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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 std::pair<G4double,G4double> RootFinder::solution;
56 55
57 namespace { << 56 const G4double RootFinder::toleranceY = 1.e-4;
58 57
59 /// \brief Tolerance on the y value << 58 G4bool RootFinder::solve(RootFunctor const * const f, const G4double x0) {
60 const G4double toleranceY = 1.e-4; << 59 // If we already have the solution, do nothing
>> 60 const G4double y0 = (*f)(x0);
>> 61 if( std::abs(y0) < toleranceY ) {
>> 62 solution = std::make_pair(x0,y0);
>> 63 return true;
>> 64 }
61 65
62 /// \brief Maximum number of iterations << 66 // Bracket the root and set the initial values
63 const G4int maxIterations=50; << 67 std::pair<G4double,G4double> bracket = bracketRoot(f,x0);
64 << 68 G4double x1 = bracket.first;
65 /** \brief Bracket the root of the funct << 69 G4double x2 = bracket.second;
66 * << 70 // If x1>x2, it means that we could not bracket the root. Return false.
67 * Tries to find a bracketing value for << 71 if(x1>x2) {
68 * << 72 // Maybe zero is a good solution?
69 * \param f pointer to a RootFunctor << 73 G4double y_at_zero = (*f)(0.);
70 * \param x0 starting value << 74 if(std::abs(y_at_zero)<=toleranceY) {
71 * \return if the root could be brackete << 75 f->cleanUp(true);
72 * bracketing the root, as a pair. If << 76 solution = std::make_pair(0.,y_at_zero);
73 * pair with first > second. << 77 return true;
74 */ << 78 } else {
75 std::pair<G4double,G4double> bracketRoot << 79 WARN("Root-finding algorithm could not bracket the root." << std::endl);
76 G4double y0 = (*f)(x0); << 80 f->cleanUp(false);
77 << 81 return false;
78 const G4double scaleFactor = 1.5; <<
79 <<
80 G4double x1; <<
81 if(x0!=0.) <<
82 x1=scaleFactor*x0; <<
83 else <<
84 x1=1.; <<
85 G4double y1 = (*f)(x1); <<
86 <<
87 if(Math::sign(y0)!=Math::sign(y1)) <<
88 return std::make_pair(x0,x1); <<
89 <<
90 const G4double scaleFactorMinus1 = 1./ <<
91 G4double oldx0, oldx1, oldy1; <<
92 G4int iterations=0; <<
93 do { <<
94 if(iterations > maxIterations) { <<
95 INCL_DEBUG("Could not bracket the <<
96 return std::make_pair((G4double) 1 <<
97 } <<
98 <<
99 oldx0=x0; <<
100 oldx1=x1; <<
101 oldy1=y1; <<
102 <<
103 x0 *= scaleFactorMinus1; <<
104 x1 *= scaleFactor; <<
105 y0 = (*f)(x0); <<
106 y1 = (*f)(x1); <<
107 iterations++; <<
108 } while(Math::sign(y0)==Math::sign(y1) <<
109 <<
110 if(Math::sign(y1)==Math::sign(oldy1)) <<
111 return std::make_pair(x0,oldx0); <<
112 else <<
113 return std::make_pair(oldx1,x1); <<
114 } 82 }
115 <<
116 } 83 }
117 84
118 Solution solve(RootFunctor const * const f << 85 G4double y1 = (*f)(x1);
119 // If we already have the solution, do n << 86 G4double y2 = (*f)(x2);
120 const G4double y0 = (*f)(x0); << 87 G4double x = x1;
121 if( std::abs(y0) < toleranceY ) { << 88 G4double y = y1;
122 return Solution(x0,y0); << 89
>> 90 /* ********************************
>> 91 * Start of the false-position loop
>> 92 * ********************************/
>> 93
>> 94 // Keep track of the last updated interval end (-1=left, 1=right)
>> 95 G4int lastUpdated = 0;
>> 96
>> 97 for(G4int iterations=0; std::abs(y) > toleranceY; iterations++) {
>> 98
>> 99 if(iterations > maxIterations) {
>> 100 WARN("Root-finding algorithm did not converge." << std::endl);
>> 101 f->cleanUp(false);
>> 102 return false;
123 } 103 }
124 104
125 // Bracket the root and set the initial << 105 // Estimate the root position by linear interpolation
