| 1 | /*************************************************************************
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| 2 | Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
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| 3 |
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| 4 | Contributors:
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| 5 | * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
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| 6 | pseudocode.
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| 7 |
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| 8 | See subroutines comments for additional copyrights.
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| 9 |
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| 10 | >>> SOURCE LICENSE >>>
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| 11 | This program is free software; you can redistribute it and/or modify
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| 12 | it under the terms of the GNU General Public License as published by
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| 13 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 14 | License, or (at your option) any later version.
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| 15 |
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| 16 | This program is distributed in the hope that it will be useful,
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| 17 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 19 | GNU General Public License for more details.
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| 20 |
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| 21 | A copy of the GNU General Public License is available at
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| 22 | http://www.fsf.org/licensing/licenses
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| 23 |
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| 24 | >>> END OF LICENSE >>>
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| 25 | *************************************************************************/
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| 26 |
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| 27 | using System;
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| 28 |
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| 29 | namespace alglib
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| 30 | {
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| 31 | public class trinverse
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| 32 | {
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| 33 | /*************************************************************************
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| 34 | Triangular matrix inversion
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| 35 |
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| 36 | The subroutine inverts the following types of matrices:
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| 37 | * upper triangular
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| 38 | * upper triangular with unit diagonal
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| 39 | * lower triangular
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| 40 | * lower triangular with unit diagonal
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| 41 |
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| 42 | In case of an upper (lower) triangular matrix, the inverse matrix will
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| 43 | also be upper (lower) triangular, and after the end of the algorithm, the
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| 44 | inverse matrix replaces the source matrix. The elements below (above) the
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| 45 | main diagonal are not changed by the algorithm.
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| 46 |
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| 47 | If the matrix has a unit diagonal, the inverse matrix also has a unit
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| 48 | diagonal, and the diagonal elements are not passed to the algorithm.
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| 49 |
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| 50 | Input parameters:
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| 51 | A - matrix.
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| 52 | Array whose indexes range within [0..N-1, 0..N-1].
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| 53 | N - size of matrix A.
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| 54 | IsUpper - True, if the matrix is upper triangular.
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| 55 | IsunitTriangular
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| 56 | - True, if the matrix has a unit diagonal.
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| 57 |
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| 58 | Output parameters:
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| 59 | A - inverse matrix (if the problem is not degenerate).
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| 60 |
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| 61 | Result:
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| 62 | True, if the matrix is not singular.
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| 63 | False, if the matrix is singular.
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| 64 |
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| 65 | -- LAPACK routine (version 3.0) --
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| 66 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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| 67 | Courant Institute, Argonne National Lab, and Rice University
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| 68 | February 29, 1992
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| 69 | *************************************************************************/
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| 70 | public static bool rmatrixtrinverse(ref double[,] a,
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| 71 | int n,
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| 72 | bool isupper,
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| 73 | bool isunittriangular)
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| 74 | {
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| 75 | bool result = new bool();
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| 76 | bool nounit = new bool();
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| 77 | int i = 0;
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| 78 | int j = 0;
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| 79 | double v = 0;
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| 80 | double ajj = 0;
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| 81 | double[] t = new double[0];
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| 82 | int i_ = 0;
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| 83 |
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| 84 | result = true;
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| 85 | t = new double[n-1+1];
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| 86 |
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| 87 | //
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| 88 | // Test the input parameters.
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| 89 | //
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| 90 | nounit = !isunittriangular;
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| 91 | if( isupper )
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| 92 | {
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| 93 |
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| 94 | //
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| 95 | // Compute inverse of upper triangular matrix.
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| 96 | //
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| 97 | for(j=0; j<=n-1; j++)
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| 98 | {
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| 99 | if( nounit )
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| 100 | {
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| 101 | if( (double)(a[j,j])==(double)(0) )
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| 102 | {
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| 103 | result = false;
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| 104 | return result;
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| 105 | }
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| 106 | a[j,j] = 1/a[j,j];
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| 107 | ajj = -a[j,j];
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| 108 | }
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| 109 | else
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| 110 | {
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| 111 | ajj = -1;
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| 112 | }
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| 113 |
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| 114 | //
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| 115 | // Compute elements 1:j-1 of j-th column.
