feat: add lapack/base/dlarfg

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

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+<!--
+
+@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.
+
+-->
+
+# dlarfg
+
+> LAPACK routine to generate a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dlarfg = require( '@stdlib/lapack/base/dlarfg' );
+```
+
+#### dlarfg( N, X, incx, out )
+
+Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 2.0, 3.0, 4.0 ] );
+var out = new Float64Array( [ 4.0, 0.0 ] );
+
+dlarfg( 4, X, 1, out );
+// X => <Float64Array>[ ~0.19, ~0.28, ~0.37 ]
+// out => <Float64Array>[ ~-6.7, ~1.6 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of rows/columns of the elementary reflector `H`.
+-   **X**: overwritten by the vector `V` on exit, expects `N - 1` indexed elements [`Float64Array`][mdn-float64array].
+-   **incx**: stride length of `X`.
+-   **out**: output [`Float64Array`][mdn-float64array], the first element of `out` represents alpha and the second element of `out` represents `tau`.
+
+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' );
+
+// Initial arrays...
+var X0 = new Float64Array( [ 0.0, 2.0, 3.0, 4.0 ] );
+var out0 = new Float64Array( [ 0.0, 4.0, 0.0 ] );
+
+// Create offset views...
+var X1 = new Float64Array( X0.buffer, X0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+dlarfg( 4, X1, 1, out1 );
+// X0 => <Float64Array>[ 0.0, ~0.19, ~0.28, ~0.37 ]
+// out0 => <Float64Array>[ 0.0, ~6.7, ~1.6 ]
+```
+
+#### dlarfg.ndarray( N, X, strideX, offsetX, out, strideOut, offsetOut )
+
+Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X` using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 2.0, 3.0, 4.0 ] );
+var out = new Float64Array( [ 4.0, 0.0 ] );
+
+dlarfg.ndarray( 4, X, 1, 0, out, 1, 0 );
+// X => <Float64Array>[ ~0.19, ~0.28, ~0.37 ]
+// out => <Float64Array>[ ~-6.7, ~1.6 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of rows/columns of the elementary reflector `H`.
+-   **X**: overwritten by the vector `V` on exit, expects `N - 1` indexed elements [`Float64Array`][mdn-float64array].
+-   **strideX**: stride length of `X`.
+-   **offsetX**: starting index of `X`.
+-   **out**: output [`Float64Array`][mdn-float64array], the first element of `out` represents alpha and the second element of `out` represents `tau`.
+-   **strideOut**: stride length of `out`.
+-   **offsetOut**: starting index of `out`.
+
+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,
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var X = new Float64Array( [ 0.0, 2.0, 3.0, 4.0 ] );
+var out = new Float64Array( [ 0.0, 4.0, 0.0 ] );
+
+dlarfg.ndarray( 4, X, 1, 1, out, 1, 1 );
+// X => <Float64Array>[ 0.0, ~0.19, ~0.28, ~0.37 ]
+// out => <Float64Array>[ 0.0, ~6.7, ~1.6 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `H` is a Householder matrix with the form `H = I - tau * [1; v] * [1, v^T]`, where `tau` is a scalar and `v` is a vector.
+-   the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
+-   the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
+-   if all elements of `X` are zero, then `tau = 0` and `H` is the identity matrix.
+-   otherwise, `1 <= tau <= 2`
+-   `dlarfg()` corresponds to the [LAPACK][lapack] routine [`dlarfg`][lapack-dlarfg].
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var dlarfg = require( '@stdlib/lapack/base/dlarfg' );
+
+var N = 4;
+
+var X = uniform( N - 1, -10, 10, {
+    'dtype': 'float64'
+});
+console.log( 'X: ', X );
+
+var alpha = 4.0;
+
+var out = new Float64Array( [ alpha, 0.0 ] );
+
+dlarfg( N, X, 1, out );
+
+console.log( 'V: ', X );
+console.log( 'beta: ', out[ 0 ] );
+console.log( 'tau: ', out[ 1 ] );
+```
+
+</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-dlarfg]: https://netlib.org/lapack/explore-html-3.6.1/d7/da9/dlarfg_8f_aabb59655e820b3551af27781bd716143.html
+
+[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/dlarfg/benchmark/benchmark.js

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+/**
+* @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 pkg = require( './../package.json' ).name;
+var dlarfg = require( './../lib/dlarfg.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 out;
+	var X;
+
+	opts = {
+		'dtype': 'float64'
+	};
+
+	X = uniform( N-1, -10.0, 10.0, opts );
+	out = uniform( 2, -10.0, 10.0, opts );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			dlarfg( N, X, 1, out );
+			if ( isnan( X[ i%X.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( X[ i%X.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 N;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		N = pow( 10, i );
+		f = createBenchmark( N );
+		bench( pkg+':size='+(N), f );
+	}
+}
+
+main();