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# zdiff

> Calculate the k-th discrete forward difference of a double-precision complex floating-point strided array.

<section class="usage">

## Usage

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

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

#### zdiff( N, k, x, strideX, N1, prepend, strideP, N2, append, strideA, out, strideOut, workspace, strideW )

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

Calculates the k-th discrete forward difference 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 );
var w = new Complex128Array( 6 );

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

The function has the following parameters:

-   **N**: number of indexed elements.
-   **k**: number of times to recursively compute differences.
-   **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 - k` elements.
-   **strideOut**: stride length for `out`.
-   **workspace**: workspace [`Complex128Array`][@stdlib/array/complex128]. Must have `N + N1 + N2 - 1` elements.
-   **strideW**: stride length for `workspace`.

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 );
var w = new Complex128Array( 4 );

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

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 );
var w = new Complex128Array( 5 );

zdiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
// out => <Complex128Array>[ 3.0, -3.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 1.0, -1.0 ]
```

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

#### zdiff.ndarray( N, k, x, strideX, offsetX, N1, prepend, strideP, offsetP, N2, append, strideA, offsetA, out, strideOut, offsetOut, workspace, strideW, offsetW )

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

Calculates the k-th discrete forward difference 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 );
var w = new Complex128Array( 6 );

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

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`.
-   **offsetW**: starting index for `workspace`.

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 );
var w = new Complex128Array( 4 );

zdiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
// out => <Complex128Array>[ 5.0, -5.0, 2.0, -2.0, 2.0, -2.0, 1.0, -1.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   When `k <= 1`, the workspace array is unused and thus ignored.
-   If `N + N1 + N2 <= 1` or `k >= N + N1 + N2`, 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 zdiff = require( '@stdlib/blas/ext/base/zdiff' );

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( 10 );
var w = new Complex128Array( 13 );

zdiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 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/zdiff.h"
```

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

#### stdlib_strided_zdiff( N, k, \*X, strideX, N1, \*Prepend, strideP, N2, \*Append, strideA, \*Out, strideOut, \*Workspace, strideW )

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

Calculates the k-th discrete forward difference 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 };
double w[] = { 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_zdiff( 5, 1, (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, (stdlib_complex128_t *)w, 1 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
-   **X**: `[in] stdlib_complex128_t*` input array.
-   **strideX**: `[in] CBLAS_INT` stride length for `X`.
-   **N1**: `[in] CBLAS_INT` number of indexed elements for `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 for `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 - k` elements.
-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
-   **Workspace**: `[out] stdlib_complex128_t*` workspace array. Must have `N + N1 + N2 - 1` elements.
-   **strideW**: `[in] CBLAS_INT` stride length for `Workspace`.

```c
void stdlib_strided_zdiff( const CBLAS_INT N, const CBLAS_INT k, 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, stdlib_complex128_t *Workspace, const CBLAS_INT strideW );
```

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

#### stdlib_strided_zdiff_ndarray( N, k, \*X, strideX, offsetX, N1, \*Prepend, strideP, offsetP, N2, \*Append, strideA, offsetA, \*Out, strideOut, offsetOut, \*Workspace, strideW, offsetW )

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

Calculates the k-th discrete forward difference 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 };
double w[] = { 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_zdiff_ndarray( 5, 1, (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, (stdlib_complex128_t *)w, 1, 0 );
```

The function accepts the following arguments:

-   **N**: `[in] CBLAS_INT` number of indexed elements.
-   **k**: `[in] CBLAS_INT` number of times to recursively compute differences.
-   **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 for `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 for `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 - k` elements.
-   **strideOut**: `[in] CBLAS_INT` stride length for `Out`.
-   **offsetOut**: `[in] CBLAS_INT` starting index for `Out`.
-   **Workspace**: `[out] stdlib_complex128_t*` workspace array. Must have `N + N1 + N2 - 1` elements.
-   **strideW**: `[in] CBLAS_INT` stride length for `Workspace`.
-   **offsetW**: `[in] CBLAS_INT` starting index for `Workspace`.

```c
void stdlib_strided_zdiff_ndarray( const CBLAS_INT N, const CBLAS_INT k, 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, stdlib_complex128_t *Workspace, const CBLAS_INT strideW, const CBLAS_INT offsetW );
```

</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/zdiff.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 };

    // Define a workspace:
    double w[] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

    // Compute forward differences:
    stdlib_strided_zdiff( 4, 1, (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, (stdlib_complex128_t *)w, 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://www.npmjs.com/package/@stdlib/array-complex128

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

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

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

</section>

<!-- /.links -->
