dsymv

Usage

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

dsymv( order, uplo, N, α, A, LDA, x, sx, β, y, sy )

Performs the matrix-vector operation y = α*A*x + β*y where α and β are scalars, x and y are N element vectors, and A is an N by N symmetric matrix.

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

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

dsymv( 'row-major', 'lower', 3, 1.0, A, 3, x, 1, 0.0, y, 1 );
// y => <Float64Array>[ 1.0, 2.0, 3.0 ]

The function has the following parameters:

• order: storage layout.
• uplo: specifies whether the upper or lower triangular part of the symmetric matrix A should be referenced.
• N: number of elements along each dimension of 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: index increment for x.
• β: scalar constant.
• y: output Float64Array.
• sy: index increment for y.

The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of x in reverse order,

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

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

dsymv( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 1.0, y, 1 );
// y => <Float64Array>[ 7.0, 10.0, 9.0 ]

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( [ 1.0, 1.0, 1.0, 1.0 ] );
var y0 = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );

// 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

dsymv( 'row-major', 'upper', 3, 1.0, A, 3, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 1.0, 4.0, 3.0, 2.0 ]

dsymv.ndarray( order, uplo, N, α, A, LDA, x, sx, ox, β, y, sy, oy )

Performs the matrix-vector operation y = α*A*x + β*y using alternative indexing semantics and where α and β are scalars, x and y are N element vectors, and A is an N by N symmetric matrix.

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

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

dsymv.ndarray( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 2, 1.0, y, 1, 0 );
// y => <Float64Array>[ 7.0, 10.0, 9.0 ]

The function has the following additional parameters:

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

dsymv.ndarray( 'row-major', 'lower', 3, 1.0, A, 3, x, -1, 2, 1.0, y, -1, 2 );
// y => <Float64Array>[ 4.0, 3.0, 2.0 ]