dgemv

Perform one of the matrix-vector operations y = α*A*x + β*y or y = α*A^T*x + β*y.

Installation

npm install @stdlib/blas-base-dgemv

Usage

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

dgemv( order, 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:

• order: 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 (a.k.a., leading dimension of the matrix A).
• x: input Float64Array.
• sx: stride length for x.
• β: scalar constant.
• y: output Float64Array.
• 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 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 ]

Notes

• dgemv() corresponds to the BLAS level 2 function dgemv.

Examples

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

var opts = {
    'dtype': 'float64'
};

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 );

dgemv( 'row-major', 'no-transpose', M, N, 1.0, A, N, x, -1, 1.0, y, -1 );
console.log( y );

C APIs

Usage

#include "stdlib/blas/base/dgemv.h"

c_dgemv( layout, trans, M, N, alpha, *A, LDA, *X, strideX, beta, *Y, strideY )

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.

#include "stdlib/blas/base/shared.h"

const double A[] = { 1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 3.0, 2.0, 1.0 };
const double x[] = { 1.0, 2.0, 3.0 };
double y[] = { 1.0, 2.0, 3.0 };

c_dgemv( CblasColMajor, CblasNoTrans, 3, 3, 1.0, A, 3, x, 1, 1.0, y, 1 );

The function accepts the following arguments:

• layout: [in] CBLAS_LAYOUT storage layout.
• trans: [in] CBLAS_TRANSPOSE specifies whether A should be transposed, conjugate-transposed, or not transposed.
• M: [in] CBLAS_INT number of rows in the matrix A.
• N: [in] CBLAS_INT number of columns in the matrix A.
• alpha: [in] double scalar constant.
• A: [in] double* input matrix.
• LDA: [in] CBLAS_INT stride of the first dimension of A (a.k.a., leading dimension of the matrix A).
• X: [in] double* first input vector.
• strideX: [in] CBLAS_INT stride length for X.
• beta: [in] double scalar constant.
• Y: [inout] double* second input vector.
• strideY: [in] CBLAS_INT stride length for Y.

void c_dgemv( const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *A, const CBLAS_INT LDA, const double *X, const CBLAS_INT strideX, const double beta, double *Y, const CBLAS_INT strideY )

c_dgemv_ndarray( trans, M, N, alpha, *A, sa1, sa2, oa, *X, sx, ox, beta, *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 indexing alternative semantics and where α and β are scalars, x and y are vectors, and A is an M by N matrix.

#include "stdlib/blas/base/shared.h"

const double A[] = { 1.0, 0.0, 0.0, 2.0, 1.0, 0.0, 3.0, 2.0, 1.0 };
const double x[] = { 1.0, 2.0, 3.0 };
double y[] = { 1.0, 2.0, 3.0 };

c_dgemv_ndarray( CblasNoTrans, 3, 3, 1.0, A, 1, 3, 0, x, 1, 0, 1.0, y, 1, 0 );

The function accepts the following arguments:

• trans: [in] CBLAS_TRANSPOSE specifies whether A should be transposed, conjugate-transposed, or not transposed.
• M: [in] CBLAS_INT number of rows in the matrix A.
• N: [in] CBLAS_INT number of columns in the matrix A.
• alpha: [in] double scalar.
• A: [in] double* input matrix.
• sa1: [in] CBLAS_INT stride of the first dimension of A.
• sa2: [in] CBLAS_INT stride of the second dimension of A.
• oa: [in] CBLAS_INT starting index for A.
• X: [in] double* first input vector.
• sx: [in] CBLAS_INT stride length for X.
• ox: [in] CBLAS_INT starting index for X.
• beta: [in] double scalar.
• Y: [inout] double* second input vector.
• sy: [in] CBLAS_INT stride length for Y.
• oy: [in] CBLAS_INT starting index for Y.

void c_dgemv_ndarray( const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const double alpha, const double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double beta, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY )

Examples

#include "stdlib/blas/base/dgemv.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Define a 3x3 matrix stored in row-major order:
    const double A[ 3*3 ] = {
        1.0, 2.0, 3.0,
        4.0, 5.0, 6.0,
        7.0, 8.0, 9.0
    };

    // Define `x` and `y` vectors:
    const double x[ 3 ] = { 1.0, 2.0, 3.0 };
    double y[ 3 ] = { 1.0, 2.0, 3.0 };

    // Specify the number of elements along each dimension of `A`:
    const int M = 3;
    const int N = 3;

    // Perform the matrix-vector operation `y = α*A*x + β*y`:
    c_dgemv( CblasRowMajor, CblasNoTrans, M, N, 1.0, A, M, x, 1, 1.0, y, 1 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "y[ %i ] = %lf\n", i, y[ i ] );
    }

    // Perform the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics:
    c_dgemv_ndarray( CblasNoTrans, M, N, 1.0, A, N, 1, 0, x, 1, 0, 1.0, y, 1, 0 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "y[ %i ] = %lf\n", i, y[ i ] );
    }
}

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.