZeroCols = IntStream.range(0, mb.getNumColumns())
+				.filter(cIdx -> mb.get(rIdx, cIdx) != 0).toArray();
+		}
+		return nonZeroCols;
+	}
+
+	public static DataCharacteristics deriveOutputCharacteristics(MMNode node, double spOut) {
+		if(node.isLeaf() ||
+			(node.getDataCharacteristics() != null && node.getDataCharacteristics().getNonZeros() != -1)) {
+			return node.getDataCharacteristics();
+		}
+
+		MMNode nodeLeft = node.getLeft();
+		MMNode nodeRight = node.getRight();
+		int leftNRow = nodeLeft.getRows();
+		int leftNCol = nodeLeft.getCols();
+		int rightNRow = nodeRight.getRows();
+		int rightNCol = nodeRight.getCols();
+		switch(node.getOp()) {
+			case MM:
+				return new MatrixCharacteristics(leftNRow, rightNCol,
+					OptimizerUtils.getNnz(leftNRow, rightNCol, spOut));
+			case MULT:
+			case PLUS:
+			case NEQZERO:
+			case EQZERO:
+				return new MatrixCharacteristics(leftNRow, leftNCol,
+					OptimizerUtils.getNnz(leftNRow, leftNCol, spOut));
+			case RBIND:
+				return new MatrixCharacteristics(leftNRow+rightNRow, leftNCol,
+					OptimizerUtils.getNnz(leftNRow+rightNRow, leftNCol, spOut));
+			case CBIND:
+				return new MatrixCharacteristics(leftNRow, leftNCol+rightNCol,
+					OptimizerUtils.getNnz(leftNRow, leftNCol+rightNCol, spOut));
+			case DIAG:
+				int ncol = (leftNCol == 1) ? leftNRow : 1;
+				return new MatrixCharacteristics(leftNRow, ncol,
+					OptimizerUtils.getNnz(leftNRow, ncol, spOut));
+			case TRANS:
+				return new MatrixCharacteristics(leftNCol, leftNRow,
+					OptimizerUtils.getNnz(leftNCol, leftNRow, spOut));
+			case RESHAPE:
+				throw new NotImplementedException("Characteristics derivation for " + node.getOp() +" has not been " +
+					"implemented yet, but could be implemented similar to EstimatorMatrixHistogram.java");
+			default:
+				throw new NotImplementedException();
+		}
+	}
+};