feat: add lapack/base/dgetf2

lib/node_modules/@stdlib/lapack/base/dgetf2/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+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.
+
+-->
+
+# dgetf2
+
+> Compute the LU factorization of a general $M$-by-$N$ matrix $A$ using partial pivoting with row interchanges.
+
+<section class="intro">
+
+The `dgetf2` routine computes an LU factorization of a general $M$-by-$N$ matrix $A$ using partial pivoting with row interchanges. The factorization has the form:
+
+```math
+A = P L U
+```
+
+where $P$ is a permutation matrix, $L$ is lower unit triangular (with ones on the diagonal), and $U$ is upper triangular.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dgetf2 = require( '@stdlib/lapack/base/dgetf2' );
+```
+
+#### dgetf2( order, M, N, A, LDA, IPIV )
+
+Computes an `LU` factorization of a general $M$-by-$N$ matrix $A$ using partial pivoting with row interchanges.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var A = new Float64Array( [ 2.0, 1.0, 4.0, 6.0 ] );
+var IPIV = new Int32Array( 2 );
+
+var info = dgetf2( 'row-major', 2, 2, A, 2, IPIV );
+// returns 0
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout (`'row-major'` or `'column-major'`).
+-   **M**: number of rows in matrix `A`.
+-   **N**: number of columns in matrix `A`.
+-   **A**: the input matrix $A$ as a [`Float64Array`][@stdlib/array/float64]. `A` is overwritten by the factors $L$ and $U$ from the factorization.
+-   **LDA**: stride of the first dimension of `A` (leading dimension of the matrix `A` if column-major, or stride between rows if row-major).
+-   **IPIV**: pivot indices as an [`Int32Array`][@stdlib/array/int32]. Pivot indices are 0-based. Should have at least $\min(M, N)$ elements.
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+// Initial arrays:
+var A0 = new Float64Array( [ 0.0, 2.0, 1.0, 4.0, 6.0 ] );
+var IPIV0 = new Int32Array( [ 0, 0, 0 ] );
+
+// Create offset views:
+var A1 = new Float64Array( A0.buffer, A0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var IPIV1 = new Int32Array( IPIV0.buffer, IPIV0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var info = dgetf2( 'row-major', 2, 2, A1, 2, IPIV1 );
+// returns 0
+```
+
+#### dgetf2.ndarray( M, N, A, sa1, sa2, oa, IPIV, si, oi )
+
+Computes an `LU` factorization of a general $M$-by-$N$ matrix $A$ using partial pivoting with row interchanges and alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var A = new Float64Array( [ 2.0, 1.0, 4.0, 6.0 ] );
+var IPIV = new Int32Array( 2 );
+
+var info = dgetf2.ndarray( 2, 2, A, 2, 1, 0, IPIV, 1, 0 );
+// returns 0
+```
+
+The function has the following additional parameters:
+
+-   **sa1**: row stride of `A`.
+-   **sa2**: column stride of `A`.
+-   **oa**: starting index of `A`.
+-   **si**: stride length for `IPIV`.
+-   **oi**: starting index of `IPIV`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var A = new Float64Array( [ 0.0, 2.0, 1.0, 4.0, 6.0 ] );
+var IPIV = new Int32Array( 3 );
+
+var info = dgetf2.ndarray( 2, 2, A, 2, 1, 1, IPIV, 1, 1 );
+// returns 0
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Both functions mutate the input arrays `A` and `IPIV`.
+
+-   Both functions return a status code indicating success or failure. The status code indicates the following conditions:
+
+    -   `0`: factorization was successful.
+    -   `>0`: $U(k, k)$ is exactly zero (where $k$ equals the status code value minus one when using zero-based indexing). The factorization has been completed, but the factor $U$ is exactly singular, and division by zero will occur if it is used to solve a system of equations.
+
+-   `dgetf2()` corresponds to the [LAPACK][LAPACK] routine [`dgetf2`][lapack-dgetf2].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var dgetf2 = require( '@stdlib/lapack/base/dgetf2' );
+
+var A = new Float64Array( [ 2.0, 1.0, 4.0, 6.0 ] );
+var IPIV = new Int32Array( 2 );
+
+var info = dgetf2( 'row-major', 2, 2, A, 2, IPIV );
+console.log( A );
+// => <Float64Array>[ 4.0, 6.0, 0.5, -2.0 ]
+
+console.log( IPIV );
+// => <Int32Array>[ 1, 1 ]
+
+console.log( info );
+// => 0
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+TODO
+```
+
+#### TODO
+
+TODO.
+
+```c
+TODO
+```
+
+TODO
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+TODO
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- Section for all links. -->
+
+<section class="links">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dgetf2]: https://www.netlib.org/lapack/explore-html/db/d4e/group__getf2_ga5f8f2998bad179dcee6a58d00599dba8.html#ga5f8f2998bad179dcee6a58d00599dba8
+
+[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
+
+[@stdlib/array/int32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/int32
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dgetf2/benchmark/benchmark.js

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2026 The Stdlib Authors.
+*
+* 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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var floor = require( '@stdlib/math/base/special/floor' );
+var Int32Array = require( '@stdlib/array/int32' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dgetf2 = require( './../lib/dgetf2.js' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} N - number of elements along each dimension
+* @returns {Function} benchmark function
+*/
+function createBenchmark( N ) {
+	var opts;
+	var IPIV;
+	var A;
+
+	opts = {
+		'dtype': 'float64'
+	};
+
+	A = uniform( N*N, -10.0, 10.0, opts );
+	IPIV = new Int32Array( N );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var z;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			z = dgetf2( 'column-major', N, N, A, N, IPIV );
+			if ( isnan( z ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var N;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+		f = createBenchmark( N );
+		bench( format( '%s:order=column-major,size=%d', pkg, N*N ), f );
+	}
+}
+
+main();