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* @license Apache-2.0
*
* Copyright (c) 2024 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MAIN //
/**
* Computes the `L * D * L^T` factorization of a real symmetric positive definite tridiagonal matrix `A`.
*
* @private
* @param {NonNegativeInteger} N - order of matrix `A`
* @param {Float64Array} D - the `N` diagonal elements of `A`
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index of `D`
* @param {Float64Array} E - the `N-1` subdiagonal elements of `A`
* @param {integer} strideE - stride length for `E`
* @param {NonNegativeInteger} offsetE - starting index of `E`
* @returns {integer} status code
*
* @example
* 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, 1, 0, E, 1, 0 );
* // D => <Float64Array>[ 4, 4.75, ~5.15789 ]
* // E => <Float64Array>[ 0.25, ~0.4210 ]
*/
function dpttrf( N, D, strideD, offsetD, E, strideE, offsetE ) {
var id;
var ie;
var v;
var i;
if ( N === 0 ) {
return 0;
}
ie = offsetE;
id = offsetD;
// Compute the `L * D * L^T` factorization of `A`...
for ( i = 0; i < N-1; i++ ) {
// If `D[k] <= 0`, then the matrix is not positive definite...
if ( D[ id ] <= 0.0 ) {
return i+1;
}
// Solve for E[k] and D[k+1]...
v = E[ ie ];
E[ ie ] = v / D[ id ];
id += strideD;
D[ id ] -= E[ ie ] * v;
ie += strideE;
}
// Check `D[k]` for positive definiteness...
if ( D[ id ] <= 0.0 ) {
return N;
}
return 0;
}
// EXPORTS //
module.exports = dpttrf;
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