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ssyr2

README.md

ssyr2

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

Usage

var ssyr2 = require( '@stdlib/blas/base/ssyr2' );

ssyr2( 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 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 ] );
var y = new Float32Array( [ 1.0, 2.0, 3.0 ] );

ssyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A, 3 );
// A => <Float32Array>[ 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 Float32Array.
  • sx: stride length for x.
  • y: second input Float32Array.
  • sy: stride length for y.
  • 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 every other element of x,

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

ssyr2( 'row-major', 'upper', 3, 1.0, x, 2, y, 1, A, 3 );
// A => <Float32Array>[ 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 Float32Array = require( '@stdlib/array/float32' );

// Initial arrays...
var x0 = new Float32Array( [ 0.0, 1.0, 1.0, 1.0 ] );
var y0 = new Float32Array( [ 0.0, 1.0, 2.0, 3.0 ] );
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
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

ssyr2( 'row-major', 'upper', 3, 1.0, x1, 1, y1, 1, A, 3 );
// A => <Float32Array>[ 3.0, 5.0, 7.0, 2.0, 5.0, 7.0, 3.0, 2.0, 7.0 ]

ssyr2.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 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 ] );
var y = new Float32Array( [ 1.0, 2.0, 3.0 ] );

ssyr2.ndarray( 'upper', 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
// A => <Float32Array>[ 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 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 ] );
var y = new Float32Array( [ 1.0, 2.0, 3.0 ] );

ssyr2.ndarray( 'upper', 3, 1.0, x, -2, 4, y, 1, 0, A, 3, 1, 0 );
// A => <Float32Array>[ 11.0, 15.0, 19.0, 2.0, 13.0, 13.0, 3.0, 2.0, 7.0 ]

Notes

  • ssyr2() corresponds to the BLAS level 2 function ssyr2.

Examples

var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ones = require( '@stdlib/array/ones' );
var ssyr2 = require( '@stdlib/blas/base/ssyr2' );

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

ssyr2( 'row-major', 'upper', 3, 1.0, x, 1, y, 1, A1, 3 );
console.log( A1 );

ssyr2.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/ssyr2.h"

c_ssyr2( 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"

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

c_ssyr2( CblasColMajor, CblasUpper, 3, 1.0f, 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] float scalar constant.
  • X: [in] float* first input array.
  • strideX: [in] CBLAS_INT stride length for X.
  • Y: [in] float* second input array.
  • strideY: [in] CBLAS_INT stride length for Y.
  • 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_ssyr2( const CBLAS_LAYOUT order, const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const float *Y, const CBLAS_INT strideY, float *A, const CBLAS_INT LDA )

c_ssyr2_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"

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

c_ssyr2_ndarray( CblasUpper, 3, 1.0f, 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] float scalar constant.
  • X: [in] float* first input array.
  • sx: [in] CBLAS_INT stride length for X.
  • ox: [in] CBLAS_INT starting index for X.
  • Y: [in] float second input array.
  • sy: [in] CBLAS_INT stride length for Y.
  • oy: [in] CBLAS_INT starting index for Y.
  • 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_ssyr2_ndarray( const CBLAS_UPLO uplo, const CBLAS_INT N, const float alpha, const float *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, const float *Y, CBLAS_INT strideY, const CBLAS_INT offsetY, float *A, const CBLAS_INT strideA1, const CBLAS_INT strideA2, const CBLAS_INT offsetA )

Examples

#include "stdlib/blas/base/ssyr2.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 `x` and `y` vectors:
    const float x[ 3 ] = { 1.0f, 2.0f, 3.0f };
    const float y[ 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 2 operation `A = α*x*y^T + α*y*x^T + A`:
    c_ssyr2( CblasColMajor, CblasUpper, N, 1.0f, x, 1, y, 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 2 operation `A = α*x*y^T + α*y*x^T + A` using alternative indexing semantics:
    c_ssyr2_ndarray( CblasUpper, N, 1.0f, x, 1, 0, y, 1, 0, A2, N, 1, 0 );

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