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 lu
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32 | {
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33 | public const int lunb = 8;
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34 |
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35 |
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36 | /*************************************************************************
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37 | LU decomposition of a general matrix of size MxN
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38 |
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39 | The subroutine calculates the LU decomposition of a rectangular general
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40 | matrix with partial pivoting (with row permutations).
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41 |
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42 | Input parameters:
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43 | A - matrix A whose indexes range within [0..M-1, 0..N-1].
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44 | M - number of rows in matrix A.
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45 | N - number of columns in matrix A.
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46 |
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47 | Output parameters:
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48 | A - matrices L and U in compact form (see below).
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49 | Array whose indexes range within [0..M-1, 0..N-1].
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50 | Pivots - permutation matrix in compact form (see below).
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51 | Array whose index ranges within [0..Min(M-1,N-1)].
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52 |
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53 | Matrix A is represented as A = P * L * U, where P is a permutation matrix,
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54 | matrix L - lower triangular (or lower trapezoid, if M>N) matrix,
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55 | U - upper triangular (or upper trapezoid, if M<N) matrix.
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56 |
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57 | Let M be equal to 4 and N be equal to 3:
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58 |
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59 | ( 1 ) ( U11 U12 U13 )
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60 | A = P1 * P2 * P3 * ( L21 1 ) * ( U22 U23 )
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61 | ( L31 L32 1 ) ( U33 )
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62 | ( L41 L42 L43 )
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63 |
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64 | Matrix L has size MxMin(M,N), matrix U has size Min(M,N)xN, matrix P(i) is
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65 | a permutation of the identity matrix of size MxM with numbers I and Pivots[I].
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66 |
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67 | The algorithm returns array Pivots and the following matrix which replaces
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68 | matrix A and contains matrices L and U in compact form (the example applies
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69 | to M=4, N=3).
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70 |
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71 | ( U11 U12 U13 )
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72 | ( L21 U22 U23 )
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73 | ( L31 L32 U33 )
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74 | ( L41 L42 L43 )
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75 |
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76 | As we can see, the unit diagonal isn't stored.
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77 |
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78 | -- LAPACK routine (version 3.0) --
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79 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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80 | Courant Institute, Argonne National Lab, and Rice University
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81 | June 30, 1992
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82 | *************************************************************************/
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83 | public static void rmatrixlu(ref double[,] a,
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84 | int m,
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85 | int n,
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86 | ref int[] pivots)
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87 | {
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88 | double[,] b = new double[0,0];
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89 | double[] t = new double[0];
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90 | int[] bp = new int[0];
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91 | int minmn = 0;
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92 | int i = 0;
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93 | int ip = 0;
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94 | int j = 0;
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95 | int j1 = 0;
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96 | int j2 = 0;
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97 | int cb = 0;
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98 | int nb = 0;
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99 | double v = 0;
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100 | int i_ = 0;
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101 | int i1_ = 0;
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102 |
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103 | System.Diagnostics.Debug.Assert(lunb>=1, "RMatrixLU internal error");
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104 | nb = lunb;
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105 |
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106 | //
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107 | // Decide what to use - blocked or unblocked code
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108 | //
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109 | if( n<=1 | Math.Min(m, n)<=nb | nb==1 )
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110 | {
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111 |
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112 | //
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113 | // Unblocked code
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114 | //
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115 | rmatrixlu2(ref a, m, n, ref pivots);
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116 | }
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117 | else
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118 | {
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119 |
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120 | //
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121 | // Blocked code.
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122 | // First, prepare temporary matrix and indices
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123 | //
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124 | b = new double[m-1+1, nb-1+1];
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125 | t = new double[n-1+1];
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126 | pivots = new int[Math.Min(m, n)-1+1];
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127 | minmn = Math.Min(m, n);
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128 | j1 = 0;
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129 | j2 = Math.Min(minmn, nb)-1;
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130 |
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131 | //
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132 | // Main cycle
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133 | //
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134 | while( j1<minmn )
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135 | {
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136 | cb = j2-j1+1;
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137 |
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138 | //
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139 | // LU factorization of diagonal and subdiagonal blocks:
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140 | // 1. Copy columns J1..J2 of A to B
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141 | // 2. LU(B)
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142 | // 3. Copy result back to A
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143 | // 4. Copy pivots, apply pivots
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144 | //
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145 | for(i=j1; i<=m-1; i++)
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146 | {
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147 | i1_ = (j1) - (0);
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148 | for(i_=0; i_<=cb-1;i_++)
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149 | {
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150 | b[i-j1,i_] = a[i,i_+i1_];
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151 | }
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152 | }
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153 | rmatrixlu2(ref b, m-j1, cb, ref bp);
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154 | for(i=j1; i<=m-1; i++)
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155 | {
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156 | i1_ = (0) - (j1);
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157 | for(i_=j1; i_<=j2;i_++)
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158 | {
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159 | a[i,i_] = b[i-j1,i_+i1_];
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160 | }
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161 | }
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162 | for(i=0; i<=cb-1; i++)
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163 | {
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164 | ip = bp[i];
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165 | pivots[j1+i] = j1+ip;
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166 | if( bp[i]!=i )
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167 | {
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168 | if( j1!=0 )
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169 | {
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170 |
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171 | //
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172 | // Interchange columns 0:J1-1
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173 | //
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174 | for(i_=0; i_<=j1-1;i_++)
