| 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 ctrinverse
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| 32 | {
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| 33 | /*************************************************************************
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| 34 | Complex 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,
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| 44 | the inverse matrix replaces the source matrix. The elements below (above)
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| 45 | the 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, the diagonal elements are not passed to the algorithm, they are
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| 49 | not changed by the algorithm.
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| 50 |
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| 51 | Input parameters:
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| 52 | A - matrix.
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| 53 | Array whose indexes range within [0..N-1,0..N-1].
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| 54 | N - size of matrix A.
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| 55 | IsUpper - True, if the matrix is upper triangular.
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| 56 | IsunitTriangular
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| 57 | - True, if the matrix has a unit diagonal.
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| 58 |
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| 59 | Output parameters:
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| 60 | A - inverse matrix (if the problem is not degenerate).
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| 61 |
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| 62 | Result:
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| 63 | True, if the matrix is not singular.
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| 64 | False, if the matrix is singular.
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| 65 |
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| 66 | -- LAPACK routine (version 3.0) --
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| 67 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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| 68 | Courant Institute, Argonne National Lab, and Rice University
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| 69 | February 29, 1992
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| 70 | *************************************************************************/
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| 71 | public static bool cmatrixtrinverse(ref AP.Complex[,] a,
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| 72 | int n,
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| 73 | bool isupper,
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| 74 | bool isunittriangular)
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| 75 | {
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| 76 | bool result = new bool();
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| 77 | bool nounit = new bool();
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| 78 | int i = 0;
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| 79 | int j = 0;
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| 80 | AP.Complex v = 0;
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| 81 | AP.Complex ajj = 0;
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| 82 | AP.Complex[] t = new AP.Complex[0];
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| 83 | int i_ = 0;
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| 84 |
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| 85 | result = true;
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| 86 | t = new AP.Complex[n-1+1];
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| 87 |
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| 88 | //
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| 89 | // Test the input parameters.
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| 90 | //
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| 91 | nounit = !isunittriangular;
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| 92 | if( isupper )
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| 93 | {
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| 94 |
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| 95 | //
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| 96 | // Compute inverse of upper triangular matrix.
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| 97 | //
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| 98 | for(j=0; j<=n-1; j++)
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| 99 | {
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| 100 | if( nounit )
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| 101 | {
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| 102 | if( a[j,j]==0 )
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| 103 | {
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| 104 | result = false;
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| 105 | return result;
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| 106 | }
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| 107 | a[j,j] = 1/a[j,j];
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| 108 | ajj = -a[j,j];
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| 109 | }
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| 110 | else
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| 111 | {
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| 112 | ajj = -1;
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| 113 | }
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| 114 |
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| 115 | //
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| 116 | // Compute elements 1:j-1 of j-th column.
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| 117 | //
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| 118 | if( j>0 )
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| 119 | {
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| 120 | for(i_=0; i_<=j-1;i_++)
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| 121 | {
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| 122 | t[i_] = a[i_,j];
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| 123 | }
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| 124 | for(i=0; i<=j-1; i++)
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| 125 | {
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| 126 | if( i+1<j )
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| 127 | {
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| 128 | v = 0.0;
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| 129 | for(i_=i+1; i_<=j-1;i_++)
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| 130 | {
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| 131 | v += a[i,i_]*t[i_];
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| 132 | }
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| 133 | }
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| 134 | else
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| 135 | {
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| 136 | v = 0;
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| 137 | }
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| 138 | if( nounit )
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| 139 | {
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| 140 | a[i,j] = v+a[i,i]*t[i];
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| 141 | }
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| 142 | else
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| 143 | {
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| 144 | a[i,j] = v+t[i];
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| 145 | }
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| 146 | }
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| 147 | for(i_=0; i_<=j-1;i_++)
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| 148 | {
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| 149 | a[i_,j] = ajj*a[i_,j];
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| 150 | }
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| 151 | }
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| 152 | }
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| 153 | }
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| 154 | else
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| 155 | {
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| 156 |
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| 157 | //
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| 158 | // Compute inverse of lower triangular matrix.
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| 159 | //
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| 160 | for(j=n-1; j>=0; j--)
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| 161 | {
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| 162 | if( nounit )
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| 163 | {
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| 164 | if( a[j,j]==0 )
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| 165 | {
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| 166 | result = false;
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| 167 | return result;
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| 168 | }
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| 169 | a[j,j] = 1/a[j,j];
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| 170 | ajj = -a[j,j];
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| 171 | }
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| 172 | else
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| 173 | {
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| 174 | ajj = -1;
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| 175 | }
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| 176 | if( j+1<n )
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| 177 | {
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| 178 |
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| 179 | //
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| 180 | // Compute elements j+1:n of j-th column.
