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cdiff

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

Installation

npm install @stdlib/blas-ext-base-cdiff

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var cdiff = require( '@stdlib/blas-ext-base-cdiff' );

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

Calculates the k-th discrete forward difference of a single-precision complex floating-point strided array.

var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex64Array( [ 1.0, -1.0 ] );
var a = new Complex64Array( [ 11.0, -11.0 ] );
var out = new Complex64Array( 6 );
var w = new Complex64Array( 6 );

cdiff( x.length, 1, x, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
// out => <Complex64Array>[ 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 Complex64Array.
• strideX: stride length for x.
• N1: number of indexed elements to prepend.
• prepend: a Complex64Array containing values to prepend prior to computing differences.
• strideP: stride length for prepend.
• N2: number of indexed elements to append.
• append: a Complex64Array containing values to append prior to computing differences.
• strideA: stride length for append.
• out: output Complex64Array. Must have N + N1 + N2 - k elements.
• strideOut: stride length for out.
• workspace: workspace Complex64Array. 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:

var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex64Array( [ 1.0, -1.0 ] );
var a = new Complex64Array( [ 11.0, -11.0 ] );
var out = new Complex64Array( 4 );
var w = new Complex64Array( 4 );

cdiff( 3, 1, x, 2, 1, p, 1, 1, a, 1, out, 1, w, 1 );
// out => <Complex64Array>[ 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 views.

var Complex64Array = require( '@stdlib/array-complex64' );

// Initial array...
var x0 = new Complex64Array( [ 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 Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

var p = new Complex64Array( [ 1.0, -1.0 ] );
var a = new Complex64Array( [ 11.0, -11.0 ] );
var out = new Complex64Array( 5 );
var w = new Complex64Array( 5 );

cdiff( x1.length, 1, x1, 1, 1, p, 1, 1, a, 1, out, 1, w, 1 );
// out => <Complex64Array>[ 3.0, -3.0, 2.0, -2.0, 2.0, -2.0, 2.0, -2.0, 1.0, -1.0 ]

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

Calculates the k-th discrete forward difference of a single-precision complex floating-point strided array using alternative indexing semantics.

var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex64Array( [ 1.0, -1.0 ] );
var a = new Complex64Array( [ 11.0, -11.0 ] );
var out = new Complex64Array( 6 );
var w = new Complex64Array( 6 );

cdiff.ndarray( x.length, 1, x, 1, 0, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
// out => <Complex64Array>[ 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 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:

var Complex64Array = require( '@stdlib/array-complex64' );

var x = new Complex64Array( [ 2.0, -2.0, 4.0, -4.0, 6.0, -6.0, 8.0, -8.0, 10.0, -10.0 ] );
var p = new Complex64Array( [ 1.0, -1.0 ] );
var a = new Complex64Array( [ 11.0, -11.0 ] );
var out = new Complex64Array( 4 );
var w = new Complex64Array( 4 );

cdiff.ndarray( 3, 1, x, 1, x.length-3, 1, p, 1, 0, 1, a, 1, 0, out, 1, 0, w, 1, 0 );
// out => <Complex64Array>[ 5.0, -5.0, 2.0, -2.0, 2.0, -2.0, 1.0, -1.0 ]

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.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Complex64Array = require( '@stdlib/array-complex64' );
var cdiff = require( '@stdlib/blas-ext-base-cdiff' );

var xbuf = discreteUniform( 20, -100, 100, {
    'dtype': 'float32'
});
var x = new Complex64Array( xbuf.buffer );
console.log( 'Input array: ', x );

var pbuf = discreteUniform( 4, -100, 100, {
    'dtype': 'float32'
});
var p = new Complex64Array( pbuf.buffer );
console.log( 'Prepend array: ', p );

var abuf = discreteUniform( 4, -100, 100, {
    'dtype': 'float32'
});
var a = new Complex64Array( abuf.buffer );
console.log( 'Append array: ', a );

var out = new Complex64Array( 10 );
var w = new Complex64Array( 13 );

cdiff( x.length, 4, x, 1, 2, p, 1, 2, a, 1, out, 1, w, 1 );
console.log( 'Output: ', out );

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C APIs

Usage

#include "stdlib/blas/ext/base/cdiff.h"

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

Calculates the k-th discrete forward difference of a single-precision complex floating-point strided array.

#include "stdlib/complex/float32/ctor.h"

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

stdlib_strided_cdiff( 5, 1, (const stdlib_complex64_t *)x, 1, 1, (const stdlib_complex64_t *)p, 1, 1, (const stdlib_complex64_t *)a, 1, (stdlib_complex64_t *)out, 1, (stdlib_complex64_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_complex64_t* input array.
• strideX: [in] CBLAS_INT stride length for X.
• N1: [in] CBLAS_INT number of indexed elements for Prepend.
• Prepend: [in] stdlib_complex64_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_complex64_t* array containing values to append prior to computing differences.
• strideA: [in] CBLAS_INT stride length for Append.
• Out: [out] stdlib_complex64_t* output array. Must have N + N1 + N2 - k elements.
• strideOut: [in] CBLAS_INT stride length for Out.
• Workspace: [out] stdlib_complex64_t* workspace array. Must have N + N1 + N2 - 1 elements.
• strideW: [in] CBLAS_INT stride length for Workspace.

void stdlib_strided_cdiff( const CBLAS_INT N, const CBLAS_INT k, const stdlib_complex64_t *X, const CBLAS_INT strideX, const CBLAS_INT N1, const stdlib_complex64_t *Prepend, const CBLAS_INT strideP, const CBLAS_INT N2, const stdlib_complex64_t *Append, const CBLAS_INT strideA, stdlib_complex64_t *Out, const CBLAS_INT strideOut, stdlib_complex64_t *Workspace, const CBLAS_INT strideW );

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

Calculates the k-th discrete forward difference of a single-precision complex floating-point strided array using alternative indexing semantics.

#include "stdlib/complex/float32/ctor.h"

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

stdlib_strided_cdiff_ndarray( 5, 1, (const stdlib_complex64_t *)x, 1, 0, 1, (const stdlib_complex64_t *)p, 1, 0, 1, (const stdlib_complex64_t *)a, 1, 0, (stdlib_complex64_t *)out, 1, 0, (stdlib_complex64_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_complex64_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_complex64_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_complex64_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_complex64_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_complex64_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.

void stdlib_strided_cdiff_ndarray( const CBLAS_INT N, const CBLAS_INT k, const stdlib_complex64_t *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const CBLAS_INT N1, const stdlib_complex64_t *Prepend, const CBLAS_INT strideP, const CBLAS_INT offsetP, const CBLAS_INT N2, const stdlib_complex64_t *Append, const CBLAS_INT strideA, const CBLAS_INT offsetA, stdlib_complex64_t *Out, const CBLAS_INT strideOut, const CBLAS_INT offsetOut, stdlib_complex64_t *Workspace, const CBLAS_INT strideW, const CBLAS_INT offsetW );

Examples

#include "stdlib/blas/ext/base/cdiff.h"
#include "stdlib/complex/float32/ctor.h"
#include <stdio.h>

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

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

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

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

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

    // Compute forward differences:
    stdlib_strided_cdiff( 4, 1, (const stdlib_complex64_t *)x, 1, 1, (const stdlib_complex64_t *)p, 1, 1, (const stdlib_complex64_t *)a, 1, (stdlib_complex64_t *)out, 1, (stdlib_complex64_t *)w, 1 );

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

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.