1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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4 | // * * |
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5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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7 | // * conditions of the Geant4 Software License, included in the file * |
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8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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9 | // * include a list of copyright holders. * |
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10 | // * * |
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11 | // * Neither the authors of this software system, nor their employing * |
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12 | // * institutes,nor the agencies providing financial support for this * |
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13 | // * work make any representation or warranty, express or implied, * |
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14 | // * regarding this software system or assume any liability for its * |
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15 | // * use. Please see the license in the file LICENSE and URL above * |
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16 | // * for the full disclaimer and the limitation of liability. * |
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17 | // * * |
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18 | // * This code implementation is the result of the scientific and * |
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19 | // * technical work of the GEANT4 collaboration. * |
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20 | // * By using, copying, modifying or distributing the software (or * |
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21 | // * any work based on the software) you agree to acknowledge its * |
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22 | // * use in resulting scientific publications, and indicate your * |
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23 | // * acceptance of all terms of the Geant4 Software license. * |
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24 | // ******************************************************************** |
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25 | // |
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26 | // $Id: G4ErrorSymMatrix.cc,v 1.3 2007/06/21 15:04:10 gunter Exp $ |
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27 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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28 | // |
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29 | // ------------------------------------------------------------ |
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30 | // GEANT 4 class implementation file |
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31 | // ------------------------------------------------------------ |
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32 | |
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33 | #include "globals.hh" |
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34 | #include <iostream> |
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35 | #include <cmath> |
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36 | |
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37 | #include "G4ErrorSymMatrix.hh" |
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38 | #include "G4ErrorMatrix.hh" |
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39 | |
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40 | // Simple operation for all elements |
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41 | |
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42 | #define SIMPLE_UOP(OPER) \ |
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43 | G4ErrorMatrixIter a=m.begin(); \ |
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44 | G4ErrorMatrixIter e=m.begin()+num_size(); \ |
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45 | for(;a<e; a++) (*a) OPER t; |
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46 | |
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47 | #define SIMPLE_BOP(OPER) \ |
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48 | G4ErrorMatrixIter a=m.begin(); \ |
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49 | G4ErrorMatrixConstIter b=m2.m.begin(); \ |
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50 | G4ErrorMatrixConstIter e=m.begin()+num_size(); \ |
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51 | for(;a<e; a++, b++) (*a) OPER (*b); |
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52 | |
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53 | #define SIMPLE_TOP(OPER) \ |
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54 | G4ErrorMatrixConstIter a=m1.m.begin(); \ |
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55 | G4ErrorMatrixConstIter b=m2.m.begin(); \ |
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56 | G4ErrorMatrixIter t=mret.m.begin(); \ |
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57 | G4ErrorMatrixConstIter e=m1.m.begin()+m1.num_size(); \ |
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58 | for( ;a<e; a++, b++, t++) (*t) = (*a) OPER (*b); |
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59 | |
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60 | #define CHK_DIM_2(r1,r2,c1,c2,fun) \ |
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61 | if (r1!=r2 || c1!=c2) { \ |
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62 | G4ErrorMatrix::error("Range error in Matrix function " #fun "(1)."); \ |
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63 | } |
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64 | |
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65 | #define CHK_DIM_1(c1,r2,fun) \ |
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66 | if (c1!=r2) { \ |
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67 | G4ErrorMatrix::error("Range error in Matrix function " #fun "(2)."); \ |
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68 | } |
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69 | |
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70 | // Constructors. (Default constructors are inlined and in .icc file) |
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71 | |
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72 | G4ErrorSymMatrix::G4ErrorSymMatrix(G4int p) |
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73 | : m(p*(p+1)/2), nrow(p) |
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74 | { |
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75 | size = nrow * (nrow+1) / 2; |
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76 | m.assign(size,0); |
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77 | } |
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78 | |
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79 | G4ErrorSymMatrix::G4ErrorSymMatrix(G4int p, G4int init) |
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80 | : m(p*(p+1)/2), nrow(p) |
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81 | { |
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82 | size = nrow * (nrow+1) / 2; |
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83 | |
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84 | m.assign(size,0); |
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85 | switch(init) |
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86 | { |
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87 | case 0: |
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88 | break; |
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89 | |
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90 | case 1: |
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91 | { |
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92 | G4ErrorMatrixIter a = m.begin(); |
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93 | for(G4int i=1;i<=nrow;i++) |
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94 | { |
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95 | *a = 1.0; |
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96 | a += (i+1); |
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97 | } |
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98 | break; |
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99 | } |
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100 | default: |
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101 | G4ErrorMatrix::error("G4ErrorSymMatrix: initialization must be 0 or 1."); |
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102 | } |
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103 | } |
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104 | |
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105 | // |
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106 | // Destructor |
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107 | // |
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108 | |
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109 | G4ErrorSymMatrix::~G4ErrorSymMatrix() |
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110 | { |
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111 | } |
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112 | |
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113 | G4ErrorSymMatrix::G4ErrorSymMatrix(const G4ErrorSymMatrix &m1) |
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114 | : m(m1.size), nrow(m1.nrow), size(m1.size) |
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115 | { |
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116 | m = m1.m; |
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117 | } |
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118 | |
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119 | // |
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120 | // |
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121 | // Sub matrix |
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122 | // |
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123 | // |
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124 | |
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125 | G4ErrorSymMatrix G4ErrorSymMatrix::sub(G4int min_row, G4int max_row) const |
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126 | { |
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127 | G4ErrorSymMatrix mret(max_row-min_row+1); |
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128 | if(max_row > num_row()) |
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129 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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130 | G4ErrorMatrixIter a = mret.m.begin(); |
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131 | G4ErrorMatrixConstIter b1 = m.begin() + (min_row+2)*(min_row-1)/2; |
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132 | for(G4int irow=1; irow<=mret.num_row(); irow++) |
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133 | { |
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134 | G4ErrorMatrixConstIter b = b1; |
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135 | for(G4int icol=1; icol<=irow; icol++) |
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136 | { |
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137 | *(a++) = *(b++); |
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138 | } |
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139 | b1 += irow+min_row-1; |
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140 | } |
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141 | return mret; |
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142 | } |
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143 | |
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144 | G4ErrorSymMatrix G4ErrorSymMatrix::sub(G4int min_row, G4int max_row) |
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145 | { |
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146 | G4ErrorSymMatrix mret(max_row-min_row+1); |
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147 | if(max_row > num_row()) |
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148 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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149 | G4ErrorMatrixIter a = mret.m.begin(); |
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150 | G4ErrorMatrixIter b1 = m.begin() + (min_row+2)*(min_row-1)/2; |
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151 | for(G4int irow=1; irow<=mret.num_row(); irow++) |
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152 | { |
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153 | G4ErrorMatrixIter b = b1; |
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154 | for(G4int icol=1; icol<=irow; icol++) |
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155 | { |
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156 | *(a++) = *(b++); |
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157 | } |
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158 | b1 += irow+min_row-1; |
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159 | } |
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160 | return mret; |
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161 | } |
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162 | |
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163 | void G4ErrorSymMatrix::sub(G4int row,const G4ErrorSymMatrix &m1) |
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164 | { |
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165 | if(row <1 || row+m1.num_row()-1 > num_row() ) |
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166 | { G4ErrorMatrix::error("G4ErrorSymMatrix::sub: Index out of range"); } |
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167 | G4ErrorMatrixConstIter a = m1.m.begin(); |
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168 | G4ErrorMatrixIter b1 = m.begin() + (row+2)*(row-1)/2; |
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169 | for(G4int irow=1; irow<=m1.num_row(); irow++) |
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170 | { |
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171 | G4ErrorMatrixIter b = b1; |
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172 | for(G4int icol=1; icol<=irow; icol++) |
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173 | { |