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| 181 | //
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| 182 | for(i_=j+1; i_<=n-1;i_++)
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| 183 | {
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| 184 | t[i_] = a[i_,j];
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| 185 | }
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| 186 | for(i=j+1; i<=n-1; i++)
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| 187 | {
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| 188 | if( i>j+1 )
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| 189 | {
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| 190 | v = 0.0;
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| 191 | for(i_=j+1; i_<=i-1;i_++)
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| 192 | {
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| 193 | v += a[i,i_]*t[i_];
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| 194 | }
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| 195 | }
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| 196 | else
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| 197 | {
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| 198 | v = 0;
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| 199 | }
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| 200 | if( nounit )
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| 201 | {
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| 202 | a[i,j] = v+a[i,i]*t[i];
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| 203 | }
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| 204 | else
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| 205 | {
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| 206 | a[i,j] = v+t[i];
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| 207 | }
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| 208 | }
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| 209 | for(i_=j+1; i_<=n-1;i_++)
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| 210 | {
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| 211 | a[i_,j] = ajj*a[i_,j];
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| 212 | }
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| 213 | }
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| 214 | }
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| 215 | }
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| 216 | return result;
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| 217 | }
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| 218 |
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| 219 |
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| 220 | public static bool complexinvtriangular(ref AP.Complex[,] a,
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| 221 | int n,
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| 222 | bool isupper,
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| 223 | bool isunittriangular)
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| 224 | {
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| 225 | bool result = new bool();
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| 226 | bool nounit = new bool();
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| 227 | int i = 0;
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| 228 | int j = 0;
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| 229 | int nmj = 0;
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| 230 | int jm1 = 0;
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| 231 | int jp1 = 0;
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| 232 | AP.Complex v = 0;
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| 233 | AP.Complex ajj = 0;
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| 234 | AP.Complex[] t = new AP.Complex[0];
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| 235 | int i_ = 0;
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| 236 |
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| 237 | result = true;
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| 238 | t = new AP.Complex[n+1];
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| 239 |
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| 240 | //
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| 241 | // Test the input parameters.
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| 242 | //
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| 243 | nounit = !isunittriangular;
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| 244 | if( isupper )
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| 245 | {
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| 246 |
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| 247 | //
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| 248 | // Compute inverse of upper triangular matrix.
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| 249 | //
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| 250 | for(j=1; j<=n; j++)
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| 251 | {
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| 252 | if( nounit )
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| 253 | {
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| 254 | if( a[j,j]==0 )
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| 255 | {
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| 256 | result = false;
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| 257 | return result;
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| 258 | }
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| 259 | a[j,j] = 1/a[j,j];
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| 260 | ajj = -a[j,j];
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| 261 | }
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| 262 | else
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| 263 | {
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| 264 | ajj = -1;
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| 265 | }
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| 266 |
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| 267 | //
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| 268 | // Compute elements 1:j-1 of j-th column.
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| 269 | //
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| 270 | if( j>1 )
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| 271 | {
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| 272 | jm1 = j-1;
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| 273 | for(i_=1; i_<=jm1;i_++)
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| 274 | {
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| 275 | t[i_] = a[i_,j];
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| 276 | }
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| 277 | for(i=1; i<=j-1; i++)
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| 278 | {
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| 279 | if( i<j-1 )
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| 280 | {
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| 281 | v = 0.0;
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| 282 | for(i_=i+1; i_<=jm1;i_++)
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| 283 | {
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| 284 | v += a[i,i_]*t[i_];
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| 285 | }
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| 286 | }
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| 287 | else
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| 288 | {
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| 289 | v = 0;
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| 290 | }
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| 291 | if( nounit )
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| 292 | {
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| 293 | a[i,j] = v+a[i,i]*t[i];
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| 294 | }
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| 295 | else
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| 296 | {
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| 297 | a[i,j] = v+t[i];
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| 298 | }
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| 299 | }
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| 300 | for(i_=1; i_<=jm1;i_++)
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| 301 | {
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| 302 | a[i_,j] = ajj*a[i_,j];
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| 303 | }
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| 304 | }
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| 305 | }
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| 306 | }
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| 307 | else
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| 308 | {
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| 309 |
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| 310 | //
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| 311 | // Compute inverse of lower triangular matrix.
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| 312 | //
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| 313 | for(j=n; j>=1; j--)
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| 314 | {
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| 315 | if( nounit )
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| 316 | {
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| 317 | if( a[j,j]==0 )
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| 318 | {
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| 319 | result = false;
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| 320 | return result;
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| 321 | }
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| 322 | a[j,j] = 1/a[j,j];
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| 323 | ajj = -a[j,j];
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| 324 | }
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| 325 | else
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| 326 | {
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| 327 | ajj = -1;
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| 328 | }
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| 329 | if( j<n )
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| 330 | {
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| 331 |
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| 332 | //
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| 333 | // Compute elements j+1:n of j-th column.
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| 334 | //
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| 335 | nmj = n-j;
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| 336 | jp1 = j+1;
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| 337 | for(i_=jp1; i_<=n;i_++)
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| 338 | {
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| 339 | t[i_] = a[i_,j];
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| 340 | }
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| 341 | for(i=j+1; i<=n; i++)
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| 342 | {
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| 343 | if( i>j+1 )
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| 344 | {
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| 345 | v = 0.0;
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| 346 | for(i_=jp1; i_<=i-1;i_++)
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| 347 | {
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| 348 | v += a[i,i_]*t[i_];
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| 349 | }
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| 350 | }
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| 351 | else
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| 352 | {
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| 353 | v = 0;
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| 354 | }
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| 355 | if( nounit )
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| 356 | {
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| 357 | a[i,j] = v+a[i,i]*t[i];
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| 358 | }
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| 359 | else
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| 360 | {
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| 361 | a[i,j] = v+t[i];
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| 362 | }
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| 363 | }
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| 364 | for(i_=jp1; i_<=n;i_++)
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| 365 | {
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| 366 | a[i_,j] = ajj*a[i_,j];
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| 367 | }
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| 368 | }
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| 369 | }
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| 370 | }
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| 371 | return result;
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| 372 | }
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| 373 | }
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| 374 | }
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