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dspmv

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 supplied in packed form.

Usage

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

dspmv( order, uplo, N, α, AP, 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 supplied in packed form AP.

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

var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, 1 );
// y => <Float64Array>[ 7.0, 12.0, 15.0 ]

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.
  • α: scalar constant.
  • AP: packed form of a symmetric matrix A stored in linear memory as a Float64Array.
  • 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 y in reverse order,

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

var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, -1 );
// y => <Float64Array>[ 15.0, 12.0, 7.0 ]

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

dspmv( 'row-major', 'upper', 2, 1.0, AP, x1, -1, 1.0, y1, -1 );
// y0 => <Float64Array>[ 0.0, 6.0, 4.0 ]

dspmv.ndarray( order, uplo, N, α, AP, oa, 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 supplied in packed form AP.

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

var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );
// y => <Float64Array>[ 7.0, 12.0, 15.0 ]

The function has the following additional parameters:

  • oa: starting index for AP.
  • 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 AP = new Float64Array( [ 0.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );

dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, 2, x, 1, 0, 1.0, y, -1, 2 );
// y => <Float64Array>[ 15.0, 12.0, 7.0 ]

Notes

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

Examples

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

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

var N = 3;
var AP = discreteUniform( N * ( N + 1 ) / 2, -10, 10, opts );

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

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

C APIs

Usage

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

c_dspmv( order, uplo, N, alpha, *AP, *X, strideX, beta, *Y, strideY )

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 supplied in packed form AP.

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

const double AP[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
const double x[] = { 1.0, 1.0, 1.0 };
double y[] = { 1.0, 1.0, 1.0 };

c_dspmv( CblasColMajor, CblasLower, 3, 1.0, AP, x, 1, 1.0, y, 1 );

The function accepts the following arguments:

  • order: [in] CBLAS_LAYOUT storage layout.
  • uplo: [in] CBLAS_UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is supplied.
  • N: [in] CBLAS_INT number of elements along each dimension of A.
  • alpha: [in] double scalar constant.
  • AP: [in] double* packed form of a symmetric matrix A.
  • X: [in] double* first input vector.
  • strideX: [in] CBLAS_INT stride length for X.
  • beta: [in] double scalar constant.
  • Y: [inout] double* second input vector.
  • strideY: [in] CBLAS_INT stride length for Y.
void c_dspmv( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *AP, const double *X, const CBLAS_INT strideX, const double beta, double *Y, const CBLAS_INT strideY )

c_dspmv_ndarray( order, uplo, N, alpha, *AP, oap, *X, sx, ox, beta, *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 supplied in packed form AP.

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

const double AP[] = { 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 };
const double x[] = { 1.0, 1.0, 1.0 };
double y[] = { 1.0, 1.0, 1.0 };

c_dspmv_ndarray( CblasColMajor, CblasLower, 3, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );

The function accepts the following arguments:

  • order: [in] CBLAS_LAYOUT storage layout.
  • uplo: [in] CBLAS_UPLO specifies whether the upper or lower triangular part of the symmetric matrix A is supplied.
  • N: [in] CBLAS_INT number of elements along each dimension of A.
  • alpha: [in] double scalar.
  • AP: [in] double* packed form of a symmetric matrix A.
  • oap: [in] CBLAS_INT starting index for AP.
  • X: [in] double* first input vector.
  • sx: [in] CBLAS_INT stride length for X.
  • ox: [in] CBLAS_INT starting index for X.
  • beta: [in] double scalar.
  • Y: [inout] double* second input vector.
  • sy: [in] CBLAS_INT stride length for Y.
  • oy: [in] CBLAS_INT starting index for Y.
void c_dspmv_ndarray( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *AP, const CBLAS_INT offsetAP, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double beta, double *Y, const CBLAS_INT strideY, const CBLAS_INT offsetY )

Examples

#include "stdlib/blas/base/dspmv.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Define `AP`, a packed form of a symmetric matrix `A`:
    const double AP[ 3*(3+1)/2 ] = {
        1.0, 2.0, 3.0, 4.0, 5.0, 6.0
    };

    // Define `x` and `y` vectors:
    const double x[ 3 ] = { 1.0, 1.0, 1.0 };
    double y[ 3 ] = { 1.0, 1.0, 1.0 };

    // Specify the number of elements along each dimension of `A`:
    const int N = 3;

    // Perform the matrix-vector operation `y = α*A*x + β*y`:
    c_dspmv( CblasColMajor, CblasLower, N, 1.0, AP, x, 1, 1.0, y, 1 );

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

    // Perform the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics:
    c_dspmv_ndarray( CblasColMajor, CblasLower, N, 1.0, AP, 0, x, 1, 0, 1.0, y, 1, 0 );

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