gaxpy

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

Usage

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

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

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

var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var y = [ 1.0, 1.0, 1.0, 1.0, 1.0 ];
var alpha = 5.0;

gaxpy( x.length, alpha, x, 1, y, 1 );
// y => [ 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 Array or typed array.
strideX: index increment for x.
y: input Array or typed array.
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 floor = require( '@stdlib/math/base/special/floor' );

var x = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var y = [ 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 ];

var alpha = 5.0;
var N = floor( x.length / 2 );

gaxpy( N, alpha, x, 2, y, -1 );
// y => [ 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 Float64Array = require( '@stdlib/array/float64' );
var floor = require( '@stdlib/math/base/special/floor' );

// Initial arrays...
var x0 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var y0 = new Float64Array( [ 7.0, 8.0, 9.0, 10.0, 11.0, 12.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*3 ); // start at 4th element

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

gaxpy( N, 5.0, x1, -2, y1, 1 );
// y0 => <Float64Array>[ 7.0, 8.0, 9.0, 40.0, 31.0, 22.0 ]

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

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

var x = [ 1.0, 2.0, 3.0, 4.0, 5.0 ];
var y = [ 1.0, 1.0, 1.0, 1.0, 1.0 ];
var alpha = 5.0;

gaxpy.ndarray( x.length, alpha, x, 1, 0, y, 1, 0 );
// y => [ 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 floor = require( '@stdlib/math/base/special/floor' );

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

var alpha = 5.0;
var N = floor( x.length / 2 );

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

Notes

If N <= 0 or alpha == 0, both functions return y unchanged.
gaxpy() corresponds to the BLAS level 1 function daxpy with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (daxpy, saxpy, etc.) are likely to be significantly more performant.

Examples

var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var gaxpy = require( '@stdlib/blas/base/gaxpy' );

var x;
var y;
var i;

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

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