1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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9 | // * include a list of copyright holders. * |
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11 | // * Neither the authors of this software system, nor their employing * |
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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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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 | // |
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27 | // $Id: G4SimplexDownhill.icc,v 1.2 2007/05/11 13:05:53 gcosmo Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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29 | // |
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30 | // Author: Tatsumi Koi (SLAC/SCCS), 2007 |
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31 | // -------------------------------------------------------------------------- |
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32 | |
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33 | #include <iostream> |
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34 | #include <numeric> |
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35 | #include <cfloat> |
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36 | |
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37 | template<class T> void G4SimplexDownhill<T>::init() |
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38 | { |
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39 | alpha = 2.0; // refrection coefficient: 0 < alpha |
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40 | beta = 0.5; // contraction coefficient: 0 < beta < 1 |
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41 | gamma = 2.0; // expantion coefficient: 1 < gamma |
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42 | |
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43 | maximum_no_trial = 10000; |
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44 | max_se = FLT_MIN; |
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45 | //max_ratio = FLT_EPSILON/1; |
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46 | max_ratio = DBL_EPSILON/1; |
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47 | minimized = false; |
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48 | } |
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49 | |
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50 | |
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51 | /* |
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52 | |
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53 | void G4SimplexDownhill<class T>:: |
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54 | SetFunction( G4int n , G4double( *afunc )( std::vector < G4double > ) ) |
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55 | { |
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56 | numberOfVariable = n; |
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57 | theFunction = afunc; |
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58 | minimized = false; |
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59 | } |
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60 | |
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61 | */ |
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62 | |
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63 | |
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64 | template<class T> |
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65 | G4double G4SimplexDownhill<T>::GetMinimum() |
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66 | { |
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67 | |
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68 | initialize(); |
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69 | |
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70 | // First Tryal; |
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71 | |
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72 | //G4cout << "Begin First Trials" << G4endl; |
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73 | doDownhill(); |
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74 | //G4cout << "End First Trials" << G4endl; |
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75 | |
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76 | std::vector< G4double >::iterator it_minh = |
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77 | std::min_element( currentHeights.begin() , currentHeights.end() ); |
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78 | G4int imin = -1; |
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79 | G4int i = 0; |
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80 | for ( std::vector< G4double >::iterator it = currentHeights.begin(); |
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81 | it != currentHeights.end(); it++ ) |
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82 | { |
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83 | if ( it == it_minh ) |
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84 | { |
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85 | imin = i; |
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86 | } |
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87 | i++; |
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88 | } |
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89 | std::vector< G4double > minimumPoint = currentSimplex[ imin ]; |
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90 | |
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91 | // Second Trial |
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92 | |
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93 | //std::vector< G4double > minimumPoint = currentSimplex[ 0 ]; |
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94 | initialize(); |
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95 | |
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96 | currentSimplex[ numberOfVariable ] = minimumPoint; |
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97 | |
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98 | //G4cout << "Begin Second Trials" << G4endl; |
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99 | doDownhill(); |
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100 | //G4cout << "End Second Trials" << G4endl; |
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101 | |
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102 | G4double sum = std::accumulate( currentHeights.begin() , |
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103 | currentHeights.end() , 0.0 ); |
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104 | G4double average = sum/(numberOfVariable+1); |
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105 | G4double minimum = average; |
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106 | |
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107 | minimized = true; |
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108 | |
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109 | return minimum; |
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110 | |
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111 | } |
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112 | |
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113 | |
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114 | |
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115 | template<class T> |
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116 | void G4SimplexDownhill<T>::initialize() |
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117 | { |
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118 | |
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119 | currentSimplex.resize( numberOfVariable+1 ); |
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120 | currentHeights.resize( numberOfVariable+1 ); |
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121 | |
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122 | for ( G4int i = 0 ; i < numberOfVariable ; i++ ) |
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123 | { |
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124 | std::vector< G4double > avec ( numberOfVariable , 0.0 ); |
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125 | avec[ i ] = 1.0; |
