@stdlib/lapack-base-spttrf

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spttrf

Compute the L * D * L^T factorization of a real symmetric positive definite tridiagonal matrix A.

Installation

npm install @stdlib/lapack-base-spttrf

Usage

var spttrf = require( '@stdlib/lapack-base-spttrf' );

spttrf( N, D, E )

Computes the L * D * L^T factorization of a real symmetric positive definite tridiagonal matrix A.

var Float32Array = require( '@stdlib/array-float32' );

var D = new Float32Array( [ 4.0, 5.0, 6.0 ] );
var E = new Float32Array( [ 1.0, 2.0 ] );

spttrf( 3, D, E );
// D => <Float32Array>[ 4, 4.75, ~5.15789 ]
// E => <Float32Array>[ 0.25, ~0.4210 ]

The function has the following parameters:

• N: order of matrix A.
• D: the N diagonal elements of A as a Float32Array.
• E: the N-1 subdiagonal elements of A as a Float32Array.

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

var Float32Array = require( '@stdlib/array-float32' );

// Initial arrays...
var D0 = new Float32Array( [ 0.0, 4.0, 5.0, 6.0 ] );
var E0 = new Float32Array( [ 0.0, 1.0, 2.0 ] );

// Create offset views...
var D1 = new Float32Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var E1 = new Float32Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

spttrf( 3, D1, E1 );
// D0 => <Float32Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
// E0 => <Float32Array>[ 0.0, 0.25, ~0.4210 ]

spttrf.ndarray( N, D, strideD, offsetD, E, strideE, offsetE )

Computes the L * D * L^T factorization of a real symmetric positive definite tridiagonal matrix A using alternative indexing semantics.

var Float32Array = require( '@stdlib/array-float32' );

var D = new Float32Array( [ 4.0, 5.0, 6.0 ] );
var E = new Float32Array( [ 1.0, 2.0 ] );

spttrf.ndarray( 3, D, 1, 0, E, 1, 0 );
// D => <Float32Array>[ 4, 4.75, ~5.15789 ]
// E => <Float32Array>[ 0.25, ~0.4210 ]

The function has the following additional parameters:

• strideD: stride length for D.
• offsetD: starting index for D.
• strideE: stride length for E.
• offsetE: starting index for E.

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 Float32Array = require( '@stdlib/array-float32' );

var D = new Float32Array( [ 0.0, 4.0, 5.0, 6.0 ] );
var E = new Float32Array( [ 0.0, 1.0, 2.0 ] );

spttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
// D => <Float32Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
// E => <Float32Array>[ 0.0, 0.25, ~0.4210 ]

Notes

• Both functions mutate the input arrays D and E.

• Both functions return a status code indicating success or failure. A status code indicates the following conditions:

  • 0: factorization was successful.
  • <0: the k-th argument had an illegal value, where -k equals the status code value.
  • 0 < k < N: the leading principal minor of order k is not positive and factorization could not be completed, where k equals the status code value.
  • N: the leading principal minor of order N is not positive, and factorization was completed.

• spttrf() corresponds to the LAPACK routine spttrf.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var spttrf = require( '@stdlib/lapack-base-spttrf' );

var opts = {
    'dtype': 'float32'
};
var D = discreteUniform( 5, 1, 5, opts );
console.log( D );

var E = discreteUniform( D.length-1, 1, 5, opts );
console.log( E );

// Perform the `L * D * L^T` factorization:
var info = spttrf( D.length, D, E );
console.log( D );
console.log( E );
console.log( info );

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C APIs

Usage

TODO

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Examples

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Notice

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.

Community

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License

See LICENSE.

Copyright

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