Geant4  10.03.p03
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G4INCLRootFinder.cc
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25 //
26 // INCL++ intra-nuclear cascade model
27 // Alain Boudard, CEA-Saclay, France
28 // Joseph Cugnon, University of Liege, Belgium
29 // Jean-Christophe David, CEA-Saclay, France
30 // Pekka Kaitaniemi, CEA-Saclay, France, and Helsinki Institute of Physics, Finland
31 // Sylvie Leray, CEA-Saclay, France
32 // Davide Mancusi, CEA-Saclay, France
33 //
34 #define INCLXX_IN_GEANT4_MODE 1
35 
36 #include "globals.hh"
37 
47 #include "G4INCLRootFinder.hh"
48 #include "G4INCLGlobals.hh"
49 #include "G4INCLLogger.hh"
50 #include <utility>
51 #include <cmath>
52 
53 namespace G4INCL {
54 
55  namespace RootFinder {
56 
57  namespace {
58 
60  const G4double toleranceY = 1.e-4;
61 
63  const G4int maxIterations=50;
64 
75  std::pair<G4double,G4double> bracketRoot(RootFunctor const * const f, G4double x0) {
76  G4double y0 = (*f)(x0);
77 
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./scaleFactor;
91  G4double oldx0, oldx1, oldy1;
92  G4int iterations=0;
93  do {
94  if(iterations > maxIterations) {
95  INCL_DEBUG("Could not bracket the root." << '\n');
96  return std::make_pair((G4double) 1.,(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)); /* Loop checking, 10.07.2015, D.Mancusi */
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  }
115 
116  }
117 
118  Solution solve(RootFunctor const * const f, const G4double x0) {
119  // If we already have the solution, do nothing
120  const G4double y0 = (*f)(x0);
121  if( std::abs(y0) < toleranceY ) {
122  return Solution(x0,y0);
123  }
124 
125  // Bracket the root and set the initial values
126  std::pair<G4double,G4double> bracket = bracketRoot(f,x0);
127  G4double x1 = bracket.first;
128  G4double x2 = bracket.second;
129  // If x1>x2, it means that we could not bracket the root. Return false.
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 could not bracket the root." << '\n');
138  f->cleanUp(false);
139  return Solution();
140  }
141  }
142 
143  G4double y1 = (*f)(x1);
144  G4double y2 = (*f)(x2);
145  G4double x = x1;
146  G4double y = y1;
147 
148  /* ********************************
149  * Start of the false-position loop
150  * ********************************/
151 
152  // Keep track of the last updated interval end (-1=left, 1=right)
153  G4int lastUpdated = 0;
154 
155  for(G4int iterations=0; std::abs(y) > toleranceY; iterations++) {
156 
157  if(iterations > maxIterations) {
158  INCL_DEBUG("Root-finding algorithm did not converge." << '\n');
159  f->cleanUp(false);
160  return Solution();
161  }
162 
163  // Estimate the root position by linear interpolation
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  }
182 
183  /* ******************************
184  * End of the false-position loop
185  * ******************************/
186 
187  f->cleanUp(true);
188  return Solution(x,y);
189  }
190 
191  } // namespace RootFinder
192 }
virtual void cleanUp(const G4bool success) const =0
tuple x
Definition: test.py:50
int G4int
Definition: G4Types.hh:78
Solution solve(RootFunctor const *const f, const G4double x0)
Numerically solve a one-dimensional equation.
double G4double
Definition: G4Types.hh:76
#define INCL_DEBUG(x)
G4int sign(const T t)
Static root-finder algorithm.