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126 | currentSimplex[ i ] = avec; |
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127 | } |
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128 | |
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129 | //std::vector< G4double > avec ( numberOfVariable , 0.0 ); |
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130 | std::vector< G4double > avec ( numberOfVariable , 1 ); |
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131 | currentSimplex[ numberOfVariable ] = avec; |
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132 | |
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133 | } |
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134 | |
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135 | |
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136 | |
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137 | template<class T> |
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138 | void G4SimplexDownhill<T>::calHeights() |
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139 | { |
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140 | |
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141 | for ( G4int i = 0 ; i <= numberOfVariable ; i++ ) |
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142 | { |
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143 | currentHeights[i] = getValue ( currentSimplex[i] ); |
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144 | } |
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145 | |
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146 | } |
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147 | |
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148 | |
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149 | |
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150 | template<class T> |
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151 | std::vector< G4double > G4SimplexDownhill<T>::calCentroid( G4int ih ) |
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152 | { |
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153 | |
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154 | std::vector< G4double > centroid ( numberOfVariable , 0.0 ); |
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155 | |
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156 | G4int i = 0; |
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157 | for ( std::vector< std::vector< G4double > >::iterator |
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158 | it = currentSimplex.begin(); it != currentSimplex.end() ; it++ ) |
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159 | { |
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160 | if ( i != ih ) |
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161 | { |
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162 | for ( G4int j = 0 ; j < numberOfVariable ; j++ ) |
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163 | { |
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164 | centroid[j] += (*it)[j]/numberOfVariable; |
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165 | } |
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166 | } |
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167 | i++; |
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168 | } |
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169 | |
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170 | return centroid; |
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171 | } |
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172 | |
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173 | |
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174 | |
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175 | template<class T> |
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176 | std::vector< G4double > G4SimplexDownhill<T>:: |
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177 | getReflectionPoint( std::vector< G4double > p , |
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178 | std::vector< G4double > centroid ) |
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179 | { |
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180 | //G4cout << "Reflection" << G4endl; |
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181 | |
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182 | std::vector< G4double > reflectionP ( numberOfVariable , 0.0 ); |
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183 | |
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184 | for ( G4int i = 0 ; i < numberOfVariable ; i++ ) |
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185 | { |
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186 | reflectionP[ i ] = ( 1 + alpha ) * centroid[ i ] - alpha * p[ i ]; |
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187 | } |
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188 | |
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189 | return reflectionP; |
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190 | } |
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191 | |
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192 | |
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193 | |
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194 | template<class T> |
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195 | std::vector< G4double > G4SimplexDownhill<T>:: |
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196 | getExpansionPoint( std::vector< G4double > p , |
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197 | std::vector< G4double > centroid ) |
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198 | { |
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199 | //G4cout << "Expantion" << G4endl; |
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200 | |
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201 | std::vector< G4double > expansionP ( numberOfVariable , 0.0 ); |
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202 | |
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203 | for ( G4int i = 0 ; i < numberOfVariable ; i++ ) |
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204 | { |
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205 | expansionP[i] = ( 1 - gamma ) * centroid[i] + gamma * p[i]; |
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206 | } |
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207 | |
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208 | return expansionP; |
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209 | } |
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210 | |
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211 | template<class T> |
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212 | std::vector< G4double > G4SimplexDownhill<T>:: |
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213 | getContractionPoint( std::vector< G4double > p , |
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214 | std::vector< G4double > centroid ) |
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215 | { |
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216 | //G4cout << "Contraction" << G4endl; |
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217 | |
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218 | std::vector< G4double > contractionP ( numberOfVariable , 0.0 ); |
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219 | |
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220 | for ( G4int i = 0 ; i < numberOfVariable ; i++ ) |
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221 | { |
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222 | contractionP[i] = ( 1 - beta ) * centroid[i] + beta * p[i]; |
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223 | } |
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224 | |
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225 | return contractionP; |
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226 | } |
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227 | |
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228 | |
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229 | |
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230 | template<class T> |
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231 | G4bool G4SimplexDownhill<T>::isItGoodEnough() |