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174 | *(b++) = *(a++); |
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175 | } |
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176 | b1 += irow+row-1; |
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177 | } |
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178 | } |
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179 | |
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180 | // |
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181 | // Direct sum of two matricies |
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182 | // |
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183 | |
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184 | G4ErrorSymMatrix dsum(const G4ErrorSymMatrix &m1, |
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185 | const G4ErrorSymMatrix &m2) |
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186 | { |
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187 | G4ErrorSymMatrix mret(m1.num_row() + m2.num_row(), 0); |
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188 | mret.sub(1,m1); |
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189 | mret.sub(m1.num_row()+1,m2); |
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190 | return mret; |
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191 | } |
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192 | |
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193 | /* ----------------------------------------------------------------------- |
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194 | This section contains support routines for matrix.h. This section contains |
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195 | The two argument functions +,-. They call the copy constructor and +=,-=. |
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196 | ----------------------------------------------------------------------- */ |
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197 | |
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198 | G4ErrorSymMatrix G4ErrorSymMatrix::operator- () const |
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199 | { |
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200 | G4ErrorSymMatrix m2(nrow); |
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201 | G4ErrorMatrixConstIter a=m.begin(); |
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202 | G4ErrorMatrixIter b=m2.m.begin(); |
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203 | G4ErrorMatrixConstIter e=m.begin()+num_size(); |
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204 | for(;a<e; a++, b++) { (*b) = -(*a); } |
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205 | return m2; |
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206 | } |
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207 | |
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208 | G4ErrorMatrix operator+(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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209 | { |
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210 | G4ErrorMatrix mret(m1); |
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211 | CHK_DIM_2(m1.num_row(),m2.num_row(), m1.num_col(),m2.num_col(),+); |
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212 | mret += m2; |
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213 | return mret; |
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214 | } |
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215 | |
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216 | G4ErrorMatrix operator+(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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217 | { |
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218 | G4ErrorMatrix mret(m2); |
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219 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),+); |
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220 | mret += m1; |
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221 | return mret; |
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222 | } |
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223 | |
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224 | G4ErrorSymMatrix operator+(const G4ErrorSymMatrix &m1, |
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225 | const G4ErrorSymMatrix &m2) |
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226 | { |
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227 | G4ErrorSymMatrix mret(m1.nrow); |
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228 | CHK_DIM_1(m1.nrow, m2.nrow,+); |
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229 | SIMPLE_TOP(+) |
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230 | return mret; |
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231 | } |
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232 | |
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233 | // |
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234 | // operator - |
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235 | // |
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236 | |
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237 | G4ErrorMatrix operator-(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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238 | { |
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239 | G4ErrorMatrix mret(m1); |
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240 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),-); |
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241 | mret -= m2; |
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242 | return mret; |
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243 | } |
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244 | |
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245 | G4ErrorMatrix operator-(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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246 | { |
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247 | G4ErrorMatrix mret(m1); |
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248 | CHK_DIM_2(m1.num_row(),m2.num_row(),m1.num_col(),m2.num_col(),-); |
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249 | mret -= m2; |
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250 | return mret; |
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251 | } |
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252 | |
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253 | G4ErrorSymMatrix operator-(const G4ErrorSymMatrix &m1, |
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254 | const G4ErrorSymMatrix &m2) |
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255 | { |
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256 | G4ErrorSymMatrix mret(m1.num_row()); |
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257 | CHK_DIM_1(m1.num_row(),m2.num_row(),-); |
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258 | SIMPLE_TOP(-) |
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259 | return mret; |
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260 | } |
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261 | |
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262 | /* ----------------------------------------------------------------------- |
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263 | This section contains support routines for matrix.h. This file contains |
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264 | The two argument functions *,/. They call copy constructor and then /=,*=. |
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265 | ----------------------------------------------------------------------- */ |
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266 | |
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267 | G4ErrorSymMatrix operator/(const G4ErrorSymMatrix &m1,G4double t) |
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268 | { |
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269 | G4ErrorSymMatrix mret(m1); |
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270 | mret /= t; |
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271 | return mret; |
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272 | } |
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273 | |
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274 | G4ErrorSymMatrix operator*(const G4ErrorSymMatrix &m1,G4double t) |
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275 | { |
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276 | G4ErrorSymMatrix mret(m1); |
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277 | mret *= t; |
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278 | return mret; |
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279 | } |
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280 | |
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281 | G4ErrorSymMatrix operator*(G4double t,const G4ErrorSymMatrix &m1) |
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282 | { |
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283 | G4ErrorSymMatrix mret(m1); |
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284 | mret *= t; |
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285 | return mret; |
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286 | } |
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287 | |
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288 | G4ErrorMatrix operator*(const G4ErrorMatrix &m1, const G4ErrorSymMatrix &m2) |
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289 | { |
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290 | G4ErrorMatrix mret(m1.num_row(),m2.num_col()); |
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291 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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292 | G4ErrorMatrixConstIter mit1, mit2, sp,snp; //mit2=0 |
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293 | G4double temp; |
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294 | G4ErrorMatrixIter mir=mret.m.begin(); |
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295 | G4int step,stept; |
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296 | for(mit1=m1.m.begin(); |
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297 | mit1<m1.m.begin()+m1.num_row()*m1.num_col(); mit1 = mit2) |
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298 | { |
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299 | for(step=1,snp=m2.m.begin();step<=m2.num_row();) |
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300 | { |
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301 | mit2=mit1; |
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302 | sp=snp; |
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303 | snp+=step; |
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304 | temp=0; |
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305 | while(sp<snp) |
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306 | { |
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307 | temp+=*(sp++)*(*(mit2++)); |
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308 | } |
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309 | sp+=step-1; |
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310 | for(stept=++step;stept<=m2.num_row();stept++) |
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311 | { |
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312 | temp+=*sp*(*(mit2++)); |
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313 | sp+=stept; |
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314 | } |
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315 | *(mir++)=temp; |
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316 | } |
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317 | } |
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318 | return mret; |
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319 | } |
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320 | |
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321 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, const G4ErrorMatrix &m2) |
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322 | { |
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323 | G4ErrorMatrix mret(m1.num_row(),m2.num_col()); |
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324 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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325 | G4int step,stept; |
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326 | G4ErrorMatrixConstIter mit1,mit2,sp,snp; |
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327 | G4double temp; |
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328 | G4ErrorMatrixIter mir=mret.m.begin(); |
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329 | for(step=1,snp=m1.m.begin();step<=m1.num_row();snp+=step++) |
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330 | { |
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331 | for(mit1=m2.m.begin();mit1<m2.m.begin()+m2.num_col();mit1++) |
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332 | { |
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333 | mit2=mit1; |
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334 | sp=snp; |
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335 | temp=0; |
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336 | while(sp<snp+step) |
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337 | { |
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338 | temp+=*mit2*(*(sp++)); |
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339 | mit2+=m2.num_col(); |
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340 | } |
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341 | sp+=step-1; |
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342 | for(stept=step+1;stept<=m1.num_row();stept++) |
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343 | { |
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344 | temp+=*mit2*(*sp); |
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345 | mit2+=m2.num_col(); |
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346 | sp+=stept; |
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347 | } |
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348 | *(mir++)=temp; |
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349 | } |
