Perform one of the matrix-vector operations
y = α*A*x + β*yory = α*A^T*x + β*y.
var ggemv = require( '@stdlib/blas/base/ggemv' );Performs one of the matrix-vector operations y = α*A*x + β*y or y = α*A^T*x + β*y, where α and β are scalars, x and y are vectors, 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, 1.0 ];
var y = [ 1.0, 1.0 ];
ggemv( 'row-major', 'no-transpose', 2, 3, 1.0, A, 3, x, 1, 1.0, y, 1 );
// y => [ 7.0, 16.0 ]The function has the following parameters:
- order: storage layout.
- trans: specifies whether
Ashould be transposed, conjugate-transposed, or not transposed. - M: number of rows in the matrix
A. - N: number of columns in the matrix
A. - α: scalar constant.
- A: input matrix stored in linear memory.
- LDA: stride of the first dimension of
A(a.k.a., leading dimension of the matrixA). - x: first input vector.
- sx: stride length for
x. - β: scalar constant.
- y: second input vector.
- sy: stride length for
y.
The stride parameters determine how operations are performed. For example, to iterate over every other element in x and y,
var A = [ 1.0, 2.0, 3.0, 4.0 ];
var x = [ 1.0, 0.0, 1.0, 0.0 ];
var y = [ 1.0, 0.0, 1.0, 0.0 ];
ggemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x, 2, 1.0, y, 2 );
// y => [ 4.0, 0.0, 8.0, 0.0 ]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 ] );
var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 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
ggemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 0.0, 8.0, 4.0 ]Performs one of the matrix-vector operations y = α*A*x + β*y or y = α*A^T*x + β*y, using alternative indexing semantics and where α and β are scalars, x and y are vectors, 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, 1.0 ];
var y = [ 1.0, 1.0 ];
ggemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => [ 7.0, 16.0 ]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 = [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ];
var x = [ 0.0, 1.0, 2.0, 3.0 ];
var y = [ 7.0, 8.0, 9.0, 10.0 ];
ggemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 1, 1.0, y, -2, 2 );
// y => [ 39.0, 8.0, 23.0, 10.0 ]ggemv()corresponds to the BLAS level 2 functiondgemvwith the exception that this implementation works with any array type, not just Float64Arrays. Depending on the environment, the typed versions (dgemv,sgemv, 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).
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ggemv = require( '@stdlib/blas/base/ggemv' );
var opts = {
'dtype': 'generic'
};
var M = 3;
var N = 3;
var A = discreteUniform( M*N, 0, 255, opts );
var x = discreteUniform( N, 0, 255, opts );
var y = discreteUniform( M, 0, 255, opts );
ggemv( 'row-major', 'no-transpose', M, N, 1.0, A, N, x, 1, 1.0, y, 1 );
console.log( y );
ggemv.ndarray( 'no-transpose', M, N, 1.0, A, N, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );