cgemv

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cgemv

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

Installation

npm install @stdlib/blas-base-cgemv

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

cgemv( 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 or y = α*A^H*x + β*y where α and β are scalars, x and y are vectors, and A is an M by N matrix.

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var A = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0 ] );
var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0 ] );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

cgemv( 'column-major', 'no-transpose', 4, 2, alpha, A, 4, x, 1, beta, y, 1 );
// y => <Complex64Array>[ -10.0, 11.0, -12.0, 14.0, -14.0, 17.0, -16.0, 20.0 ]

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 Complex64Array.
LDA: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).
x: input Complex64Array.
sx: stride length for x.
β: scalar constant.
y: output Complex64Array.
sy: stride length for y.

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

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var A = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0 ] );
var x = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 3.0, 3.0, 0.0, 0.0, 4.0, 4.0 ] );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

cgemv( 'column-major', 'no-transpose', 4, 2, alpha, A, 4, x, 2, beta, y, 2 );
// y => <Complex64Array>[ -10.0, 11.0, 0.0, 0.0, -12.0, 14.0, 0.0, 0.0, -14.0, 17.0, 0.0, 0.0, -16.0, 20.0 ]

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

var Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

// Initial arrays...
var x0 = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0 ] );
var y0 = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0 ] );
var A = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0 ] );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

// Create offset views...
var x1 = new Complex64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element
var y1 = new Complex64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd complex element

cgemv( 'column-major', 'no-transpose', 4, 2, alpha, A, 4, x1, 1, beta, y1, 1 );
// y1 => <Complex64Array>[ -10.0, 11.0, -12.0, 14.0, -14.0, 17.0, -16.0, 20.0 ]

cgemv.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 or y = α*A^H*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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var A = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0 ] );
var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0 ] );
var y = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0 ] );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

cgemv.ndarray( 'no-transpose', 4, 2, alpha, A, 1, 4, 0, x, 1, 0, beta, y, 1, 0 );
// y => <Complex64Array>[ -10.0, 11.0, -12.0, 14.0, -14.0, 17.0, -16.0, 20.0 ]

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 Complex64Array = require( '@stdlib/array-complex64' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );

var A = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0, 6.0, 6.0, 7.0, 7.0, 8.0, 8.0 ] );
var x = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0 ] );
var y = new Complex64Array( [ 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 1.0, 1.0 ] );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

cgemv.ndarray( 'no-transpose', 4, 2, alpha, A, 1, 4, 0, x, 1, 1, beta, y, -2, 6 );
// y => <Complex64Array>[ -16.0, 20.0, 0.0, 0.0, -14.0, 17.0, 0.0, 0.0, -12.0, 14.0, 0.0, 0.0, -10.0, 11.0 ]

Notes

cgemv() corresponds to the BLAS level 2 function cgemv.

Examples

var discreteUniform = require( '@stdlib/random-base-discrete-uniform' );
var Complex64 = require( '@stdlib/complex-float32-ctor' );
var filledarrayBy = require( '@stdlib/array-filled-by' );
var logEach = require( '@stdlib/console-log-each' );
var cgemv = require( '@stdlib/blas-base-cgemv' );

function rand() {
    return new Complex64( discreteUniform( 0, 255 ), discreteUniform( -128, 127 ) );
}

var M = 3;
var N = 3;

var A = filledarrayBy( M*N, 'complex64', rand );
var x = filledarrayBy( N, 'complex64', rand );
var y = filledarrayBy( M, 'complex64', rand );

var alpha = new Complex64( 0.5, 0.5 );
var beta = new Complex64( 0.5, -0.5 );

cgemv( 'column-major', 'no-transpose', M, N, alpha, A, M, x, 1, beta, y, 1 );

// Print the results:
logEach( '%s', x );

cgemv.ndarray( 'no-transpose', M, N, alpha, A, 1, M, 0, x, 1, 0, beta, y, 1, 0 );

// Print the results:
logEach( '%s', x );

C APIs

Usage

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

c_cgemv( 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 or Y = α*A^H*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"
#include "stdlib/complex/float32/ctor.h"

const float A[] = {
    1.0f, 1.0f, 2.0f, 2.0f,
    3.0f, 3.0f, 4.0f, 4.0f,
    5.0f, 5.0f, 6.0f, 6.0f,
    7.0f, 7.0f, 8.0f, 8.0f
};
const float x[] = { 1.0f, 1.0f, 2.0f, 2.0f };
float y[] = { 1.0f, 1.0f, 2.0f, 2.0f, 3.0f, 3.0f, 4.0f, 4.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 0.5f, 0.5f );
const stdlib_complex64_t beta = stdlib_complex64( 0.5f, -0.5f );

c_cgemv( CblasColMajor, CblasNoTrans, 4, 2, alpha, (void *)A, 4, (void *)x, 1, beta, (void *)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] stdlib_complex64_t scalar constant.
A: [in] void* input matrix.
LDA: [in] CBLAS_INT stride of the first dimension of A (a.k.a., leading dimension of the matrix A).
X: [in] void* first input vector.
strideX: [in] CBLAS_INT stride length for X.
beta: [in] stdlib_complex64_t scalar constant.
Y: [inout] void* second input vector.
strideY: [in] CBLAS_INT stride length for Y.