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350 | } |
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351 | return mret; |
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352 | } |
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353 | |
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354 | G4ErrorMatrix operator*(const G4ErrorSymMatrix &m1, const G4ErrorSymMatrix &m2) |
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355 | { |
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356 | G4ErrorMatrix mret(m1.num_row(),m1.num_row()); |
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357 | CHK_DIM_1(m1.num_col(),m2.num_row(),*); |
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358 | G4int step1,stept1,step2,stept2; |
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359 | G4ErrorMatrixConstIter snp1,sp1,snp2,sp2; |
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360 | G4double temp; |
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361 | G4ErrorMatrixIter mr = mret.m.begin(); |
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362 | for(step1=1,snp1=m1.m.begin();step1<=m1.num_row();snp1+=step1++) |
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363 | { |
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364 | for(step2=1,snp2=m2.m.begin();step2<=m2.num_row();) |
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365 | { |
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366 | sp1=snp1; |
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367 | sp2=snp2; |
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368 | snp2+=step2; |
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369 | temp=0; |
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370 | if(step1<step2) |
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371 | { |
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372 | while(sp1<snp1+step1) |
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373 | { temp+=(*(sp1++))*(*(sp2++)); } |
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374 | sp1+=step1-1; |
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375 | for(stept1=step1+1;stept1!=step2+1;sp1+=stept1++) |
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376 | { temp+=(*sp1)*(*(sp2++)); } |
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377 | sp2+=step2-1; |
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378 | for(stept2=++step2;stept2<=m2.num_row();sp1+=stept1++,sp2+=stept2++) |
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379 | { temp+=(*sp1)*(*sp2); } |
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380 | } |
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381 | else |
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382 | { |
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383 | while(sp2<snp2) |
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384 | { temp+=(*(sp1++))*(*(sp2++)); } |
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385 | sp2+=step2-1; |
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386 | for(stept2=++step2;stept2!=step1+1;sp2+=stept2++) |
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387 | { temp+=(*(sp1++))*(*sp2); } |
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388 | sp1+=step1-1; |
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389 | for(stept1=step1+1;stept1<=m1.num_row();sp1+=stept1++,sp2+=stept2++) |
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390 | { temp+=(*sp1)*(*sp2); } |
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391 | } |
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392 | *(mr++)=temp; |
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393 | } |
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394 | } |
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395 | return mret; |
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396 | } |
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397 | |
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398 | /* ----------------------------------------------------------------------- |
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399 | This section contains the assignment and inplace operators =,+=,-=,*=,/=. |
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400 | ----------------------------------------------------------------------- */ |
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401 | |
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402 | G4ErrorMatrix & G4ErrorMatrix::operator+=(const G4ErrorSymMatrix &m2) |
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403 | { |
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404 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=); |
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405 | G4int n = num_col(); |
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406 | G4ErrorMatrixConstIter sjk = m2.m.begin(); |
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407 | G4ErrorMatrixIter m1j = m.begin(); |
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408 | G4ErrorMatrixIter mj = m.begin(); |
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409 | // j >= k |
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410 | for(G4int j=1;j<=num_row();j++) |
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411 | { |
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412 | G4ErrorMatrixIter mjk = mj; |
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413 | G4ErrorMatrixIter mkj = m1j; |
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414 | for(G4int k=1;k<=j;k++) |
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415 | { |
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416 | *(mjk++) += *sjk; |
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417 | if(j!=k) *mkj += *sjk; |
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418 | sjk++; |
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419 | mkj += n; |
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420 | } |
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421 | mj += n; |
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422 | m1j++; |
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423 | } |
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424 | return (*this); |
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425 | } |
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426 | |
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427 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator+=(const G4ErrorSymMatrix &m2) |
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428 | { |
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429 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),+=); |
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430 | SIMPLE_BOP(+=) |
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431 | return (*this); |
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432 | } |
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433 | |
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434 | G4ErrorMatrix & G4ErrorMatrix::operator-=(const G4ErrorSymMatrix &m2) |
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435 | { |
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436 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=); |
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437 | G4int n = num_col(); |
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438 | G4ErrorMatrixConstIter sjk = m2.m.begin(); |
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439 | G4ErrorMatrixIter m1j = m.begin(); |
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440 | G4ErrorMatrixIter mj = m.begin(); |
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441 | // j >= k |
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442 | for(G4int j=1;j<=num_row();j++) |
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443 | { |
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444 | G4ErrorMatrixIter mjk = mj; |
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445 | G4ErrorMatrixIter mkj = m1j; |
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446 | for(G4int k=1;k<=j;k++) |
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447 | { |
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448 | *(mjk++) -= *sjk; |
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449 | if(j!=k) *mkj -= *sjk; |
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450 | sjk++; |
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451 | mkj += n; |
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452 | } |
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453 | mj += n; |
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454 | m1j++; |
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455 | } |
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456 | return (*this); |
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457 | } |
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458 | |
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459 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator-=(const G4ErrorSymMatrix &m2) |
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460 | { |
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461 | CHK_DIM_2(num_row(),m2.num_row(),num_col(),m2.num_col(),-=); |
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462 | SIMPLE_BOP(-=) |
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463 | return (*this); |
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464 | } |
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465 | |
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466 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator/=(G4double t) |
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467 | { |
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468 | SIMPLE_UOP(/=) |
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469 | return (*this); |
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470 | } |
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471 | |
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472 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator*=(G4double t) |
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473 | { |
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474 | SIMPLE_UOP(*=) |
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475 | return (*this); |
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476 | } |
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477 | |
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478 | G4ErrorMatrix & G4ErrorMatrix::operator=(const G4ErrorSymMatrix &m1) |
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479 | { |
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480 | if(m1.nrow*m1.nrow != size) |
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481 | { |
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482 | size = m1.nrow * m1.nrow; |
---|
483 | m.resize(size); |
---|
484 | } |
---|
485 | nrow = m1.nrow; |
---|
486 | ncol = m1.nrow; |
---|
487 | G4int n = ncol; |
---|
488 | G4ErrorMatrixConstIter sjk = m1.m.begin(); |
---|
489 | G4ErrorMatrixIter m1j = m.begin(); |
---|
490 | G4ErrorMatrixIter mj = m.begin(); |
---|
491 | // j >= k |
---|
492 | for(G4int j=1;j<=num_row();j++) |
---|
493 | { |
---|
494 | G4ErrorMatrixIter mjk = mj; |
---|
495 | G4ErrorMatrixIter mkj = m1j; |
---|
496 | for(G4int k=1;k<=j;k++) |
---|
497 | { |
---|
498 | *(mjk++) = *sjk; |
---|
499 | if(j!=k) *mkj = *sjk; |
---|
500 | sjk++; |
---|
501 | mkj += n; |
---|
502 | } |
---|
503 | mj += n; |
---|
504 | m1j++; |
---|
505 | } |
---|
506 | return (*this); |
---|
507 | } |
---|
508 | |
---|
509 | G4ErrorSymMatrix & G4ErrorSymMatrix::operator=(const G4ErrorSymMatrix &m1) |
---|
510 | { |
---|
511 | if(m1.nrow != nrow) |
---|
512 | { |
---|
513 | nrow = m1.nrow; |
---|
514 | size = m1.size; |
---|
515 | m.resize(size); |
---|
516 | } |
---|
517 | m = m1.m; |
---|
518 | return (*this); |
---|
519 | } |
---|
520 | |
---|
521 | // Print the Matrix. |
---|
522 | |
---|
523 | std::ostream& operator<<(std::ostream &s, const G4ErrorSymMatrix &q) |
---|
524 | { |
---|
525 | s << G4endl; |
---|
526 | |
---|
527 | // Fixed format needs 3 extra characters for field, |
---|
528 | // while scientific needs 7 |
---|
529 | |
---|
530 | G4int width; |
---|
531 | if(s.flags() & std::ios::fixed) |
---|
532 | { |
---|
533 | width = s.precision()+3; |
---|
534 | } |
---|
535 | else |
---|
536 | { |
---|
537 | width = s.precision()+7; |
---|
538 | } |
---|
539 | for(G4int irow = 1; irow<= q.num_row(); irow++) |
---|
540 | { |
---|
541 | for(G4int icol = 1; icol <= q.num_col(); icol++) |
---|
542 | { |
---|
543 | s.width(width); |
---|
544 | s << q(irow,icol) << " "; |
---|
545 | } |
---|
546 | s << G4endl; |
---|
547 | } |
---|
548 | return s; |
---|
549 | } |
---|
550 | |
---|
551 | G4ErrorSymMatrix G4ErrorSymMatrix:: |
---|
552 | apply(G4double (*f)(G4double, G4int, G4int)) const |
---|
553 | { |
---|
554 | G4ErrorSymMatrix mret(num_row()); |
---|
555 | G4ErrorMatrixConstIter a = m.begin(); |
---|
556 | G4ErrorMatrixIter b = mret.m.begin(); |
---|
557 | for(G4int ir=1;ir<=num_row();ir++) |
---|
558 | { |
---|
559 | for(G4int ic=1;ic<=ir;ic++) |
---|
560 | { |
---|
561 | *(b++) = (*f)(*(a++), ir, ic); |
---|
562 | } |
---|
563 | } |
---|
564 | return mret; |
---|
565 | } |
---|
566 | |
---|
567 | void G4ErrorSymMatrix::assign (const G4ErrorMatrix &m1) |
---|
568 | { |
---|
569 | if(m1.nrow != nrow) |
---|
570 | { |
---|
571 | nrow = m1.nrow; |
---|
572 | size = nrow * (nrow+1) / 2; |
---|
573 | m.resize(size); |
---|
574 | } |
---|
575 | G4ErrorMatrixConstIter a = m1.m.begin(); |
---|
576 | G4ErrorMatrixIter b = m.begin(); |
---|
577 | for(G4int r=1;r<=nrow;r++) |
---|
578 | { |
---|
579 | G4ErrorMatrixConstIter d = a; |
---|
580 | for(G4int c=1;c<=r;c++) |
---|
581 | { |
---|
582 | *(b++) = *(d++); |
---|
583 | } |
---|
584 | a += nrow; |
---|
585 | } |
---|
586 | } |
---|
587 | |
---|
588 | G4ErrorSymMatrix G4ErrorSymMatrix::similarity(const G4ErrorMatrix &m1) const |
---|
589 | { |
---|
590 | G4ErrorSymMatrix mret(m1.num_row()); |
---|
591 | G4ErrorMatrix temp = m1*(*this); |
---|
592 | |
---|
593 | // If m1*(*this) has correct dimensions, then so will the m1.T multiplication. |
---|
594 | // So there is no need to check dimensions again. |
---|
595 | |
---|
596 | G4int n = m1.num_col(); |
---|
597 | G4ErrorMatrixIter mr = mret.m.begin(); |
---|
598 | G4ErrorMatrixIter tempr1 = temp.m.begin(); |
---|
599 | for(G4int r=1;r<=mret.num_row();r++) |
---|
600 | { |
---|
