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feat: add blas/ext/base/zediff #13024

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384 changes: 384 additions & 0 deletions lib/node_modules/@stdlib/blas/ext/base/zediff/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.

-->

# zediff

> Calculate the differences between consecutive elements of a double-precision complex floating-point strided array.

<section class="usage">

## Usage

```javascript
var zediff = require( '@stdlib/blas/ext/base/zediff' );
```

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

#### zediff( N, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut )

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

Calculates the differences between consecutive elements of a double-precision complex floating-point strided array.

<!-- eslint-disable max-len -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex128Array( [ 1.0, -1.0 ] );
var a = new Complex128Array( [ 11.0, -11.0 ] );
var out = new Complex128Array( 6 );

zediff( x.length, x, 1, 1, p, 1, 1, a, 1, out, 1 );
// out => <Complex128Array>[ 1.0, -1.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 11.0, -11.0 ]
```

The function has the following parameters:

- **N**: number of indexed elements.
- **x**: input [`Complex128Array`][@stdlib/array/complex128].
- **strideX**: stride length for `x`.
- **N1**: number of indexed elements to `prepend`.
- **prepend**: a [`Complex128Array`][@stdlib/array/complex128] containing values to prepend prior to computing differences.
- **strideP**: stride length for `prepend`.
- **N2**: number of indexed elements to `append`.
- **append**: a [`Complex128Array`][@stdlib/array/complex128] containing values to append prior to computing differences.
- **strideA**: stride length for `append`.
- **out**: output [`Complex128Array`][@stdlib/array/complex128]. Must have `N + N1 + N2 - 1` elements.
- **strideOut**: stride length for `out`.

The `N` and stride parameters determine which elements in the strided array are accessed at runtime. For example, to compute differences of every other element:

<!-- eslint-disable max-len -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex128Array( [ 1.0, -1.0 ] );
var a = new Complex128Array( [ 11.0, -11.0 ] );
var out = new Complex128Array( 4 );

zediff( 3, x, 2, 1, p, 1, 1, a, 1, out, 1 );
// out => <Complex128Array>[ 1.0, -1.0, 4.0, -4.0, 4.0, -4.0, 11.0, -11.0 ]
```

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

<!-- eslint-disable max-len -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );

// Initial array...
var x0 = new Complex128Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );

// Create an offset view...
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var p = new Complex128Array( [ 1.0, -1.0 ] );
var a = new Complex128Array( [ 11.0, -11.0 ] );
var out = new Complex128Array( 5 );

zediff( x1.length, x1, 1, 1, p, 1, 1, a, 1, out, 1 );
// out => <Complex128Array>[ 1.0, -1.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 11.0, -11.0 ]
```

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

#### zediff.ndarray( N, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut )

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

Calculates the differences between consecutive elements of a double-precision complex floating-point strided array using alternative indexing semantics.

<!-- eslint-disable max-len -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex128Array( [ 1.0, -1.0 ] );
var a = new Complex128Array( [ 11.0, -11.0 ] );
var out = new Complex128Array( 6 );

zediff.ndarray( x.length, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0 );
// out => <Complex128Array>[ 1.0, -1.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 11.0, -11.0 ]
```

The function has the following additional parameters:

- **offsetX**: starting index for `x`.
- **offsetP**: starting index for `prepend`.
- **offsetA**: starting index for `append`.
- **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 three elements:

<!-- eslint-disable max-len -->

```javascript
var Complex128Array = require( '@stdlib/array/complex128' );

var x = new Complex128Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex128Array( [ 1.0, -1.0 ] );
var a = new Complex128Array( [ 11.0, -11.0 ] );
var out = new Complex128Array( 4 );

zediff.ndarray( 3, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0 );
// out => <Complex128Array>[ 1.0, -1.0, 2.0, -2.0, 2.0, -2.0, 11.0, -11.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

- If `N + N1 + N2 <= 1`, both functions return the output array unchanged.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var Complex128Array = require( '@stdlib/array/complex128' );
var zediff = require( '@stdlib/blas/ext/base/zediff' );

var xbuf = discreteUniform( 20, -100, 100, {
'dtype': 'float64'
});
var x = new Complex128Array( xbuf.buffer );
console.log( 'Input array: ', x );

var pbuf = discreteUniform( 4, -100, 100, {
'dtype': 'float64'
});
var p = new Complex128Array( pbuf.buffer );
console.log( 'Prepend array: ', p );

var abuf = discreteUniform( 4, -100, 100, {
'dtype': 'float64'
});
var a = new Complex128Array( abuf.buffer );
console.log( 'Append array: ', a );

var out = new Complex128Array( 13 );

zediff( x.length, x, 1, 2, p, 1, 2, a, 1, out, 1 );
console.log( 'Output: ', 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/zediff.h"
```

