dspr

Usage

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

dspr( order, uplo, N, α, x, sx, AP )

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 supplied in packed form.

var Float64Array = require( '@stdlib/array/float64' );

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

dspr( 'row-major', 'upper', 3, 1.0, x, 1, AP );
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 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 is supplied.
• N: number of elements along each dimension of A.
• α: scalar constant.
• x: input Float64Array.
• sx: index increment for x.
• AP: packed form of a symmetric matrix A stored as a Float64Array.

The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of x in reverse order,

var Float64Array = require( '@stdlib/array/float64' );

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

dspr( 'row-major', 'upper', 3, 1.0, x, -1, AP );
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ]

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

// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dspr( 'row-major', 'upper', 3, 1.0, x1, -1, AP );
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ]

dspr.ndarray( uplo, N, α, x, sx, ox, AP, sap, oap )

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 supplied in packed form.

var Float64Array = require( '@stdlib/array/float64' );

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

dspr.ndarray( 'row-major', 'lower', 3, 1.0, x, 1, 0, AP, 1, 0 );
// AP => <Float64Array>[ 2.0, 3.0, 6.0, 4.0, 8.0, 12.0 ]

The function has the following additional parameters:

• ox: starting index for x.
• sap: AP stride length.
• oap: starting index for AP.

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

dspr.ndarray( 'row-major', 'upper', 3, 1.0, x, -1, 2, AP, 1, 0 );
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ]