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Compute the
L * D * L^T
factorization of a real symmetric positive definite tridiagonal matrixA
.
var dpttrf = require( '@stdlib/lapackbasedpttrf' );
Computes the L * D * L^T
factorization of a real symmetric positive definite tridiagonal matrix A
.
var Float64Array = require( '@stdlib/arrayfloat64' );
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 ofA
as aFloat64Array
. 
E: the N1 subdiagonal elements of
A
as aFloat64Array
.
Note that indexing is relative to the first index. To introduce an offset, use typed array
views.
var Float64Array = require( '@stdlib/arrayfloat64' );
// 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 ]
Computes the L * D * L^T
factorization of a real symmetric positive definite tridiagonal matrix A
using alternative indexing semantics.
var Float64Array = require( '@stdlib/arrayfloat64' );
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/arrayfloat64' );
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 ]

Both functions mutate the input arrays
D
andE
. 
Both functions return a status code indicating success or failure. A status code indicates the following conditions:

0
: factorization was successful. 
<0
: the kth argument had an illegal value, wherek
equals the status code value. 
0 < k < N
: the leading principal minor of orderk
is not positive and factorization could not be completed, wherek
equals the status code value. 
N
: the leading principal minor of orderN
is not positive, and factorization was completed.

var discreteUniform = require( '@stdlib/randomarraydiscreteuniform' );
var dpttrf = require( '@stdlib/lapackbasedpttrf' );
var opts = {
'dtype': 'float64'
};
var D = discreteUniform( 5, 1, 5, opts );
console.log( D );
var E = discreteUniform( D.length1, 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 );
npm install @stdlib/lapackbasedpttrf
TODO
TODO.
TODO
TODO
TODO
TODO
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.
See LICENSE.
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