feat: add blas/ext/base/dcartesian-power

lib/node_modules/@stdlib/blas/ext/base/dcartesian-power/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.
+
+-->
+
+# dcartesianPower
+
+> Compute the Cartesian power for a double-precision floating-point strided array.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dcartesianPower = require( '@stdlib/blas/ext/base/dcartesian-power' );
+```
+
+#### dcartesianPower( order, N, k, x, strideX, out, LDO )
+
+Computes the Cartesian power for a double-precision floating-point strided array.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0 ] );
+var out = new Float64Array( 8 );
+
+dcartesianPower( 'row-major', x.length, 2, x, 1, out, 2 );
+// out => <Float64Array>[ 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.
+-   **k**: power.
+-   **x**: input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **out**: output [`Float64Array`][@stdlib/array/float64].
+-   **LDO**: stride length between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of `out`).
+
+The `N`, `k`, and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the Cartesian power of every other element:
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 0.0, 2.0, 0.0 ] );
+var out = new Float64Array( 8 );
+
+dcartesianPower( 'row-major', 2, 2, x, 2, out, 2 );
+// out => <Float64Array>[ 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 );
+
+dcartesianPower( 'row-major', 2, 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 -->
+
+#### dcartesianPower.ndarray( N, k, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Computes the Cartesian power for a double-precision floating-point strided array using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 1.0, 2.0 ] );
+var out = new Float64Array( 8 );
+
+dcartesianPower.ndarray( x.length, 2, x, 1, 0, out, 2, 1, 0 );
+// out => <Float64Array>[ 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.
+-   **k**: power.
+-   **x**: input [`Float64Array`][@stdlib/array/float64].
+-   **strideX**: stride length for `x`.
+-   **offsetX**: starting index for `x`.
+-   **out**: output [`Float64Array`][@stdlib/array/float64].
+-   **strideOut1**: stride length of the first dimension of `out`.
+-   **strideOut2**: stride length of 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 Float64Array = require( '@stdlib/array/float64' );
+
+var x = new Float64Array( [ 0.0, 0.0, 1.0, 2.0 ] );
+var out = new Float64Array( 8 );
+
+dcartesianPower.ndarray( 2, 2, x, 1, 2, out, 2, 1, 0 );
+// out => <Float64Array>[ 1.0, 1.0, 1.0, 2.0, 2.0, 1.0, 2.0, 2.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   `k`-tuples are stored as rows in the output matrix, where the `j`-th column contains the `j`-th element of each tuple.
+-   For an input array of length `N`, the output array must contain at least `N^k * k` indexed elements.
+-   For row-major order, the `LDO` parameter must be greater than or equal to `max(1,k)`. For column-major order, the `LDO` parameter must be greater than or equal to `max(1,N^k)`.
+-   If `N <= 0` or `k <= 0`, both functions return `out` unchanged.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var Float64Array = require( '@stdlib/array/float64' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var dcartesianPower = require( '@stdlib/blas/ext/base/dcartesian-power' );
+
+var N = 2;
+var k = 3;
+var x = discreteUniform( N, 1, 10, {
+    'dtype': 'float64'
+});
+console.log( x );
+
+var out = new Float64Array( pow( N, k ) * k );
+dcartesianPower( 'row-major', N, k, x, 1, out, k );
+console.log( out );
+```
+
+</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
+#include "stdlib/blas/ext/base/dcartesianpower.h"
+```
+
+#### stdlib_strided_dcartesian_power( order, N, k, \*X, strideX, \*Out, LDO )
+
+Computes the Cartesian power for a double-precision floating-point strided array.
+
+```c
+#include "stdlib/blas/base/shared.h"
+
+const double x[] = { 1.0, 2.0 };
+double out[ 8 ];
+
+stdlib_strided_dcartesian_power( CblasRowMajor, 2, 2, x, 1, out, 2 );
+```
+
+The function accepts the following arguments:
+
+-   **order**: `[in] CBLAS_LAYOUT` storage layout.
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **k**: `[in] CBLAS_INT` power.
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **Out**: `[out] double*` output array.
+-   **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 `max(1,k)`. For column-major order, must be greater than or equal to `max(1,N^k)`.
+
+```c
+void stdlib_strided_dcartesian_power( const CBLAS_LAYOUT order, const CBLAS_INT N, const CBLAS_INT k, const double *X, const CBLAS_INT strideX, double *Out, const CBLAS_INT LDO );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### stdlib_strided_dcartesian_power_ndarray( N, k, \*X, strideX, offsetX, \*Out, strideOut1, strideOut2, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Computes the Cartesian power for a double-precision floating-point strided array using alternative indexing semantics.
+
+```c
+const double x[] = { 1.0, 2.0 };
+double out[ 8 ];
+
+stdlib_strided_dcartesian_power_ndarray( 2, 2, x, 1, 0, out, 2, 1, 0 );
+```
+
+The function accepts the following arguments:
+
+-   **N**: `[in] CBLAS_INT` number of indexed elements.
+-   **k**: `[in] CBLAS_INT` power.
+-   **X**: `[in] double*` input array.
+-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
+-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
+-   **Out**: `[out] double*` output array.
+-   **strideOut1**: `[in] CBLAS_INT` stride length of the first dimension of `Out`.
+-   **strideOut2**: `[in] CBLAS_INT` stride length of the second dimension of `Out`.
+-   **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
+
+```c
+void stdlib_strided_dcartesian_power_ndarray( const CBLAS_INT N, const CBLAS_INT k, 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 );
+```
+
+</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
+#include "stdlib/blas/ext/base/dcartesianpower.h"
+#include "stdlib/blas/base/shared.h"
+#include <stdio.h>
+#include <math.h>
+
+int main( void ) {
+    // Create a strided input array:
+    const double x[] = { 1.0, 2.0 };
+
+    // Specify the number of indexed elements and power:
+    const int N = 2;
+    const int k = 2;
+
+    // Create an output array (N^k tuples, each tuple has k elements):
+    double out[ 8 ];
+
+    // Specify strides:
+    const int strideX = 1;
+    const int LDO = 2;
+
+    // Compute the Cartesian power:
+    stdlib_strided_dcartesian_power( CblasRowMajor, N, k, x, strideX, out, LDO );
+
+    // Print the result:
+    const int len = (int)pow( N, k );
+    for ( int i = 0; i < len; i++ ) {
+        printf( "out[ %i ] = ( %lf, %lf )\n", i, out[ i*2 ], out[ (i*2)+1 ] );
+    }
+}
+```
+
+</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">
+
+[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+</section>
+
+<!-- /.links -->