gger

Perform the rank 1 operation A = α*x*y^T + A.

Installation

npm install @stdlib/blas-base-gger

Usage

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

gger( order, M, N, α, x, sx, y, sy, A, lda )

Performs the rank 1 operation A = α*x*y^T + A, where α is a scalar, x is an M element vector, y is an N element vector, and A is an M by N matrix.

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

gger( 'row-major', 2, 3, 1.0, x, 1, y, 1, A, 3 );
// A => [ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

The function has the following parameters:

• order: storage layout.
• M: number of rows in the matrix A.
• N: number of columns in the matrix A.
• α: scalar constant.
• x: an M element input array.
• sx: stride length for x.
• y: an N element input array.
• sy: stride length for y.
• A: input matrix stored in linear memory.
• lda: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).

The stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to iterate over every other element in x and y,

var A = [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ];
var x = [ 1.0, 0.0, 1.0, 0.0 ];
var y = [ 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ];

gger( 'column-major', 2, 3, 1.0, x, 2, y, 2, A, 2 );
// A => [ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

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

var Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 1.0, 1.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );

// 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*1 ); // start at 2nd element

gger( 'column-major', 2, 3, 1.0, x1, -1, y1, -1, A, 2 );
// A => <Float64Array>[ 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

gger.ndarray( M, N, α, x, sx, ox, y, sy, oy, A, sa1, sa2, oa )

Performs the rank 1 operation A = α*x*y^T + A, using alternative indexing semantics and where α is a scalar, x is an M element vector, y is an N element vector, and A is an M by N matrix.

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

gger.ndarray( 2, 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
// A => [ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0 ]

The function has the following additional parameters:

• sa1: stride of the first dimension of A.
• sa2: stride of the second dimension of A.
• oa: starting index for A.
• ox: starting index for x.
• oy: 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,

var Float64Array = require( '@stdlib/array-float64' );

var A = [ 0.0, 0.0, 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ];
var x = [ 0.0, 1.0, 0.0, 1.0, 0.0 ];
var y = [ 0.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0 ];

gger.ndarray( 2, 3, 1.0, x, 2, 1, y, 2, 1, A, 1, 2, 2 );
// A => [ 0.0, 0.0, 2.0, 5.0, 3.0, 6.0, 4.0, 7.0 ]

Notes

• gger() corresponds to the BLAS level 2 function dger with the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dger, sger, etc.) are likely to be significantly more performant.
• Both functions support array-like objects having getter and setter accessors for array element access (e.g., @stdlib/array-base/accessor).

Examples

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

var opts = {
    'dtype': 'generic'
};

var M = 3;
var N = 5;

var A = discreteUniform( M*N, 0, 255, opts );
var x = discreteUniform( M, 0, 255, opts );
var y = discreteUniform( N, 0, 255, opts );

gger( 'row-major', M, N, 1.0, x, 1, y, 1, A, N );
console.log( A );

gger.ndarray( M, N, 1.0, x, 1, 0, y, 1, 0, A, 1, M, 0 );
console.log( A );

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

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.