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# dcartesianProduct

> Compute the Cartesian product for two double-precision floating-point strided arrays.

<section class="usage">

## Usage

```javascript
var dcartesianProduct = require( '@stdlib/blas/ext/base/dcartesian-product' );
```

#### dcartesianProduct( order, M, N, x, strideX, y, strideY, out, LDO )

Computes the Cartesian product for two double-precision floating-point strided arrays.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 2.0 ] );
var y = new Float64Array( [ 3.0, 4.0 ] );
var out = new Float64Array( 8 );

// Compute the Cartesian product:
dcartesianProduct( 'row-major', x.length, y.length, x, 1, y, 1, out, 2 );
// out => <Float64Array>[ 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0 ]
```

The function has the following parameters:

-   **order**: storage layout.
-   **M**: number of indexed elements in `x`.
-   **N**: number of indexed elements in `y`.
-   **x**: first input [`Float64Array`][@stdlib/array/float64].
-   **strideX**: stride length for `x`.
-   **y**: second input [`Float64Array`][@stdlib/array/float64].
-   **strideY**: stride length for `y`.
-   **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 `M`, `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the Cartesian product of every other element:

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 0.0, 2.0, 0.0 ] );
var y = new Float64Array( [ 3.0, 0.0, 4.0, 0.0 ] );
var out = new Float64Array( 8 );

// Compute the Cartesian product:
dcartesianProduct( 'row-major', 2, 2, x, 2, y, 2, out, 2 );
// out => <Float64Array>[ 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0 ]
```

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 arrays...
var x0 = new Float64Array( [ 0.0, 1.0, 2.0 ] );
var y0 = new Float64Array( [ 0.0, 3.0, 4.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var out = new Float64Array( 8 );

// Compute the Cartesian product:
dcartesianProduct( 'row-major', 2, 2, x1, 1, y1, 1, out, 2 );
// out => <Float64Array>[ 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0 ]
```

<!--lint disable maximum-heading-length-->

#### dcartesianProduct.ndarray( M, N, x, strideX, offsetX, y, strideY, offsetY, out, strideOut1, strideOut2, offsetOut )

<!--lint enable maximum-heading-length-->

Computes the Cartesian product for two double-precision floating-point strided arrays using alternative indexing semantics.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 1.0, 2.0 ] );
var y = new Float64Array( [ 3.0, 4.0 ] );
var out = new Float64Array( 8 );

// Compute the Cartesian product:
dcartesianProduct.ndarray( x.length, y.length, x, 1, 0, y, 1, 0, out, 2, 1, 0 );
// out => <Float64Array>[ 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **offsetY**: starting index for `y`.
-   **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 Float64Array = require( '@stdlib/array/float64' );

var x = new Float64Array( [ 0.0, 0.0, 1.0, 2.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 3.0, 4.0 ] );
var out = new Float64Array( 8 );

// Compute the Cartesian product:
dcartesianProduct.ndarray( 2, 2, x, 1, 2, y, 1, 2, out, 2, 1, 0 );
// out => <Float64Array>[ 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `M <= 0` or `N <= 0`, both functions return `out` unchanged.
-   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 input arrays `x` of length `M` and `y` of length `N`, the output array must contain at least `M * 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,M*N)`.

</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 dcartesianProduct = require( '@stdlib/blas/ext/base/dcartesian-product' );

var M = 3;
var N = 2;
var x = discreteUniform( M, 1, 10, {
    'dtype': 'float64'
});
console.log( x );

var y = discreteUniform( N, 1, 10, {
    'dtype': 'float64'
});
console.log( y );

var out = new Float64Array( M * N * 2 );

// Compute the Cartesian product:
dcartesianProduct( 'row-major', M, N, x, 1, y, 1, out, 2 );
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/dcartesianproduct.h"
```

<!--lint disable maximum-heading-length-->

#### stdlib_strided_dcartesian_product( order, M, N, \*X, strideX, \*Y, strideY, \*Out, LDO )

<!--lint enable maximum-heading-length-->

Computes the Cartesian product for two double-precision floating-point strided arrays.

```c
#include "stdlib/blas/base/shared.h"

const double x[] = { 1.0, 2.0 };
const double y[] = { 3.0, 4.0 };
double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dcartesian_product( CblasRowMajor, 2, 2, x, 1, y, 1, out, 2 );
```

The function accepts the following arguments:

-   **order**: `[in] CBLAS_LAYOUT` storage layout.
-   **M**: `[in] CBLAS_INT` number of indexed elements in `X`.
-   **N**: `[in] CBLAS_INT` number of indexed elements in `Y`.
-   **X**: `[in] double*` first input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **Y**: `[in] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
-   **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 `2`. For column-major order, must be greater than or equal to `max(1,M*N)`.

```c
void stdlib_strided_dcartesian_product( const CBLAS_LAYOUT order, const CBLAS_INT M, const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY, double *Out, const CBLAS_INT LDO );
```

<!--lint disable maximum-heading-length-->

#### stdlib_strided_dcartesian_product_ndarray( M, N, \*X, strideX, offsetX, \*Y, strideY, offsetY, \*Out, strideOut1, strideOut2, offsetOut )

<!--lint enable maximum-heading-length-->

Computes the Cartesian product for two double-precision floating-point strided arrays using alternative indexing semantics.

```c
const double x[] = { 1.0, 2.0 };
const double y[] = { 3.0, 4.0 };
double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dcartesian_product_ndarray( 2, 2, x, 1, 0, y, 1, 0, out, 2, 1, 0 );
```

The function accepts the following arguments:

-   **M**: `[in] CBLAS_INT` number of indexed elements in `X`.
-   **N**: `[in] CBLAS_INT` number of indexed elements in `Y`.
-   **X**: `[in] double*` first input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **offsetX**: `[in] CBLAS_INT` starting index for `X`.
-   **Y**: `[in] double*` second input array.
-   **strideY**: `[in] CBLAS_INT` stride length for `Y`.
-   **offsetY**: `[in] CBLAS_INT` starting index for `Y`.
-   **Out**: `[out] double*` output array.
-   **strideOut1**: `[in] CBLAS_INT` stride length for the first dimension of `Out`.
-   **strideOut2**: `[in] CBLAS_INT` stride length for the second dimension of `Out`.
-   **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.

```c
void stdlib_strided_dcartesian_product_ndarray( const CBLAS_INT M, const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY, 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/dcartesianproduct.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Create strided input arrays:
    const double X[] = { 1.0, 2.0, 3.0, 4.0 };
    const double Y[] = { 5.0, 6.0, 7.0, 8.0 };

    // Specify the number of indexed elements:
    const int M = 4;
    const int N = 4;

    // Create an output array (M*N pairs, each pair has 2 elements):
    double out[ 32 ];

    // Specify strides:
    const int strideX = 1;
    const int strideY = 1;
    const int LDO = 2;

    // Compute the Cartesian product:
    stdlib_strided_dcartesian_product( CblasRowMajor, M, N, X, strideX, Y, strideY, out, LDO );

    // Print the result:
    for ( int i = 0; i < M*N; 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://www.npmjs.com/package/@stdlib/array-float64

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

</section>

<!-- /.links -->