void c_cgemv( const CBLAS_LAYOUT layout, const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const stdlib_complex64_t alpha, const void *A, const CBLAS_INT LDA, const void *X, const CBLAS_INT strideX, const stdlib_complex64_t beta, void *Y, const CBLAS_INT strideY )

c_cgemv_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 or Y = α*A^H*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.

#include "stdlib/blas/base/shared.h"
#include "stdlib/complex/float32/ctor.h"

const float A[] = {
    1.0f, 1.0f, 2.0f, 2.0f,
    3.0f, 3.0f, 4.0f, 4.0f,
    5.0f, 5.0f, 6.0f, 6.0f,
    7.0f, 7.0f, 8.0f, 8.0f
};
const float x[] = { 1.0f, 1.0f, 2.0f, 2.0f };
float y[] = { 1.0f, 1.0f, 2.0f, 2.0f, 3.0f, 3.0f, 4.0f, 4.0f };
const stdlib_complex64_t alpha = stdlib_complex64( 0.5f, 0.5f );
const stdlib_complex64_t beta = stdlib_complex64( 0.5f, -0.5f );

c_cgemv( CblasNoTrans, 4, 2, alpha, (void *)A, 1, 4, (void *)x, 1, 0, beta, (void *)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] stdlib_complex64_t scalar constant.
A: [in] void* 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] void* first input vector.
sx: [in] CBLAS_INT stride length for X.
ox: [in] CBLAS_INT starting index for X.
beta: [in] stdlib_complex64_t scalar constant.
Y: [inout] void* second input vector.
sy: [in] CBLAS_INT stride length for Y.
oy: [in] CBLAS_INT starting index for Y.

void c_cgemv_ndarray( const CBLAS_TRANSPOSE trans, const CBLAS_INT M, const CBLAS_INT N, const stdlib_complex64_t alpha, const void *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA, const void *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const stdlib_complex64_t beta, void *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY )

Examples

#include "stdlib/blas/base/cgemv.h"
#include "stdlib/blas/base/shared.h"
#include "stdlib/complex/float32/ctor.h"
#include <stdio.h>

int main( void ) {
    // Define a 3x3 matrix stored in row-major order:
    const float A[ 3*3*2 ] = {
        1.0f, 1.0f, 2.0f, 2.0f, 3.0f, 3.0f,
        4.0f, 4.0f, 5.0f, 5.0f, 6.0f, 6.0f,
        7.0f, 7.0f, 8.0f, 8.0f, 9.0f, 9.0f
    };

    // Define `x` and `y` vectors:
    const float x[ 3*2 ] = { 1.0f, 1.0f, 2.0f, 2.0f, 3.0f, 3.0f };
    float y[ 3*2 ] = { 3.0f, 3.0f, 2.0f, 2.0f, 1.0f, 1.0f };

    // Create complex scalars:
    const stdlib_complex64_t alpha = stdlib_complex64( 0.5f, 0.5f );
    const stdlib_complex64_t beta = stdlib_complex64( 0.5f, -0.5f );

    // 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_cgemv( CblasRowMajor, CblasNoTrans, M, N, alpha, (void *)A, M, (void *)x, 1, beta, (void *)y, 1 );

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "y[ %i ] = %f + %fj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }

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

    // Print the result:
    for ( int i = 0; i < N; i++ ) {
        printf( "y[ %i ] = %f + %fj\n", i, y[ i*2 ], y[ (i*2)+1 ] );
    }
}

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.

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cgemv

Installation

Usage

cgemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )

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

Notes

Examples

C APIs

Usage

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

c_cgemv_ndarray( trans, M, N, alpha, A, sa1, sa2, oa, X, sx, ox, beta, *Y, sy, oy )

Examples

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cgemv

Installation

Usage

cgemv( order, trans, M, N, α, A, LDA, x, sx, β, y, sy )

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

Notes

Examples

C APIs

Usage

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

c_cgemv_ndarray( trans, M, N, alpha, *A, sa1, sa2, oa, *X, sx, ox, beta, *Y, sy, oy )

Examples

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

c_cgemv_ndarray( trans, M, N, alpha, A, sa1, sa2, oa, X, sx, ox, beta, *Y, sy, oy )

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