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| 116 | //
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| 117 | if( j>0 )
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| 118 | {
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| 119 | for(i_=0; i_<=j-1;i_++)
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| 120 | {
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| 121 | t[i_] = a[i_,j];
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| 122 | }
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| 123 | for(i=0; i<=j-1; i++)
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| 124 | {
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| 125 | if( i<j-1 )
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| 126 | {
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| 127 | v = 0.0;
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| 128 | for(i_=i+1; i_<=j-1;i_++)
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| 129 | {
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| 130 | v += a[i,i_]*t[i_];
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| 131 | }
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| 132 | }
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| 133 | else
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| 134 | {
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| 135 | v = 0;
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| 136 | }
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| 137 | if( nounit )
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| 138 | {
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| 139 | a[i,j] = v+a[i,i]*t[i];
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| 140 | }
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| 141 | else
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| 142 | {
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| 143 | a[i,j] = v+t[i];
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| 144 | }
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| 145 | }
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| 146 | for(i_=0; i_<=j-1;i_++)
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| 147 | {
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| 148 | a[i_,j] = ajj*a[i_,j];
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| 149 | }
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| 150 | }
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| 151 | }
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| 152 | }
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| 153 | else
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| 154 | {
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| 155 |
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| 156 | //
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| 157 | // Compute inverse of lower triangular matrix.
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| 158 | //
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| 159 | for(j=n-1; j>=0; j--)
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| 160 | {
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| 161 | if( nounit )
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| 162 | {
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| 163 | if( (double)(a[j,j])==(double)(0) )
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| 164 | {
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| 165 | result = false;
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| 166 | return result;
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| 167 | }
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| 168 | a[j,j] = 1/a[j,j];
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| 169 | ajj = -a[j,j];
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| 170 | }
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| 171 | else
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| 172 | {
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| 173 | ajj = -1;
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| 174 | }
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| 175 | if( j<n-1 )
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| 176 | {
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| 177 |
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| 178 | //
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| 179 | // Compute elements j+1:n of j-th column.
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| 180 | //
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| 181 | for(i_=j+1; i_<=n-1;i_++)
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| 182 | {
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| 183 | t[i_] = a[i_,j];
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| 184 | }
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| 185 | for(i=j+1; i<=n-1; i++)
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| 186 | {
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| 187 | if( i>j+1 )
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| 188 | {
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| 189 | v = 0.0;
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| 190 | for(i_=j+1; i_<=i-1;i_++)
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| 191 | {
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| 192 | v += a[i,i_]*t[i_];
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| 193 | }
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| 194 | }
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| 195 | else
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| 196 | {
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| 197 | v = 0;
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| 198 | }
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| 199 | if( nounit )
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| 200 | {
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| 201 | a[i,j] = v+a[i,i]*t[i];
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| 202 | }
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| 203 | else
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| 204 | {
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| 205 | a[i,j] = v+t[i];
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| 206 | }
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| 207 | }
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| 208 | for(i_=j+1; i_<=n-1;i_++)
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| 209 | {
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| 210 | a[i_,j] = ajj*a[i_,j];
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| 211 | }
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| 212 | }
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| 213 | }
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| 214 | }
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| 215 | return result;
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| 216 | }
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| 217 |
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| 218 |
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| 219 | public static bool invtriangular(ref double[,] a,
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| 220 | int n,
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| 221 | bool isupper,
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| 222 | bool isunittriangular)
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| 223 | {
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| 224 | bool result = new bool();
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| 225 | bool nounit = new bool();
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| 226 | int i = 0;
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| 227 | int j = 0;
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| 228 | int nmj = 0;
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| 229 | int jm1 = 0;
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| 230 | int jp1 = 0;
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| 231 | double v = 0;
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| 232 | double ajj = 0;
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| 233 | double[] t = new double[0];
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| 234 | int i_ = 0;
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| 235 |
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| 236 | result = true;
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| 237 | t = new double[n+1];
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| 238 |
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| 239 | //
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| 240 | // Test the input parameters.