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175 | {
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176 | t[i_] = a[j1+i,i_];
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177 | }
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178 | for(i_=0; i_<=j1-1;i_++)
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179 | {
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180 | a[j1+i,i_] = a[j1+ip,i_];
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181 | }
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182 | for(i_=0; i_<=j1-1;i_++)
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183 | {
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184 | a[j1+ip,i_] = t[i_];
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185 | }
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186 | }
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187 | if( j2<n-1 )
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188 | {
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189 |
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190 | //
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191 | // Interchange the rest of the matrix, if needed
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192 | //
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193 | for(i_=j2+1; i_<=n-1;i_++)
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194 | {
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195 | t[i_] = a[j1+i,i_];
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196 | }
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197 | for(i_=j2+1; i_<=n-1;i_++)
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198 | {
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199 | a[j1+i,i_] = a[j1+ip,i_];
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200 | }
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201 | for(i_=j2+1; i_<=n-1;i_++)
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202 | {
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203 | a[j1+ip,i_] = t[i_];
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204 | }
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205 | }
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206 | }
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207 | }
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208 |
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209 | //
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210 | // Compute block row of U
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211 | //
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212 | if( j2<n-1 )
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213 | {
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214 | for(i=j1+1; i<=j2; i++)
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215 | {
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216 | for(j=j1; j<=i-1; j++)
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217 | {
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218 | v = a[i,j];
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219 | for(i_=j2+1; i_<=n-1;i_++)
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220 | {
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221 | a[i,i_] = a[i,i_] - v*a[j,i_];
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222 | }
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223 | }
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224 | }
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225 | }
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226 |
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227 | //
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228 | // Update trailing submatrix
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229 | //
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230 | if( j2<n-1 )
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231 | {
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232 | for(i=j2+1; i<=m-1; i++)
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233 | {
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234 | for(j=j1; j<=j2; j++)
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235 | {
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236 | v = a[i,j];
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237 | for(i_=j2+1; i_<=n-1;i_++)
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238 | {
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239 | a[i,i_] = a[i,i_] - v*a[j,i_];
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240 | }
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241 | }
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242 | }
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243 | }
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244 |
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245 | //
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246 | // Next step
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247 | //
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248 | j1 = j2+1;
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249 | j2 = Math.Min(minmn, j1+nb)-1;
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250 | }
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251 | }
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252 | }
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253 |
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254 |
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255 | public static void ludecomposition(ref double[,] a,
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256 | int m,
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257 | int n,
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258 | ref int[] pivots)
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259 | {
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260 | int i = 0;
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261 | int j = 0;
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262 | int jp = 0;
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263 | double[] t1 = new double[0];
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264 | double s = 0;
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265 | int i_ = 0;
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266 |
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267 | pivots = new int[Math.Min(m, n)+1];
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268 | t1 = new double[Math.Max(m, n)+1];
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269 | System.Diagnostics.Debug.Assert(m>=0 & n>=0, "Error in LUDecomposition: incorrect function arguments");
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270 |
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271 | //
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272 | // Quick return if possible
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273 | //
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274 | if( m==0 | n==0 )
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275 | {
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276 | return;
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277 | }
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278 | for(j=1; j<=Math.Min(m, n); j++)
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279 | {
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280 |
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281 | //
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282 | // Find pivot and test for singularity.
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283 | //
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284 | jp = j;
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285 | for(i=j+1; i<=m; i++)
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286 | {
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287 | if( (double)(Math.Abs(a[i,j]))>(double)(Math.Abs(a[jp,j])) )
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288 | {
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289 | jp = i;
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290 | }
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291 | }
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292 | pivots[j] = jp;
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293 | if( (double)(a[jp,j])!=(double)(0) )
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294 | {
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295 |
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296 | //
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297 | //Apply the interchange to rows
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298 | //
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299 | if( jp!=j )
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300 | {
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301 | for(i_=1; i_<=n;i_++)
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302 | {
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303 | t1[i_] = a[j,i_];
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304 | }
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305 | for(i_=1; i_<=n;i_++)
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306 | {
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307 | a[j,i_] = a[jp,i_];
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308 | }
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309 | for(i_=1; i_<=n;i_++)
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310 | {
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311 | a[jp,i_] = t1[i_];
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312 | }
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313 | }
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314 |
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315 | //
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316 | //Compute elements J+1:M of J-th column.
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317 | //
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318 | if( j<m )
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319 | {
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320 |
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321 | //
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322 | // CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
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323 | //
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324 | jp = j+1;
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325 | s = 1/a[j,j];
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326 | for(i_=jp; i_<=m;i_++)
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327 | {
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328 | a[i_,j] = s*a[i_,j];
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329 | }
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330 | }
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331 | }
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332 | if( j<Math.Min(m, n) )
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333 | {
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334 |
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335 | //
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336 | //Update trailing submatrix.
