ssyr

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

Installation

npm install @stdlib/blas-base-ssyr

Usage

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

ssyr( order, uplo, N, α, x, sx, A, LDA )

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.

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

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

ssyr( 'row-major', 'upper', 3, 1.0, x, 1, A, 3 );
// A => <Float32Array>[ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 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 should be referenced.
• N: number of elements along each dimension of A.
• α: scalar constant.
• x: input Float32Array.
• sx: stride length for x.
• A: input matrix stored in linear memory as a Float32Array.
• LDA: stride of the first dimension of A (a.k.a., leading dimension of the matrix A).

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

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

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

ssyr( 'row-major', 'upper', 3, 1.0, x1, -1, A, 3 );
// A => <Float32Array>[ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ]

ssyr.ndarray( uplo, N, α, x, sx, ox, A, sa1, sa2, oa )

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.

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

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

ssyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A, 3, 1, 0 );
// A => <Float32Array>[ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ]

The function has the following additional parameters:

• ox: starting index for x.
• sa1: stride of the first dimension of A.
• sa2: stride of the second dimension of A.
• oa: starting index for A.

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

ssyr.ndarray( 'upper', 3, 1.0, x, -2, 4, A, 3, 1, 0 );
// A => <Float32Array>[ 26.0, 17.0, 8.0, 2.0, 10.0, 5.0, 3.0, 2.0, 2.0 ]

Notes

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

Examples

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

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

var N = 3;

// Create N-by-N symmetric matrices:
var A1 = ones( N*N, opts.dtype );
var A2 = ones( N*N, opts.dtype );

// Create a random vector:
var x = discreteUniform( N, -10.0, 10.0, opts );

ssyr( 'row-major', 'upper', 3, 1.0, x, 1, A1, 3 );
console.log( A1 );

ssyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A2, 3, 1, 0 );
console.log( A2 );

C APIs

Usage

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

c_ssyr( layout, uplo, N, alpha, *X, sx, *A, LDA )

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.

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

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

c_ssyr( CblasColMajor, CblasUpper, 3, 1.0, x, 1, A, 3 );

The function accepts the following arguments:

• layout: [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 constant.
• X: [in] float* input array.
• sx: [in] CBLAS_INT stride length for X.
• A: [inout] float* input matrix.
• LDA: [in] CBLAS_INT stride of the first dimension of A (a.k.a., leading dimension of the matrix A).

void c_ssyr( const CBLAS_LAYOUT layout, const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, float *A, const CBLAS_INT LDA )

c_ssyr_ndarray( uplo, N, alpha, *X, sx, ox, *A, sa1, sa2, oa )

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.

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

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

c_ssyr_ndarray( CblasUpper, 3, 1.0, x, 1, 0, A, 3, 1, 0 );

The function accepts the following arguments:

• 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 constant.
• X: [in] float* input array.
• sx: [in] CBLAS_INT stride length for X.
• ox: [in] CBLAS_INT starting index for X.
• A: [inout] float* input matrix.
• sa1: [in] CBLAS_INT stride of the first dimension of A.
• sa2: [in] CBLAS_INT stride of the second dimension of A.
• oa: [in] CBLAS_INT starting index for A.

void c_ssyr_ndarray( const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, float *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA )

Examples

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

int main( void ) {
    // Define 3x3 symmetric matrices stored in row-major layout:
    float A1[ 3*3 ] = {
        1.0f, 2.0f, 3.0f,
        2.0f, 1.0f, 2.0f,
        3.0f, 2.0f, 1.0f
    };

    float A2[ 3*3 ] = {
        1.0f, 2.0f, 3.0f,
        2.0f, 1.0f, 2.0f,
        3.0f, 2.0f, 1.0f
    };

    // Define a vector:
    const float x[ 3 ] = { 1.0f, 2.0f, 3.0f };

    // Specify the number of elements along each dimension of `A1` and `A2`:
    const int N = 3;

    // Perform the symmetric rank 1 operation `A = α*x*x^T + A`:
    c_ssyr( CblasColMajor, CblasUpper, N, 1.0f, x, 1, A1, N );

    // Print the result:
    for ( int i = 0; i < N*N; i++ ) {
        printf( "A1[ %i ] = %f\n", i, A1[ i ] );
    }

    // Perform the symmetric rank 1 operation `A = α*x*x^T + A` using alternative indexing semantics:
    c_ssyr_ndarray( CblasUpper, N, 1.0, x, 1, 0, A2, N, 1, 0 );

    // Print the result:
    for ( int i = 0; i < N*N; i++ ) {
        printf( "A2[ %i ] = %f\n", i, A[ i ] );
    }
}

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.

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License

See LICENSE.

Copyright

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