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| 241 | //
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| 242 | nounit = !isunittriangular;
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| 243 | if( isupper )
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| 244 | {
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| 245 |
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| 246 | //
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| 247 | // Compute inverse of upper triangular matrix.
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| 248 | //
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| 249 | for(j=1; j<=n; j++)
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| 250 | {
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| 251 | if( nounit )
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| 252 | {
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| 253 | if( (double)(a[j,j])==(double)(0) )
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| 254 | {
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| 255 | result = false;
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| 256 | return result;
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| 257 | }
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| 258 | a[j,j] = 1/a[j,j];
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| 259 | ajj = -a[j,j];
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| 260 | }
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| 261 | else
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| 262 | {
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| 263 | ajj = -1;
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| 264 | }
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| 265 |
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| 266 | //
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| 267 | // Compute elements 1:j-1 of j-th column.
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| 268 | //
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| 269 | if( j>1 )
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| 270 | {
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| 271 | jm1 = j-1;
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| 272 | for(i_=1; i_<=jm1;i_++)
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| 273 | {
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| 274 | t[i_] = a[i_,j];
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| 275 | }
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| 276 | for(i=1; i<=j-1; i++)
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| 277 | {
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| 278 | if( i<j-1 )
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| 279 | {
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| 280 | v = 0.0;
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| 281 | for(i_=i+1; i_<=jm1;i_++)
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| 282 | {
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| 283 | v += a[i,i_]*t[i_];
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| 284 | }
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| 285 | }
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| 286 | else
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| 287 | {
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| 288 | v = 0;
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| 289 | }
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| 290 | if( nounit )
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| 291 | {
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| 292 | a[i,j] = v+a[i,i]*t[i];
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| 293 | }
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| 294 | else
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| 295 | {
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| 296 | a[i,j] = v+t[i];
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| 297 | }
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| 298 | }
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| 299 | for(i_=1; i_<=jm1;i_++)
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| 300 | {
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| 301 | a[i_,j] = ajj*a[i_,j];
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| 302 | }
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| 303 | }
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| 304 | }
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| 305 | }
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| 306 | else
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| 307 | {
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| 308 |
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| 309 | //
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| 310 | // Compute inverse of lower triangular matrix.
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| 311 | //
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| 312 | for(j=n; j>=1; j--)
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| 313 | {
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| 314 | if( nounit )
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| 315 | {
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| 316 | if( (double)(a[j,j])==(double)(0) )
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| 317 | {
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| 318 | result = false;
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| 319 | return result;
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| 320 | }
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| 321 | a[j,j] = 1/a[j,j];
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| 322 | ajj = -a[j,j];
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| 323 | }
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| 324 | else
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| 325 | {
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| 326 | ajj = -1;
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| 327 | }
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| 328 | if( j<n )
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| 329 | {
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| 330 |
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| 331 | //
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| 332 | // Compute elements j+1:n of j-th column.
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| 333 | //
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| 334 | nmj = n-j;
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| 335 | jp1 = j+1;
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| 336 | for(i_=jp1; i_<=n;i_++)
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| 337 | {
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| 338 | t[i_] = a[i_,j];
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| 339 | }
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| 340 | for(i=j+1; i<=n; i++)
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| 341 | {
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| 342 | if( i>j+1 )
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| 343 | {
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| 344 | v = 0.0;
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| 345 | for(i_=jp1; i_<=i-1;i_++)
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| 346 | {
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| 347 | v += a[i,i_]*t[i_];
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| 348 | }
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| 349 | }
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| 350 | else
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| 351 | {
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| 352 | v = 0;
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| 353 | }
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| 354 | if( nounit )
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| 355 | {
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| 356 | a[i,j] = v+a[i,i]*t[i];
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| 357 | }
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| 358 | else
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| 359 | {
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| 360 | a[i,j] = v+t[i];
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| 361 | }
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| 362 | }
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| 363 | for(i_=jp1; i_<=n;i_++)
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| 364 | {
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| 365 | a[i_,j] = ajj*a[i_,j];
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| 366 | }
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| 367 | }
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| 368 | }
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| 369 | }
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| 370 | return result;
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| 371 | }
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| 372 | }
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| 373 | }
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