dsymv

Perform 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.

Installation

npm install @stdlib/blas-base-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 ]

Notes

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

Examples

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

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

var N = 3;
var A = ones( N*N, opts.dtype );

var x = discreteUniform( N, 0, 255, opts );
var y = discreteUniform( N, 0, 255, opts );

dsymv.ndarray( 'row-major', 'upper', N, 1.0, A, N, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );

C APIs

Usage

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Examples

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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.

Copyright

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