Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 14x 2x 2x 12x 12x 12x 12x 12x 12x 12x 12x 14x 60x 60x 12x 12x 14x 36x 36x 12x 14x 36x 36x 36x 36x 36x 36x 24x 24x 24x 24x 24x 36x 12x 12x 12x 12x 12x 12x 12x 12x 12x 12x 36x 12x 12x 12x 12x 12x 12x 12x 12x 12x 8x 8x 8x 8x 8x 12x 4x 4x 4x 4x 4x 4x 4x 4x 12x 12x 12x 14x 50x 4x 4x 50x 8x 8x 14x 3x 3x 3x 3x 3x | /**
* @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
*
* - 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 + dui ] = 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;
|