126 std::pair<G4double,G4double> bracket = b << 106 x = (y1*x2-y2*x1)/(y1-y2);
127 G4double x1 = bracket.first; << 107
128 G4double x2 = bracket.second; << 108 // Update the value of the function
129 // If x1>x2, it means that we could not << 109 y = (*f)(x);
130 if(x1>x2) { <<
131 // Maybe zero is a good solution? <<
132 G4double y_at_zero = (*f)(0.); <<
133 if(std::abs(y_at_zero)<=toleranceY) { <<
134 f->cleanUp(true); <<
135 return Solution(0.,y_at_zero); <<
136 } else { <<
137 INCL_DEBUG("Root-finding algorithm c <<
138 f->cleanUp(false); <<
139 return Solution(); <<
140 } <<
141 } <<
142 110
143 G4double y1 = (*f)(x1); << 111 // Update the bracketing interval
144 G4double y2 = (*f)(x2); << 112 if(Math::sign(y) == Math::sign(y1)) {
145 G4double x = x1; << 113 x1=x;
146 G4double y = y1; << 114 y1=y;
147 << 115 if(lastUpdated==-1) y2 *= 0.5;
148 /* ******************************** << 116 lastUpdated = -1;
149 * Start of the false-position loop << 117 } else {
150 * ********************************/ << 118 x2=x;
151 << 119 y2=y;
152 // Keep track of the last updated interv << 120 if(lastUpdated==1) y1 *= 0.5;
153 G4int lastUpdated = 0; << 121 lastUpdated = 1;
154 <<
155 for(G4int iterations=0; std::abs(y) > to <<
156 <<
157 if(iterations > maxIterations) { <<
158 INCL_DEBUG("Root-finding algorithm d <<
159 f->cleanUp(false); <<
160 return Solution(); <<
161 } <<
162 <<
163 // Estimate the root position by linea <<
164 x = (y1*x2-y2*x1)/(y1-y2); <<
165 <<
166 // Update the value of the function <<
167 y = (*f)(x); <<
168 <<
169 // Update the bracketing interval <<
170 if(Math::sign(y) == Math::sign(y1)) { <<
171 x1=x; <<
172 y1=y; <<
173 if(lastUpdated==-1) y2 *= 0.5; <<
174 lastUpdated = -1; <<
175 } else { <<
176 x2=x; <<
177 y2=y; <<
178 if(lastUpdated==1) y1 *= 0.5; <<
179 lastUpdated = 1; <<
180 } <<
181 } 122 }
>> 123 }
182 124
183 /* ****************************** << 125 /* ******************************
184 * End of the false-position loop << 126 * End of the false-position loop
185 * ******************************/ << 127 * ******************************/
>> 128
>> 129 solution = std::make_pair(x,y);
>> 130 f->cleanUp(true);
>> 131 return true;
>> 132 }
>> 133
>> 134 std::pair<G4double,G4double> RootFinder::bracketRoot(RootFunctor const * const f, G4double x0) {
>> 135 G4double y0 = (*f)(x0);
>> 136
>> 137 const G4double scaleFactor = 1.5;
>> 138
>> 139 G4double x1;
>> 140 if(x0!=0.)
>> 141 x1=scaleFactor*x0;
>> 142 else
>> 143 x1=1.;
>> 144 G4double y1 = (*f)(x1);
>> 145
>> 146 if(Math::sign(y0)!=Math::sign(y1))
>> 147 return std::make_pair(x0,x1);
>> 148
>> 149 const G4double scaleFactorMinus1 = 1./scaleFactor;
>> 150 G4double oldx0, oldx1, oldy1;
>> 151 G4int iterations=0;
>> 152 do {
>> 153 if(iterations > maxIterations) {
>> 154 DEBUG("Could not bracket the root." << std::endl);
>> 155 return std::make_pair((G4double) 1.,(G4double) -1.);
>> 156 }
186 157
187 f->cleanUp(true); << 158 oldx0=x0;
188 return Solution(x,y); << 159 oldx1=x1;
189 } << 160 oldy1=y1;
>> 161
>> 162 x0 *= scaleFactorMinus1;
>> 163 x1 *= scaleFactor;
>> 164 y0 = (*f)(x0);
>> 165 y1 = (*f)(x1);
>> 166 iterations++;
>> 167 } while(Math::sign(y0)==Math::sign(y1));
>> 168
>> 169 if(Math::sign(y1)==Math::sign(oldy1))
>> 170 return std::make_pair(x0,oldx0);
>> 171 else
>> 172 return std::make_pair(oldx1,x1);
>> 173 }
190 174
191 } // namespace RootFinder <<
192 } 175 }
193 176