601 | G4ErrorMatrixConstIter m1c1 = m1.m.begin(); |
---|
602 | for(G4int c=1;c<=r;c++) |
---|
603 | { |
---|
604 | G4double tmp = 0.0; |
---|
605 | G4ErrorMatrixIter tempri = tempr1; |
---|
606 | G4ErrorMatrixConstIter m1ci = m1c1; |
---|
607 | for(G4int i=1;i<=m1.num_col();i++) |
---|
608 | { |
---|
609 | tmp+=(*(tempri++))*(*(m1ci++)); |
---|
610 | } |
---|
611 | *(mr++) = tmp; |
---|
612 | m1c1 += n; |
---|
613 | } |
---|
614 | tempr1 += n; |
---|
615 | } |
---|
616 | return mret; |
---|
617 | } |
---|
618 | |
---|
619 | G4ErrorSymMatrix G4ErrorSymMatrix::similarity(const G4ErrorSymMatrix &m1) const |
---|
620 | { |
---|
621 | G4ErrorSymMatrix mret(m1.num_row()); |
---|
622 | G4ErrorMatrix temp = m1*(*this); |
---|
623 | G4int n = m1.num_col(); |
---|
624 | G4ErrorMatrixIter mr = mret.m.begin(); |
---|
625 | G4ErrorMatrixIter tempr1 = temp.m.begin(); |
---|
626 | for(G4int r=1;r<=mret.num_row();r++) |
---|
627 | { |
---|
628 | G4ErrorMatrixConstIter m1c1 = m1.m.begin(); |
---|
629 | G4int c; |
---|
630 | for(c=1;c<=r;c++) |
---|
631 | { |
---|
632 | G4double tmp = 0.0; |
---|
633 | G4ErrorMatrixIter tempri = tempr1; |
---|
634 | G4ErrorMatrixConstIter m1ci = m1c1; |
---|
635 | G4int i; |
---|
636 | for(i=1;i<c;i++) |
---|
637 | { |
---|
638 | tmp+=(*(tempri++))*(*(m1ci++)); |
---|
639 | } |
---|
640 | for(i=c;i<=m1.num_col();i++) |
---|
641 | { |
---|
642 | tmp+=(*(tempri++))*(*(m1ci)); |
---|
643 | m1ci += i; |
---|
644 | } |
---|
645 | *(mr++) = tmp; |
---|
646 | m1c1 += c; |
---|
647 | } |
---|
648 | tempr1 += n; |
---|
649 | } |
---|
650 | return mret; |
---|
651 | } |
---|
652 | |
---|
653 | G4ErrorSymMatrix G4ErrorSymMatrix::similarityT(const G4ErrorMatrix &m1) const |
---|
654 | { |
---|
655 | G4ErrorSymMatrix mret(m1.num_col()); |
---|
656 | G4ErrorMatrix temp = (*this)*m1; |
---|
657 | G4int n = m1.num_col(); |
---|
658 | G4ErrorMatrixIter mrc = mret.m.begin(); |
---|
659 | G4ErrorMatrixIter temp1r = temp.m.begin(); |
---|
660 | for(G4int r=1;r<=mret.num_row();r++) |
---|
661 | { |
---|
662 | G4ErrorMatrixConstIter m11c = m1.m.begin(); |
---|
663 | for(G4int c=1;c<=r;c++) |
---|
664 | { |
---|
665 | G4double tmp = 0.0; |
---|
666 | G4ErrorMatrixIter tempir = temp1r; |
---|
667 | G4ErrorMatrixConstIter m1ic = m11c; |
---|
668 | for(G4int i=1;i<=m1.num_row();i++) |
---|
669 | { |
---|
670 | tmp+=(*(tempir))*(*(m1ic)); |
---|
671 | tempir += n; |
---|
672 | m1ic += n; |
---|
673 | } |
---|
674 | *(mrc++) = tmp; |
---|
675 | m11c++; |
---|
676 | } |
---|
677 | temp1r++; |
---|
678 | } |
---|
679 | return mret; |
---|
680 | } |
---|
681 | |
---|
682 | void G4ErrorSymMatrix::invert(G4int &ifail) |
---|
683 | { |
---|
684 | ifail = 0; |
---|
685 | |
---|
686 | switch(nrow) |
---|
687 | { |
---|
688 | case 3: |
---|
689 | { |
---|
690 | G4double det, temp; |
---|
691 | G4double t1, t2, t3; |
---|
692 | G4double c11,c12,c13,c22,c23,c33; |
---|
693 | c11 = (*(m.begin()+2)) * (*(m.begin()+5)) |
---|
694 | - (*(m.begin()+4)) * (*(m.begin()+4)); |
---|
695 | c12 = (*(m.begin()+4)) * (*(m.begin()+3)) |
---|
696 | - (*(m.begin()+1)) * (*(m.begin()+5)); |
---|
697 | c13 = (*(m.begin()+1)) * (*(m.begin()+4)) |
---|
698 | - (*(m.begin()+2)) * (*(m.begin()+3)); |
---|
699 | c22 = (*(m.begin()+5)) * (*m.begin()) |
---|
700 | - (*(m.begin()+3)) * (*(m.begin()+3)); |
---|
701 | c23 = (*(m.begin()+3)) * (*(m.begin()+1)) |
---|
702 | - (*(m.begin()+4)) * (*m.begin()); |
---|
703 | c33 = (*m.begin()) * (*(m.begin()+2)) |
---|
704 | - (*(m.begin()+1)) * (*(m.begin()+1)); |
---|
705 | t1 = std::fabs(*m.begin()); |
---|
706 | t2 = std::fabs(*(m.begin()+1)); |
---|
707 | t3 = std::fabs(*(m.begin()+3)); |
---|
708 | if (t1 >= t2) |
---|
709 | { |
---|
710 | if (t3 >= t1) |
---|
711 | { |
---|
712 | temp = *(m.begin()+3); |
---|
713 | det = c23*c12-c22*c13; |
---|
714 | } |
---|
715 | else |
---|
716 | { |
---|
717 | temp = *m.begin(); |
---|
718 | det = c22*c33-c23*c23; |
---|
719 | } |
---|
720 | } |
---|
721 | else if (t3 >= t2) |
---|
722 | { |
---|
723 | temp = *(m.begin()+3); |
---|
724 | det = c23*c12-c22*c13; |
---|
725 | } |
---|
726 | else |
---|
727 | { |
---|
728 | temp = *(m.begin()+1); |
---|
729 | det = c13*c23-c12*c33; |
---|
730 | } |
---|
731 | if (det==0) |
---|
732 | { |
---|
733 | ifail = 1; |
---|
734 | return; |
---|
735 | } |
---|
736 | { |
---|
737 | G4double s = temp/det; |
---|
738 | G4ErrorMatrixIter mm = m.begin(); |
---|
739 | *(mm++) = s*c11; |
---|
740 | *(mm++) = s*c12; |
---|
741 | *(mm++) = s*c22; |
---|
742 | *(mm++) = s*c13; |
---|
743 | *(mm++) = s*c23; |
---|
744 | *(mm) = s*c33; |
---|
745 | } |
---|
746 | } |
---|
747 | break; |
---|
748 | case 2: |
---|
749 | { |
---|
750 | G4double det, temp, s; |
---|
751 | det = (*m.begin())*(*(m.begin()+2)) - (*(m.begin()+1))*(*(m.begin()+1)); |
---|
752 | if (det==0) |
---|
753 | { |
---|
754 | ifail = 1; |
---|
755 | return; |
---|
756 | } |
---|
757 | s = 1.0/det; |
---|
758 | *(m.begin()+1) *= -s; |
---|
759 | temp = s*(*(m.begin()+2)); |
---|
760 | *(m.begin()+2) = s*(*m.begin()); |
---|
761 | *m.begin() = temp; |
---|
762 | break; |
---|
763 | } |
---|
764 | case 1: |
---|
765 | { |
---|
766 | if ((*m.begin())==0) |
---|
767 | { |
---|
768 | ifail = 1; |
---|
769 | return; |
---|
770 | } |
---|
771 | *m.begin() = 1.0/(*m.begin()); |
---|
772 | break; |
---|
773 | } |
---|
774 | case 5: |
---|
775 | { |
---|
776 | invert5(ifail); |
---|
777 | return; |
---|
778 | } |
---|
779 | case 6: |
---|
780 | { |
---|
781 | invert6(ifail); |
---|
782 | return; |
---|
783 | } |
---|
784 | case 4: |
---|
785 | { |
---|
786 | invert4(ifail); |
---|
787 | return; |
---|
788 | } |
---|
789 | default: |
---|
790 | { |
---|
791 | invertBunchKaufman(ifail); |
---|
792 | return; |
---|
793 | } |
---|
794 | } |
---|
795 | return; // inversion successful |
---|
796 | } |
---|
797 | |
---|
798 | G4double G4ErrorSymMatrix::determinant() const |
---|
799 | { |
---|
800 | static const G4int max_array = 20; |
---|
801 | |
---|
802 | // ir must point to an array which is ***1 longer than*** nrow |
---|
803 | |
---|
804 | static std::vector<G4int> ir_vec (max_array+1); |
---|
805 | if (ir_vec.size() <= static_cast<unsigned int>(nrow)) |
---|
806 | { |
---|
807 | ir_vec.resize(nrow+1); |
---|
808 | } |
---|
809 | G4int * ir = &ir_vec[0]; |
---|
810 | |
---|
811 | G4double det; |
---|
812 | G4ErrorMatrix mt(*this); |
---|
813 | G4int i = mt.dfact_matrix(det, ir); |
---|
814 | if(i==0) { return det; } |
---|
815 | return 0.0; |
---|
816 | } |
---|
817 | |
---|
818 | G4double G4ErrorSymMatrix::trace() const |
---|
819 | { |
---|
820 | G4double t = 0.0; |
---|
821 | for (G4int i=0; i<nrow; i++) |
---|
822 | { t += *(m.begin() + (i+3)*i/2); } |
---|
823 | return t; |
---|
824 | } |
---|
825 | |
---|
826 | void G4ErrorSymMatrix::invertBunchKaufman(G4int &ifail) |
---|
827 | { |
---|
828 | // Bunch-Kaufman diagonal pivoting method |
---|
829 | // It is decribed in J.R. Bunch, L. Kaufman (1977). |
---|
830 | // "Some Stable Methods for Calculating Inertia and Solving Symmetric |
---|
831 | // Linear Systems", Math. Comp. 31, p. 162-179. or in Gene H. Golub, |
---|
832 | // Charles F. van Loan, "Matrix Computations" (the second edition |
---|
833 | // has a bug.) and implemented in "lapack" |
---|
834 | // Mario Stanke, 09/97 |
---|
835 | |
---|
836 | G4int i, j, k, s; |
---|
837 | G4int pivrow; |
---|
838 | |
---|
839 | // Establish the two working-space arrays needed: x and piv are |
---|
840 | // used as pointers to arrays of doubles and ints respectively, each |
---|
841 | // of length nrow. We do not want to reallocate each time through |
---|
842 | // unless the size needs to grow. We do not want to leak memory, even |
---|
843 | // by having a new without a delete that is only done once. |
---|
844 | |
---|
845 | static const G4int max_array = 25; |
---|
846 | static std::vector<G4double> xvec (max_array); |
---|
847 | static std::vector<G4int> pivv (max_array); |
---|
848 | typedef std::vector<G4int>::iterator pivIter; |
---|
849 | if (xvec.size() < static_cast<unsigned int>(nrow)) xvec.resize(nrow); |
---|
850 | if (pivv.size() < static_cast<unsigned int>(nrow)) pivv.resize(nrow); |
---|
851 | // Note - resize should do nothing if the size is already larger than nrow, |
---|
852 | // but on VC++ there are indications that it does so we check. |
---|
853 | // Note - the data elements in a vector are guaranteed to be contiguous, |
---|
854 | // so x[i] and piv[i] are optimally fast. |
---|
855 | G4ErrorMatrixIter x = xvec.begin(); |
---|
856 | // x[i] is used as helper storage, needs to have at least size nrow. |
---|
857 | pivIter piv = pivv.begin(); |
---|
858 | // piv[i] is used to store details of exchanges |
---|
859 | |
---|
860 | G4double temp1, temp2; |
---|
861 | G4ErrorMatrixIter ip, mjj, iq; |
---|
862 | G4double lambda, sigma; |
---|
863 | const G4double alpha = .6404; // = (1+sqrt(17))/8 |
---|
864 | const G4double epsilon = 32*DBL_EPSILON; |
---|
865 | // whenever a sum of two doubles is below or equal to epsilon |
---|
866 | // it is set to zero. |
---|
867 | // this constant could be set to zero but then the algorithm |
---|
868 | // doesn't neccessarily detect that a matrix is singular |
---|
869 | |
---|
870 | for (i = 0; i < nrow; i++) |
---|
871 | { |
---|
872 | piv[i] = i+1; |
---|
873 | } |
---|
874 | |
---|
875 | ifail = 0; |
---|
876 | |
---|
877 | // compute the factorization P*A*P^T = L * D * L^T |
---|
878 | // L is unit lower triangular, D is direct sum of 1x1 and 2x2 matrices |
---|
879 | // L and D^-1 are stored in A = *this, P is stored in piv[] |
---|
880 | |
---|
881 | for (j=1; j < nrow; j+=s) // main loop over columns |
---|
882 | { |
---|
883 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
884 | lambda = 0; // compute lambda = max of A(j+1:n,j) |
---|
885 | pivrow = j+1; |
---|
886 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
887 | for (i=j+1; i <= nrow ; ip += i++) |
---|
888 | { |
---|
889 | if (std::fabs(*ip) > lambda) |
---|
890 | { |
---|
891 | lambda = std::fabs(*ip); |
---|
892 | pivrow = i; |
---|
893 | } |
---|
894 | } |
---|
895 | if (lambda == 0 ) |
---|
896 | { |
---|
897 | if (*mjj == 0) |
---|
898 | { |
---|
899 | ifail = 1; |
---|
900 | return; |
---|
901 | } |
---|
902 | s=1; |
---|
903 | *mjj = 1./ *mjj; |
---|
904 | } |
---|
905 | else |
---|
906 | { |
---|
907 | if (std::fabs(*mjj) >= lambda*alpha) |
---|
908 | { |
---|
909 | s=1; |
---|
910 | pivrow=j; |
---|
911 | } |
---|
912 | else |
---|
913 | { |
---|
914 | sigma = 0; // compute sigma = max A(pivrow, j:pivrow-1) |
---|
915 | ip = m.begin() + pivrow*(pivrow-1)/2+j-1; |
---|
916 | for (k=j; k < pivrow; k++) |
---|
917 | { |
---|
918 | if (std::fabs(*ip) > sigma) |
---|
919 | sigma = std::fabs(*ip); |
---|
920 | ip++; |
---|
921 | } |
---|
922 | if (sigma * std::fabs(*mjj) >= alpha * lambda * lambda) |
---|
923 | { |
---|
924 | s=1; |
---|
925 | pivrow = j; |
---|
926 | } |
---|
927 | else if (std::fabs(*(m.begin()+pivrow*(pivrow-1)/2+pivrow-1)) |
---|
928 | >= alpha * sigma) |
---|
929 | { s=1; } |
---|
930 | else |
---|
931 | { s=2; } |
---|
932 | } |
---|
933 | if (pivrow == j) // no permutation neccessary |
---|
934 | { |
---|
935 | piv[j-1] = pivrow; |
---|
936 | if (*mjj == 0) |
---|
937 | { |
---|
938 | ifail=1; |
---|
939 | return; |
---|
940 | } |
---|
941 | temp2 = *mjj = 1./ *mjj; // invert D(j,j) |
---|
942 | |
---|
943 | // update A(j+1:n, j+1,n) |
---|
944 | for (i=j+1; i <= nrow; i++) |
---|
945 | { |
---|
946 | temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2; |
---|
947 | ip = m.begin()+i*(i-1)/2+j; |
---|
948 | for (k=j+1; k<=i; k++) |
---|
949 | { |
---|
950 | *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1); |
---|
951 | if (std::fabs(*ip) <= epsilon) |
---|
952 | { *ip=0; } |
---|
953 | ip++; |
---|
954 | } |
---|
955 | } |
---|
956 | // update L |
---|
957 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
958 | for (i=j+1; i <= nrow; ip += i++) |
---|
959 | { |
---|
960 | *ip *= temp2; |
---|
961 | } |
---|
962 | } |
---|
963 | else if (s==1) // 1x1 pivot |
---|
964 | { |
---|
965 | piv[j-1] = pivrow; |
---|
966 | |
---|
967 | // interchange rows and columns j and pivrow in |
---|
968 | // submatrix (j:n,j:n) |
---|
969 | ip = m.begin() + pivrow*(pivrow-1)/2 + j; |
---|
970 | for (i=j+1; i < pivrow; i++, ip++) |
---|
971 | { |
---|
972 | temp1 = *(m.begin() + i*(i-1)/2 + j-1); |
---|
973 | *(m.begin() + i*(i-1)/2 + j-1)= *ip; |
---|
974 | *ip = temp1; |
---|
975 | } |
---|
976 | temp1 = *mjj; |
---|
977 | *mjj = *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1); |
---|
978 | *(m.begin()+pivrow*(pivrow-1)/2+pivrow-1) = temp1; |
---|
979 | ip = m.begin() + (pivrow+1)*pivrow/2 + j-1; |
---|
980 | iq = ip + pivrow-j; |
---|
981 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
982 | { |
---|
983 | temp1 = *iq; |
---|
984 | *iq = *ip; |
---|
985 | *ip = temp1; |
---|
986 | } |
---|
987 | |
---|
988 | if (*mjj == 0) |
---|
989 | { |
---|
990 | ifail = 1; |
---|
991 | return; |
---|
992 | } |
---|
993 | temp2 = *mjj = 1./ *mjj; // invert D(j,j) |
---|
994 | |
---|
995 | // update A(j+1:n, j+1:n) |
---|
996 | for (i = j+1; i <= nrow; i++) |
---|
997 | { |
---|
998 | temp1 = *(m.begin() + i*(i-1)/2 + j-1) * temp2; |
---|
999 | ip = m.begin()+i*(i-1)/2+j; |
---|
1000 | for (k=j+1; k<=i; k++) |
---|
1001 | { |
---|
1002 | *ip -= temp1 * *(m.begin() + k*(k-1)/2 + j-1); |
---|
1003 | if (std::fabs(*ip) <= epsilon) |
---|
1004 | { *ip=0; } |
---|
1005 | ip++; |
---|
1006 | } |
---|
1007 | } |
---|
1008 | // update L |
---|
1009 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
1010 | for (i=j+1; i<=nrow; ip += i++) |
---|
1011 | { |
---|
1012 | *ip *= temp2; |
---|
1013 | } |
---|
1014 | } |
---|
1015 | else // s=2, ie use a 2x2 pivot |
---|
1016 | { |
---|
1017 | piv[j-1] = -pivrow; |
---|
1018 | piv[j] = 0; // that means this is the second row of a 2x2 pivot |
---|
1019 | |
---|
1020 | if (j+1 != pivrow) |
---|
1021 | { |
---|
1022 | // interchange rows and columns j+1 and pivrow in |
---|
1023 | // submatrix (j:n,j:n) |
---|
1024 | ip = m.begin() + pivrow*(pivrow-1)/2 + j+1; |
---|
1025 | for (i=j+2; i < pivrow; i++, ip++) |
---|
1026 | { |
---|
1027 | temp1 = *(m.begin() + i*(i-1)/2 + j); |
---|
1028 | *(m.begin() + i*(i-1)/2 + j) = *ip; |
---|
1029 | *ip = temp1; |
---|
1030 | } |
---|
1031 | temp1 = *(mjj + j + 1); |
---|
1032 | *(mjj + j + 1) = |
---|
1033 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1); |
---|
1034 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1; |
---|
1035 | temp1 = *(mjj + j); |
---|
1036 | *(mjj + j) = *(m.begin() + pivrow*(pivrow-1)/2 + j-1); |
---|
1037 | *(m.begin() + pivrow*(pivrow-1)/2 + j-1) = temp1; |
