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dsyr2

README.md

dsyr2

Perform the symmetric rank 2 operation A = α*x*y^T + α*y*x^T + A.

Usage

var dsyr2 = require( '@stdlib/blas/base/dsyr2' );

dsyr2( order, uplo, N, α, x, sx, y, sy, A, LDA )

Performs the symmetric rank 2 operation A = α*x*y^T + α*y*x^T + A, where α is a scalar, x and y are N element vectors, 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 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A, 3 );
// A => <Float64Array>[ 3.0, 6.0, 9.0, 2.0, 9.0, 14.0, 3.0, 2.0, 19.0 ]

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: first input Float64Array.
  • sx: stride length for x.
  • y: second input Float64Array.
  • sy: stride length for y.
  • 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 every other element of x,

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

dsyr2( 'row-major', 'upper', 3, 1.0, x, 2, y, 1, A, 3 );
// A => <Float64Array>[ 3.0, 7.0, 11.0, 2.0, 13.0, 21.0, 3.0, 2.0, 31.0 ]

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, 1.0 ] );
var y0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
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
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dsyr2( 'row-major', 'upper', 3, 1.0, x1, 1, y1, 1, A, 3 );
// A => <Float64Array>[ 3.0, 5.0, 7.0, 2.0, 5.0, 7.0, 3.0, 2.0, 7.0 ]

dsyr2.ndarray( uplo, N, α, x, sx, ox, y, sy, oy, A, sa1, sa2, oa )

Performs the symmetric rank 2 operation A = α*x*y^T + α*y*x^T + A, using alternative indexing semantics and where α is a scalar, x and y are N element vectors, 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 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsyr2.ndarray( 'upper', 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
// A => <Float64Array>[ 3.0, 6.0, 9.0, 2.0, 9.0, 14.0, 3.0, 2.0, 19.0 ]

The function has the following additional parameters:

  • ox: starting index for x.
  • oy: starting index for y.
  • 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 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );

dsyr2.ndarray( 'upper', 3, 1.0, x, -2, 4, y, 1, 0, A, 3, 1, 0 );
// A => <Float64Array>[ 11.0, 15.0, 19.0, 2.0, 13.0, 13.0, 3.0, 2.0, 7.0 ]

Notes

  • dsyr2() corresponds to the BLAS level 2 function dsyr2.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ones = require( '@stdlib/array/ones' );
var dsyr2 = require( '@stdlib/blas/base/dsyr2' );

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 random vectors:
var x = discreteUniform( N, -10.0, 10.0, opts );
var y = discreteUniform( N, -10.0, 10.0, opts );

dsyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A1, 3 );
console.log( A1 );

dsyr2.ndarray( 'upper', 3, 1.0, x, 1, 0, y, 1, 0, A2, 3, 1, 0 );
console.log( A2 );

C APIs

Usage

#include "stdlib/blas/base/dsyr2.h"

c_dsyr2( order, uplo, N, alpha, *X, sx, *Y, sy, *A, LDA )

Performs the symmetric rank 2 operation A = α*x*y^T + α*y*x^T + A where α is a scalar, x and y are N element vectors, 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 };
const double y[] = { 1.0, 2.0, 3.0 };

c_dsyr2( CblasColMajor, CblasUpper, 3, 1.0, x, 1, y, 1, A, 3 );

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] double scalar constant.
  • X: [in] double* first input array.
  • strideX: [in] CBLAS_INT stride length for X.
  • Y: [in] double* second input array.
  • strideY: [in] CBLAS_INT stride length for Y.
  • 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_dsyr2( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const double *Y, const CBLAS_INT strideY, double *A, const CBLAS_INT LDA )

c_dsyr2_ndarray( uplo, N, alpha, *X, sx, ox, *Y, sy, oy, *A, sa1, sa2, oa )

Performs the symmetric rank 2 operation A = α*x*y^T + α*y*x^T + A, using alternative indexing semantics and where α is a scalar, x and y are N element vectors, 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 };
const double y[] = { 1.0, 2.0, 3.0 };

c_dsyr2_ndarray( CblasUpper, 3, 1.0, x, 1, 0, y, 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* first input array.
  • sx: [in] CBLAS_INT stride length for X.
  • ox: [in] CBLAS_INT starting index for X.
  • Y: [in] double second input array.
  • sy: [in] CBLAS_INT stride length for Y.
  • oy: [in] CBLAS_INT starting index for Y.
  • 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_dsyr2_ndarray( const CBLAS_UPLO uplo, const CBLAS_INT N, const double alpha, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const double *Y, CBLAS_INT strideY, const CBLAS_INT offsetY, double *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA )

Examples

#include "stdlib/blas/base/dsyr2.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 `x` and `y` vectors:
    const double x[ 3 ] = { 1.0, 2.0, 3.0 };
    const double y[ 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 2 operation `A = α*x*y^T + α*y*x^T + A`:
    c_dsyr2( CblasColMajor, CblasUpper, N, 1.0, x, 1, y, 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 2 operation `A = α*x*y^T + α*y*x^T + A` using alternative indexing semantics:
    c_dsyr2_ndarray( CblasUpper, N, 1.0, x, 1, 0, y, 1, 0, A2, N, 1, 0 );

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