# @stdlib/lapack-base-dpttrf

0.1.0 • Public • Published

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# dpttrf

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

## Usage

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

#### 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:

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

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

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 );```

## Installation

`npm install @stdlib/lapack-base-dpttrf`

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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.

## Package Sidebar

### Install

`npm i @stdlib/lapack-base-dpttrf`

### Repository

github.com/stdlib-js/lapack-base-dpttrf

stdlib.io

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