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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 for complex-valued data.

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, 0.0, 0.0, 2.0, 2.0 ] );
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, 3, 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, 4, x, 1, beta, y, 1 );

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

cgemv.ndarray( 'no-transpose', M, N, alpha, A, 1, 4, 0, x, 1, 0, beta, y, 1, 0 );

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

C APIs

Usage

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Examples

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