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

Usage

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

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

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

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

var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex64( 2.0, 2.0 );

caxpy( 3, alpha, x, 1, y, 1 );
// y => <Complex64Array>[ -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 Complex64 constant.
• x: first input Complex64Array.
• strideX: index increment for x.
• y: second input Complex64Array.
• strideY: index increment for y.

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

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

var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex64( 2.0, 2.0 );

caxpy( 2, alpha, x, 2, y, 2 );
// y => <Complex64Array>[ -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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

// Initial arrays...
var x0 = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y0 = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

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

// Create offset views...
var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Complex64Array( y0.buffer, y0.BYTES_PER_ELEMENT*2 ); // start at 3rd element

// Scales values of `x0` by `alpha` starting from second index and add the result to `y0` starting from third index...
caxpy( 2, alpha, x1, 1, y1, 1 );
// y0 => <Complex64Array>[ 1.0, 1.0, 1.0, 1.0, -1.0, 15.0, -1.0, 23.0 ]

caxpy.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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex64( 2.0, 2.0 );

caxpy.ndarray( 3, alpha, x, 1, 0, y, 1, 0 );
// y => <Complex64Array>[ -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 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 x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = new Complex64( 2.0, 2.0 );

caxpy.ndarray( 3, alpha, x, 1, 1, y, 1, 1 );
// y => <Complex64Array>[ 1.0, 1.0, -1.0, 15.0, -1.0, 23.0, -1.0, 31.0 ]

Notes

• If N <= 0, both functions return y 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 x = filledarrayBy( 10, 'complex64', rand );
var y = filledarrayBy( 10, 'complex64', rand );
var yc = ccopy( y.length, y, 1, zeros( y.length, 'complex64' ), 1 );

var alpha = new Complex64( 2.0, 2.0 );

// Scale values from `x` by `alpha` and add the result to `y`:
caxpy( x.length, alpha, x, 1, y, 1 );

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

C APIs

Usage

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

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

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

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

float X[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
float Y[] = { -1.0f, -2.0f, -3.0f, -4.0f, -5.0f, -6.0f, -7.0f, -8.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 2.0f );

c_caxpy( 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_complex64_t scalar constant.
• X: [in] void* input array.
• strideX: [in] CBLAS_INT index increment for X.
• Y: [inout] void* output array.
• strideY: [in] CBLAS_INT index increment for Y.

void c_caxpy( const CBLAS_INT N, const stdlib_complex64_t alpha, const void *X, const CBLAS_INT strideX, void *Y, const CBLAS_INT strideY );

c_caxpy_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/float32/ctor.h"

float X[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
float Y[] = { -1.0f, -2.0f, -3.0f, -4.0f, -5.0f, -6.0f, -7.0f, -8.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 2.0f );

c_caxpy_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_complex64_t scalar constant.
• X: [in] void* input array.
• strideX: [in] CBLAS_INT index increment for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Y: [inout] void* output array.
• strideY: [in] CBLAS_INT index increment for Y.
• offsetY: [in] CBLAS_INT starting index for Y.

void c_caxpy_ndarray( const CBLAS_INT N, const stdlib_complex64_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/caxpy.h"
#include "stdlib/complex/float32/ctor.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays of interleaved real and imaginary components...
    float X[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
    float Y[] = { -1.0f, -2.0f, -3.0f, -4.0f, -5.0f, -6.0f, -7.0f, -8.0f };

    // Create a complex scalar:
    const stdlib_complex64_t alpha = stdlib_complex64( 2.0f, 2.0f );

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

    // Specify strides...
    const int strideX = 1;
    const int strideY = 1;

    // Scale values from `X` by `alpha` and adds the result to `Y`:
    c_caxpy( N, alpha, (void *)X, strideX, (void *)Y, strideY );

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

    // Scales values from `X` by `alpha` and adds the result to `Y` using alternative indexing semantics:
    c_caxpy_ndarray( N, alpha, (void *)X, -strideX, 3, (void *)Y, -strideY, 3 );

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

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.

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License

See LICENSE.

Copyright

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