---|
1038 | ip = m.begin() + (pivrow+1)*pivrow/2 + j; |
---|
1039 | iq = ip + pivrow-(j+1); |
---|
1040 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
1041 | { |
---|
1042 | temp1 = *iq; |
---|
1043 | *iq = *ip; |
---|
1044 | *ip = temp1; |
---|
1045 | } |
---|
1046 | } |
---|
1047 | // invert D(j:j+1,j:j+1) |
---|
1048 | temp2 = *mjj * *(mjj + j + 1) - *(mjj + j) * *(mjj + j); |
---|
1049 | if (temp2 == 0) |
---|
1050 | { |
---|
1051 | G4cerr |
---|
1052 | << "G4ErrorSymMatrix::bunch_invert: error in pivot choice" |
---|
1053 | << G4endl; |
---|
1054 | } |
---|
1055 | temp2 = 1. / temp2; |
---|
1056 | |
---|
1057 | // this quotient is guaranteed to exist by the choice |
---|
1058 | // of the pivot |
---|
1059 | |
---|
1060 | temp1 = *mjj; |
---|
1061 | *mjj = *(mjj + j + 1) * temp2; |
---|
1062 | *(mjj + j + 1) = temp1 * temp2; |
---|
1063 | *(mjj + j) = - *(mjj + j) * temp2; |
---|
1064 | |
---|
1065 | if (j < nrow-1) // otherwise do nothing |
---|
1066 | { |
---|
1067 | // update A(j+2:n, j+2:n) |
---|
1068 | for (i=j+2; i <= nrow ; i++) |
---|
1069 | { |
---|
1070 | ip = m.begin() + i*(i-1)/2 + j-1; |
---|
1071 | temp1 = *ip * *mjj + *(ip + 1) * *(mjj + j); |
---|
1072 | if (std::fabs(temp1 ) <= epsilon) |
---|
1073 | { temp1 = 0; } |
---|
1074 | temp2 = *ip * *(mjj + j) + *(ip + 1) * *(mjj + j + 1); |
---|
1075 | if (std::fabs(temp2 ) <= epsilon) |
---|
1076 | { temp2 = 0; } |
---|
1077 | for (k = j+2; k <= i ; k++) |
---|
1078 | { |
---|
1079 | ip = m.begin() + i*(i-1)/2 + k-1; |
---|
1080 | iq = m.begin() + k*(k-1)/2 + j-1; |
---|
1081 | *ip -= temp1 * *iq + temp2 * *(iq+1); |
---|
1082 | if (std::fabs(*ip) <= epsilon) |
---|
1083 | { *ip = 0; } |
---|
1084 | } |
---|
1085 | } |
---|
1086 | // update L |
---|
1087 | for (i=j+2; i <= nrow ; i++) |
---|
1088 | { |
---|
1089 | ip = m.begin() + i*(i-1)/2 + j-1; |
---|
1090 | temp1 = *ip * *mjj + *(ip+1) * *(mjj + j); |
---|
1091 | if (std::fabs(temp1) <= epsilon) |
---|
1092 | { temp1 = 0; } |
---|
1093 | *(ip+1) = *ip * *(mjj + j) + *(ip+1) * *(mjj + j + 1); |
---|
1094 | if (std::fabs(*(ip+1)) <= epsilon) |
---|
1095 | { *(ip+1) = 0; } |
---|
1096 | *ip = temp1; |
---|
1097 | } |
---|
1098 | } |
---|
1099 | } |
---|
1100 | } |
---|
1101 | } // end of main loop over columns |
---|
1102 | |
---|
1103 | if (j == nrow) // the the last pivot is 1x1 |
---|
1104 | { |
---|
1105 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
1106 | if (*mjj == 0) |
---|
1107 | { |
---|
1108 | ifail = 1; |
---|
1109 | return; |
---|
1110 | } |
---|
1111 | else |
---|
1112 | { |
---|
1113 | *mjj = 1. / *mjj; |
---|
1114 | } |
---|
1115 | } // end of last pivot code |
---|
1116 | |
---|
1117 | // computing the inverse from the factorization |
---|
1118 | |
---|
1119 | for (j = nrow ; j >= 1 ; j -= s) // loop over columns |
---|
1120 | { |
---|
1121 | mjj = m.begin() + j*(j-1)/2 + j-1; |
---|
1122 | if (piv[j-1] > 0) // 1x1 pivot, compute column j of inverse |
---|
1123 | { |
---|
1124 | s = 1; |
---|
1125 | if (j < nrow) |
---|
1126 | { |
---|
1127 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
1128 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
1129 | { |
---|
1130 | x[i] = *ip; |
---|
1131 | } |
---|
1132 | for (i=j+1; i<=nrow ; i++) |
---|
1133 | { |
---|
1134 | temp2=0; |
---|
1135 | ip = m.begin() + i*(i-1)/2 + j; |
---|
1136 | for (k=0; k <= i-j-1; k++) |
---|
1137 | { temp2 += *ip++ * x[k]; } |
---|
1138 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
1139 | { temp2 += *ip * x[k]; } |
---|
1140 | *(m.begin()+ i*(i-1)/2 + j-1) = -temp2; |
---|
1141 | } |
---|
1142 | temp2 = 0; |
---|
1143 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
1144 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
1145 | { temp2 += x[k] * *ip; } |
---|
1146 | *mjj -= temp2; |
---|
1147 | } |
---|
1148 | } |
---|
1149 | else //2x2 pivot, compute columns j and j-1 of the inverse |
---|
1150 | { |
---|
1151 | if (piv[j-1] != 0) |
---|
1152 | { G4cerr << "error in piv" << piv[j-1] << G4endl; } |
---|
1153 | s=2; |
---|
1154 | if (j < nrow) |
---|
1155 | { |
---|
1156 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
1157 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
1158 | { |
---|
1159 | x[i] = *ip; |
---|
1160 | } |
---|
1161 | for (i=j+1; i<=nrow ; i++) |
---|
1162 | { |
---|
1163 | temp2 = 0; |
---|
1164 | ip = m.begin() + i*(i-1)/2 + j; |
---|
1165 | for (k=0; k <= i-j-1; k++) |
---|
1166 | { temp2 += *ip++ * x[k]; } |
---|
1167 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
1168 | { temp2 += *ip * x[k]; } |
---|
1169 | *(m.begin()+ i*(i-1)/2 + j-1) = -temp2; |
---|
1170 | } |
---|
1171 | temp2 = 0; |
---|
1172 | ip = m.begin() + (j+1)*j/2 + j-1; |
---|
1173 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
1174 | { temp2 += x[k] * *ip; } |
---|
1175 | *mjj -= temp2; |
---|
1176 | temp2 = 0; |
---|
1177 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
1178 | for (i=j+1; i <= nrow; ip += i++) |
---|
1179 | { temp2 += *ip * *(ip+1); } |
---|
1180 | *(mjj-1) -= temp2; |
---|
1181 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
1182 | for (i=0; i < nrow-j; ip += 1+j+i++) |
---|
1183 | { |
---|
1184 | x[i] = *ip; |
---|
1185 | } |
---|
1186 | for (i=j+1; i <= nrow ; i++) |
---|
1187 | { |
---|
1188 | temp2 = 0; |
---|
1189 | ip = m.begin() + i*(i-1)/2 + j; |
---|
1190 | for (k=0; k <= i-j-1; k++) |
---|
1191 | { temp2 += *ip++ * x[k]; } |
---|
1192 | for (ip += i-1; k < nrow-j; ip += 1+j+k++) |
---|
1193 | { temp2 += *ip * x[k]; } |
---|
1194 | *(m.begin()+ i*(i-1)/2 + j-2)= -temp2; |
---|
1195 | } |
---|
1196 | temp2 = 0; |
---|
1197 | ip = m.begin() + (j+1)*j/2 + j-2; |
---|
1198 | for (k=0; k < nrow-j; ip += 1+j+k++) |
---|
1199 | { temp2 += x[k] * *ip; } |
---|
1200 | *(mjj-j) -= temp2; |
---|
1201 | } |
---|
1202 | } |
---|
1203 | |
---|
1204 | // interchange rows and columns j and piv[j-1] |
---|
1205 | // or rows and columns j and -piv[j-2] |
---|
1206 | |
---|
1207 | pivrow = (piv[j-1]==0)? -piv[j-2] : piv[j-1]; |
---|
1208 | ip = m.begin() + pivrow*(pivrow-1)/2 + j; |
---|
1209 | for (i=j+1;i < pivrow; i++, ip++) |
---|
1210 | { |
---|
1211 | temp1 = *(m.begin() + i*(i-1)/2 + j-1); |
---|
1212 | *(m.begin() + i*(i-1)/2 + j-1) = *ip; |
---|
1213 | *ip = temp1; |
---|
1214 | } |
---|
1215 | temp1 = *mjj; |
---|
1216 | *mjj = *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1); |
---|
1217 | *(m.begin() + pivrow*(pivrow-1)/2 + pivrow-1) = temp1; |
---|
1218 | if (s==2) |
---|
1219 | { |
---|
1220 | temp1 = *(mjj-1); |
---|
1221 | *(mjj-1) = *( m.begin() + pivrow*(pivrow-1)/2 + j-2); |
---|
1222 | *( m.begin() + pivrow*(pivrow-1)/2 + j-2) = temp1; |
---|
1223 | } |
---|
1224 | |
---|
1225 | ip = m.begin() + (pivrow+1)*pivrow/2 + j-1; // &A(i,j) |
---|
1226 | iq = ip + pivrow-j; |
---|
1227 | for (i = pivrow+1; i <= nrow; ip += i, iq += i++) |
---|
1228 | { |
---|
1229 | temp1 = *iq; |
---|
1230 | *iq = *ip; |
---|
1231 | *ip = temp1; |
---|
1232 | } |
---|
1233 | } // end of loop over columns (in computing inverse from factorization) |
---|
1234 | |
---|
1235 | return; // inversion successful |
---|
1236 | } |
---|
1237 | |
---|
1238 | G4double G4ErrorSymMatrix::posDefFraction5x5 = 1.0; |
---|
1239 | G4double G4ErrorSymMatrix::posDefFraction6x6 = 1.0; |
---|
1240 | G4double G4ErrorSymMatrix::adjustment5x5 = 0.0; |
---|
1241 | G4double G4ErrorSymMatrix::adjustment6x6 = 0.0; |
---|
1242 | const G4double G4ErrorSymMatrix::CHOLESKY_THRESHOLD_5x5 = .5; |
---|
1243 | const G4double G4ErrorSymMatrix::CHOLESKY_THRESHOLD_6x6 = .2; |
---|
1244 | const G4double G4ErrorSymMatrix::CHOLESKY_CREEP_5x5 = .005; |
---|
1245 | const G4double G4ErrorSymMatrix::CHOLESKY_CREEP_6x6 = .002; |
---|
1246 | |
---|
1247 | // Aij are indices for a 6x6 symmetric matrix. |
---|
1248 | // The indices for 5x5 or 4x4 symmetric matrices are the same, |
---|
1249 | // ignoring all combinations with an index which is inapplicable. |
---|
1250 | |
---|
1251 | #define A00 0 |
---|
1252 | #define A01 1 |
---|
1253 | #define A02 3 |
---|
1254 | #define A03 6 |
---|
1255 | #define A04 10 |
---|
1256 | #define A05 15 |
---|
1257 | |
---|
1258 | #define A10 1 |
---|
1259 | #define A11 2 |
---|
1260 | #define A12 4 |
---|
1261 | #define A13 7 |
---|
1262 | #define A14 11 |
---|
1263 | #define A15 16 |
---|
1264 | |
---|
1265 | #define A20 3 |
---|
1266 | #define A21 4 |
---|
1267 | #define A22 5 |
---|
1268 | #define A23 8 |
---|
1269 | #define A24 12 |
---|
1270 | #define A25 17 |
---|
1271 | |
---|
1272 | #define A30 6 |
---|
1273 | #define A31 7 |
---|
1274 | #define A32 8 |
---|
1275 | #define A33 9 |
---|
1276 | #define A34 13 |
---|
1277 | #define A35 18 |
---|
1278 | |
---|
1279 | #define A40 10 |
---|
1280 | #define A41 11 |
---|
1281 | #define A42 12 |
---|
1282 | #define A43 13 |
---|
1283 | #define A44 14 |
---|
1284 | #define A45 19 |
---|
1285 | |
---|
1286 | #define A50 15 |
---|
1287 | #define A51 16 |
---|
1288 | #define A52 17 |
---|
1289 | #define A53 18 |
---|
1290 | #define A54 19 |
---|
1291 | #define A55 20 |
---|
1292 | |
---|
1293 | void G4ErrorSymMatrix::invert5(G4int & ifail) |
---|
1294 | { |
---|
1295 | if (posDefFraction5x5 >= CHOLESKY_THRESHOLD_5x5) |
---|
1296 | { |
---|
1297 | invertCholesky5(ifail); |
---|
1298 | posDefFraction5x5 = .9*posDefFraction5x5 + .1*(1-ifail); |
---|
1299 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
1300 | { |
---|
1301 | invertHaywood5(ifail); |
---|
1302 | } |
---|
1303 | } |
---|
1304 | else |
---|
1305 | { |
---|
1306 | if (posDefFraction5x5 + adjustment5x5 >= CHOLESKY_THRESHOLD_5x5) |
---|
1307 | { |
---|
1308 | invertCholesky5(ifail); |
---|
1309 | posDefFraction5x5 = .9*posDefFraction5x5 + .1*(1-ifail); |
---|
1310 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
1311 | { |
---|
1312 | invertHaywood5(ifail); |
---|
1313 | adjustment5x5 = 0; |
---|
1314 | } |
---|
1315 | } |
---|
1316 | else |
---|
1317 | { |
---|
1318 | invertHaywood5(ifail); |
---|
1319 | adjustment5x5 += CHOLESKY_CREEP_5x5; |
---|
1320 | } |
---|
1321 | } |
---|
1322 | return; |
---|
1323 | } |
---|
1324 | |
---|
1325 | void G4ErrorSymMatrix::invert6(G4int & ifail) |
---|
1326 | { |
---|
1327 | if (posDefFraction6x6 >= CHOLESKY_THRESHOLD_6x6) |
---|
1328 | { |
---|
1329 | invertCholesky6(ifail); |
---|
1330 | posDefFraction6x6 = .9*posDefFraction6x6 + .1*(1-ifail); |
---|
1331 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
1332 | { |
---|
1333 | invertHaywood6(ifail); |
---|
1334 | } |
---|
1335 | } |
---|
1336 | else |
---|
1337 | { |
---|
1338 | if (posDefFraction6x6 + adjustment6x6 >= CHOLESKY_THRESHOLD_6x6) |
---|
1339 | { |
---|
1340 | invertCholesky6(ifail); |
---|
1341 | posDefFraction6x6 = .9*posDefFraction6x6 + .1*(1-ifail); |
---|
1342 | if (ifail!=0) // Cholesky failed -- invert using Haywood |
---|
1343 | { |
---|
1344 | invertHaywood6(ifail); |
---|
1345 | adjustment6x6 = 0; |
---|
1346 | } |
---|
1347 | } |
---|
1348 | else |
---|
1349 | { |
---|
1350 | invertHaywood6(ifail); |
---|
1351 | adjustment6x6 += CHOLESKY_CREEP_6x6; |
---|
1352 | } |
---|
1353 | } |
---|
1354 | return; |
---|
1355 | } |
---|
1356 | |
---|
1357 | void G4ErrorSymMatrix::invertHaywood5 (G4int & ifail) |
---|
1358 | { |
---|
1359 | ifail = 0; |
---|
1360 | |
---|
1361 | // Find all NECESSARY 2x2 dets: (25 of them) |
---|
1362 | |
---|
1363 | G4double Det2_23_01 = m[A20]*m[A31] - m[A21]*m[A30]; |
---|
1364 | G4double Det2_23_02 = m[A20]*m[A32] - m[A22]*m[A30]; |
---|
1365 | G4double Det2_23_03 = m[A20]*m[A33] - m[A23]*m[A30]; |
---|
1366 | G4double Det2_23_12 = m[A21]*m[A32] - m[A22]*m[A31]; |
---|
1367 | G4double Det2_23_13 = m[A21]*m[A33] - m[A23]*m[A31]; |
---|
1368 | G4double Det2_23_23 = m[A22]*m[A33] - m[A23]*m[A32]; |
---|
1369 | G4double Det2_24_01 = m[A20]*m[A41] - m[A21]*m[A40]; |
---|
1370 | G4double Det2_24_02 = m[A20]*m[A42] - m[A22]*m[A40]; |
---|
1371 | G4double Det2_24_03 = m[A20]*m[A43] - m[A23]*m[A40]; |
---|
1372 | G4double Det2_24_04 = m[A20]*m[A44] - m[A24]*m[A40]; |
---|
1373 | G4double Det2_24_12 = m[A21]*m[A42] - m[A22]*m[A41]; |
---|
1374 | G4double Det2_24_13 = m[A21]*m[A43] - m[A23]*m[A41]; |
---|
1375 | G4double Det2_24_14 = m[A21]*m[A44] - m[A24]*m[A41]; |
---|
1376 | G4double Det2_24_23 = m[A22]*m[A43] - m[A23]*m[A42]; |
---|
1377 | G4double Det2_24_24 = m[A22]*m[A44] - m[A24]*m[A42]; |
---|
1378 | G4double Det2_34_01 = m[A30]*m[A41] - m[A31]*m[A40]; |
---|
1379 | G4double Det2_34_02 = m[A30]*m[A42] - m[A32]*m[A40]; |
---|
1380 | G4double Det2_34_03 = m[A30]*m[A43] - m[A33]*m[A40]; |
---|
1381 | G4double Det2_34_04 = m[A30]*m[A44] - m[A34]*m[A40]; |
---|
1382 | G4double Det2_34_12 = m[A31]*m[A42] - m[A32]*m[A41]; |
---|
1383 | G4double Det2_34_13 = m[A31]*m[A43] - m[A33]*m[A41]; |
---|
1384 | G4double Det2_34_14 = m[A31]*m[A44] - m[A34]*m[A41]; |
---|
1385 | G4double Det2_34_23 = m[A32]*m[A43] - m[A33]*m[A42]; |
---|
1386 | G4double Det2_34_24 = m[A32]*m[A44] - m[A34]*m[A42]; |
---|
1387 | G4double Det2_34_34 = m[A33]*m[A44] - m[A34]*m[A43]; |
---|
1388 | |
---|
1389 | // Find all NECESSARY 3x3 dets: (30 of them) |
---|
1390 | |
---|
1391 | G4double Det3_123_012 = m[A10]*Det2_23_12 - m[A11]*Det2_23_02 |
---|
1392 | + m[A12]*Det2_23_01; |
---|
1393 | G4double Det3_123_013 = m[A10]*Det2_23_13 - m[A11]*Det2_23_03 |
---|
1394 | + m[A13]*Det2_23_01; |
---|
1395 | G4double Det3_123_023 = m[A10]*Det2_23_23 - m[A12]*Det2_23_03 |
---|
1396 | + m[A13]*Det2_23_02; |
---|
1397 | G4double Det3_123_123 = m[A11]*Det2_23_23 - m[A12]*Det2_23_13 |
---|
1398 | + m[A13]*Det2_23_12; |
---|
1399 | G4double Det3_124_012 = m[A10]*Det2_24_12 - m[A11]*Det2_24_02 |
---|
1400 | + m[A12]*Det2_24_01; |
---|
1401 | G4double Det3_124_013 = m[A10]*Det2_24_13 - m[A11]*Det2_24_03 |
---|
1402 | + m[A13]*Det2_24_01; |
---|
1403 | G4double Det3_124_014 = m[A10]*Det2_24_14 - m[A11]*Det2_24_04 |
---|
1404 | + m[A14]*Det2_24_01; |
---|
1405 | G4double Det3_124_023 = m[A10]*Det2_24_23 - m[A12]*Det2_24_03 |
---|
1406 | + m[A13]*Det2_24_02; |
---|
1407 | G4double Det3_124_024 = m[A10]*Det2_24_24 - m[A12]*Det2_24_04 |
---|
1408 | + m[A14]*Det2_24_02; |
---|
1409 | G4double Det3_124_123 = m[A11]*Det2_24_23 - m[A12]*Det2_24_13 |
---|
1410 | + m[A13]*Det2_24_12; |
---|
1411 | G4double Det3_124_124 = m[A11]*Det2_24_24 - m[A12]*Det2_24_14 |
---|
1412 | + m[A14]*Det2_24_12; |
---|
1413 | G4double Det3_134_012 = m[A10]*Det2_34_12 - m[A11]*Det2_34_02 |
---|
1414 | + m[A12]*Det2_34_01; |
---|
1415 | G4double Det3_134_013 = m[A10]*Det2_34_13 - m[A11]*Det2_34_03 |
---|
1416 | + m[A13]*Det2_34_01; |
---|
1417 | G4double Det3_134_014 = m[A10]*Det2_34_14 - m[A11]*Det2_34_04 |
---|
1418 | + m[A14]*Det2_34_01; |
---|