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232 | { |
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233 | G4bool result = false; |
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234 | |
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235 | G4double sum = std::accumulate( currentHeights.begin() , |
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236 | currentHeights.end() , 0.0 ); |
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237 | G4double average = sum/(numberOfVariable+1); |
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238 | //G4cout << "average " << average << G4endl; |
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239 | |
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240 | G4double delta = 0.0; |
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241 | for ( G4int i = 0 ; i <= numberOfVariable ; i++ ) |
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242 | { |
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243 | delta += std::abs ( currentHeights[ i ] - average ); |
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244 | } |
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245 | //G4cout << "ratio of delta to average is " |
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246 | // << delta / (numberOfVariable+1) / average << G4endl; |
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247 | |
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248 | if ( delta/(numberOfVariable+1)/average < max_ratio ) |
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249 | { |
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250 | result = true; |
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251 | } |
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252 | |
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253 | /* |
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254 | G4double sigma = 0.0; |
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255 | G4cout << "average " << average << G4endl; |
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256 | for ( G4int i = 0 ; i <= numberOfVariable ; i++ ) |
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257 | { |
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258 | sigma += ( currentHeights[ i ] - average ) |
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259 | *( currentHeights[ i ] - average ); |
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260 | } |
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261 | |
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262 | G4cout << "standard error of hs " |
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263 | << std::sqrt ( sigma ) / (numberOfVariable+1) << G4endl; |
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264 | if ( std::sqrt ( sigma ) / (numberOfVariable+1) < max_se ) |
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265 | { |
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266 | result = true; |
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267 | } |
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268 | */ |
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269 | |
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270 | return result; |
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271 | } |
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272 | |
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273 | |
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274 | |
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275 | template<class T> |
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276 | void G4SimplexDownhill<T>::doDownhill() |
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277 | { |
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278 | |
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279 | G4int nth_trial = 0; |
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280 | |
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281 | while ( nth_trial < maximum_no_trial ) |
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282 | { |
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283 | |
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284 | /* |
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285 | G4cout << "Begining " << nth_trial << "th trial " << G4endl; |
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286 | for ( G4int j = 0 ; j <= numberOfVariable ; j++ ) |
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287 | { |
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288 | G4cout << "SimplexPoint " << j << ": "; |
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289 | for ( G4int i = 0 ; i < numberOfVariable ; i++ ) |
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290 | { |
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291 | G4cout << currentSimplex[j][i] |
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292 | << " "; |
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293 | } |
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294 | G4cout << G4endl; |
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295 | } |
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296 | */ |
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297 | |
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298 | calHeights(); |
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299 | |
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300 | if ( isItGoodEnough() ) |
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301 | { |
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302 | break; |
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303 | } |
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304 | |
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305 | std::vector< G4double >::iterator it_maxh = |
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306 | std::max_element( currentHeights.begin() , currentHeights.end() ); |
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307 | std::vector< G4double >::iterator it_minh = |
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308 | std::min_element( currentHeights.begin() , currentHeights.end() );; |
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309 | |
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310 | G4double h_H = *it_maxh; |
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311 | G4double h_L = *it_minh; |
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312 | |
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313 | G4int ih = 0;; |
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314 | G4int il = 0; |
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315 | G4double h_H2 =0.0; |
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316 | G4int i = 0; |
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317 | for ( std::vector< G4double >::iterator |
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318 | it = currentHeights.begin(); it != currentHeights.end(); it++ ) |
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319 | { |
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320 | if ( it == it_maxh ) |
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321 | { |
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322 | ih = i; |
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323 | } |
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324 | else |
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325 | { |
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326 | h_H2 = std::max( h_H2 , *it ); |
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327 | } |
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328 | |
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329 | if ( it == it_minh ) |
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330 | { |
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331 | il = i; |
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332 | } |
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333 | i++; |
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334 | } |
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335 | |
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336 | //G4cout << "max " << h_H << " " << ih << G4endl; |
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337 | //G4cout << "max-dash " << h_H2 << G4endl; |
