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sspr

README.md

sspr

Perform the symmetric rank 1 operation A = α*x*x^T + A.

Usage

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

sspr( order, uplo, N, α, x, sx, AP )

Performs the symmetric rank 1 operation A = α*x*x^T + A where α is a scalar, x is an N element vector, and A is an N by N symmetric matrix supplied in packed form.

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

var AP = new Float32Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );

sspr( 'row-major', 'upper', 3, 1.0, x, 1, AP );
// AP => <Float32Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 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: number of elements along each dimension of A.
  • α: scalar constant.
  • x: input Float32Array.
  • sx: index increment for x.
  • AP: packed form of a symmetric matrix A stored as a Float32Array.

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

var AP = new Float32Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] );
var x = new Float32Array( [ 3.0, 2.0, 1.0 ] );

sspr( 'row-major', 'upper', 3, 1.0, x, -1, AP );
// AP => <Float32Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 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, 3.0, 2.0, 1.0 ] );
var AP = new Float32Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] );

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

sspr( 'row-major', 'upper', 3, 1.0, x1, -1, AP );
// AP => <Float32Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ]

sspr.ndarray( uplo, N, α, x, sx, ox, AP, sap, oap )

Performs the symmetric rank 1 operation A = α*x*x^T + A, using alternative indexing semantics and where α is a scalar, x is an N element vector, and A is an N by N symmetric matrix supplied in packed form.

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

var AP = new Float32Array( [ 1.0, 1.0, 2.0, 1.0, 2.0, 3.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );

sspr.ndarray( 'row-major', 'lower', 3, 1.0, x, 1, 0, AP, 1, 0 );
// AP => <Float32Array>[ 2.0, 3.0, 6.0, 4.0, 8.0, 12.0 ]

The function has the following additional parameters:

  • ox: starting index for x.
  • sap: AP stride length.
  • oap: starting index for AP.

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 AP = new Float32Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] );
var x = new Float32Array( [ 3.0, 2.0, 1.0 ] );

sspr.ndarray( 'row-major', 'upper', 3, 1.0, x, -1, 2, AP, 1, 0 );
// AP => <Float32Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ]

Notes

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

Examples

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

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

var N = 5;

var AP = discreteUniform( N * ( N + 1 ) / 2, -10.0, 10.0, opts );
var x = discreteUniform( N, -10.0, 10.0, opts );

sspr( 'column-major', 'upper', N, 1.0, x, 1, AP );
console.log( AP );

sspr.ndarray( 'column-major', 'upper', N, 1.0, x, 1, 0, AP, 1, 0 );
console.log( AP );

C APIs

Usage

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

c_sspr( order, uplo, N, alpha, *X, strideX, *AP )

Performs the symmetric rank 1 operation A = α*x*x^T + A where α is a scalar, x is an N element vector, and A is an N by N symmetric matrix supplied in packed form.

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

float AP[] = { 1.0f, 2.0f, 3.0f, 1.0f, 2.0f, 1.0f };
const float x[] = { 1.0f, 2.0f, 3.0f };

c_sspr( CblasColMajor, CblasUpper, 3, 1.0f, x, 1, AP );

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 should be referenced.
  • N: [in] CBLAS_INT number of elements along each dimension of A.
  • alpha: [in] float scalar.
  • X: [in] float* input vector.
  • strideX: [in] CBLAS_INT stride length for X.
  • AP: [inout] float* packed form of a symmetric matrix A.
void c_sspr( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, float *AP )

c_sspr_ndarray( order, uplo, N, alpha, *X, strideX, offsetX, *AP, strideAP, offsetAP )

Performs the symmetric rank 1 operation A = α*x*x^T + A where α is a scalar, x is an N element vector, and A is an N by N symmetric matrix supplied in packed form using alternative indexing semantics.

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

float AP[] = { 1.0f, 2.0f, 3.0f, 1.0f, 2.0f, 1.0f };
const float x[] = { 1.0f, 2.0f, 3.0f };

c_sspr_ndarray( CblasColMajor, CblasUpper, 3, 1.0f, x, 1, AP, 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 should be referenced.
  • N: [in] CBLAS_INT number of elements along each dimension of A.
  • alpha: [in] float scalar.
  • X: [in] float* input vector.
  • strideX: [in] CBLAS_INT stride length for X.
  • offsetX: [in] CBLAS_INT starting index for X.
  • AP: [inout] float* packed form of a symmetric matrix A.
  • strideAP: [in] CBLAS_INT stride length for AP.
  • offsetAP: [in] CBLAS_INT starting index for AP.
void c_sspr_ndarray( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *AP, const CBLAS_INT strideAP, const CBLAS_INT offsetAP )

Examples

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

int main( void ) {
    // Create strided arrays:
    float AP[] = { 1.0f, 2.0f, 3.0f, 1.0f, 2.0f, 1.0f };
    const float x[] = { 1.0f, 2.0f, 3.0f };

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

    // Perform the symmetric rank 1 operation `A = α*x*x^T + A`:
    c_sspr( CblasRowMajor, CblasUpper, N, 1.0f, x, 1, AP );

    // Print the result:
    for ( int i = 0; i < N*(N+1)/2; i++ ) {
        printf( "AP[ %i ] = %f\n", i, AP[ i ] );
    }

    // Perform the symmetric rank 1 operation `A = α*x*x^T + A` using alternative indexing semantics:
    c_sspr_ndarray( CblasRowMajor, CblasUpper, N, 1.0f, x, 1, 0, AP, 1, 0 );

    // Print the result:
    for ( int i = 0; i < N*(N+1)/2; i++ ) {
        printf( "AP[ %i ] = %f\n", i, AP[ i ] );
    }
}