[833] | 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 | // |
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| 27 | // $Id: G4SimplexDownhill.icc,v 1.2 2007/05/11 13:05:53 gcosmo Exp $ |
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[1337] | 28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $ |
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[833] | 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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