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sspr

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

Installation

npm install @stdlib/blas-base-sspr

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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 );

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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 ] );
    }
}

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.