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About stdlib...

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dspr

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Perform the symmetric rank 1 operation A = α*x*x^T + A.

Usage

import dspr from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-dspr@esm/index.mjs';

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.

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

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,

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

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.

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

// 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.

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

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,

import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@esm/index.mjs';

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 ]

Notes

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

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">

import discreteUniform from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-array-discrete-uniform@esm/index.mjs';
import dspr from 'https://cdn.jsdelivr.net/gh/stdlib-js/blas-base-dspr@esm/index.mjs';

var opts = {
    'dtype': 'float64'
};

var N = 5;

var AP = discreteUniform( N * ( N + 1 ) / 2, -10.0, 10.0, opts );
var x = discreteUniform( N, -10.0, 10.0, opts );

dspr( 'column-major', 'upper', N, 1.0, x, 1, AP );
console.log( AP );

dspr.ndarray( 'column-major', 'upper', N, 1.0, x, 1, 0, AP, 1, 0 );
console.log( AP );

</script>
</body>
</html>

Notice

This package is part of stdlib, a standard library 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.

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.