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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 5.0, 8.0, 0.0, 0.0, 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: index increment 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 every other element of x in reverse order,

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 ] );

dsyr( 'row-major', 'upper', 3, 1.0, x, -2, A, 3 );
// A => <Float64Array>[ 26.0, 17.0, 8.0, 0.0, 10.0, 5.0, 0.0, 0.0, 2.0 ]

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( [ 1.0, 1.0, 1.0, 1.0 ] );
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

dsyr( 'row-major', 'upper', 3, 1.0, x1, -1, A, 3 );
// A => <Float64Array>[ 2.0, 3.0, 4.0, 0.0, 2.0, 3.0, 0.0, 0.0, 2.0 ]

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, 0.0, 1.0, 2.0, 0.0, 0.0, 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, 0.0, 5.0, 8.0, 0.0, 0.0, 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, 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 ] );

dsyr.ndarray( 'upper', 3, 1.0, x, -2, 4, A, 3, 1, 0 );
// A => <Float64Array>[ 26.0, 17.0, 8.0, 0.0, 10.0, 5.0, 0.0, 0.0, 2.0 ]