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338 | //G4cout << "min " << h_L << " " << il << G4endl; |
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339 | |
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340 | std::vector< G4double > centroidPoint = calCentroid ( ih ); |
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341 | |
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342 | // REFLECTION |
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343 | std::vector< G4double > reflectionPoint = |
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344 | getReflectionPoint( currentSimplex[ ih ] , centroidPoint ); |
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345 | |
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346 | G4double h = getValue( reflectionPoint ); |
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347 | |
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348 | if ( h <= h_L ) |
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349 | { |
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350 | // EXPANSION |
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351 | std::vector< G4double > expansionPoint = |
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352 | getExpansionPoint( reflectionPoint , centroidPoint ); |
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353 | G4double hh = getValue( expansionPoint ); |
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354 | |
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355 | if ( hh <= h_L ) |
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356 | { |
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357 | // Replace |
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358 | currentSimplex[ ih ] = expansionPoint; |
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359 | //G4cout << "A" << G4endl; |
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360 | } |
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361 | else |
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362 | { |
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363 | // Replace |
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364 | currentSimplex[ ih ] = reflectionPoint; |
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365 | //G4cout << "B1" << G4endl; |
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366 | } |
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367 | } |
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368 | else |
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369 | { |
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370 | if ( h <= h_H2 ) |
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371 | { |
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372 | // Replace |
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373 | currentSimplex[ ih ] = reflectionPoint; |
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374 | //G4cout << "B2" << G4endl; |
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375 | } |
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376 | else |
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377 | { |
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378 | if ( h <= h_H ) |
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379 | { |
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380 | // Replace |
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381 | currentSimplex[ ih ] = reflectionPoint; |
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382 | //G4cout << "BC" << G4endl; |
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383 | } |
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384 | // CONTRACTION |
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385 | std::vector< G4double > contractionPoint = |
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386 | getContractionPoint( currentSimplex[ ih ] , centroidPoint ); |
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387 | G4double hh = getValue( contractionPoint ); |
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388 | if ( hh <= h_H ) |
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389 | { |
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390 | // Replace |
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391 | currentSimplex[ ih ] = contractionPoint; |
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392 | //G4cout << "C" << G4endl; |
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393 | } |
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394 | else |
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395 | { |
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396 | // Replace |
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397 | for ( G4int j = 0 ; j <= numberOfVariable ; j++ ) |
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398 | { |
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399 | std::vector< G4double > vec ( numberOfVariable , 0.0 ); |
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400 | for ( G4int k = 0 ; k < numberOfVariable ; k++ ) |
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401 | { |
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402 | vec[ k ] = ( currentSimplex[ j ][ k ] |
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403 | + currentSimplex[ il ][ k ] ) / 2.0; |
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404 | } |
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405 | currentSimplex[ j ] = vec; |
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406 | } |
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407 | //G4cout << "D" << G4endl; |
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408 | } |
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409 | } |
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410 | |
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411 | } |
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412 | |
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413 | nth_trial++; |
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414 | } |
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415 | } |
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416 | |
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417 | |
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418 | |
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419 | template<class T> |
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420 | std::vector< G4double > G4SimplexDownhill<T>::GetMinimumPoint() |
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421 | { |
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422 | if ( minimized != true ) |
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423 | { |
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424 | GetMinimum(); |
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425 | } |
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426 | |
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427 | std::vector< G4double >::iterator it_minh = |
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428 | std::min_element( currentHeights.begin() , currentHeights.end() );; |
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429 | G4int imin = -1; |
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430 | G4int i = 0; |
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431 | for ( std::vector< G4double >::iterator |
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432 | it = currentHeights.begin(); it != currentHeights.end(); it++ ) |
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433 | { |
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434 | if ( it == it_minh ) |
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435 | { |
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436 | imin = i; |
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437 | } |
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438 | i++; |
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439 | } |
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440 | std::vector< G4double > minimumPoint = currentSimplex[ imin ]; |
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441 | |
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442 | return minimumPoint; |
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443 | } |
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