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saxpy

Multiply a vector x by a constant alpha and add the result to y.

Installation

npm install @stdlib/blas-base-saxpy

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

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

Multiplies a vector x by a constant alpha and adds the result to y.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

saxpy( x.length, alpha, x, 1, y, 1 );
// y => <Float32Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

The function has the following parameters:

• N: number of indexed elements.
• alpha: numeric constant.
• x: input Float32Array.
• strideX: index increment for x.
• y: output Float32Array.
• strideY: index increment for y.

The N and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to multiply every other value in x by alpha and add the result to the first N elements of y in reverse order,

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ] );

var alpha = 5.0;

saxpy( 3, alpha, x, 2, y, -1 );
// y => <Float32Array>[ 26.0, 16.0, 6.0, 1.0, 1.0, 1.0 ]

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

var Float32Array = require( '@stdlib/array-float32' );

// Initial arrays...
var x0 = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

saxpy( 3, 5.0, x1, -2, y1, 1 );
// y0 => <Float32Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]

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

Multiplies a vector x by a constant alpha and adds the result to y using alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
var alpha = 5.0;

saxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => <Float32Array>[ 6.0, 11.0, 16.0, 21.0, 26.0 ]

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 multiply every other value in x by a constant alpha starting from the second value and add to the last N elements in y where x[i] -> y[n], x[i+2] -> y[n-1],...,

var Float32Array = require( '@stdlib/array-float32' );

var x = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y = new Float32Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

var alpha = 5.0;

saxpy.ndarray( 3, alpha, x, 2, 1, y, -1, y.length-1 );
// y => <Float32Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]

Notes

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

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var saxpy = require( '@stdlib/blas-base-saxpy' );

var opts = {
    'dtype': 'float32'
};
var x = discreteUniform( 10, 0, 100, opts );
console.log( x );

var y = discreteUniform( x.length, 0, 10, opts );
console.log( y );

saxpy.ndarray( x.length, 5.0, x, 1, 0, y, -1, y.length-1 );
console.log( y );

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C APIs

Usage

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

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

Multiplies a vector X by a constant and adds the result to Y.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

c_saxpy( 4, 5.0f, x, 1, y, 1 );

The function accepts the following arguments:

• N: [in] CBLAS_INT number of indexed elements.
• alpha: [in] float scalar constant.
• X: [in] float* input array.
• strideX: [in] CBLAS_INT index increment for X.
• Y: [inout] float* output array.
• strideY: [in CBLAS_INT index increment for Y.

void c_saxpy( const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, float *Y, const CBLAS_INT strideY );

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

Multiplies a vector X by a constant and adds the result to Y using alternative indexing semantics.

const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f };
float y[] = { 0.0f, 0.0f, 0.0f, 0.0f };

c_saxpy_ndarray( 4, 5.0f, x, 1, 0, y, 1, 0 );

The function accepts the following arguments:

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

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

Examples

#include "stdlib/blas/base/saxpy.h"
#include <stdio.h>

int main( void ) {
    // Create strided arrays:
    const float x[] = { 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f };
    float y[] = { 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f };

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

    // Specify stride lengths:
    const int strideX = 2;
    const int strideY = -2;

    // Compute `a*x + y`:
    c_saxpy( N, 5.0f, x, strideX, y, strideY );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %f\n", i, y[ i ] );
    }

    // Compute `a*x + y`:
    c_saxpy_ndarray( N, 5.0f, x, strideX, 1, y, strideY, 7 );

    // Print the result:
    for ( int i = 0; i < 8; i++ ) {
        printf( "y[ %i ] = %f\n", i, y[ i ] );
    }
}

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See Also

• @stdlib/blas-base/daxpy: multiply a vector x by a constant and add the result to y.
• @stdlib/blas-base/gaxpy: multiply x by a constant and add the result to y.

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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.