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Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 17 // * 17 // * * 18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // INCL++ intra-nuclear cascade model 26 // INCL++ intra-nuclear cascade model 27 // Alain Boudard, CEA-Saclay, France 27 // Alain Boudard, CEA-Saclay, France 28 // Joseph Cugnon, University of Liege, Belgium 28 // Joseph Cugnon, University of Liege, Belgium 29 // Jean-Christophe David, CEA-Saclay, France 29 // Jean-Christophe David, CEA-Saclay, France 30 // Pekka Kaitaniemi, CEA-Saclay, France, and H 30 // Pekka Kaitaniemi, CEA-Saclay, France, and Helsinki Institute of Physics, Finland 31 // Sylvie Leray, CEA-Saclay, France 31 // Sylvie Leray, CEA-Saclay, France 32 // Davide Mancusi, CEA-Saclay, France 32 // Davide Mancusi, CEA-Saclay, France 33 // 33 // 34 #define INCLXX_IN_GEANT4_MODE 1 34 #define INCLXX_IN_GEANT4_MODE 1 35 35 36 #include "globals.hh" 36 #include "globals.hh" 37 37 38 /** \file G4INCLRootFinder.hh 38 /** \file G4INCLRootFinder.hh 39 * \brief Static root-finder algorithm. 39 * \brief Static root-finder algorithm. 40 * 40 * 41 * Provides a stateless root-finder algorithm. 41 * Provides a stateless root-finder algorithm. 42 * 42 * 43 * \date 2nd March 2011 43 * \date 2nd March 2011 44 * \author Davide Mancusi 44 * \author Davide Mancusi 45 */ 45 */ 46 46 47 #include "G4INCLRootFinder.hh" 47 #include "G4INCLRootFinder.hh" 48 #include "G4INCLGlobals.hh" 48 #include "G4INCLGlobals.hh" 49 #include "G4INCLLogger.hh" 49 #include "G4INCLLogger.hh" 50 #include <utility> 50 #include <utility> 51 #include <cmath> 51 #include <cmath> 52 52 53 namespace G4INCL { 53 namespace G4INCL { 54 54 55 namespace RootFinder { 55 namespace RootFinder { 56 56 57 namespace { 57 namespace { 58 58 59 /// \brief Tolerance on the y value 59 /// \brief Tolerance on the y value 60 const G4double toleranceY = 1.e-4; 60 const G4double toleranceY = 1.e-4; 61 61 62 /// \brief Maximum number of iterations 62 /// \brief Maximum number of iterations for convergence 63 const G4int maxIterations=50; 63 const G4int maxIterations=50; 64 64 65 /** \brief Bracket the root of the funct 65 /** \brief Bracket the root of the function f. 66 * 66 * 67 * Tries to find a bracketing value for 67 * Tries to find a bracketing value for the function root. 68 * 68 * 69 * \param f pointer to a RootFunctor 69 * \param f pointer to a RootFunctor 70 * \param x0 starting value 70 * \param x0 starting value 71 * \return if the root could be brackete 71 * \return if the root could be bracketed, returns two values of x 72 * bracketing the root, as a pair. If 72 * bracketing the root, as a pair. If the bracketing failed, returns a 73 * pair with first > second. 73 * pair with first > second. 74 */ 74 */ 75 std::pair<G4double,G4double> bracketRoot 75 std::pair<G4double,G4double> bracketRoot(RootFunctor const * const f, G4double x0) { 76 G4double y0 = (*f)(x0); 76 G4double y0 = (*f)(x0); 77 77 78 const G4double scaleFactor = 1.5; 78 const G4double scaleFactor = 1.5; 79 79 80 G4double x1; 80 G4double x1; 81 if(x0!=0.) 81 if(x0!=0.) 82 x1=scaleFactor*x0; 82 x1=scaleFactor*x0; 83 else 83 else 84 x1=1.; 84 x1=1.; 85 G4double y1 = (*f)(x1); 85 G4double y1 = (*f)(x1); 86 86 87 if(Math::sign(y0)!=Math::sign(y1)) 87 if(Math::sign(y0)!=Math::sign(y1)) 88 return std::make_pair(x0,x1); 88 return std::make_pair(x0,x1); 89 89 90 const G4double scaleFactorMinus1 = 1./ 90 const G4double scaleFactorMinus1 = 1./scaleFactor; 91 G4double oldx0, oldx1, oldy1; 91 G4double oldx0, oldx1, oldy1; 92 G4int iterations=0; 92 G4int iterations=0; 93 do { 93 do { 94 if(iterations > maxIterations) { 94 if(iterations > maxIterations) { 95 INCL_DEBUG("Could not bracket the 95 INCL_DEBUG("Could not bracket the root." << '\n'); 96 return std::make_pair((G4double) 1 96 return std::make_pair((G4double) 1.,(G4double) -1.); 97 } 97 } 98 98 99 oldx0=x0; 99 oldx0=x0; 100 oldx1=x1; 100 oldx1=x1; 101 oldy1=y1; 101 oldy1=y1; 102 102 103 x0 *= scaleFactorMinus1; 103 x0 *= scaleFactorMinus1; 104 x1 *= scaleFactor; 104 x1 *= scaleFactor; 105 y0 = (*f)(x0); 105 y0 = (*f)(x0); 106 y1 = (*f)(x1); 106 y1 = (*f)(x1); 107 iterations++; 107 iterations++; 108 } while(Math::sign(y0)==Math::sign(y1) 108 } while(Math::sign(y0)==Math::sign(y1)); /* Loop checking, 10.07.2015, D.Mancusi */ 109 109 110 if(Math::sign(y1)==Math::sign(oldy1)) 110 if(Math::sign(y1)==Math::sign(oldy1)) 111 return std::make_pair(x0,oldx0); 111 return std::make_pair(x0,oldx0); 112 else 112 else 113 return std::make_pair(oldx1,x1); 113 return std::make_pair(oldx1,x1); 114 } 114 } 115 115 116 } 116 } 117 117 118 Solution solve(RootFunctor const * const f 118 Solution solve(RootFunctor const * const f, const G4double x0) { 119 // If we already have the solution, do n 119 // If we already have the solution, do nothing 120 const G4double y0 = (*f)(x0); 120 const G4double y0 = (*f)(x0); 121 if( std::abs(y0) < toleranceY ) { 121 if( std::abs(y0) < toleranceY ) { 122 return Solution(x0,y0); 122 return Solution(x0,y0); 123 } 123 } 124 124 125 // Bracket the root and set the initial 125 // Bracket the root and set the initial values 126 std::pair<G4double,G4double> bracket = b 126 std::pair<G4double,G4double> bracket = bracketRoot(f,x0); 127 G4double x1 = bracket.first; 127 G4double x1 = bracket.first; 128 G4double x2 = bracket.second; 128 G4double x2 = bracket.second; 129 // If x1>x2, it means that we could not 129 // If x1>x2, it means that we could not bracket the root. Return false. 130 if(x1>x2) { 130 if(x1>x2) { 131 // Maybe zero is a good solution? 131 // Maybe zero is a good solution? 132 G4double y_at_zero = (*f)(0.); 132 G4double y_at_zero = (*f)(0.); 133 if(std::abs(y_at_zero)<=toleranceY) { 133 if(std::abs(y_at_zero)<=toleranceY) { 134 f->cleanUp(true); 134 f->cleanUp(true); 135 return Solution(0.,y_at_zero); 135 return Solution(0.,y_at_zero); 136 } else { 136 } else { 137 INCL_DEBUG("Root-finding algorithm c 137 INCL_DEBUG("Root-finding algorithm could not bracket the root." << '\n'); 138 f->cleanUp(false); 138 f->cleanUp(false); 139 return Solution(); 139 return Solution(); 140 } 140 } 141 } 141 } 142 142 143 G4double y1 = (*f)(x1); 143 G4double y1 = (*f)(x1); 144 G4double y2 = (*f)(x2); 144 G4double y2 = (*f)(x2); 145 G4double x = x1; 145 G4double x = x1; 146 G4double y = y1; 146 G4double y = y1; 147 147 148 /* ******************************** 148 /* ******************************** 149 * Start of the false-position loop 149 * Start of the false-position loop 150 * ********************************/ 150 * ********************************/ 151 151 152 // Keep track of the last updated interv 152 // Keep track of the last updated interval end (-1=left, 1=right) 153 G4int lastUpdated = 0; 153 G4int lastUpdated = 0; 154 154 155 for(G4int iterations=0; std::abs(y) > to 155 for(G4int iterations=0; std::abs(y) > toleranceY; iterations++) { 156 156 157 if(iterations > maxIterations) { 157 if(iterations > maxIterations) { 158 INCL_DEBUG("Root-finding algorithm d 158 INCL_DEBUG("Root-finding algorithm did not converge." << '\n'); 159 f->cleanUp(false); 159 f->cleanUp(false); 160 return Solution(); 160 return Solution(); 161 } 161 } 162 162 163 // Estimate the root position by linea 163 // Estimate the root position by linear interpolation 164 x = (y1*x2-y2*x1)/(y1-y2); 164 x = (y1*x2-y2*x1)/(y1-y2); 165 165 166 // Update the value of the function 166 // Update the value of the function 167 y = (*f)(x); 167 y = (*f)(x); 168 168 169 // Update the bracketing interval 169 // Update the bracketing interval 170 if(Math::sign(y) == Math::sign(y1)) { 170 if(Math::sign(y) == Math::sign(y1)) { 171 x1=x; 171 x1=x; 172 y1=y; 172 y1=y; 173 if(lastUpdated==-1) y2 *= 0.5; 173 if(lastUpdated==-1) y2 *= 0.5; 174 lastUpdated = -1; 174 lastUpdated = -1; 175 } else { 175 } else { 176 x2=x; 176 x2=x; 177 y2=y; 177 y2=y; 178 if(lastUpdated==1) y1 *= 0.5; 178 if(lastUpdated==1) y1 *= 0.5; 179 lastUpdated = 1; 179 lastUpdated = 1; 180 } 180 } 181 } 181 } 182 182 183 /* ****************************** 183 /* ****************************** 184 * End of the false-position loop 184 * End of the false-position loop 185 * ******************************/ 185 * ******************************/ 186 186 187 f->cleanUp(true); 187 f->cleanUp(true); 188 return Solution(x,y); 188 return Solution(x,y); 189 } 189 } 190 190 191 } // namespace RootFinder 191 } // namespace RootFinder 192 } 192 } 193 193