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