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# 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://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/blas/ext/base/dcartesian-square]: https://github.com/stdlib-js/blas/tree/main/ext/base/dcartesian-square

[@stdlib/blas/ext/base/scartesian-square]: https://github.com/stdlib-js/blas/tree/main/ext/base/scartesian-square

<!-- <related-links> -->

<!-- </related-links> -->

</section>

<!-- /.links -->
