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Perform the symmetric rank 2 operation
A = α*x*y^T + α*y*x^T + A.
npm install @stdlib/blas-base-dsyr2Alternatively,
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scripttag without installation and bundlers, use the ES Module available on theesmbranch (see README). - If you are using Deno, visit the
denobranch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch (see README).
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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.
var dsyr2 = require( '@stdlib/blas-base-dsyr2' );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
Ashould 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 matrixA).
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 ]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 ]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 );#include "stdlib/blas/base/dsyr2.h"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_LAYOUTstorage layout. - uplo:
[in] CBLAS_UPLOspecifies whether the upper or lower triangular part of the symmetric matrixAshould be referenced. - N:
[in] CBLAS_INTnumber of elements along each dimension ofA. - alpha:
[in] doublescalar constant. - X:
[in] double*first input array. - strideX:
[in] CBLAS_INTstride length forX. - Y:
[in] double*second input array. - strideY:
[in] CBLAS_INTstride length forY. - A:
[inout] double*input matrix. - LDA:
[in] CBLAS_INTstride of the first dimension ofA(a.k.a., leading dimension of the matrixA).
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 )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_UPLOspecifies whether the upper or lower triangular part of the symmetric matrixAshould be referenced. - N:
[in] CBLAS_INTnumber of elements along each dimension ofA. - alpha:
[in] doublescalar constant. - X:
[in] double*first input array. - sx:
[in] CBLAS_INTstride length forX. - ox:
[in] CBLAS_INTstarting index forX. - Y:
[in] doublesecond input array. - sy:
[in] CBLAS_INTstride length forY. - oy:
[in] CBLAS_INTstarting index forY. - A:
[inout] double*input matrix. - sa1:
[in] CBLAS_INTstride of the first dimension ofA. - sa2:
[in] CBLAS_INTstride of the second dimension ofA. - oa:
[in] CBLAS_INTstarting index forA.
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 )#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 ] );
}
}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.
See LICENSE.
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