1419 | G4double Det3_134_023 = m[A10]*Det2_34_23 - m[A12]*Det2_34_03 |
---|
1420 | + m[A13]*Det2_34_02; |
---|
1421 | G4double Det3_134_024 = m[A10]*Det2_34_24 - m[A12]*Det2_34_04 |
---|
1422 | + m[A14]*Det2_34_02; |
---|
1423 | G4double Det3_134_034 = m[A10]*Det2_34_34 - m[A13]*Det2_34_04 |
---|
1424 | + m[A14]*Det2_34_03; |
---|
1425 | G4double Det3_134_123 = m[A11]*Det2_34_23 - m[A12]*Det2_34_13 |
---|
1426 | + m[A13]*Det2_34_12; |
---|
1427 | G4double Det3_134_124 = m[A11]*Det2_34_24 - m[A12]*Det2_34_14 |
---|
1428 | + m[A14]*Det2_34_12; |
---|
1429 | G4double Det3_134_134 = m[A11]*Det2_34_34 - m[A13]*Det2_34_14 |
---|
1430 | + m[A14]*Det2_34_13; |
---|
1431 | G4double Det3_234_012 = m[A20]*Det2_34_12 - m[A21]*Det2_34_02 |
---|
1432 | + m[A22]*Det2_34_01; |
---|
1433 | G4double Det3_234_013 = m[A20]*Det2_34_13 - m[A21]*Det2_34_03 |
---|
1434 | + m[A23]*Det2_34_01; |
---|
1435 | G4double Det3_234_014 = m[A20]*Det2_34_14 - m[A21]*Det2_34_04 |
---|
1436 | + m[A24]*Det2_34_01; |
---|
1437 | G4double Det3_234_023 = m[A20]*Det2_34_23 - m[A22]*Det2_34_03 |
---|
1438 | + m[A23]*Det2_34_02; |
---|
1439 | G4double Det3_234_024 = m[A20]*Det2_34_24 - m[A22]*Det2_34_04 |
---|
1440 | + m[A24]*Det2_34_02; |
---|
1441 | G4double Det3_234_034 = m[A20]*Det2_34_34 - m[A23]*Det2_34_04 |
---|
1442 | + m[A24]*Det2_34_03; |
---|
1443 | G4double Det3_234_123 = m[A21]*Det2_34_23 - m[A22]*Det2_34_13 |
---|
1444 | + m[A23]*Det2_34_12; |
---|
1445 | G4double Det3_234_124 = m[A21]*Det2_34_24 - m[A22]*Det2_34_14 |
---|
1446 | + m[A24]*Det2_34_12; |
---|
1447 | G4double Det3_234_134 = m[A21]*Det2_34_34 - m[A23]*Det2_34_14 |
---|
1448 | + m[A24]*Det2_34_13; |
---|
1449 | G4double Det3_234_234 = m[A22]*Det2_34_34 - m[A23]*Det2_34_24 |
---|
1450 | + m[A24]*Det2_34_23; |
---|
1451 | |
---|
1452 | // Find all NECESSARY 4x4 dets: (15 of them) |
---|
1453 | |
---|
1454 | G4double Det4_0123_0123 = m[A00]*Det3_123_123 - m[A01]*Det3_123_023 |
---|
1455 | + m[A02]*Det3_123_013 - m[A03]*Det3_123_012; |
---|
1456 | G4double Det4_0124_0123 = m[A00]*Det3_124_123 - m[A01]*Det3_124_023 |
---|
1457 | + m[A02]*Det3_124_013 - m[A03]*Det3_124_012; |
---|
1458 | G4double Det4_0124_0124 = m[A00]*Det3_124_124 - m[A01]*Det3_124_024 |
---|
1459 | + m[A02]*Det3_124_014 - m[A04]*Det3_124_012; |
---|
1460 | G4double Det4_0134_0123 = m[A00]*Det3_134_123 - m[A01]*Det3_134_023 |
---|
1461 | + m[A02]*Det3_134_013 - m[A03]*Det3_134_012; |
---|
1462 | G4double Det4_0134_0124 = m[A00]*Det3_134_124 - m[A01]*Det3_134_024 |
---|
1463 | + m[A02]*Det3_134_014 - m[A04]*Det3_134_012; |
---|
1464 | G4double Det4_0134_0134 = m[A00]*Det3_134_134 - m[A01]*Det3_134_034 |
---|
1465 | + m[A03]*Det3_134_014 - m[A04]*Det3_134_013; |
---|
1466 | G4double Det4_0234_0123 = m[A00]*Det3_234_123 - m[A01]*Det3_234_023 |
---|
1467 | + m[A02]*Det3_234_013 - m[A03]*Det3_234_012; |
---|
1468 | G4double Det4_0234_0124 = m[A00]*Det3_234_124 - m[A01]*Det3_234_024 |
---|
1469 | + m[A02]*Det3_234_014 - m[A04]*Det3_234_012; |
---|
1470 | G4double Det4_0234_0134 = m[A00]*Det3_234_134 - m[A01]*Det3_234_034 |
---|
1471 | + m[A03]*Det3_234_014 - m[A04]*Det3_234_013; |
---|
1472 | G4double Det4_0234_0234 = m[A00]*Det3_234_234 - m[A02]*Det3_234_034 |
---|
1473 | + m[A03]*Det3_234_024 - m[A04]*Det3_234_023; |
---|
1474 | G4double Det4_1234_0123 = m[A10]*Det3_234_123 - m[A11]*Det3_234_023 |
---|
1475 | + m[A12]*Det3_234_013 - m[A13]*Det3_234_012; |
---|
1476 | G4double Det4_1234_0124 = m[A10]*Det3_234_124 - m[A11]*Det3_234_024 |
---|
1477 | + m[A12]*Det3_234_014 - m[A14]*Det3_234_012; |
---|
1478 | G4double Det4_1234_0134 = m[A10]*Det3_234_134 - m[A11]*Det3_234_034 |
---|
1479 | + m[A13]*Det3_234_014 - m[A14]*Det3_234_013; |
---|
1480 | G4double Det4_1234_0234 = m[A10]*Det3_234_234 - m[A12]*Det3_234_034 |
---|
1481 | + m[A13]*Det3_234_024 - m[A14]*Det3_234_023; |
---|
1482 | G4double Det4_1234_1234 = m[A11]*Det3_234_234 - m[A12]*Det3_234_134 |
---|
1483 | + m[A13]*Det3_234_124 - m[A14]*Det3_234_123; |
---|
1484 | |
---|
1485 | // Find the 5x5 det: |
---|
1486 | |
---|
1487 | G4double det = m[A00]*Det4_1234_1234 |
---|
1488 | - m[A01]*Det4_1234_0234 |
---|
1489 | + m[A02]*Det4_1234_0134 |
---|
1490 | - m[A03]*Det4_1234_0124 |
---|
1491 | + m[A04]*Det4_1234_0123; |
---|
1492 | |
---|
1493 | if ( det == 0 ) |
---|
1494 | { |
---|
1495 | ifail = 1; |
---|
1496 | return; |
---|
1497 | } |
---|
1498 | |
---|
1499 | G4double oneOverDet = 1.0/det; |
---|
1500 | G4double mn1OverDet = - oneOverDet; |
---|
1501 | |
---|
1502 | m[A00] = Det4_1234_1234 * oneOverDet; |
---|
1503 | m[A01] = Det4_1234_0234 * mn1OverDet; |
---|
1504 | m[A02] = Det4_1234_0134 * oneOverDet; |
---|
1505 | m[A03] = Det4_1234_0124 * mn1OverDet; |
---|
1506 | m[A04] = Det4_1234_0123 * oneOverDet; |
---|
1507 | |
---|
1508 | m[A11] = Det4_0234_0234 * oneOverDet; |
---|
1509 | m[A12] = Det4_0234_0134 * mn1OverDet; |
---|
1510 | m[A13] = Det4_0234_0124 * oneOverDet; |
---|
1511 | m[A14] = Det4_0234_0123 * mn1OverDet; |
---|
1512 | |
---|
1513 | m[A22] = Det4_0134_0134 * oneOverDet; |
---|
1514 | m[A23] = Det4_0134_0124 * mn1OverDet; |
---|
1515 | m[A24] = Det4_0134_0123 * oneOverDet; |
---|
1516 | |
---|
1517 | m[A33] = Det4_0124_0124 * oneOverDet; |
---|
1518 | m[A34] = Det4_0124_0123 * mn1OverDet; |
---|
1519 | |
---|
1520 | m[A44] = Det4_0123_0123 * oneOverDet; |
---|
1521 | |
---|
1522 | return; |
---|
1523 | } |
---|
1524 | |
---|
1525 | void G4ErrorSymMatrix::invertHaywood6 (G4int & ifail) |
---|
1526 | { |
---|
1527 | ifail = 0; |
---|
1528 | |
---|
1529 | // Find all NECESSARY 2x2 dets: (39 of them) |
---|
1530 | |
---|
1531 | G4double Det2_34_01 = m[A30]*m[A41] - m[A31]*m[A40]; |
---|
1532 | G4double Det2_34_02 = m[A30]*m[A42] - m[A32]*m[A40]; |
---|
1533 | G4double Det2_34_03 = m[A30]*m[A43] - m[A33]*m[A40]; |
---|
1534 | G4double Det2_34_04 = m[A30]*m[A44] - m[A34]*m[A40]; |
---|
1535 | G4double Det2_34_12 = m[A31]*m[A42] - m[A32]*m[A41]; |
---|
1536 | G4double Det2_34_13 = m[A31]*m[A43] - m[A33]*m[A41]; |
---|
1537 | G4double Det2_34_14 = m[A31]*m[A44] - m[A34]*m[A41]; |
---|
1538 | G4double Det2_34_23 = m[A32]*m[A43] - m[A33]*m[A42]; |
---|
1539 | G4double Det2_34_24 = m[A32]*m[A44] - m[A34]*m[A42]; |
---|
1540 | G4double Det2_34_34 = m[A33]*m[A44] - m[A34]*m[A43]; |
---|
1541 | G4double Det2_35_01 = m[A30]*m[A51] - m[A31]*m[A50]; |
---|
1542 | G4double Det2_35_02 = m[A30]*m[A52] - m[A32]*m[A50]; |
---|
1543 | G4double Det2_35_03 = m[A30]*m[A53] - m[A33]*m[A50]; |
---|
1544 | G4double Det2_35_04 = m[A30]*m[A54] - m[A34]*m[A50]; |
---|
1545 | G4double Det2_35_05 = m[A30]*m[A55] - m[A35]*m[A50]; |
---|
1546 | G4double Det2_35_12 = m[A31]*m[A52] - m[A32]*m[A51]; |
---|
1547 | G4double Det2_35_13 = m[A31]*m[A53] - m[A33]*m[A51]; |
---|
1548 | G4double Det2_35_14 = m[A31]*m[A54] - m[A34]*m[A51]; |
---|
1549 | G4double Det2_35_15 = m[A31]*m[A55] - m[A35]*m[A51]; |
---|
1550 | G4double Det2_35_23 = m[A32]*m[A53] - m[A33]*m[A52]; |
---|
1551 | G4double Det2_35_24 = m[A32]*m[A54] - m[A34]*m[A52]; |
---|
1552 | G4double Det2_35_25 = m[A32]*m[A55] - m[A35]*m[A52]; |
---|
1553 | G4double Det2_35_34 = m[A33]*m[A54] - m[A34]*m[A53]; |
---|
1554 | G4double Det2_35_35 = m[A33]*m[A55] - m[A35]*m[A53]; |
---|
1555 | G4double Det2_45_01 = m[A40]*m[A51] - m[A41]*m[A50]; |
---|
1556 | G4double Det2_45_02 = m[A40]*m[A52] - m[A42]*m[A50]; |
---|
1557 | G4double Det2_45_03 = m[A40]*m[A53] - m[A43]*m[A50]; |
---|
1558 | G4double Det2_45_04 = m[A40]*m[A54] - m[A44]*m[A50]; |
---|
1559 | G4double Det2_45_05 = m[A40]*m[A55] - m[A45]*m[A50]; |
---|
1560 | G4double Det2_45_12 = m[A41]*m[A52] - m[A42]*m[A51]; |
---|
1561 | G4double Det2_45_13 = m[A41]*m[A53] - m[A43]*m[A51]; |
---|
1562 | G4double Det2_45_14 = m[A41]*m[A54] - m[A44]*m[A51]; |
---|
1563 | G4double Det2_45_15 = m[A41]*m[A55] - m[A45]*m[A51]; |
---|
1564 | G4double Det2_45_23 = m[A42]*m[A53] - m[A43]*m[A52]; |
---|
1565 | G4double Det2_45_24 = m[A42]*m[A54] - m[A44]*m[A52]; |
---|
1566 | G4double Det2_45_25 = m[A42]*m[A55] - m[A45]*m[A52]; |
---|
1567 | G4double Det2_45_34 = m[A43]*m[A54] - m[A44]*m[A53]; |
---|
1568 | G4double Det2_45_35 = m[A43]*m[A55] - m[A45]*m[A53]; |
---|
1569 | G4double Det2_45_45 = m[A44]*m[A55] - m[A45]*m[A54]; |
---|
1570 | |
---|
1571 | // Find all NECESSARY 3x3 dets: (65 of them) |
---|
1572 | |
---|
1573 | G4double Det3_234_012 = m[A20]*Det2_34_12 - m[A21]*Det2_34_02 |
---|
1574 | + m[A22]*Det2_34_01; |
---|
1575 | G4double Det3_234_013 = m[A20]*Det2_34_13 - m[A21]*Det2_34_03 |
---|
1576 | + m[A23]*Det2_34_01; |
---|
1577 | G4double Det3_234_014 = m[A20]*Det2_34_14 - m[A21]*Det2_34_04 |
---|
1578 | + m[A24]*Det2_34_01; |
---|
1579 | G4double Det3_234_023 = m[A20]*Det2_34_23 - m[A22]*Det2_34_03 |
---|
1580 | + m[A23]*Det2_34_02; |
---|
1581 | G4double Det3_234_024 = m[A20]*Det2_34_24 - m[A22]*Det2_34_04 |
---|
1582 | + m[A24]*Det2_34_02; |
---|
1583 | G4double Det3_234_034 = m[A20]*Det2_34_34 - m[A23]*Det2_34_04 |
---|
1584 | + m[A24]*Det2_34_03; |
---|
1585 | G4double Det3_234_123 = m[A21]*Det2_34_23 - m[A22]*Det2_34_13 |
---|
1586 | + m[A23]*Det2_34_12; |
---|
1587 | G4double Det3_234_124 = m[A21]*Det2_34_24 - m[A22]*Det2_34_14 |
---|
1588 | + m[A24]*Det2_34_12; |
---|
1589 | G4double Det3_234_134 = m[A21]*Det2_34_34 - m[A23]*Det2_34_14 |
---|
1590 | + m[A24]*Det2_34_13; |
---|
1591 | G4double Det3_234_234 = m[A22]*Det2_34_34 - m[A23]*Det2_34_24 |
---|
1592 | + m[A24]*Det2_34_23; |
---|
1593 | G4double Det3_235_012 = m[A20]*Det2_35_12 - m[A21]*Det2_35_02 |
---|
1594 | + m[A22]*Det2_35_01; |
---|
1595 | G4double Det3_235_013 = m[A20]*Det2_35_13 - m[A21]*Det2_35_03 |
---|
1596 | + m[A23]*Det2_35_01; |
---|
1597 | G4double Det3_235_014 = m[A20]*Det2_35_14 - m[A21]*Det2_35_04 |
---|
1598 | + m[A24]*Det2_35_01; |
---|
1599 | G4double Det3_235_015 = m[A20]*Det2_35_15 - m[A21]*Det2_35_05 |
---|
1600 | + m[A25]*Det2_35_01; |
---|
1601 | G4double Det3_235_023 = m[A20]*Det2_35_23 - m[A22]*Det2_35_03 |
---|
1602 | + m[A23]*Det2_35_02; |
---|
1603 | G4double Det3_235_024 = m[A20]*Det2_35_24 - m[A22]*Det2_35_04 |
---|
1604 | + m[A24]*Det2_35_02; |
---|
1605 | G4double Det3_235_025 = m[A20]*Det2_35_25 - m[A22]*Det2_35_05 |
---|
1606 | + m[A25]*Det2_35_02; |
---|
1607 | G4double Det3_235_034 = m[A20]*Det2_35_34 - m[A23]*Det2_35_04 |
---|
1608 | + m[A24]*Det2_35_03; |
---|
1609 | G4double Det3_235_035 = m[A20]*Det2_35_35 - m[A23]*Det2_35_05 |
---|
1610 | + m[A25]*Det2_35_03; |
---|
1611 | G4double Det3_235_123 = m[A21]*Det2_35_23 - m[A22]*Det2_35_13 |
---|
1612 | + m[A23]*Det2_35_12; |
---|
1613 | G4double Det3_235_124 = m[A21]*Det2_35_24 - m[A22]*Det2_35_14 |
---|
1614 | + m[A24]*Det2_35_12; |
---|
1615 | G4double Det3_235_125 = m[A21]*Det2_35_25 - m[A22]*Det2_35_15 |
---|
1616 | + m[A25]*Det2_35_12; |
---|
1617 | G4double Det3_235_134 = m[A21]*Det2_35_34 - m[A23]*Det2_35_14 |
---|
1618 | + m[A24]*Det2_35_13; |
---|
1619 | G4double Det3_235_135 = m[A21]*Det2_35_35 - m[A23]*Det2_35_15 |
---|
1620 | + m[A25]*Det2_35_13; |
---|
1621 | G4double Det3_235_234 = m[A22]*Det2_35_34 - m[A23]*Det2_35_24 |
---|
1622 | + m[A24]*Det2_35_23; |
---|
1623 | G4double Det3_235_235 = m[A22]*Det2_35_35 - m[A23]*Det2_35_25 |
---|
1624 | + m[A25]*Det2_35_23; |
---|
1625 | G4double Det3_245_012 = m[A20]*Det2_45_12 - m[A21]*Det2_45_02 |
---|
1626 | + m[A22]*Det2_45_01; |
---|
1627 | G4double Det3_245_013 = m[A20]*Det2_45_13 - m[A21]*Det2_45_03 |
---|
1628 | + m[A23]*Det2_45_01; |
---|
1629 | G4double Det3_245_014 = m[A20]*Det2_45_14 - m[A21]*Det2_45_04 |
---|
1630 | + m[A24]*Det2_45_01; |
---|
1631 | G4double Det3_245_015 = m[A20]*Det2_45_15 - m[A21]*Det2_45_05 |
---|
1632 | + m[A25]*Det2_45_01; |
---|
1633 | G4double Det3_245_023 = m[A20]*Det2_45_23 - m[A22]*Det2_45_03 |
---|
1634 | + m[A23]*Det2_45_02; |
---|
1635 | G4double Det3_245_024 = m[A20]*Det2_45_24 - m[A22]*Det2_45_04 |
---|
1636 | + m[A24]*Det2_45_02; |
---|
1637 | G4double Det3_245_025 = m[A20]*Det2_45_25 - m[A22]*Det2_45_05 |
---|
1638 | + m[A25]*Det2_45_02; |
---|
1639 | G4double Det3_245_034 = m[A20]*Det2_45_34 - m[A23]*Det2_45_04 |
---|
1640 | + m[A24]*Det2_45_03; |
---|
1641 | G4double Det3_245_035 = m[A20]*Det2_45_35 - m[A23]*Det2_45_05 |
---|
1642 | + m[A25]*Det2_45_03; |
---|
1643 | G4double Det3_245_045 = m[A20]*Det2_45_45 - m[A24]*Det2_45_05 |
---|
1644 | + m[A25]*Det2_45_04; |
---|
1645 | G4double Det3_245_123 = m[A21]*Det2_45_23 - m[A22]*Det2_45_13 |
---|
1646 | + m[A23]*Det2_45_12; |
---|
1647 | G4double Det3_245_124 = m[A21]*Det2_45_24 - m[A22]*Det2_45_14 |
---|
1648 | + m[A24]*Det2_45_12; |
---|
1649 | G4double Det3_245_125 = m[A21]*Det2_45_25 - m[A22]*Det2_45_15 |
---|
1650 | + m[A25]*Det2_45_12; |
---|
1651 | G4double Det3_245_134 = m[A21]*Det2_45_34 - m[A23]*Det2_45_14 |
---|
1652 | + m[A24]*Det2_45_13; |
---|
1653 | G4double Det3_245_135 = m[A21]*Det2_45_35 - m[A23]*Det2_45_15 |
---|
1654 | + m[A25]*Det2_45_13; |
---|
1655 | G4double Det3_245_145 = m[A21]*Det2_45_45 - m[A24]*Det2_45_15 |
---|
1656 | + m[A25]*Det2_45_14; |
---|
1657 | G4double Det3_245_234 = m[A22]*Det2_45_34 - m[A23]*Det2_45_24 |
---|
1658 | + m[A24]*Det2_45_23; |
---|
1659 | G4double Det3_245_235 = m[A22]*Det2_45_35 - m[A23]*Det2_45_25 |
---|
1660 | + m[A25]*Det2_45_23; |
---|
1661 | G4double Det3_245_245 = m[A22]*Det2_45_45 - m[A24]*Det2_45_25 |
---|
1662 | + m[A25]*Det2_45_24; |
---|
1663 | G4double Det3_345_012 = m[A30]*Det2_45_12 - m[A31]*Det2_45_02 |
---|
1664 | + m[A32]*Det2_45_01; |
---|
1665 | G4double Det3_345_013 = m[A30]*Det2_45_13 - m[A31]*Det2_45_03 |
---|
1666 | + m[A33]*Det2_45_01; |
---|
1667 | G4double Det3_345_014 = m[A30]*Det2_45_14 - m[A31]*Det2_45_04 |
---|
1668 | + m[A34]*Det2_45_01; |
---|
1669 | G4double Det3_345_015 = m[A30]*Det2_45_15 - m[A31]*Det2_45_05 |
---|
1670 | + m[A35]*Det2_45_01; |
---|
1671 | G4double Det3_345_023 = m[A30]*Det2_45_23 - m[A32]*Det2_45_03 |
---|
1672 | + m[A33]*Det2_45_02; |
---|
1673 | G4double Det3_345_024 = m[A30]*Det2_45_24 - m[A32]*Det2_45_04 |
---|
1674 | + m[A34]*Det2_45_02; |
---|
1675 | G4double Det3_345_025 = m[A30]*Det2_45_25 - m[A32]*Det2_45_05 |
---|
1676 | + m[A35]*Det2_45_02; |
---|
1677 | G4double Det3_345_034 = m[A30]*Det2_45_34 - m[A33]*Det2_45_04 |
---|
1678 | + m[A34]*Det2_45_03; |
---|
1679 | G4double Det3_345_035 = m[A30]*Det2_45_35 - m[A33]*Det2_45_05 |
---|
1680 | + m[A35]*Det2_45_03; |
---|
1681 | G4double Det3_345_045 = m[A30]*Det2_45_45 - m[A34]*Det2_45_05 |
---|
1682 | + m[A35]*Det2_45_04; |
---|
1683 | G4double Det3_345_123 = m[A31]*Det2_45_23 - m[A32]*Det2_45_13 |
---|
1684 | + m[A33]*Det2_45_12; |
---|
1685 | G4double Det3_345_124 = m[A31]*Det2_45_24 - m[A32]*Det2_45_14 |
---|
1686 | + m[A34]*Det2_45_12; |
---|
1687 | G4double Det3_345_125 = m[A31]*Det2_45_25 - m[A32]*Det2_45_15 |
---|
1688 | + m[A35]*Det2_45_12; |
