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ssbmv

Perform the matrix-vector operation y = alpha*A*x + beta*y where alpha and beta are scalars, x and y are N element vectors, and A is an N by N symmetric band matrix, with K super-diagonals.

Usage

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

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

Performs the matrix-vector operation y = alpha*A*x + beta*y where alpha and beta are scalars, x and y are N element vectors, and A is an N by N symmetric band matrix, with K super-diagonals.

var Float32Array = require( '@stdlib/array/float32' );

var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );

ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, 1 );
// y => <Float32Array>[ 10.0, 25.0, 10.0 ]

The function has the following parameters:

  • order: storage layout.
  • uplo: specifies whether the upper or lower triangular part of the symmetric matrix A is supplied.
  • N: specifies the order of the matrix A.
  • K: specifies the number of super-diagonals of the matrix A
  • α: scalar constant.
  • A: packed banded form of a symmetric matrix A stored in linear memory as a Float32Array.
  • LDA: stride of the first dimension of A (a.k.a., leading dimension of the matrix A)
  • x: input Float32Array.
  • sx: index increment for x.
  • β: scalar constant.
  • y: output Float32Array.
  • 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 y in reverse order,

var Float32Array = require( '@stdlib/array/float32' );

var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );

ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x, 1, 0.0, y, -1 );
// y => <Float32Array>[ 10.0, 25.0, 10.0 ]

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

var Float32Array = require( '@stdlib/array/float32' );

// Initial arrays...
var x0 = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var y0 = new Float32Array( [ 0.0, 0.0, 0.0, 0.0 ] );
var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );

// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

ssbmv( 'row-major', 'lower', 3, 1, 1.0, A, 2, x1, 1, 0.0, y1, 1 );
// y0 => <Float32Array>[ 0.0, 10.0, 25.0, 10.0 ]

ssbmv.ndarray( uplo, N, K, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy )

Performs the matrix-vector operation y = alpha*A*x + beta*y using alternative indexing semantics where alpha and beta are scalars, x and y are N element vectors, and A is an N by N symmetric band matrix, with K super-diagonals.

var Float32Array = require( '@stdlib/array/float32' );

var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );

ssbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 0, 0.0, y, 1, 0 );
// y => <Float32Array>[ 10.0, 25.0, 10.0 ]

The function has the following additional parameters:

  • oa: starting index for A.
  • sa1: first dimension index increment for A.
  • sa2: second dimension index increment 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 Float32Array = require( '@stdlib/array/float32' );

var A = new Float32Array( [ 1.0, 2.0, 4.0, 3.0, 5.0, 0.0 ] );
var x = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
var y = new Float32Array( [ 0.0, 0.0, 0.0, 0.0 ] );

ssbmv.ndarray( 'lower', 3, 1, 1.0, A, 2, 1, 0, x, 1, 1, 0.0, y, 1, 1 );
// y => <Float32Array>[ 0.0, 10.0, 25.0, 10.0 ]

Notes

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

Examples

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

var opts = {
    'dtype': 'float32'
};

var N = 3;
var A = [ 1, 2, 0, 3, 4, 5 ];

var x = discreteUniform( N, -10, 10, opts );
var y = discreteUniform( N, -10, 10, opts );

ssbmv.ndarray( 'upper', N, 1, 1.0, A, 1, 2, 0, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );

C APIs

Usage

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Examples

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