saxpy

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

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 );

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 ] );
    }
}

See Also

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