dsyr2

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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 9.0, 14.0, 0.0, 0.0, 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: index increment for x.
• y: second input Float64Array.
• sy: index increment 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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 13.0, 21.0, 0.0, 0.0, 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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 5.0, 7.0, 0.0, 0.0, 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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 9.0, 14.0, 0.0, 0.0, 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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 13.0, 13.0, 0.0, 0.0, 7.0 ]