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feat: add blas/ext/base/dcartesian-square
PR-URL: #10797 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Closes: stdlib-js/metr-issue-tracker#172
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‎lib/node_modules/@stdlib/blas/ext/base/dcartesian-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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# dcartesianSquare
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> Compute the Cartesian square for a double-precision floating-point strided array.
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<section class="usage">
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## Usage
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```javascript
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var dcartesianSquare = require( '@stdlib/blas/ext/base/dcartesian-square' );
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```
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#### dcartesianSquare( order, N, x, strideX, out, LDO )
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Computes the Cartesian square for a double-precision floating-point strided array.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, 2.0 ] );
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var out = new Float64Array( 8 );
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dcartesianSquare( 'row-major', x.length, x, 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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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 [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length for `x`.
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- **out**: output [`Float64Array`][@stdlib/array/float64].
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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 Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, 0.0, 2.0, 0.0 ] );
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var out = new Float64Array( 8 );
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dcartesianSquare( 'row-major', 2, x, 2, 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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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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dcartesianSquare( '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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#### dcartesianSquare.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 double-precision floating-point strided array using alternative indexing semantics.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 1.0, 2.0 ] );
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var out = new Float64Array( 8 );
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dcartesianSquare.ndarray( x.length, x, 1, 0, out, 2, 1, 0 );
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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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The function has the following parameters:
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- **N**: number of indexed elements.
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- **x**: input [`Float64Array`][@stdlib/array/float64].
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- **strideX**: stride length for `x`.
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- **offsetX**: starting index for `x`.
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- **out**: output [`Float64Array`][@stdlib/array/float64].
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- **strideOut1**: stride length of the first dimension of `out`.
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- **strideOut2**: stride length of 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 Float64Array = require( '@stdlib/array/float64' );
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var x = new Float64Array( [ 0.0, 0.0, 1.0, 2.0 ] );
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var out = new Float64Array( 8 );
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dcartesianSquare.ndarray( 2, x, 1, 2, out, 2, 1, 0 );
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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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</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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</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 Float64Array = require( '@stdlib/array/float64' );
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var dcartesianSquare = require( '@stdlib/blas/ext/base/dcartesian-square' );
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var N = 2;
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var x = discreteUniform( N, 1, 10, {
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'dtype': 'float64'
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});
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console.log( x );
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var out = new Float64Array( N * N * 2 );
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dcartesianSquare( '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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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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#include "stdlib/blas/ext/base/dcartesiansquare.h"
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```
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#### stdlib_strided_dcartesian_square( order, N, \*X, strideX, \*Out, LDO )
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Computes the Cartesian square for a double-precision floating-point strided array.
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```c
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#include "stdlib/blas/base/shared.h"
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const double x[] = { 1.0, 2.0 };
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double out[ 8 ];
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stdlib_strided_dcartesian_square( CblasRowMajor, 2, x, 1, out, 2 );
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```
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The function accepts the following arguments:
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- **order**: `[in] CBLAS_LAYOUT` storage layout.
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] double*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **Out**: `[out] double*` output array.
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- **LDO**: `[in] CBLAS_INT` stride length between successive contiguous vectors of the matrix `Out` (a.k.a., leading dimension of `Out`). For row-major order, must be greater than or equal to `2`. For column-major order, must be greater than or equal to `max(1,N*N)`.
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```c
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void stdlib_strided_dcartesian_square( const CBLAS_LAYOUT order, const CBLAS_INT N, const double *X, const CBLAS_INT strideX, double *Out, const CBLAS_INT LDO );
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```
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<!-- lint disable maximum-heading-length -->
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#### stdlib_strided_dcartesian_square_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 double-precision floating-point strided array using alternative indexing semantics.
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```c
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const double x[] = { 1.0, 2.0 };
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double out[ 8 ];
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stdlib_strided_dcartesian_square_ndarray( 2, x, 1, 0, out, 2, 1, 0 );
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```
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The function accepts the following arguments:
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- **N**: `[in] CBLAS_INT` number of indexed elements.
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- **X**: `[in] double*` input array.
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- **strideX**: `[in] CBLAS_INT` stride length for `X`.
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- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
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- **Out**: `[out] double*` output array.
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- **strideOut1**: `[in] CBLAS_INT` stride length of the first dimension of `Out`.
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- **strideOut2**: `[in] CBLAS_INT` stride length of the second dimension of `Out`.
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- **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
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```c
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void stdlib_strided_dcartesian_square_ndarray( const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Out, const CBLAS_INT strideOut1, const CBLAS_INT strideOut2, const CBLAS_INT offsetOut );
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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#include "stdlib/blas/ext/base/dcartesiansquare.h"
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#include "stdlib/blas/base/shared.h"
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#include <stdio.h>
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int main( void ) {
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// Create a strided input array:
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const double x[] = { 1.0, 2.0 };
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// Specify the number of indexed elements:
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const int N = 2;
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// Create an output array (N*N pairs, each pair has 2 elements):
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double out[ 8 ];
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// Specify strides:
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const int strideX = 1;
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const int LDO = 2;
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// Compute the Cartesian square:
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stdlib_strided_dcartesian_square( CblasRowMajor, N, x, strideX, out, LDO );
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// Print the result:
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for ( int i = 0; i < N*N; i++ ) {
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printf( "out[ %i ] = ( %lf, %lf )\n", i, out[ i*2 ], out[ (i*2)+1 ] );
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}
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}
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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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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[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

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