@stdlib/blas-base-saxpy

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


Keywords
stdlib, stdmath, mathematics, math, blas, level 1, saxpy, daxpy, axpy, linear, algebra, subroutines, add, alpha, vector, array, ndarray, float32, float, single, float32array, javascript, level-1, node, node-js, nodejs
License
Apache-2.0
Install
npm install @stdlib/blas-base-saxpy@0.0.5

Documentation

saxpy

NPM version Build Status Coverage Status dependencies

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

Installation

npm install @stdlib/blas-base-saxpy

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: input Float32Array.
  • strideY: index increment for y.

The N and stride parameters determine which elements in x and y 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 floor = require( '@stdlib/math-base-special-floor' );

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;
var N = floor( x.length / 2 );

saxpy( N, 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' );
var floor = require( '@stdlib/math-base-special-floor' );

// 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

var N = floor( x0.length / 2 );

saxpy( N, 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 offsetX and offsetY 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 floor = require( '@stdlib/math-base-special-floor' );

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;
var N = floor( x.length / 2 );

saxpy.ndarray( N, 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 randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var Float32Array = require( '@stdlib/array-float32' );
var saxpy = require( '@stdlib/blas-base-saxpy' );

var x;
var y;
var i;

x = new Float32Array( 10 );
y = new Float32Array( 10 );
for ( i = 0; i < x.length; i++ ) {
    x[ i ] = round( randu()*100.0 );
    y[ i ] = round( randu()*10.0 );
}
console.log( x );
console.log( y );

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

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

Chat


License

See LICENSE.

Copyright

Copyright © 2016-2021. The Stdlib Authors.