feat: add blas/ext/base/gcompanion

lib/node_modules/@stdlib/blas/ext/base/gcompanion/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.
+
+-->
+
+# gcompanion
+
+> Generate a companion matrix.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gcompanion = require( '@stdlib/blas/ext/base/gcompanion' );
+```
+
+#### gcompanion( order, N, x, strideX, out, ldo )
+
+Generates a companion matrix.
+
+```javascript
+var x = [ 1.0, 2.0, 3.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+gcompanion( 'row-major', 3, x, 1, out, 2 );
+// out => [ -2.0, -3.0, 1.0, 0.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: row-major (C-style) or column-major (Fortran-style) order.
+-   **N**: number of indexed elements in `x`.
+-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array] containing polynomial coefficients in order of decreasing degree, with the first indexed element being the leading coefficient. The leading coefficient must not be zero.
+-   **strideX**: stride length for `x`.
+-   **out**: output matrix.
+-   **ldo**: stride between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of the matrix `out`). Must be greater than or equal to `max(1,N-1)`.
+
+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, max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays:
+var x0 = new Float64Array( [ 999.0, 1.0, 2.0, 3.0 ] );
+var out0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 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
+
+gcompanion( 'row-major', 3, x1, 1, out1, 2 );
+// out0 => <Float64Array>[ 0.0, -2.0, -3.0, 1.0, 0.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### gcompanion.ndarray( N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Generates a companion matrix using alternative indexing semantics.
+
+```javascript
+var x = [ 1.0, 2.0, 3.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+gcompanion.ndarray( 3, x, 1, 0, out, 2, 1, 0 );
+// out => [ -2.0, -3.0, 1.0, 0.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **strideOut1**: stride length for the first dimension of `out`.
+-   **strideOut2**: stride length for the second dimension of `out`.
+-   **offsetOut**: starting index for `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, to start writing matrix elements from the second element of the output array:
+
+```javascript
+var x = [ 1.0, 2.0, 3.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gcompanion.ndarray( 3, x, 1, 0, out, 2, 1, 1 );
+// out => [ 0.0, -2.0, -3.0, 1.0, 0.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 1`, both functions return `out` unchanged.
+-   Given `N` polynomial coefficients, both functions generate an `(N-1)`-by-`(N-1)` matrix in which the first row contains the remaining coefficients negated and divided by the leading coefficient and ones are placed along the first subdiagonal.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var gcompanion = require( '@stdlib/blas/ext/base/gcompanion' );
+
+var N = 5;
+var order = 'row-major';
+var shape = [ N-1, N-1 ];
+var strides = shape2strides( shape, order );
+
+var x = discreteUniform( N, 1, 10, {
+    'dtype': 'generic'
+});
+console.log( x );
+
+var out = zeros( ( N-1 )*( N-1 ), 'generic' );
+
+gcompanion( order, N, x, 1, out, N-1 );
+console.log( ndarray2array( out, shape, strides, 0, order ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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">
+
+[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/ext/base/gcompanion/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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var gcompanion = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out;
+	var x;
+
+	x = uniform( len, 1.0, 10.0, options );
+	out = zeros( ( len-1 ) * ( len-1 ), options.dtype );
+
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			x[ 0 ] += 0.1;
+			v = gcompanion( 'row-major', len, x, 1, out, len-1 );
+			if ( isnan( v[ i%v.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v[ i%v.length ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 3; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();