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

#### stdlib_strided_zediff( N, \*X, strideX, N1, \*Prepend, strideP, N2, \*Append, strideA, \*Out, strideOut )

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

Calculates the differences between consecutive elements of a double-precision complex floating-point strided array.

```c
#include "stdlib/complex/float64/ctor.h"

const double x[] = { 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 };
const double p[] = { 1.0, -1.0 };
const double a[] = { 11.0, -11.0 };
double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_zediff( 5, (const stdlib_complex128_t *)x, 1, 1, (const stdlib_complex128_t *)p, 1, 1, (const stdlib_complex128_t *)a, 1, (stdlib_complex128_t *)out, 1 );
```

The function accepts the following arguments:

- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[in] stdlib_complex128_t*` input array.
- **strideX**: `[in] CBLAS_INT` stride length for `X`.
- **N1**: `[in] CBLAS_INT` number of indexed elements to prepend.
- **Prepend**: `[in] stdlib_complex128_t*` array containing values to prepend prior to computing differences.
- **strideP**: `[in] CBLAS_INT` stride length for `Prepend`.
- **N2**: `[in] CBLAS_INT` number of indexed elements to append.
- **Append**: `[in] stdlib_complex128_t*` array containing values to append prior to computing differences.
- **strideA**: `[in] CBLAS_INT` stride length for `Append`.
- **Out**: `[out] stdlib_complex128_t*` output array. Must have `N + N1 + N2 - 1` elements.
- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.

```c
void stdlib_strided_zediff( const CBLAS_INT N, const stdlib_complex128_t *X, const CBLAS_INT strideX, const CBLAS_INT N1, const stdlib_complex128_t *Prepend, const CBLAS_INT strideP, const CBLAS_INT N2, const stdlib_complex128_t *Append, const CBLAS_INT strideA, stdlib_complex128_t *Out, const CBLAS_INT strideOut );
```

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

#### stdlib_strided_zediff_ndarray( N, \*X, strideX, offsetX, N1, \*Prepend, strideP, offsetP, N2, \*Append, strideA, offsetA, \*Out, strideOut, offsetOut )

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

Calculates the differences between consecutive elements of a double-precision complex floating-point strided array using alternative indexing semantics.

```c
#include "stdlib/complex/float64/ctor.h"

const double x[] = { 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 };
const double p[] = { 1.0, -1.0 };
const double a[] = { 11.0, -11.0 };
double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_zediff_ndarray( 5, (const stdlib_complex128_t *)x, 1, 0, 1, (const stdlib_complex128_t *)p, 1, 0, 1, (const stdlib_complex128_t *)a, 1, 0, (stdlib_complex128_t *)out, 1, 0 );
```

The function accepts the following arguments:

- **N**: `[in] CBLAS_INT` number of indexed elements.
- **X**: `[in] stdlib_complex128_t*` input array.
- **strideX**: `[in] CBLAS_INT` stride length for `X`.
- **offsetX**: `[in] CBLAS_INT` starting index for `X`.
- **N1**: `[in] CBLAS_INT` number of indexed elements to prepend.
- **Prepend**: `[in] stdlib_complex128_t*` array containing values to prepend prior to computing differences.
- **strideP**: `[in] CBLAS_INT` stride length for `Prepend`.
- **offsetP**: `[in] CBLAS_INT` starting index for `Prepend`.
- **N2**: `[in] CBLAS_INT` number of indexed elements to append.
- **Append**: `[in] stdlib_complex128_t*` array containing values to append prior to computing differences.
- **strideA**: `[in] CBLAS_INT` stride length for `Append`.
- **offsetA**: `[in] CBLAS_INT` starting index for `Append`.
- **Out**: `[out] stdlib_complex128_t*` output array. Must have `N + N1 + N2 - 1` elements.
- **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
- **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.

```c
void stdlib_strided_zediff_ndarray( const CBLAS_INT N, const stdlib_complex128_t *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const CBLAS_INT N1, const stdlib_complex128_t *Prepend, const CBLAS_INT strideP, const CBLAS_INT offsetP, const CBLAS_INT N2, const stdlib_complex128_t *Append, const CBLAS_INT strideA, const CBLAS_INT offsetA, stdlib_complex128_t *Out, const CBLAS_INT strideOut, 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/zediff.h"
#include "stdlib/complex/float64/ctor.h"
#include <stdio.h>

int main( void ) {
// Create a strided array of interleaved real and imaginary components:
const double x[] = { 1.0, -1.0, 2.0, -2.0, 3.0, -3.0, 4.0, -4.0 };

// Define a list of values to prepend:
const double p[] = { 0.0, 0.0 };

// Define a list of values to append:
const double a[] = { 5.0, -5.0 };

// Define an output array:
double out[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

// Compute differences:
stdlib_strided_zediff( 4, (const stdlib_complex128_t *)x, 1, 1, (const stdlib_complex128_t *)p, 1, 1, (const stdlib_complex128_t *)a, 1, (stdlib_complex128_t *)out, 1 );

// Print the result:
for ( int i = 0; i < 10; i++ ) {
printf( "out[ %i ] = %lf\n", i, out[ i ] );
}
}
```

</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/complex128]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/complex128

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

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

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

</section>

<!-- /.links -->
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