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* @license Apache-2.0
*
* Copyright (c) 2025 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';
// MODULES //
var abs = require( '@stdlib/math/base/special/abs' );
// MAIN //
/**
* Computes an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges.
*
* ## Notes
*
* - On exit, `DL` is overwritten by the multipliers that define the matrix `L` from the `LU` factorization of `A`.
* - On exit, `D` is overwritten by the diagonal elements of the upper triangular matrix `U` from the `LU` factorization of `A`.
* - On exit, `DU` is overwritten by the elements of the first super-diagonal of `U`.
* - On exit, `DU2` is overwritten by the elements of the second super-diagonal of `U`.
* - On exit, for 0 <= i < n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
*
* @private
* @param {NonNegativeInteger} N - order of matrix A.
* @param {Float64Array} DL - sub diagonal elements of A.
* @param {integer} sdl - stride length for `DL`
* @param {NonNegativeInteger} odl - starting index of `DL`
* @param {Float64Array} D - diagonal elements of A.
* @param {integer} sd - stride length for `D`
* @param {NonNegativeInteger} od - starting index of `D`
* @param {Float64Array} DU - super diagonal elements of A.
* @param {integer} sdu - stride length for `DU`
* @param {NonNegativeInteger} odu - starting index of `DU`
* @param {Float64Array} DU2 - vector to store the second super diagonal of `U`
* @param {integer} sdu2 - stride length for `DU2`
* @param {NonNegativeInteger} odu2 - starting index of `DU2`
* @param {Int32Array} IPIV - vector of pivot indices
* @param {integer} si - stride length for `IPIV`
* @param {NonNegativeInteger} oi - starting index of `IPIV`
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' )
*
* var DL = new Float64Array( [ 1.0, 1.0 ] );
* var D = new Float64Array( [ 2.0, 3.0, 1.0 ] );
* var DU = new Float64Array( [ 1.0, 1.0 ] );
* var DU2 = new Float64Array( 1 );
* var IPIV = new Int32Array( 3 );
*
* dgttrf( 3, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 );
* // DL => <Float64Array>[ 0.5, 0.4 ]
* // D => <Float64Array>[ 2, 2.5, 0.6 ]
* // DU => <Float64Array>[ 1, 1 ]
* // DU2 => <Float64Array>[ 0 ]
* // IPIV => <Int32Array>[ 0, 1, 2 ]
*/
function dgttrf( N, DL, sdl, odl, D, sd, od, DU, sdu, odu, DU2, sdu2, odu2, IPIV, si, oi ) { // eslint-disable-line max-len, max-params
var fact;
var temp;
var idu2;
var idu;
var idl;
var dli;
var dui;
var id;
var ip;
var di;
var ii;
var i;
// Quick return if possible
if ( N === 0 ) {
return 0;
}
idl = odl;
id = od;
idu = odu;
idu2 = odu2;
ip = oi;
// Initialise ith element of IPIV as i
for ( i = 0; i < N; i++ ) {
IPIV[ ip + (si*i) ] = i;
}
// Initialise ith element of DU2 as 0
for ( i = 0; i < N-2; i++ ) {
DU2[ idu + (sdu*i) ] = 0;
}
for ( i = 0; i < N-2; i++ ) {
di = sd * i;
dli = sdl * i;
ii = si * i;
dui = sdu * i;
if ( abs( D[ id + di ] ) >= abs( DL[ idl + dli ] ) ) { // No row interchange required, eleminate ith element of DL
if ( D[ id ] !== 0.0 ) {
fact = DL[ idl + dli ] / D[ id + di ];
DL[ idl + dli ] = fact;
D[ id + di + sd ] = D[ id + di + sd ] - ( fact*DU[ idu + dui ] ); // eslint-disable-line max-len
}
} else { // Interchange the ith and (i+1)th rows and eliminate ith element of DL
fact = D[ id + di ] / DL[ idl + dli ];
D[ id + di ] = DL[ idl + dli ];
DL[ idl + dli ] = fact;
temp = DU[ idu + dui ];
DU[ idu + dui ] = D[ id + di + sd ];
D[ id + di + sd ] = temp - ( fact * D[ id + di + sd ] );
DU2[ idu2 + ( sdu2 * i ) ] = DU[ idu + dui + sdu ];
DU[ idu + dui + sdu ] = -fact * DU[ idu + dui + sdu ];
IPIV[ ip + ii ] = i + 1;
}
}
if ( N > 1 ) {
i = N - 2;
di = sd * i;
dli = sdl * i;
ii = si * i;
dui = sdu * i;
if ( abs( D[ id + di ] ) >= abs( DL[ idl + dli ] ) ) {
if ( D[ id + di ] !== 0 ) {
fact = DL[ idl + dli ] / D[ id + di ];
DL[ idl + dli ] = fact;
D[ id + di + sd ] = D[ id + di + sd ] - (fact*DU[ idu + dui ]);
}
} else {
fact = D[ id + di ] / DL[ idl + dli ];
D[ id + di ] = DL[ idl + dli ];
DL[ idl + dli ] = fact;
temp = DU[ idu + dui ];
DU[ idu + dui ] = D[ id + di + sd ];
D[ id + di + sd ] = temp - ( fact * D[ id + di + sd ] );
IPIV[ ip + ii ] = i + 1;
}
}
// Check for a 0 on the diagonal of U
for ( i = 0; i < N; i++ ) {
if ( D[ sd * i ] === 0.0 ) {
return i;
}
}
return 0;
}
// EXPORTS //
module.exports = dgttrf;
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