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dpttrf

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

Usage

To use in Observable,

dpttrf = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/lapack-base-dpttrf@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var dpttrf = require( 'path/to/vendor/umd/lapack-base-dpttrf/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/lapack-base-dpttrf@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.dpttrf;
})();
</script>

dpttrf( N, D, E )

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

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

var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
var E = new Float64Array( [ 1.0, 2.0 ] );

dpttrf( 3, D, E );
// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
// E => <Float64Array>[ 0.25, ~0.4210 ]

The function has the following parameters:

• N: order of matrix A.
• D: the N diagonal elements of A as a Float64Array.
• E: the N-1 subdiagonal elements of A as a Float64Array.

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 D0 = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
var E0 = new Float64Array( [ 0.0, 1.0, 2.0 ] );

// Create offset views...
var D1 = new Float64Array( D0.buffer, D0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var E1 = new Float64Array( E0.buffer, E0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

dpttrf( 3, D1, E1 );
// D0 => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
// E0 => <Float64Array>[ 0.0, 0.25, ~0.4210 ]

dpttrf.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 Float64Array = require( '@stdlib/array-float64' );

var D = new Float64Array( [ 4.0, 5.0, 6.0 ] );
var E = new Float64Array( [ 1.0, 2.0 ] );

dpttrf.ndarray( 3, D, 1, 0, E, 1, 0 );
// D => <Float64Array>[ 4, 4.75, ~5.15789 ]
// E => <Float64Array>[ 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 Float64Array = require( '@stdlib/array-float64' );

var D = new Float64Array( [ 0.0, 4.0, 5.0, 6.0 ] );
var E = new Float64Array( [ 0.0, 1.0, 2.0 ] );

dpttrf.ndarray( 3, D, 1, 1, E, 1, 1 );
// D => <Float64Array>[ 0.0, 4.0, 4.75, ~5.15789 ]
// E => <Float64Array>[ 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.

• dpttrf() corresponds to the LAPACK routine dpttrf.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-array-discrete-uniform@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/lapack-base-dpttrf@umd/browser.js"></script>
<script type="text/javascript">
(function () {

var opts = {
    'dtype': 'float64'
};
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 = dpttrf( D.length, D, E );
console.log( D );
console.log( E );
console.log( info );

})();
</script>
</body>
</html>

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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

Copyright © 2016-2025. The Stdlib Authors.