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feat: add blas/ext/base/gcartesian-square
PR-URL: #11828 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#491
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‎lib/node_modules/@stdlib/blas/ext/base/gcartesian-square/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# gcartesianSquare
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> Compute the Cartesian square for a strided array.
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<section class="usage">
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## Usage
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```javascript
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var gcartesianSquare = require( '@stdlib/blas/ext/base/gcartesian-square' );
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```
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#### gcartesianSquare( order, N, x, strideX, out, LDO )
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Computes the Cartesian square for a strided array.
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```javascript
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var x = [ 1.0, 2.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gcartesianSquare( 'row-major', x.length, x, 1, out, 2 );
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// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout. Must be either `'row-major'` or `'column-major'`.
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- **N**: number of indexed elements.
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- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideX**: stride length for `x`.
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- **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **LDO**: stride length between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of `out`).
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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:
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```javascript
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var x = [ 1.0, 0.0, 2.0, 0.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gcartesianSquare( 'row-major', 2, x, 2, out, 2 );
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// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial array:
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var x0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
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// Create an offset view:
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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// Output array:
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var out = new Float64Array( 8 );
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gcartesianSquare( 'row-major', 2, x1, 1, out, 2 );
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// out => <Float64Array>[ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
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```
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<!-- lint disable maximum-heading-length -->
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#### gcartesianSquare.ndarray( N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut )
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<!-- lint enable maximum-heading-length -->
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Computes the Cartesian square for a strided array using alternative indexing semantics.
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```javascript
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var x = [ 1.0, 2.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gcartesianSquare.ndarray( x.length, x, 1, 0, out, 2, 1, 0 );
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// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
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```
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The function has the following parameters:
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- **N**: number of indexed elements.
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- **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideX**: stride length for `x`.
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- **offsetX**: starting index for `x`.
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- **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
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- **strideOut1**: stride length for the first dimension of `out`.
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- **strideOut2**: stride length for the second dimension of `out`.
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- **offsetOut**: starting index for `out`.
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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:
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```javascript
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var x = [ 0.0, 0.0, 1.0, 2.0 ];
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var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
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gcartesianSquare.ndarray( 2, x, 1, 2, out, 2, 1, 0 );
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// out => [ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- 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.
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- For an input array of length `N`, the output array must contain at least `N * N * 2` indexed elements.
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- 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)`.
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- If `N <= 0`, both functions return `out` unchanged.
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- 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]).
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- 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.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var gcartesianSquare = require( '@stdlib/blas/ext/base/gcartesian-square' );
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var N = 2;
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var x = discreteUniform( N, 1, 10, {
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'dtype': 'generic'
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});
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console.log( x );
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var out = zeros( N*N*2, 'generic' );
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gcartesianSquare( 'row-major', N, x, 1, out, 2 );
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console.log( out );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
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[@stdlib/blas/ext/base/dcartesian-square]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/dcartesian-square
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[@stdlib/blas/ext/base/scartesian-square]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/blas/ext/base/scartesian-square
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<!-- <related-links> -->
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<!-- </related-links> -->
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/ext/base/gcartesian-square/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2026 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var zeros = require( '@stdlib/array/zeros' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var gcartesianSquare = require( './../lib/main.js' );
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// VARIABLES //
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var options = {
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'dtype': 'generic'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var out = zeros( len * len * 2, options.dtype );
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var x = uniform( len, -10.0, 10.0, options );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var y;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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x[ 0 ] += 0.1;
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y = gcartesianSquare( 'row-major', x.length, x, 1, out, 2 );
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if ( isnan( y[ i%y.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y[ i%y.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 3; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s:len=%d', pkg, len ), f );
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}
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}
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main();

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