dsyr

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

Installation

npm install @stdlib/blas-base-dsyr

Usage

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

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

var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsyr( 'row-major', 'upper', 3, 1.0, x, 1, A, 3 );
// A => <Float64Array>[ 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 Float64Array.
• sx: stride length for x.
• A: input matrix stored in linear memory as a Float64Array.
• 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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] );
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );

dsyr( 'row-major', 'upper', 3, 1.0, x, -1, A, 3 );
// A => <Float64Array>[ 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 Float64Array = require( '@stdlib/array-float64' );

// Initial arrays...
var x0 = new Float64Array( [ 0.0, 3.0, 2.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] );

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dsyr( 'row-major', 'upper', 3, 1.0, x1, -1, A, 3 );
// A => <Float64Array>[ 2.0, 4.0, 6.0, 2.0, 5.0, 8.0, 3.0, 2.0, 10.0 ]

dsyr.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 Float64Array = require( '@stdlib/array-float64' );

var A = new Float64Array( [ 1.0, 2.0, 3.0, 2.0, 1.0, 2.0, 3.0, 2.0, 1.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsyr.ndarray( 'upper', 3, 1.0, x, 1, 0, A, 3, 1, 0 );
// A => <Float64Array>[ 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 Float64Array = require( '@stdlib/array-float64' );

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

dsyr.ndarray( 'upper', 3, 1.0, x, -2, 4, A, 3, 1, 0 );
// A => <Float64Array>[ 26.0, 17.0, 8.0, 2.0, 10.0, 5.0, 3.0, 2.0, 2.0 ]

Notes

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

Examples

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

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

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 );

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

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

C APIs

Usage

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

c_dsyr( 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"

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

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

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

c_dsyr_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"

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

c_dsyr_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] double scalar constant.
• X: [in] double* input array.
• sx: [in] CBLAS_INT stride length for X.
• ox: [in] CBLAS_INT starting index for X.
• A: [inout] double* 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_dsyr_ndarray( const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA )

Examples

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

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

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

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

    // 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_dsyr( CblasColMajor, CblasUpper, N, 1.0, x, 1, A1, N );

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

    // Perform the symmetric rank 1 operation `A = α*x*x^T + A` using alternative indexing semantics:
    c_dsyr_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 ] = %lf\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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.