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337 | //CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,A( J+1, J+1 ), LDA )
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338 | //
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339 | jp = j+1;
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340 | for(i=j+1; i<=m; i++)
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341 | {
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342 | s = a[i,j];
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343 | for(i_=jp; i_<=n;i_++)
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344 | {
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345 | a[i,i_] = a[i,i_] - s*a[j,i_];
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346 | }
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347 | }
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348 | }
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349 | }
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350 | }
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351 |
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352 |
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353 | public static void ludecompositionunpacked(double[,] a,
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354 | int m,
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355 | int n,
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356 | ref double[,] l,
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357 | ref double[,] u,
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358 | ref int[] pivots)
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359 | {
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360 | int i = 0;
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361 | int j = 0;
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362 | int minmn = 0;
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363 |
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364 | a = (double[,])a.Clone();
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365 |
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366 | if( m==0 | n==0 )
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367 | {
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368 | return;
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369 | }
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370 | minmn = Math.Min(m, n);
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371 | l = new double[m+1, minmn+1];
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372 | u = new double[minmn+1, n+1];
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373 | ludecomposition(ref a, m, n, ref pivots);
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374 | for(i=1; i<=m; i++)
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375 | {
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376 | for(j=1; j<=minmn; j++)
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377 | {
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378 | if( j>i )
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379 | {
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380 | l[i,j] = 0;
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381 | }
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382 | if( j==i )
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383 | {
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384 | l[i,j] = 1;
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385 | }
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386 | if( j<i )
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387 | {
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388 | l[i,j] = a[i,j];
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389 | }
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390 | }
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391 | }
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392 | for(i=1; i<=minmn; i++)
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393 | {
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394 | for(j=1; j<=n; j++)
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395 | {
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396 | if( j<i )
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397 | {
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398 | u[i,j] = 0;
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399 | }
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400 | if( j>=i )
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401 | {
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402 | u[i,j] = a[i,j];
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403 | }
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404 | }
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405 | }
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406 | }
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407 |
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408 |
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409 | /*************************************************************************
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410 | Level 2 BLAS version of RMatrixLU
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411 |
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412 | -- LAPACK routine (version 3.0) --
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413 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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414 | Courant Institute, Argonne National Lab, and Rice University
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415 | June 30, 1992
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416 | *************************************************************************/
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417 | private static void rmatrixlu2(ref double[,] a,
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418 | int m,
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419 | int n,
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420 | ref int[] pivots)
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421 | {
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422 | int i = 0;
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423 | int j = 0;
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424 | int jp = 0;
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425 | double[] t1 = new double[0];
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426 | double s = 0;
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427 | int i_ = 0;
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428 |
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429 | pivots = new int[Math.Min(m-1, n-1)+1];
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430 | t1 = new double[Math.Max(m-1, n-1)+1];
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431 | System.Diagnostics.Debug.Assert(m>=0 & n>=0, "Error in LUDecomposition: incorrect function arguments");
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432 |
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433 | //
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434 | // Quick return if possible
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435 | //
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436 | if( m==0 | n==0 )
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437 | {
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438 | return;
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439 | }
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440 | for(j=0; j<=Math.Min(m-1, n-1); j++)
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441 | {
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442 |
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443 | //
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444 | // Find pivot and test for singularity.
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445 | //
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446 | jp = j;
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447 | for(i=j+1; i<=m-1; i++)
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448 | {
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449 | if( (double)(Math.Abs(a[i,j]))>(double)(Math.Abs(a[jp,j])) )
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450 | {
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451 | jp = i;
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452 | }
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453 | }
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454 | pivots[j] = jp;
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455 | if( (double)(a[jp,j])!=(double)(0) )
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456 | {
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457 |
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458 | //
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459 | //Apply the interchange to rows
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460 | //
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461 | if( jp!=j )
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462 | {
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463 | for(i_=0; i_<=n-1;i_++)
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464 | {
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465 | t1[i_] = a[j,i_];
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466 | }
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467 | for(i_=0; i_<=n-1;i_++)
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468 | {
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469 | a[j,i_] = a[jp,i_];
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470 | }
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471 | for(i_=0; i_<=n-1;i_++)
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472 | {
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473 | a[jp,i_] = t1[i_];
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474 | }
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475 | }
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476 |
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477 | //
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478 | //Compute elements J+1:M of J-th column.
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479 | //
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480 | if( j<m )
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481 | {
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482 | jp = j+1;
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483 | s = 1/a[j,j];
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484 | for(i_=jp; i_<=m-1;i_++)
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485 | {
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486 | a[i_,j] = s*a[i_,j];
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487 | }
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488 | }
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489 | }
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490 | if( j<Math.Min(m, n)-1 )
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491 | {
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492 |
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493 | //
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494 | //Update trailing submatrix.
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495 | //
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496 | jp = j+1;
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497 | for(i=j+1; i<=m-1; i++)
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498 | {
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499 | s = a[i,j];
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500 | for(i_=jp; i_<=n-1;i_++)
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501 | {
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502 | a[i,i_] = a[i,i_] - s*a[j,i_];
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503 | }
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504 | }
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505 | }
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506 | }
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507 | }
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508 | }
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509 | }
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