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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 tridiagonal matrix `A` using elimination with partial pivoting and row interchanges.
*
* ## Notes
*
* - `DL` is overwritten by the multipliers that define the matrix `L` from the `LU` factorization of `A`.
* - `D` is overwritten by the diagonal elements of the upper triangular matrix `U` from the `LU` factorization of `A`.
* - `DU` is overwritten by the elements of the first super-diagonal of `U`.
* - `DU2` is overwritten by the elements of the second super-diagonal of `U`.
* - 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 - number of rows/columns in `A`
* @param {Float64Array} DL - the first sub diagonal of `A`, expects N-1 indexed elements
* @param {integer} strideDL - stride length for `DL`
* @param {NonNegativeInteger} offsetDL - starting index of `DL`
* @param {Float64Array} D - the diagonal of `A`, expects N indexed elements
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index of `D`
* @param {Float64Array} DU - the first super-diagonal of `A`, expects N-1 indexed elements
* @param {integer} strideDU - stride length for `DU`
* @param {NonNegativeInteger} offsetDU - starting index of `DU`
* @param {Float64Array} DU2 - the second super-diagonal of `U`, expects N-2 indexed elements
* @param {integer} strideDU2 - stride length for `DU2`
* @param {NonNegativeInteger} offsetDU2 - starting index of `DU2`
* @param {Int32Array} IPIV - vector of pivot indices, expects N indexed elements
* @param {integer} strideIPIV - stride length for `IPIV`
* @param {NonNegativeInteger} offsetIPIV - 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( [ 0.0 ] );
* var IPIV = new Int32Array( [ 0, 0, 0 ] );
*
* 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, strideDL, offsetDL, D, strideD, offsetD, DU, strideDU, offsetDU, DU2, strideDU2, offsetDU2, IPIV, strideIPIV, offsetIPIV ) { // eslint-disable-line max-len, max-params
var fact;
var temp;
var idu2;
var idu;
var idl;
var id;
var ip;
var i;
// Quick return if possible
if ( N === 0 ) {
return 0;
}
idu2 = offsetDU2;
ip = offsetIPIV;
// Initialize ith element of IPIV as i
for ( i = 0; i < N; i++ ) {
IPIV[ ip ] = i;
if ( i < N-2 ) {
// Initialize ith element of DU2 as 0
DU2[ idu2 ] = 0;
}
ip += strideIPIV;
idu2 += strideDU2;
}
// Set the pointers to the starting indices
idu2 = offsetDU2;
ip = offsetIPIV;
idl = offsetDL;
id = offsetD;
idu = offsetDU;
for ( i = 0; i < N-2; i++ ) {
if ( abs( D[ id ] ) >= abs( DL[ idl ] ) ) { // No row interchange required, eleminate ith element of DL
if ( D[ id ] !== 0.0 ) {
fact = DL[ idl ] / D[ id ];
DL[ idl ] = fact;
D[ id + strideD ] = D[ id + strideD ] - ( fact*DU[ idu ] );
}
} else { // Interchange the ith and (i+1)th rows and eliminate ith element of DL
fact = D[ id ] / DL[ idl ];
D[ id ] = DL[ idl ];
DL[ idl ] = fact;
temp = DU[ idu ];
DU[ idu ] = D[ id + strideD ];
D[ id + strideD ] = temp - ( fact*D[ id + strideD ] );
DU2[ idu2 ] = DU[ idu + strideDU ];
DU[ idu + strideDU ] = -fact*DU[ idu + strideDU ];
IPIV[ ip ] = i + 1;
}
id += strideD;
idl += strideDL;
idu += strideDU;
idu2 += strideDU2;
ip += strideIPIV;
}
if ( N > 1 ) {
// Perform the final (N-2)th iteration separately for the last two rows
i = N - 2;
if ( abs( D[ id ] ) >= abs( DL[ idl ] ) ) {
if ( D[ id ] !== 0 ) {
fact = DL[ idl ] / D[ id ];
DL[ idl ] = fact;
D[ id + strideD ] = D[ id + strideD ] - ( fact * DU[ idu ] );
}
} else {
fact = D[ id ] / DL[ idl ];
D[ id ] = DL[ idl ];
DL[ idl ] = fact;
temp = DU[ idu ];
DU[ idu ] = D[ id + strideD ];
D[ id + strideD ] = temp - ( fact*D[ id + strideD ] );
IPIV[ ip ] = i + 1;
}
}
id = offsetD;
// Check if U is singular
for ( i = 0; i < N; i++ ) {
if ( D[ id ] === 0.0 ) {
return i;
}
id += strideD;
}
return 0;
}
// EXPORTS //
module.exports = dgttrf;
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