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zaxpy

Scale a double-precision complex floating-point vector by a double-precision complex floating-point constant and add the result to a double-precision complex floating-point vector.

Installation

npm install @stdlib/blas-base-zaxpy

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 zaxpy = require( '@stdlib/blas-base-zaxpy' );

zaxpy( N, alpha, x, strideX, y, strideY )

Scales values from x by alpha and adds the result to y.

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy( 3, alpha, x, 1, y, 1 );
// y => <Complex128Array>[ -1.0, 7.0, -1.0, 15.0, -1.0, 23.0 ]

The function has the following parameters:

• N: number of indexed elements.
• alpha: scalar Complex128 constant.
• x: first input Complex128Array.
• strideX: stride length for x.
• y: second input Complex128Array.
• strideY: stride length for y.

The N and stride parameters determine how elements from x are scaled by alpha and added to y. For example, to scale every other element in x by alpha and add the result to every other element of y,

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy( 2, alpha, x, 2, y, 2 );
// y => <Complex128Array>[ -1.0, 7.0, 1.0, 1.0, -1.0, 23.0, 1.0, 1.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

// Initial arrays...
var x0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y0 = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

// Define a scalar constant:
var alpha = new Complex128( 2.0, 2.0 );

// Create offset views...
var x1 = new Complex128Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Complex128Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Perform operation:
zaxpy( 2, alpha, x1, 1, y1, 1 );
// y0 => <Complex128Array>[ 1.0, 1.0, 1.0, 1.0, -1.0, 15.0, -1.0, 23.0 ]

zaxpy.ndarray( N, alpha, x, strideX, offsetX, y, strideY, offsetY )

Scales values from x by alpha and adds the result to y using alternative indexing semantics.

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, alpha, x, 1, 0, y, 1, 0 );
// y => <Complex128Array>[ -1.0, 7.0, -1.0, 15.0, -1.0, 23.0 ]

The function has the following additional parameters:

• offsetX: starting index for x.
• offsetY: starting index for y.

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 scale elements in the first input strided array starting from the second element and add the result to the second input array starting from the second element,

var Complex128Array = require( '@stdlib/array-complex128' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );

var x = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, alpha, x, 1, 1, y, 1, 1 );
// y => <Complex128Array>[ 1.0, 1.0, -1.0, 15.0, -1.0, 23.0, -1.0, 31.0 ]

Notes

• If N <= 0 or alpha == 0, both functions return y unchanged.
• zaxpy() corresponds to the BLAS level 1 function zaxpy.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex128 = require( '@stdlib/complex-float64-ctor' );
var zcopy = require( '@stdlib/blas-base-zcopy' );
var zeros = require( '@stdlib/array-zeros' );
var logEach = require( '@stdlib/console-log-each' );
var zaxpy = require( '@stdlib/blas-base-zaxpy' );

function rand() {
    return new Complex128( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var x = filledarrayBy( 10, 'complex128', rand );
var y = filledarrayBy( 10, 'complex128', rand );
var yc1 = zcopy( y.length, y, 1, zeros( y.length, 'complex128' ), 1 );

var alpha = new Complex128( 2.0, 2.0 );

// Perform operation:
zaxpy( x.length, alpha, x, 1, yc1, 1 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', alpha, x, y, yc1 );

var yc2 = zcopy( y.length, y, 1, zeros( y.length, 'complex128' ), 1 );

// Perform operation using alternative indexing semantics:
zaxpy.ndarray( x.length, alpha, x, 1, 0, yc2, 1, 0 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', alpha, x, y, yc2 );

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C APIs

Usage

#include "stdlib/blas/base/zaxpy.h"

c_zaxpy( N, alpha, *X, strideX, *Y, strideY )

Scales values from X by alpha and adds the result to Y.

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

const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double y[] = { -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0, -8.0 };
const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

c_zaxpy( 4, alpha, (void *)x, 1, (void *)y, 1 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• alpha: [in] stdlib_complex128_t scalar constant.
• X: [in] void* input array.
• strideX: [in] CBLAS_INT stride length for X.
• Y: [inout] void* output array.
• strideY: [in] CBLAS_INT stride length for Y.

void c_zaxpy( const CBLAS_INT N, const stdlib_complex128_t alpha, const void *X, const CBLAS_INT strideX, void *Y, const CBLAS_INT strideY );

c_zaxpy_ndarray( N, alpha, *X, strideX, offsetX, *Y, strideY, offsetY )

Scales values from X by alpha and adds the result to Y using alternative indexing semantics.

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

const double x[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 };
double y[] = { -1.0, -2.0, -3.0, -4.0, -5.0, -6.0, -7.0, -8.0 };
const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

c_zaxpy_ndarray( 4, alpha, (void *)x, 1, 0, (void *)y, 1, 0 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• alpha: [in] stdlib_complex128_t scalar constant.
• X: [in] void* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [inout] void* output array.
• strideY: [in] CBLAS_INT stride length for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

void c_zaxpy_ndarray( const CBLAS_INT N, const stdlib_complex128_t alpha, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY );

Examples

#include "stdlib/blas/base/zaxpy.h"
#include "stdlib/complex/float64/ctor.h"
#include <stdio.h>

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

    // Create a complex scalar:
    const stdlib_complex128_t alpha = stdlib_complex128( 2.0, 2.0 );

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

    // Specify stride lengths:
    const int strideX = 1;
    const int strideY = 1;

    // Perform operation:
    c_zaxpy( N, alpha, (void *)x, strideX, (void *)y, strideY );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "zaxpy[ %i ] = %lf + %lfj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }

    // Perform operation using alternative indexing semantics:
    c_zaxpy_ndarray( N, alpha, (void *)x, strideX, 0, (void *)y, strideY, 0 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "zaxpy[ %i ] = %lf + %lfj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }
}

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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 © 2016-2025. The Stdlib Authors.