dgemv

Usage

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

dgemv( ord, trans, M, N, α, A, LDA, x, sx, β, y, sy )

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

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0 ] );

dgemv( 'row-major', 'no-transpose', 2, 3, 1.0, A, 3, x, 1, 1.0, y, 1 );
// y => <Float64Array>[ 7.0, 16.0 ]

The function has the following parameters:

• ord: storage layout.
• trans: specifies whether A should 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 as a Float64Array.
• lda: stride of the first dimension of A (leading dimension of A).
• x: input Float64Array.
• sx: index increment for x.
• β: scalar constant.
• y: output Float64Array.
• sy: index increment for y.

The stride parameters determine how operations are performed. For example, to iterate over every other element in x and y,

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

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
var x = new Float64Array( [ 1.0, 0.0, 1.0, 0.0 ] );
var y = new Float64Array( [ 1.0, 0.0, 1.0, 0.0 ] );

dgemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x, 2, 1.0, y, 2 );
// y => <Float64Array>[ 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

dgemv( 'row-major', 'no-transpose', 2, 2, 1.0, A, 2, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 0.0, 8.0, 4.0 ]

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

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

var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0 ] );

dgemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => <Float64Array>[ 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 = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var y = new Float64Array( [ 7.0, 8.0, 9.0, 10.0 ] );

dgemv.ndarray( 'no-transpose', 2, 3, 1.0, A, 3, 1, 0, x, 1, 1, 1.0, y, -2, 2 );
// y => <Float64Array>[ 39, 8, 23, 10 ]