---|
1689 | G4double Det3_345_134 = m[A31]*Det2_45_34 - m[A33]*Det2_45_14 |
---|
1690 | + m[A34]*Det2_45_13; |
---|
1691 | G4double Det3_345_135 = m[A31]*Det2_45_35 - m[A33]*Det2_45_15 |
---|
1692 | + m[A35]*Det2_45_13; |
---|
1693 | G4double Det3_345_145 = m[A31]*Det2_45_45 - m[A34]*Det2_45_15 |
---|
1694 | + m[A35]*Det2_45_14; |
---|
1695 | G4double Det3_345_234 = m[A32]*Det2_45_34 - m[A33]*Det2_45_24 |
---|
1696 | + m[A34]*Det2_45_23; |
---|
1697 | G4double Det3_345_235 = m[A32]*Det2_45_35 - m[A33]*Det2_45_25 |
---|
1698 | + m[A35]*Det2_45_23; |
---|
1699 | G4double Det3_345_245 = m[A32]*Det2_45_45 - m[A34]*Det2_45_25 |
---|
1700 | + m[A35]*Det2_45_24; |
---|
1701 | G4double Det3_345_345 = m[A33]*Det2_45_45 - m[A34]*Det2_45_35 |
---|
1702 | + m[A35]*Det2_45_34; |
---|
1703 | |
---|
1704 | // Find all NECESSARY 4x4 dets: (55 of them) |
---|
1705 | |
---|
1706 | G4double Det4_1234_0123 = m[A10]*Det3_234_123 - m[A11]*Det3_234_023 |
---|
1707 | + m[A12]*Det3_234_013 - m[A13]*Det3_234_012; |
---|
1708 | G4double Det4_1234_0124 = m[A10]*Det3_234_124 - m[A11]*Det3_234_024 |
---|
1709 | + m[A12]*Det3_234_014 - m[A14]*Det3_234_012; |
---|
1710 | G4double Det4_1234_0134 = m[A10]*Det3_234_134 - m[A11]*Det3_234_034 |
---|
1711 | + m[A13]*Det3_234_014 - m[A14]*Det3_234_013; |
---|
1712 | G4double Det4_1234_0234 = m[A10]*Det3_234_234 - m[A12]*Det3_234_034 |
---|
1713 | + m[A13]*Det3_234_024 - m[A14]*Det3_234_023; |
---|
1714 | G4double Det4_1234_1234 = m[A11]*Det3_234_234 - m[A12]*Det3_234_134 |
---|
1715 | + m[A13]*Det3_234_124 - m[A14]*Det3_234_123; |
---|
1716 | G4double Det4_1235_0123 = m[A10]*Det3_235_123 - m[A11]*Det3_235_023 |
---|
1717 | + m[A12]*Det3_235_013 - m[A13]*Det3_235_012; |
---|
1718 | G4double Det4_1235_0124 = m[A10]*Det3_235_124 - m[A11]*Det3_235_024 |
---|
1719 | + m[A12]*Det3_235_014 - m[A14]*Det3_235_012; |
---|
1720 | G4double Det4_1235_0125 = m[A10]*Det3_235_125 - m[A11]*Det3_235_025 |
---|
1721 | + m[A12]*Det3_235_015 - m[A15]*Det3_235_012; |
---|
1722 | G4double Det4_1235_0134 = m[A10]*Det3_235_134 - m[A11]*Det3_235_034 |
---|
1723 | + m[A13]*Det3_235_014 - m[A14]*Det3_235_013; |
---|
1724 | G4double Det4_1235_0135 = m[A10]*Det3_235_135 - m[A11]*Det3_235_035 |
---|
1725 | + m[A13]*Det3_235_015 - m[A15]*Det3_235_013; |
---|
1726 | G4double Det4_1235_0234 = m[A10]*Det3_235_234 - m[A12]*Det3_235_034 |
---|
1727 | + m[A13]*Det3_235_024 - m[A14]*Det3_235_023; |
---|
1728 | G4double Det4_1235_0235 = m[A10]*Det3_235_235 - m[A12]*Det3_235_035 |
---|
1729 | + m[A13]*Det3_235_025 - m[A15]*Det3_235_023; |
---|
1730 | G4double Det4_1235_1234 = m[A11]*Det3_235_234 - m[A12]*Det3_235_134 |
---|
1731 | + m[A13]*Det3_235_124 - m[A14]*Det3_235_123; |
---|
1732 | G4double Det4_1235_1235 = m[A11]*Det3_235_235 - m[A12]*Det3_235_135 |
---|
1733 | + m[A13]*Det3_235_125 - m[A15]*Det3_235_123; |
---|
1734 | G4double Det4_1245_0123 = m[A10]*Det3_245_123 - m[A11]*Det3_245_023 |
---|
1735 | + m[A12]*Det3_245_013 - m[A13]*Det3_245_012; |
---|
1736 | G4double Det4_1245_0124 = m[A10]*Det3_245_124 - m[A11]*Det3_245_024 |
---|
1737 | + m[A12]*Det3_245_014 - m[A14]*Det3_245_012; |
---|
1738 | G4double Det4_1245_0125 = m[A10]*Det3_245_125 - m[A11]*Det3_245_025 |
---|
1739 | + m[A12]*Det3_245_015 - m[A15]*Det3_245_012; |
---|
1740 | G4double Det4_1245_0134 = m[A10]*Det3_245_134 - m[A11]*Det3_245_034 |
---|
1741 | + m[A13]*Det3_245_014 - m[A14]*Det3_245_013; |
---|
1742 | G4double Det4_1245_0135 = m[A10]*Det3_245_135 - m[A11]*Det3_245_035 |
---|
1743 | + m[A13]*Det3_245_015 - m[A15]*Det3_245_013; |
---|
1744 | G4double Det4_1245_0145 = m[A10]*Det3_245_145 - m[A11]*Det3_245_045 |
---|
1745 | + m[A14]*Det3_245_015 - m[A15]*Det3_245_014; |
---|
1746 | G4double Det4_1245_0234 = m[A10]*Det3_245_234 - m[A12]*Det3_245_034 |
---|
1747 | + m[A13]*Det3_245_024 - m[A14]*Det3_245_023; |
---|
1748 | G4double Det4_1245_0235 = m[A10]*Det3_245_235 - m[A12]*Det3_245_035 |
---|
1749 | + m[A13]*Det3_245_025 - m[A15]*Det3_245_023; |
---|
1750 | G4double Det4_1245_0245 = m[A10]*Det3_245_245 - m[A12]*Det3_245_045 |
---|
1751 | + m[A14]*Det3_245_025 - m[A15]*Det3_245_024; |
---|
1752 | G4double Det4_1245_1234 = m[A11]*Det3_245_234 - m[A12]*Det3_245_134 |
---|
1753 | + m[A13]*Det3_245_124 - m[A14]*Det3_245_123; |
---|
1754 | G4double Det4_1245_1235 = m[A11]*Det3_245_235 - m[A12]*Det3_245_135 |
---|
1755 | + m[A13]*Det3_245_125 - m[A15]*Det3_245_123; |
---|
1756 | G4double Det4_1245_1245 = m[A11]*Det3_245_245 - m[A12]*Det3_245_145 |
---|
1757 | + m[A14]*Det3_245_125 - m[A15]*Det3_245_124; |
---|
1758 | G4double Det4_1345_0123 = m[A10]*Det3_345_123 - m[A11]*Det3_345_023 |
---|
1759 | + m[A12]*Det3_345_013 - m[A13]*Det3_345_012; |
---|
1760 | G4double Det4_1345_0124 = m[A10]*Det3_345_124 - m[A11]*Det3_345_024 |
---|
1761 | + m[A12]*Det3_345_014 - m[A14]*Det3_345_012; |
---|
1762 | G4double Det4_1345_0125 = m[A10]*Det3_345_125 - m[A11]*Det3_345_025 |
---|
1763 | + m[A12]*Det3_345_015 - m[A15]*Det3_345_012; |
---|
1764 | G4double Det4_1345_0134 = m[A10]*Det3_345_134 - m[A11]*Det3_345_034 |
---|
1765 | + m[A13]*Det3_345_014 - m[A14]*Det3_345_013; |
---|
1766 | G4double Det4_1345_0135 = m[A10]*Det3_345_135 - m[A11]*Det3_345_035 |
---|
1767 | + m[A13]*Det3_345_015 - m[A15]*Det3_345_013; |
---|
1768 | G4double Det4_1345_0145 = m[A10]*Det3_345_145 - m[A11]*Det3_345_045 |
---|
1769 | + m[A14]*Det3_345_015 - m[A15]*Det3_345_014; |
---|
1770 | G4double Det4_1345_0234 = m[A10]*Det3_345_234 - m[A12]*Det3_345_034 |
---|
1771 | + m[A13]*Det3_345_024 - m[A14]*Det3_345_023; |
---|
1772 | G4double Det4_1345_0235 = m[A10]*Det3_345_235 - m[A12]*Det3_345_035 |
---|
1773 | + m[A13]*Det3_345_025 - m[A15]*Det3_345_023; |
---|
1774 | G4double Det4_1345_0245 = m[A10]*Det3_345_245 - m[A12]*Det3_345_045 |
---|
1775 | + m[A14]*Det3_345_025 - m[A15]*Det3_345_024; |
---|
1776 | G4double Det4_1345_0345 = m[A10]*Det3_345_345 - m[A13]*Det3_345_045 |
---|
1777 | + m[A14]*Det3_345_035 - m[A15]*Det3_345_034; |
---|
1778 | G4double Det4_1345_1234 = m[A11]*Det3_345_234 - m[A12]*Det3_345_134 |
---|
1779 | + m[A13]*Det3_345_124 - m[A14]*Det3_345_123; |
---|
1780 | G4double Det4_1345_1235 = m[A11]*Det3_345_235 - m[A12]*Det3_345_135 |
---|
1781 | + m[A13]*Det3_345_125 - m[A15]*Det3_345_123; |
---|
1782 | G4double Det4_1345_1245 = m[A11]*Det3_345_245 - m[A12]*Det3_345_145 |
---|
1783 | + m[A14]*Det3_345_125 - m[A15]*Det3_345_124; |
---|
1784 | G4double Det4_1345_1345 = m[A11]*Det3_345_345 - m[A13]*Det3_345_145 |
---|
1785 | + m[A14]*Det3_345_135 - m[A15]*Det3_345_134; |
---|
1786 | G4double Det4_2345_0123 = m[A20]*Det3_345_123 - m[A21]*Det3_345_023 |
---|
1787 | + m[A22]*Det3_345_013 - m[A23]*Det3_345_012; |
---|
1788 | G4double Det4_2345_0124 = m[A20]*Det3_345_124 - m[A21]*Det3_345_024 |
---|
1789 | + m[A22]*Det3_345_014 - m[A24]*Det3_345_012; |
---|
1790 | G4double Det4_2345_0125 = m[A20]*Det3_345_125 - m[A21]*Det3_345_025 |
---|
1791 | + m[A22]*Det3_345_015 - m[A25]*Det3_345_012; |
---|
1792 | G4double Det4_2345_0134 = m[A20]*Det3_345_134 - m[A21]*Det3_345_034 |
---|
1793 | + m[A23]*Det3_345_014 - m[A24]*Det3_345_013; |
---|
1794 | G4double Det4_2345_0135 = m[A20]*Det3_345_135 - m[A21]*Det3_345_035 |
---|
1795 | + m[A23]*Det3_345_015 - m[A25]*Det3_345_013; |
---|
1796 | G4double Det4_2345_0145 = m[A20]*Det3_345_145 - m[A21]*Det3_345_045 |
---|
1797 | + m[A24]*Det3_345_015 - m[A25]*Det3_345_014; |
---|
1798 | G4double Det4_2345_0234 = m[A20]*Det3_345_234 - m[A22]*Det3_345_034 |
---|
1799 | + m[A23]*Det3_345_024 - m[A24]*Det3_345_023; |
---|
1800 | G4double Det4_2345_0235 = m[A20]*Det3_345_235 - m[A22]*Det3_345_035 |
---|
1801 | + m[A23]*Det3_345_025 - m[A25]*Det3_345_023; |
---|
1802 | G4double Det4_2345_0245 = m[A20]*Det3_345_245 - m[A22]*Det3_345_045 |
---|
1803 | + m[A24]*Det3_345_025 - m[A25]*Det3_345_024; |
---|
1804 | G4double Det4_2345_0345 = m[A20]*Det3_345_345 - m[A23]*Det3_345_045 |
---|
1805 | + m[A24]*Det3_345_035 - m[A25]*Det3_345_034; |
---|
1806 | G4double Det4_2345_1234 = m[A21]*Det3_345_234 - m[A22]*Det3_345_134 |
---|
1807 | + m[A23]*Det3_345_124 - m[A24]*Det3_345_123; |
---|
1808 | G4double Det4_2345_1235 = m[A21]*Det3_345_235 - m[A22]*Det3_345_135 |
---|
1809 | + m[A23]*Det3_345_125 - m[A25]*Det3_345_123; |
---|
1810 | G4double Det4_2345_1245 = m[A21]*Det3_345_245 - m[A22]*Det3_345_145 |
---|
1811 | + m[A24]*Det3_345_125 - m[A25]*Det3_345_124; |
---|
1812 | G4double Det4_2345_1345 = m[A21]*Det3_345_345 - m[A23]*Det3_345_145 |
---|
1813 | + m[A24]*Det3_345_135 - m[A25]*Det3_345_134; |
---|
1814 | G4double Det4_2345_2345 = m[A22]*Det3_345_345 - m[A23]*Det3_345_245 |
---|
1815 | + m[A24]*Det3_345_235 - m[A25]*Det3_345_234; |
---|
1816 | |
---|
1817 | // Find all NECESSARY 5x5 dets: (19 of them) |
---|
1818 | |
---|
1819 | G4double Det5_01234_01234 = m[A00]*Det4_1234_1234 - m[A01]*Det4_1234_0234 |
---|
1820 | + m[A02]*Det4_1234_0134 - m[A03]*Det4_1234_0124 + m[A04]*Det4_1234_0123; |
---|
1821 | G4double Det5_01235_01234 = m[A00]*Det4_1235_1234 - m[A01]*Det4_1235_0234 |
---|
1822 | + m[A02]*Det4_1235_0134 - m[A03]*Det4_1235_0124 + m[A04]*Det4_1235_0123; |
---|
1823 | G4double Det5_01235_01235 = m[A00]*Det4_1235_1235 - m[A01]*Det4_1235_0235 |
---|
1824 | + m[A02]*Det4_1235_0135 - m[A03]*Det4_1235_0125 + m[A05]*Det4_1235_0123; |
---|
1825 | G4double Det5_01245_01234 = m[A00]*Det4_1245_1234 - m[A01]*Det4_1245_0234 |
---|
1826 | + m[A02]*Det4_1245_0134 - m[A03]*Det4_1245_0124 + m[A04]*Det4_1245_0123; |
---|
1827 | G4double Det5_01245_01235 = m[A00]*Det4_1245_1235 - m[A01]*Det4_1245_0235 |
---|
1828 | + m[A02]*Det4_1245_0135 - m[A03]*Det4_1245_0125 + m[A05]*Det4_1245_0123; |
---|
1829 | G4double Det5_01245_01245 = m[A00]*Det4_1245_1245 - m[A01]*Det4_1245_0245 |
---|
1830 | + m[A02]*Det4_1245_0145 - m[A04]*Det4_1245_0125 + m[A05]*Det4_1245_0124; |
---|
1831 | G4double Det5_01345_01234 = m[A00]*Det4_1345_1234 - m[A01]*Det4_1345_0234 |
---|
1832 | + m[A02]*Det4_1345_0134 - m[A03]*Det4_1345_0124 + m[A04]*Det4_1345_0123; |
---|
1833 | G4double Det5_01345_01235 = m[A00]*Det4_1345_1235 - m[A01]*Det4_1345_0235 |
---|
1834 | + m[A02]*Det4_1345_0135 - m[A03]*Det4_1345_0125 + m[A05]*Det4_1345_0123; |
---|
1835 | G4double Det5_01345_01245 = m[A00]*Det4_1345_1245 - m[A01]*Det4_1345_0245 |
---|
1836 | + m[A02]*Det4_1345_0145 - m[A04]*Det4_1345_0125 + m[A05]*Det4_1345_0124; |
---|
1837 | G4double Det5_01345_01345 = m[A00]*Det4_1345_1345 - m[A01]*Det4_1345_0345 |
---|
1838 | + m[A03]*Det4_1345_0145 - m[A04]*Det4_1345_0135 + m[A05]*Det4_1345_0134; |
---|
1839 | G4double Det5_02345_01234 = m[A00]*Det4_2345_1234 - m[A01]*Det4_2345_0234 |
---|
1840 | + m[A02]*Det4_2345_0134 - m[A03]*Det4_2345_0124 + m[A04]*Det4_2345_0123; |
---|
1841 | G4double Det5_02345_01235 = m[A00]*Det4_2345_1235 - m[A01]*Det4_2345_0235 |
---|
1842 | + m[A02]*Det4_2345_0135 - m[A03]*Det4_2345_0125 + m[A05]*Det4_2345_0123; |
---|
1843 | G4double Det5_02345_01245 = m[A00]*Det4_2345_1245 - m[A01]*Det4_2345_0245 |
---|
1844 | + m[A02]*Det4_2345_0145 - m[A04]*Det4_2345_0125 + m[A05]*Det4_2345_0124; |
---|
1845 | G4double Det5_02345_01345 = m[A00]*Det4_2345_1345 - m[A01]*Det4_2345_0345 |
---|
1846 | + m[A03]*Det4_2345_0145 - m[A04]*Det4_2345_0135 + m[A05]*Det4_2345_0134; |
---|
1847 | G4double Det5_02345_02345 = m[A00]*Det4_2345_2345 - m[A02]*Det4_2345_0345 |
---|
1848 | + m[A03]*Det4_2345_0245 - m[A04]*Det4_2345_0235 + m[A05]*Det4_2345_0234; |
---|
1849 | G4double Det5_12345_01234 = m[A10]*Det4_2345_1234 - m[A11]*Det4_2345_0234 |
---|
1850 | + m[A12]*Det4_2345_0134 - m[A13]*Det4_2345_0124 + m[A14]*Det4_2345_0123; |
---|
1851 | G4double Det5_12345_01235 = m[A10]*Det4_2345_1235 - m[A11]*Det4_2345_0235 |
---|
1852 | + m[A12]*Det4_2345_0135 - m[A13]*Det4_2345_0125 + m[A15]*Det4_2345_0123; |
---|
1853 | G4double Det5_12345_01245 = m[A10]*Det4_2345_1245 - m[A11]*Det4_2345_0245 |
---|
1854 | + m[A12]*Det4_2345_0145 - m[A14]*Det4_2345_0125 + m[A15]*Det4_2345_0124; |
---|
1855 | G4double Det5_12345_01345 = m[A10]*Det4_2345_1345 - m[A11]*Det4_2345_0345 |
---|
1856 | + m[A13]*Det4_2345_0145 - m[A14]*Det4_2345_0135 + m[A15]*Det4_2345_0134; |
---|
1857 | G4double Det5_12345_02345 = m[A10]*Det4_2345_2345 - m[A12]*Det4_2345_0345 |
---|
1858 | + m[A13]*Det4_2345_0245 - m[A14]*Det4_2345_0235 + m[A15]*Det4_2345_0234; |
---|
1859 | G4double Det5_12345_12345 = m[A11]*Det4_2345_2345 - m[A12]*Det4_2345_1345 |
---|
1860 | + m[A13]*Det4_2345_1245 - m[A14]*Det4_2345_1235 + m[A15]*Det4_2345_1234; |
---|
1861 | |
---|
1862 | // Find the determinant |
---|
1863 | |
---|
1864 | G4double det = m[A00]*Det5_12345_12345 |
---|
1865 | - m[A01]*Det5_12345_02345 |
---|
1866 | + m[A02]*Det5_12345_01345 |
---|
1867 | - m[A03]*Det5_12345_01245 |
---|
1868 | + m[A04]*Det5_12345_01235 |
---|
1869 | - m[A05]*Det5_12345_01234; |
---|
1870 | |
---|
1871 | if ( det == 0 ) |
---|
1872 | { |
---|
1873 | ifail = 1; |
---|
1874 | return; |
---|
1875 | } |
---|
1876 | |
---|
1877 | G4double oneOverDet = 1.0/det; |
---|
1878 | G4double mn1OverDet = - oneOverDet; |
---|
1879 | |
---|
1880 | m[A00] = Det5_12345_12345*oneOverDet; |
---|
1881 | m[A01] = Det5_12345_02345*mn1OverDet; |
---|
1882 | m[A02] = Det5_12345_01345*oneOverDet; |
---|
1883 | m[A03] = Det5_12345_01245*mn1OverDet; |
---|
1884 | m[A04] = Det5_12345_01235*oneOverDet; |
---|
1885 | m[A05] = Det5_12345_01234*mn1OverDet; |
---|
1886 | |
---|
1887 | m[A11] = Det5_02345_02345*oneOverDet; |
---|
1888 | m[A12] = Det5_02345_01345*mn1OverDet; |
---|
1889 | m[A13] = Det5_02345_01245*oneOverDet; |
---|
1890 | m[A14] = Det5_02345_01235*mn1OverDet; |
---|
1891 | m[A15] = Det5_02345_01234*oneOverDet; |
---|
1892 | |
---|
1893 | m[A22] = Det5_01345_01345*oneOverDet; |
---|
1894 | m[A23] = Det5_01345_01245*mn1OverDet; |
---|
1895 | m[A24] = Det5_01345_01235*oneOverDet; |
---|
1896 | m[A25] = Det5_01345_01234*mn1OverDet; |
---|
1897 | |
---|
1898 | m[A33] = Det5_01245_01245*oneOverDet; |
---|
1899 | m[A34] = Det5_01245_01235*mn1OverDet; |
---|
1900 | m[A35] = Det5_01245_01234*oneOverDet; |
---|
1901 | |
---|
1902 | m[A44] = Det5_01235_01235*oneOverDet; |
---|
1903 | m[A45] = Det5_01235_01234*mn1OverDet; |
---|
1904 | |
---|
1905 | m[A55] = Det5_01234_01234*oneOverDet; |
---|
1906 | |
---|
1907 | return; |
---|
1908 | } |
---|
1909 | |
---|
1910 | void G4ErrorSymMatrix::invertCholesky5 (G4int & ifail) |
---|
1911 | { |
---|
1912 | |
---|
1913 | // Invert by |
---|
1914 | // |
---|
1915 | // a) decomposing M = G*G^T with G lower triangular |
---|
1916 | // (if M is not positive definite this will fail, leaving this unchanged) |
---|
1917 | // b) inverting G to form H |
---|
1918 | // c) multiplying H^T * H to get M^-1. |
---|
1919 | // |
---|
1920 | // If the matrix is pos. def. it is inverted and 1 is returned. |
---|
