feat: add blas/ext/base/gcartesian-square

lib/node_modules/@stdlib/blas/ext/base/gcartesian-square/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.
+
+-->
+
+# gcartesianSquare
+
+> Compute the Cartesian square for a strided array.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var gcartesianSquare = require( '@stdlib/blas/ext/base/gcartesian-square' );
+```
+
+#### gcartesianSquare( order, N, x, strideX, out, LDO )
+
+Computes the Cartesian square for a strided array.
+
+```javascript
+var x = [ 1.0, 2.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gcartesianSquare( 'row-major', x.length, x, 1, out, 2 );
+// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout. Must be either `'row-major'` or `'column-major'`.
+-   **N**: number of indexed elements.
+-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideX**: stride length for `x`.
+-   **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **LDO**: stride length between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of `out`).
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the Cartesian square of every other element:
+
+```javascript
+var x = [ 1.0, 0.0, 2.0, 0.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gcartesianSquare( 'row-major', 2, x, 2, out, 2 );
+// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial array:
+var x0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
+
+// Create an offset view:
+var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+// Output array:
+var out = new Float64Array( 8 );
+
+gcartesianSquare( 'row-major', 2, x1, 1, out, 2 );
+// out => <Float64Array>[ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### gcartesianSquare.ndarray( N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Computes the Cartesian square for a strided array using alternative indexing semantics.
+
+```javascript
+var x = [ 1.0, 2.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gcartesianSquare.ndarray( x.length, x, 1, 0, out, 2, 1, 0 );
+// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideX**: stride length for `x`.
+-   **offsetX**: starting index for `x`.
+-   **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **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 access only the last two elements:
+
+```javascript
+var x = [ 0.0, 0.0, 1.0, 2.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+gcartesianSquare.ndarray( 2, x, 1, 2, out, 2, 1, 0 );
+// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   Pairs are stored as rows in the output matrix, where the first column contains the first element of each pair and the second column contains the second element.
+-   For an input array of length `N`, the output array must contain at least `N * N * 2` indexed elements.
+-   For row-major order, the `LDO` parameter must be greater than or equal to `2`. For column-major order, the `LDO` parameter must be greater than or equal to `max(1,N*N)`.
+-   If `N <= 0`, both functions return `out` unchanged.
+-   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]).
+-   Depending on the environment, the typed versions ([`dcartesianSquare`][@stdlib/blas/ext/base/dcartesian-square], [`scartesianSquare`][@stdlib/blas/ext/base/scartesian-square], etc.) are likely to be significantly more performant.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var gcartesianSquare = require( '@stdlib/blas/ext/base/gcartesian-square' );
+
+var N = 2;
+var x = discreteUniform( N, 1, 10, {
+    'dtype': 'generic'
+});
+console.log( x );
+
+var out = zeros( N*N*2, 'generic' );
+gcartesianSquare( 'row-major', N, x, 1, out, 2 );
+console.log( out );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- 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
+
+[@stdlib/blas/ext/base/dcartesian-square]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/dcartesian-square
+
+[@stdlib/blas/ext/base/scartesian-square]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/scartesian-square
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/blas/ext/base/gcartesian-square/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 zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var gcartesianSquare = 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 = zeros( len * len * 2, options.dtype );
+	var x = uniform( len, -10.0, 10.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var y;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			x[ 0 ] += 0.1;
+			y = gcartesianSquare( 'row-major', x.length, x, 1, out, 2 );
+			if ( isnan( y[ i%y.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( y[ i%y.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();