feat: add lapack/base/dorg2r

lib/node_modules/@stdlib/lapack/base/dorg2r/README.md

@@ -0,0 +1,254 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# dorg2r
+
+> LAPACK routine to generate an M-by-N real matrix Q with orthonormal columns.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dorg2r = require( '@stdlib/lapack/base/dorg2r' );
+```
+
+#### dorg2r( order, M, N, K, A, LDA, tau, work )
+
+Generates an M-by-N real matrix Q with orthonormal columns. The matrix Q is defined as the first N columns of a product of K elementary reflectors of order M. `Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var tau = new Float64Array( [ 0.0, 0.0 ] );
+var work = new Float64Array( 10 );
+
+dorg2r( 'column-major', 3, 2, 2, A, 3, tau, work );
+// A => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **M**: number of rows in matrix `A`.
+-   **N**: number of columns in matrix `A`.
+-   **K**: number of elementary reflectors whose product defines the matrix Q.
+-   **A**: input matrix (overwritten by Householder vectors from `dgeqrf`) stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **LDA**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
+-   **tau**: vector of K scalar factors of the elementary reflectors as a [`Float64Array`][mdn-float64array].
+-   **work**: workspace array as a [`Float64Array`][mdn-float64array].
+
+The function returns the input matrix `A` overwritten with the orthogonal matrix Q.
+
+#### dorg2r.ndarray( M, N, K, A, sa1, sa2, oa, tau, st, ot, work, sw, ow )
+
+Generates an M-by-N real matrix Q with orthonormal columns using alternative indexing semantics. The matrix Q is defined as the first N columns of a product of K elementary reflectors of order M. `Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var tau = new Float64Array( [ 0.0, 0.0 ] );
+var work = new Float64Array( 10 );
+
+dorg2r.ndarray( 3, 2, 2, A, 1, 3, 0, tau, 1, 0, work, 1, 0 );
+// A => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **M**: number of rows in matrix `A`.
+-   **N**: number of columns in matrix `A`.
+-   **K**: number of elementary reflectors whose product defines the matrix Q.
+-   **A**: input matrix (overwritten by Householder vectors from `dgeqrf`) stored in linear memory as a [`Float64Array`][mdn-float64array].
+-   **sa1**: stride of the first dimension of `A`.
+-   **sa2**: stride of the second dimension of `A`.
+-   **oa**: index offset for `A`.
+-   **tau**: vector of K scalar factors of the elementary reflectors as a [`Float64Array`][mdn-float64array].
+-   **st**: stride length for `tau`.
+-   **ot**: index offset for `tau`.
+-   **work**: workspace array as a [`Float64Array`][mdn-float64array].
+-   **sw**: stride length for `work`.
+-   **ow**: index offset for `work`.
+
+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 A = new Float64Array( [ 0.0, 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
+var tau = new Float64Array( [ 0.0, 0.0, 0.0, 0.0 ] );
+var work = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+dorg2r.ndarray( 3, 2, 2, A, 1, 3, 3, tau, 1, 2, work, 1, 0 );
+// A => <Float64Array>[ 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notess
+
+-   The function overwrites the input matrix `A` with the orthogonal matrix `Q`.
+-   The matrix Q is generated from the Householder vectors and scalar factors returned by `dgeqrf`.
+-   `dorg2r()` corresponds to the [LAPACK][LAPACK] function [`dorg2r`][lapack-dorg2r].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var dorg2r = require( '@stdlib/lapack/base/dorg2r' );
+
+// Specify matrix meta data:
+var M = 4;
+var N = 3;
+var K = 2;
+
+// Create a matrix stored in linear memory:
+var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );
+console.log( 'Original matrix A containing Householder vectors:' );
+console.log( ndarray2array( A, [ M, N ], [ 1, M ], 0, 'column-major' ) );
+
+// Define scalar factors of the elementary reflectors:
+var tau = new Float64Array( [ 1.2, 0.8 ] );
+
+// Create workspace array:
+var work = new Float64Array( N );
+
+// Generate the orthogonal matrix Q:
+dorg2r( 'column-major', M, N, K, A, M, tau, work );
+console.log( 'Resulting orthogonal matrix Q:' );
+console.log( ndarray2array( A, [ M, N ], [ 1, M ], 0, 'column-major' ) );
+```
+
+</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 related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[lapack]: https://www.netlib.org/lapack/explore-html/
+
+[lapack-dorg2r]: https://netlib.org/lapack/explore-html/da/da2/group__ung2r_ga8877e79ab6e262ae7497f11d8534635c.html#ga8877e79ab6e262ae7497f11d8534635c
+
+[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/lapack/base/dorg2r/benchmark/benchmark.js

@@ -0,0 +1,123 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 pkg = require( './../package.json' ).name;
+var dorg2r = require( './../lib/dorg2r.js' );
+
+
+// VARIABLES //
+
+var LAYOUTS = [
+	'row-major',
+	'column-major'
+];
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {string} order - storage layout
+* @param {PositiveInteger} N - matrix order (N-by-N)
+* @returns {Function} benchmark function
+*/
+function createBenchmark( order, N ) {
+	var work;
+	var opts;
+	var tau;
+	var A;
+
+	opts = {
+		'dtype': 'float64'
+	};
+
+	// Random input matrix and auxiliary arrays:
+	A = uniform( N*N, -1.0, 1.0, opts );
+	tau = uniform( N, 0.1, 1.0, opts );
+	work = uniform( N, 0.0, 0.0, opts );
+
+	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 = dorg2r( order, N, N, 0, A, N, tau, work );
+			if ( isnan( z[ i%z.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( z[ i%z.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var min;
+	var max;
+	var ord;
+	var N;
+	var f;
+	var i;
+	var k;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( k = 0; k < LAYOUTS.length; k++ ) {
+		ord = LAYOUTS[ k ];
+		for ( i = min; i <= max; i++ ) {
+			N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
+			f = createBenchmark( ord, N );
+			bench( pkg+':order='+ord+',size='+(N*N), f );
+		}
+	}
+}
+
+main();