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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