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caxpy

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

Installation

npm install @stdlib/blas-base-caxpy

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

caxpy( N, ca, cx, strideX, cy, strideY )

Scales values from cx by ca and adds the result to cy.

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var cy = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var ca = new Complex64( 2.0, 2.0 );

caxpy( 3, ca, cx, 1, cy, 1 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

The function has the following parameters:

• N: number of indexed elements.
• ca: scalar Complex64 constant.
• cx: first input Complex64Array.
• strideX: index increment for cx.
• cy: second input Complex64Array.
• strideY: index increment for cy.

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

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var ca = new Complex64( 2.0, 2.0 );

caxpy( 2, ca, cx, 2, cy, 2 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

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

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

// Initial arrays...
var cx0 = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy0 = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

// Define a scalar constant:
var ca = new Complex64( 2.0, 2.0 );

// Create offset views...
var cx1 = new Complex64Array( cx0.buffer, cx0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var cy1 = new Complex64Array( cy0.buffer, cy0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Scales values of `cx0` by `ca` starting from second index and add the result to `cy0` starting from third index...
caxpy( 2, ca, cx1, 1, cy1, 1 );

var z = cy0.get( 2 );
// returns <Complex64>

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

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

caxpy.ndarray( N, ca, cx, strideX, offsetX, cy, strideY, offsetY )

Scales values from cx by ca and adds the result to cy using alternative indexing semantics.

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var cy = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var ca = new Complex64( 2.0, 2.0 );

caxpy.ndarray( 3, ca, cx, 1, 0, cy, 1, 0 );

var z = cy.get( 0 );
// returns <Complex64>

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

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

The function has the following additional parameters:

• offsetX: starting index for cx.
• offsetY: starting index for cy.

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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var realf = require( '@stdlib/complex-float32-real' );
var imagf = require( '@stdlib/complex-float32-imag' );

var cx = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var cy = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var ca = new Complex64( 2.0, 2.0 );

caxpy.ndarray( 3, ca, cx, 1, 1, cy, 1, 1 );

var z = cy.get( 3 );
// returns <Complex64>

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

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

Notes

• If N <= 0, both functions return cy unchanged.
• caxpy() corresponds to the BLAS level 1 function caxpy.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var ccopy = require( '@stdlib/blas-base-ccopy' );
var zeros = require( '@stdlib/array-zeros' );
var logEach = require( '@stdlib/console-log-each' );
var caxpy = require( '@stdlib/blas-base-caxpy' );

function rand() {
    return new Complex64( discreteUniform( 0, 10 ), discreteUniform( -5, 5 ) );
}

var cx = filledarrayBy( 10, 'complex64', rand );
var cy = filledarrayBy( 10, 'complex64', rand );
var cyc = ccopy( cy.length, cy, 1, zeros( cy.length, 'complex64' ), 1 );

var ca = new Complex64( 2.0, 2.0 );

// Scale values from `cx` by `ca` and add the result to `cy`:
caxpy( cx.length, ca, cx, 1, cy, 1 );

// Print the results:
logEach( '(%s)*(%s) + (%s) = %s', ca, cx, cyc, cy );

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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 © 2016-2024. The Stdlib Authors.