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 cinverse
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32 | {
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33 | /*************************************************************************
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34 | Inversion of a complex matrix given by its LU decomposition.
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35 |
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36 | Input parameters:
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37 | A - LU decomposition of the matrix (output of CMatrixLU subroutine).
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38 | Pivots - table of permutations which were made during the LU decomposition
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39 | (the output of CMatrixLU subroutine).
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40 | N - size of matrix A.
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41 |
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42 | Output parameters:
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43 | A - inverse of matrix A.
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44 | Array whose indexes range within [0..N-1, 0..N-1].
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45 |
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46 | Result:
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47 | True, if the matrix is not singular.
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48 | False, if the matrix is singular.
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49 |
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50 | -- LAPACK routine (version 3.0) --
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51 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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52 | Courant Institute, Argonne National Lab, and Rice University
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53 | February 29, 1992
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54 | *************************************************************************/
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55 | public static bool cmatrixluinverse(ref AP.Complex[,] a,
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56 | ref int[] pivots,
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57 | int n)
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58 | {
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59 | bool result = new bool();
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60 | AP.Complex[] work = new AP.Complex[0];
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61 | int i = 0;
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62 | int iws = 0;
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63 | int j = 0;
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64 | int jb = 0;
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65 | int jj = 0;
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66 | int jp = 0;
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67 | AP.Complex v = 0;
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68 | int i_ = 0;
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69 |
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70 | result = true;
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71 |
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72 | //
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73 | // Quick return if possible
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74 | //
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75 | if( n==0 )
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76 | {
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77 | return result;
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78 | }
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79 | work = new AP.Complex[n-1+1];
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80 |
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81 | //
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82 | // Form inv(U)
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83 | //
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84 | if( !ctrinverse.cmatrixtrinverse(ref a, n, true, false) )
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85 | {
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86 | result = false;
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87 | return result;
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88 | }
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89 |
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90 | //
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91 | // Solve the equation inv(A)*L = inv(U) for inv(A).
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92 | //
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93 | for(j=n-1; j>=0; j--)
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94 | {
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95 |
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96 | //
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97 | // Copy current column of L to WORK and replace with zeros.
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98 | //
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99 | for(i=j+1; i<=n-1; i++)
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100 | {
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101 | work[i] = a[i,j];
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102 | a[i,j] = 0;
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103 | }
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104 |
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105 | //
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106 | // Compute current column of inv(A).
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107 | //
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108 | if( j<n-1 )
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109 | {
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110 | for(i=0; i<=n-1; i++)
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111 | {
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112 | v = 0.0;
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113 | for(i_=j+1; i_<=n-1;i_++)
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114 | {
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115 | v += a[i,i_]*work[i_];
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116 | }
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117 | a[i,j] = a[i,j]-v;
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118 | }
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119 | }
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120 | }
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121 |
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122 | //
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123 | // Apply column interchanges.
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124 | //
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125 | for(j=n-2; j>=0; j--)
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126 | {
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127 | jp = pivots[j];
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128 | if( jp!=j )
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129 | {
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130 | for(i_=0; i_<=n-1;i_++)
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131 | {
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132 | work[i_] = a[i_,j];
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133 | }
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134 | for(i_=0; i_<=n-1;i_++)
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135 | {
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136 | a[i_,j] = a[i_,jp];
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137 | }
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138 | for(i_=0; i_<=n-1;i_++)
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139 | {
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140 | a[i_,jp] = work[i_];
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141 | }
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142 | }
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143 | }
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144 | return result;
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145 | }
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146 |
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147 |
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148 | /*************************************************************************
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149 | Inversion of a general complex matrix.
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150 |
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151 | Input parameters:
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152 | A - matrix. Array whose indexes range within [0..N-1, 0..N-1].
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153 | N - size of matrix A.
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154 |
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155 | Output parameters:
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156 | A - inverse of matrix A.
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157 | Array whose indexes range within [0..N-1, 0..N-1].
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158 |
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159 | Result:
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160 | True, if the matrix is not singular.
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161 | False, if the matrix is singular.
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162 |
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163 | -- ALGLIB --
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164 | Copyright 2005 by Bochkanov Sergey
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165 | *************************************************************************/
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166 | public static bool cmatrixinverse(ref AP.Complex[,] a,
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167 | int n)
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168 | {
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169 | bool result = new bool();
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170 | int[] pivots = new int[0];
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171 |
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172 | clu.cmatrixlu(ref a, n, n, ref pivots);
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173 | result = cmatrixluinverse(ref a, ref pivots, n);
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174 | return result;
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175 | }
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176 |
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177 |
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178 | public static bool complexinverselu(ref AP.Complex[,] a,
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179 | ref int[] pivots,
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180 | int n)
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181 | {
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182 | bool result = new bool();
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183 | AP.Complex[] work = new AP.Complex[0];
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184 | int i = 0;
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185 | int iws = 0;
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186 | int j = 0;
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187 | int jb = 0;
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188 | int jj = 0;
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189 | int jp = 0;
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190 | int jp1 = 0;
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191 | AP.Complex v = 0;
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192 | int i_ = 0;
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193 |
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194 | result = true;
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195 |
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196 | //
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197 | // Quick return if possible
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198 | //
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199 | if( n==0 )
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200 | {
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201 | return result;
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202 | }
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203 | work = new AP.Complex[n+1];
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204 |
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205 | //
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206 | // Form inv(U)
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207 | //
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208 | if( !ctrinverse.complexinvtriangular(ref a, n, true, false) )
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209 | {
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210 | result = false;
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211 | return result;
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212 | }
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213 |
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214 | //
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215 | // Solve the equation inv(A)*L = inv(U) for inv(A).
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216 | //
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217 | for(j=n; j>=1; j--)
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218 | {
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219 |
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220 | //
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221 | // Copy current column of L to WORK and replace with zeros.
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222 | //
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223 | for(i=j+1; i<=n; i++)
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224 | {
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225 | work[i] = a[i,j];
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226 | a[i,j] = 0;
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227 | }
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228 |
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229 | //
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230 | // Compute current column of inv(A).
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231 | //
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232 | if( j<n )
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233 | {
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234 | jp1 = j+1;
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235 | for(i=1; i<=n; i++)
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236 | {
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237 | v = 0.0;
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238 | for(i_=jp1; i_<=n;i_++)
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239 | {
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240 | v += a[i,i_]*work[i_];
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241 | }
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242 | a[i,j] = a[i,j]-v;
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243 | }
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244 | }
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245 | }
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246 |
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247 | //
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248 | // Apply column interchanges.
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249 | //
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250 | for(j=n-1; j>=1; j--)
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251 | {
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252 | jp = pivots[j];
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253 | if( jp!=j )
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254 | {
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255 | for(i_=1; i_<=n;i_++)
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256 | {
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257 | work[i_] = a[i_,j];
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258 | }
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259 | for(i_=1; i_<=n;i_++)
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260 | {
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261 | a[i_,j] = a[i_,jp];
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262 | }
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263 | for(i_=1; i_<=n;i_++)
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264 | {
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265 | a[i_,jp] = work[i_];
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266 | }
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267 | }
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268 | }
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269 | return result;
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270 | }
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271 |
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272 |
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273 | public static bool complexinverse(ref AP.Complex[,] a,
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274 | int n)
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275 | {
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276 | bool result = new bool();
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277 | int[] pivots = new int[0];
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278 |
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279 | clu.complexludecomposition(ref a, n, n, ref pivots);
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280 | result = complexinverselu(ref a, ref pivots, n);
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281 | return result;
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282 | }
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283 | }
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284 | }
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