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, za, zx, strideX, zy, strideY )

Scales values from zx by za and adds the result to zy.

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

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var za = new Complex128( 2.0, 2.0 );

zaxpy( 3, za, zx, 1, zy, 1 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns -1.0

var im = imag( z );
// returns 7.0

The function has the following parameters:

N: number of indexed elements.
za: scalar Complex128 constant.
zx: first input Complex128Array.
strideX: index increment for zx.
zy: second input Complex128Array.
strideY: index increment for zy.

The N and stride parameters determine how values from zx are scaled by za and added to zy. For example, to scale every other value in zx by za and add the result to every other value of zy,

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

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var za = new Complex128( 2.0, 2.0 );

zaxpy( 2, za, zx, 2, zy, 2 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns -1.0

var im = imag( z );
// returns 7.0

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' );
var real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

// Initial arrays...
var zx0 = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy0 = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

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

// Create offset views...
var zx1 = new Complex128Array( zx0.buffer, zx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var zy1 = new Complex128Array( zy0.buffer, zy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Scales values of `zx0` by `za` starting from second index and add the result to `zy0` starting from third index...
zaxpy( 2, za, zx1, 1, zy1, 1 );

var z = zy0.get( 2 );
// returns <Complex128>

var re = real( z );
// returns -1.0

var im = imag( z );
// returns 15.0

zaxpy.ndarray( N, za, zx, strideX, offsetX, zy, strideY, offsetY )

Scales values from zx by za and adds the result to zy using alternative indexing semantics.

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

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var za = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, za, zx, 1, 0, zy, 1, 0 );

var z = zy.get( 0 );
// returns <Complex128>

var re = real( z );
// returns -1.0

var im = imag( z );
// returns 7.0

The function has the following additional parameters:

offsetX: starting index for zx.
offsetY: starting index for zy.

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 values 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 real = require( '@stdlib/complex-float64-real' );
var imag = require( '@stdlib/complex-float64-imag' );

var zx = new Complex128Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var zy = new Complex128Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var za = new Complex128( 2.0, 2.0 );

zaxpy.ndarray( 3, za, zx, 1, 1, zy, 1, 1 );

var z = zy.get( 3 );
// returns <Complex128>

var re = real( z );
// returns -1.0

var im = imag( z );
// returns 31.0

Notes

If N <= 0, both functions return zy 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 zx = filledarrayBy( 10, 'complex128', rand );
var zy = filledarrayBy( 10, 'complex128', rand );
var zyc = zcopy( zy.length, zy, 1, zeros( zy.length, 'complex128' ), 1 );

var za = new Complex128( 2.0, 2.0 );

// Scale values from `zx` by `za` and add the result to `zy`:
zaxpy( zx.length, za, zx, 1, zy, 1 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', za, zx, zyc, zy );

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.