1921 | // If the matrix is not pos. def. it remains unaltered and 0 is returned. |
---|
1922 | |
---|
1923 | G4double h10; // below-diagonal elements of H |
---|
1924 | G4double h20, h21; |
---|
1925 | G4double h30, h31, h32; |
---|
1926 | G4double h40, h41, h42, h43; |
---|
1927 | |
---|
1928 | G4double h00, h11, h22, h33, h44; // 1/diagonal elements of G = |
---|
1929 | // diagonal elements of H |
---|
1930 | |
---|
1931 | G4double g10; // below-diagonal elements of G |
---|
1932 | G4double g20, g21; |
---|
1933 | G4double g30, g31, g32; |
---|
1934 | G4double g40, g41, g42, g43; |
---|
1935 | |
---|
1936 | ifail = 1; // We start by assuing we won't succeed... |
---|
1937 | |
---|
1938 | // Form G -- compute diagonal members of H directly rather than of G |
---|
1939 | //------- |
---|
1940 | |
---|
1941 | // Scale first column by 1/sqrt(A00) |
---|
1942 | |
---|
1943 | h00 = m[A00]; |
---|
1944 | if (h00 <= 0) { return; } |
---|
1945 | h00 = 1.0 / std::sqrt(h00); |
---|
1946 | |
---|
1947 | g10 = m[A10] * h00; |
---|
1948 | g20 = m[A20] * h00; |
---|
1949 | g30 = m[A30] * h00; |
---|
1950 | g40 = m[A40] * h00; |
---|
1951 | |
---|
1952 | // Form G11 (actually, just h11) |
---|
1953 | |
---|
1954 | h11 = m[A11] - (g10 * g10); |
---|
1955 | if (h11 <= 0) { return; } |
---|
1956 | h11 = 1.0 / std::sqrt(h11); |
---|
1957 | |
---|
1958 | // Subtract inter-column column dot products from rest of column 1 and |
---|
1959 | // scale to get column 1 of G |
---|
1960 | |
---|
1961 | g21 = (m[A21] - (g10 * g20)) * h11; |
---|
1962 | g31 = (m[A31] - (g10 * g30)) * h11; |
---|
1963 | g41 = (m[A41] - (g10 * g40)) * h11; |
---|
1964 | |
---|
1965 | // Form G22 (actually, just h22) |
---|
1966 | |
---|
1967 | h22 = m[A22] - (g20 * g20) - (g21 * g21); |
---|
1968 | if (h22 <= 0) { return; } |
---|
1969 | h22 = 1.0 / std::sqrt(h22); |
---|
1970 | |
---|
1971 | // Subtract inter-column column dot products from rest of column 2 and |
---|
1972 | // scale to get column 2 of G |
---|
1973 | |
---|
1974 | g32 = (m[A32] - (g20 * g30) - (g21 * g31)) * h22; |
---|
1975 | g42 = (m[A42] - (g20 * g40) - (g21 * g41)) * h22; |
---|
1976 | |
---|
1977 | // Form G33 (actually, just h33) |
---|
1978 | |
---|
1979 | h33 = m[A33] - (g30 * g30) - (g31 * g31) - (g32 * g32); |
---|
1980 | if (h33 <= 0) { return; } |
---|
1981 | h33 = 1.0 / std::sqrt(h33); |
---|
1982 | |
---|
1983 | // Subtract inter-column column dot product from A43 and scale to get G43 |
---|
1984 | |
---|
1985 | g43 = (m[A43] - (g30 * g40) - (g31 * g41) - (g32 * g42)) * h33; |
---|
1986 | |
---|
1987 | // Finally form h44 - if this is possible inversion succeeds |
---|
1988 | |
---|
1989 | h44 = m[A44] - (g40 * g40) - (g41 * g41) - (g42 * g42) - (g43 * g43); |
---|
1990 | if (h44 <= 0) { return; } |
---|
1991 | h44 = 1.0 / std::sqrt(h44); |
---|
1992 | |
---|
1993 | // Form H = 1/G -- diagonal members of H are already correct |
---|
1994 | //------------- |
---|
1995 | |
---|
1996 | // The order here is dictated by speed considerations |
---|
1997 | |
---|
1998 | h43 = -h33 * g43 * h44; |
---|
1999 | h32 = -h22 * g32 * h33; |
---|
2000 | h42 = -h22 * (g32 * h43 + g42 * h44); |
---|
2001 | h21 = -h11 * g21 * h22; |
---|
2002 | h31 = -h11 * (g21 * h32 + g31 * h33); |
---|
2003 | h41 = -h11 * (g21 * h42 + g31 * h43 + g41 * h44); |
---|
2004 | h10 = -h00 * g10 * h11; |
---|
2005 | h20 = -h00 * (g10 * h21 + g20 * h22); |
---|
2006 | h30 = -h00 * (g10 * h31 + g20 * h32 + g30 * h33); |
---|
2007 | h40 = -h00 * (g10 * h41 + g20 * h42 + g30 * h43 + g40 * h44); |
---|
2008 | |
---|
2009 | // Change this to its inverse = H^T*H |
---|
2010 | //------------------------------------ |
---|
2011 | |
---|
2012 | m[A00] = h00 * h00 + h10 * h10 + h20 * h20 + h30 * h30 + h40 * h40; |
---|
2013 | m[A01] = h10 * h11 + h20 * h21 + h30 * h31 + h40 * h41; |
---|
2014 | m[A11] = h11 * h11 + h21 * h21 + h31 * h31 + h41 * h41; |
---|
2015 | m[A02] = h20 * h22 + h30 * h32 + h40 * h42; |
---|
2016 | m[A12] = h21 * h22 + h31 * h32 + h41 * h42; |
---|
2017 | m[A22] = h22 * h22 + h32 * h32 + h42 * h42; |
---|
2018 | m[A03] = h30 * h33 + h40 * h43; |
---|
2019 | m[A13] = h31 * h33 + h41 * h43; |
---|
2020 | m[A23] = h32 * h33 + h42 * h43; |
---|
2021 | m[A33] = h33 * h33 + h43 * h43; |
---|
2022 | m[A04] = h40 * h44; |
---|
2023 | m[A14] = h41 * h44; |
---|
2024 | m[A24] = h42 * h44; |
---|
2025 | m[A34] = h43 * h44; |
---|
2026 | m[A44] = h44 * h44; |
---|
2027 | |
---|
2028 | ifail = 0; |
---|
2029 | return; |
---|
2030 | } |
---|
2031 | |
---|
2032 | void G4ErrorSymMatrix::invertCholesky6 (G4int & ifail) |
---|
2033 | { |
---|
2034 | // Invert by |
---|
2035 | // |
---|
2036 | // a) decomposing M = G*G^T with G lower triangular |
---|
2037 | // (if M is not positive definite this will fail, leaving this unchanged) |
---|
2038 | // b) inverting G to form H |
---|
2039 | // c) multiplying H^T * H to get M^-1. |
---|
2040 | // |
---|
2041 | // If the matrix is pos. def. it is inverted and 1 is returned. |
---|
2042 | // If the matrix is not pos. def. it remains unaltered and 0 is returned. |
---|
2043 | |
---|
2044 | G4double h10; // below-diagonal elements of H |
---|
2045 | G4double h20, h21; |
---|
2046 | G4double h30, h31, h32; |
---|
2047 | G4double h40, h41, h42, h43; |
---|
2048 | G4double h50, h51, h52, h53, h54; |
---|
2049 | |
---|
2050 | G4double h00, h11, h22, h33, h44, h55; // 1/diagonal elements of G = |
---|
2051 | // diagonal elements of H |
---|
2052 | |
---|
2053 | G4double g10; // below-diagonal elements of G |
---|
2054 | G4double g20, g21; |
---|
2055 | G4double g30, g31, g32; |
---|
2056 | G4double g40, g41, g42, g43; |
---|
2057 | G4double g50, g51, g52, g53, g54; |
---|
2058 | |
---|
2059 | ifail = 1; // We start by assuing we won't succeed... |
---|
2060 | |
---|
2061 | // Form G -- compute diagonal members of H directly rather than of G |
---|
2062 | //------- |
---|
2063 | |
---|
2064 | // Scale first column by 1/sqrt(A00) |
---|
2065 | |
---|
2066 | h00 = m[A00]; |
---|
2067 | if (h00 <= 0) { return; } |
---|
2068 | h00 = 1.0 / std::sqrt(h00); |
---|
2069 | |
---|
2070 | g10 = m[A10] * h00; |
---|
2071 | g20 = m[A20] * h00; |
---|
2072 | g30 = m[A30] * h00; |
---|
2073 | g40 = m[A40] * h00; |
---|
2074 | g50 = m[A50] * h00; |
---|
2075 | |
---|
2076 | // Form G11 (actually, just h11) |
---|
2077 | |
---|
2078 | h11 = m[A11] - (g10 * g10); |
---|
2079 | if (h11 <= 0) { return; } |
---|
2080 | h11 = 1.0 / std::sqrt(h11); |
---|
2081 | |
---|
2082 | // Subtract inter-column column dot products from rest of column 1 and |
---|
2083 | // scale to get column 1 of G |
---|
2084 | |
---|
2085 | g21 = (m[A21] - (g10 * g20)) * h11; |
---|
2086 | g31 = (m[A31] - (g10 * g30)) * h11; |
---|
2087 | g41 = (m[A41] - (g10 * g40)) * h11; |
---|
2088 | g51 = (m[A51] - (g10 * g50)) * h11; |
---|
2089 | |
---|
2090 | // Form G22 (actually, just h22) |
---|
2091 | |
---|
2092 | h22 = m[A22] - (g20 * g20) - (g21 * g21); |
---|
2093 | if (h22 <= 0) { return; } |
---|
2094 | h22 = 1.0 / std::sqrt(h22); |
---|
2095 | |
---|
2096 | // Subtract inter-column column dot products from rest of column 2 and |
---|
2097 | // scale to get column 2 of G |
---|
2098 | |
---|
2099 | g32 = (m[A32] - (g20 * g30) - (g21 * g31)) * h22; |
---|
2100 | g42 = (m[A42] - (g20 * g40) - (g21 * g41)) * h22; |
---|
2101 | g52 = (m[A52] - (g20 * g50) - (g21 * g51)) * h22; |
---|
2102 | |
---|
2103 | // Form G33 (actually, just h33) |
---|
2104 | |
---|
2105 | h33 = m[A33] - (g30 * g30) - (g31 * g31) - (g32 * g32); |
---|
2106 | if (h33 <= 0) { return; } |
---|
2107 | h33 = 1.0 / std::sqrt(h33); |
---|
2108 | |
---|
2109 | // Subtract inter-column column dot products from rest of column 3 and |
---|
2110 | // scale to get column 3 of G |
---|
2111 | |
---|
2112 | g43 = (m[A43] - (g30 * g40) - (g31 * g41) - (g32 * g42)) * h33; |
---|
2113 | g53 = (m[A53] - (g30 * g50) - (g31 * g51) - (g32 * g52)) * h33; |
---|
2114 | |
---|
2115 | // Form G44 (actually, just h44) |
---|
2116 | |
---|
2117 | h44 = m[A44] - (g40 * g40) - (g41 * g41) - (g42 * g42) - (g43 * g43); |
---|
2118 | if (h44 <= 0) { return; } |
---|
2119 | h44 = 1.0 / std::sqrt(h44); |
---|
2120 | |
---|
2121 | // Subtract inter-column column dot product from M54 and scale to get G54 |
---|
2122 | |
---|
2123 | g54 = (m[A54] - (g40 * g50) - (g41 * g51) - (g42 * g52) - (g43 * g53)) * h44; |
---|
2124 | |
---|
2125 | // Finally form h55 - if this is possible inversion succeeds |
---|
2126 | |
---|
2127 | h55 = m[A55] - (g50*g50) - (g51*g51) - (g52*g52) - (g53*g53) - (g54*g54); |
---|
2128 | if (h55 <= 0) { return; } |
---|
2129 | h55 = 1.0 / std::sqrt(h55); |
---|
2130 | |
---|
2131 | // Form H = 1/G -- diagonal members of H are already correct |
---|
2132 | //------------- |
---|
2133 | |
---|
2134 | // The order here is dictated by speed considerations |
---|
2135 | |
---|
2136 | h54 = -h44 * g54 * h55; |
---|
2137 | h43 = -h33 * g43 * h44; |
---|
2138 | h53 = -h33 * (g43 * h54 + g53 * h55); |
---|
2139 | h32 = -h22 * g32 * h33; |
---|
2140 | h42 = -h22 * (g32 * h43 + g42 * h44); |
---|
2141 | h52 = -h22 * (g32 * h53 + g42 * h54 + g52 * h55); |
---|
2142 | h21 = -h11 * g21 * h22; |
---|
2143 | h31 = -h11 * (g21 * h32 + g31 * h33); |
---|
2144 | h41 = -h11 * (g21 * h42 + g31 * h43 + g41 * h44); |
---|
2145 | h51 = -h11 * (g21 * h52 + g31 * h53 + g41 * h54 + g51 * h55); |
---|
2146 | h10 = -h00 * g10 * h11; |
---|
2147 | h20 = -h00 * (g10 * h21 + g20 * h22); |
---|
2148 | h30 = -h00 * (g10 * h31 + g20 * h32 + g30 * h33); |
---|
2149 | h40 = -h00 * (g10 * h41 + g20 * h42 + g30 * h43 + g40 * h44); |
---|
2150 | h50 = -h00 * (g10 * h51 + g20 * h52 + g30 * h53 + g40 * h54 + g50 * h55); |
---|
2151 | |
---|
2152 | // Change this to its inverse = H^T*H |
---|
2153 | //------------------------------------ |
---|
2154 | |
---|
2155 | m[A00] = h00 * h00 + h10 * h10 + h20 * h20 + h30 * h30 + h40 * h40 + h50*h50; |
---|
2156 | m[A01] = h10 * h11 + h20 * h21 + h30 * h31 + h40 * h41 + h50 * h51; |
---|
2157 | m[A11] = h11 * h11 + h21 * h21 + h31 * h31 + h41 * h41 + h51 * h51; |
---|
2158 | m[A02] = h20 * h22 + h30 * h32 + h40 * h42 + h50 * h52; |
---|
2159 | m[A12] = h21 * h22 + h31 * h32 + h41 * h42 + h51 * h52; |
---|
2160 | m[A22] = h22 * h22 + h32 * h32 + h42 * h42 + h52 * h52; |
---|
2161 | m[A03] = h30 * h33 + h40 * h43 + h50 * h53; |
---|
2162 | m[A13] = h31 * h33 + h41 * h43 + h51 * h53; |
---|
2163 | m[A23] = h32 * h33 + h42 * h43 + h52 * h53; |
---|
2164 | m[A33] = h33 * h33 + h43 * h43 + h53 * h53; |
---|
2165 | m[A04] = h40 * h44 + h50 * h54; |
---|
2166 | m[A14] = h41 * h44 + h51 * h54; |
---|
2167 | m[A24] = h42 * h44 + h52 * h54; |
---|
2168 | m[A34] = h43 * h44 + h53 * h54; |
---|
2169 | m[A44] = h44 * h44 + h54 * h54; |
---|
2170 | m[A05] = h50 * h55; |
---|
2171 | m[A15] = h51 * h55; |
---|
2172 | m[A25] = h52 * h55; |
---|
2173 | m[A35] = h53 * h55; |
---|
2174 | m[A45] = h54 * h55; |
---|
2175 | m[A55] = h55 * h55; |
---|
2176 | |
---|
2177 | ifail = 0; |
---|
2178 | return; |
---|
2179 | } |
---|
2180 | |
---|
2181 | void G4ErrorSymMatrix::invert4 (G4int & ifail) |
---|
2182 | { |
---|
2183 | ifail = 0; |
---|
2184 | |
---|
2185 | // Find all NECESSARY 2x2 dets: (14 of them) |
---|
2186 | |
---|
2187 | G4double Det2_12_01 = m[A10]*m[A21] - m[A11]*m[A20]; |
---|
2188 | G4double Det2_12_02 = m[A10]*m[A22] - m[A12]*m[A20]; |
---|
2189 | G4double Det2_12_12 = m[A11]*m[A22] - m[A12]*m[A21]; |
---|
2190 | G4double Det2_13_01 = m[A10]*m[A31] - m[A11]*m[A30]; |
---|
2191 | G4double Det2_13_02 = m[A10]*m[A32] - m[A12]*m[A30]; |
---|
2192 | G4double Det2_13_03 = m[A10]*m[A33] - m[A13]*m[A30]; |
---|
2193 | G4double Det2_13_12 = m[A11]*m[A32] - m[A12]*m[A31]; |
---|
2194 | G4double Det2_13_13 = m[A11]*m[A33] - m[A13]*m[A31]; |
---|
2195 | G4double Det2_23_01 = m[A20]*m[A31] - m[A21]*m[A30]; |
---|
2196 | G4double Det2_23_02 = m[A20]*m[A32] - m[A22]*m[A30]; |
---|
2197 | G4double Det2_23_03 = m[A20]*m[A33] - m[A23]*m[A30]; |
---|
2198 | G4double Det2_23_12 = m[A21]*m[A32] - m[A22]*m[A31]; |
---|
2199 | G4double Det2_23_13 = m[A21]*m[A33] - m[A23]*m[A31]; |
---|
2200 | G4double Det2_23_23 = m[A22]*m[A33] - m[A23]*m[A32]; |
---|
2201 | |
---|
2202 | // Find all NECESSARY 3x3 dets: (10 of them) |
---|
2203 | |
---|
2204 | G4double Det3_012_012 = m[A00]*Det2_12_12 - m[A01]*Det2_12_02 |
---|
2205 | + m[A02]*Det2_12_01; |
---|
2206 | G4double Det3_013_012 = m[A00]*Det2_13_12 - m[A01]*Det2_13_02 |
---|
2207 | + m[A02]*Det2_13_01; |
---|
2208 | G4double Det3_013_013 = m[A00]*Det2_13_13 - m[A01]*Det2_13_03 |
---|
2209 | + m[A03]*Det2_13_01; |
---|
2210 | G4double Det3_023_012 = m[A00]*Det2_23_12 - m[A01]*Det2_23_02 |
---|
2211 | + m[A02]*Det2_23_01; |
---|
2212 | G4double Det3_023_013 = m[A00]*Det2_23_13 - m[A01]*Det2_23_03 |
---|
2213 | + m[A03]*Det2_23_01; |
---|
2214 | G4double Det3_023_023 = m[A00]*Det2_23_23 - m[A02]*Det2_23_03 |
---|
2215 | + m[A03]*Det2_23_02; |
---|
2216 | G4double Det3_123_012 = m[A10]*Det2_23_12 - m[A11]*Det2_23_02 |
---|
2217 | + m[A12]*Det2_23_01; |
---|
2218 | G4double Det3_123_013 = m[A10]*Det2_23_13 - m[A11]*Det2_23_03 |
---|
2219 | + m[A13]*Det2_23_01; |
---|
2220 | G4double Det3_123_023 = m[A10]*Det2_23_23 - m[A12]*Det2_23_03 |
---|
2221 | + m[A13]*Det2_23_02; |
---|
2222 | G4double Det3_123_123 = m[A11]*Det2_23_23 - m[A12]*Det2_23_13 |
---|
2223 | + m[A13]*Det2_23_12; |
---|
2224 | |
---|
2225 | // Find the 4x4 det: |
---|
2226 | |
---|
2227 | G4double det = m[A00]*Det3_123_123 |
---|
2228 | - m[A01]*Det3_123_023 |
---|
2229 | + m[A02]*Det3_123_013 |
---|
2230 | - m[A03]*Det3_123_012; |
---|
2231 | |
---|
2232 | if ( det == 0 ) |
---|
2233 | { |
---|
2234 | ifail = 1; |
---|
2235 | return; |
---|
2236 | } |
---|
2237 | |
---|
2238 | G4double oneOverDet = 1.0/det; |
---|
2239 | G4double mn1OverDet = - oneOverDet; |
---|
2240 | |
---|
2241 | m[A00] = Det3_123_123 * oneOverDet; |
---|
2242 | m[A01] = Det3_123_023 * mn1OverDet; |
---|
2243 | m[A02] = Det3_123_013 * oneOverDet; |
---|
2244 | m[A03] = Det3_123_012 * mn1OverDet; |
---|
2245 | |
---|
2246 | |
---|
2247 | m[A11] = Det3_023_023 * oneOverDet; |
---|
2248 | m[A12] = Det3_023_013 * mn1OverDet; |
---|
2249 | m[A13] = Det3_023_012 * oneOverDet; |
---|
2250 | |
---|
2251 | m[A22] = Det3_013_013 * oneOverDet; |
---|
2252 | m[A23] = Det3_013_012 * mn1OverDet; |
---|
2253 | |
---|
2254 | m[A33] = Det3_012_012 * oneOverDet; |
---|
2255 | |
---|
2256 | return; |
---|
2257 | } |
---|
2258 | |
---|
2259 | void G4ErrorSymMatrix::invertHaywood4 (G4int & ifail) |
---|
2260 | { |
---|
2261 | invert4(ifail); // For the 4x4 case, the method we use for invert is already |
---|
2262 | // the Haywood method. |
---|
2263 | } |
---|
2264 | |
---|