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Geant4/global/HEPNumerics/src/G4SimpleIntegration.cc

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Differences between /global/HEPNumerics/src/G4SimpleIntegration.cc (Version 11.3.0) and /global/HEPNumerics/src/G4SimpleIntegration.cc (Version 10.7.p1)


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 24 // *******************************************     24 // ********************************************************************
 25 //                                                 25 //
 26 // G4SimpleIntegration class implementation        26 // G4SimpleIntegration class implementation
 27 //                                                 27 //
 28 // Author: V.Grichine, 26.03.1997                  28 // Author: V.Grichine, 26.03.1997
 29 // -------------------------------------------     29 // --------------------------------------------------------------------
 30                                                    30 
 31 #include "G4SimpleIntegration.hh"                  31 #include "G4SimpleIntegration.hh"
 32 #include "globals.hh"                              32 #include "globals.hh"
 33                                                    33 
 34 G4SimpleIntegration::G4SimpleIntegration(funct     34 G4SimpleIntegration::G4SimpleIntegration(function pFunction)
 35   : fFunction(pFunction)                           35   : fFunction(pFunction)
 36 {}                                                 36 {}
 37                                                    37 
 38 G4SimpleIntegration::G4SimpleIntegration(funct     38 G4SimpleIntegration::G4SimpleIntegration(function pFunction,
 39                                          G4dou     39                                          G4double pTolerance)
 40   : fFunction(pFunction)                           40   : fFunction(pFunction)
 41   , fTolerance(pTolerance)                         41   , fTolerance(pTolerance)
 42 {}                                                 42 {}
 43                                                    43 
                                                   >>  44 G4SimpleIntegration::~G4SimpleIntegration() {}
                                                   >>  45 
 44 // Simple integration methods                      46 // Simple integration methods
 45                                                    47 
 46 G4double G4SimpleIntegration::Trapezoidal(G4do     48 G4double G4SimpleIntegration::Trapezoidal(G4double xInitial, G4double xFinal,
 47                                           G4in     49                                           G4int iterationNumber)
 48 {                                                  50 {
 49   G4double Step = (xFinal - xInitial) / iterat     51   G4double Step = (xFinal - xInitial) / iterationNumber;
 50   G4double mean = (fFunction(xInitial) + fFunc     52   G4double mean = (fFunction(xInitial) + fFunction(xFinal)) * 0.5;
 51   G4double x    = xInitial;                        53   G4double x    = xInitial;
 52   for(G4int i = 1; i < iterationNumber; ++i)       54   for(G4int i = 1; i < iterationNumber; ++i)
 53   {                                                55   {
 54     x += Step;                                     56     x += Step;
 55     mean += fFunction(x);                          57     mean += fFunction(x);
 56   }                                                58   }
 57   return mean * Step;                              59   return mean * Step;
 58 }                                                  60 }
 59                                                    61 
 60 G4double G4SimpleIntegration::MidPoint(G4doubl     62 G4double G4SimpleIntegration::MidPoint(G4double xInitial, G4double xFinal,
 61                                        G4int i     63                                        G4int iterationNumber)
 62 {                                                  64 {
 63   G4double Step = (xFinal - xInitial) / iterat     65   G4double Step = (xFinal - xInitial) / iterationNumber;
 64   G4double x    = xInitial + 0.5 * Step;           66   G4double x    = xInitial + 0.5 * Step;
 65   G4double mean = fFunction(x);                    67   G4double mean = fFunction(x);
 66   for(G4int i = 1; i < iterationNumber; ++i)       68   for(G4int i = 1; i < iterationNumber; ++i)
 67   {                                                69   {
 68     x += Step;                                     70     x += Step;
 69     mean += fFunction(x);                          71     mean += fFunction(x);
 70   }                                                72   }
 71   return mean * Step;                              73   return mean * Step;
 72 }                                                  74 }
 73                                                    75 
 74 G4double G4SimpleIntegration::Gauss(G4double x     76 G4double G4SimpleIntegration::Gauss(G4double xInitial, G4double xFinal,
 75                                     G4int iter     77                                     G4int iterationNumber)
 76 {                                                  78 {
 77   G4double x                 = 0.;                 79   G4double x                 = 0.;
 78   static const G4double root = 1.0 / std::sqrt     80   static const G4double root = 1.0 / std::sqrt(3.0);
 79   G4double Step              = (xFinal - xInit     81   G4double Step              = (xFinal - xInitial) / (2.0 * iterationNumber);
 80   G4double delta             = Step * root;        82   G4double delta             = Step * root;
 81   G4double mean              = 0.0;                83   G4double mean              = 0.0;
 82   for(G4int i = 0; i < iterationNumber; ++i)       84   for(G4int i = 0; i < iterationNumber; ++i)
 83   {                                                85   {
 84     x = (2 * i + 1) * Step;                        86     x = (2 * i + 1) * Step;
 85     mean += (fFunction(x + delta) + fFunction(     87     mean += (fFunction(x + delta) + fFunction(x - delta));
 86   }                                                88   }
 87   return mean * Step;                              89   return mean * Step;
 88 }                                                  90 }
 89                                                    91 
 90 G4double G4SimpleIntegration::Simpson(G4double     92 G4double G4SimpleIntegration::Simpson(G4double xInitial, G4double xFinal,
 91                                       G4int it     93                                       G4int iterationNumber)
 92 {                                                  94 {
 93   G4double Step  = (xFinal - xInitial) / itera     95   G4double Step  = (xFinal - xInitial) / iterationNumber;
 94   G4double x     = xInitial;                       96   G4double x     = xInitial;
 95   G4double xPlus = xInitial + 0.5 * Step;          97   G4double xPlus = xInitial + 0.5 * Step;
 96   G4double mean  = (fFunction(xInitial) + fFun     98   G4double mean  = (fFunction(xInitial) + fFunction(xFinal)) * 0.5;
 97   G4double sum   = fFunction(xPlus);               99   G4double sum   = fFunction(xPlus);
 98   for(G4int i = 1; i < iterationNumber; ++i)      100   for(G4int i = 1; i < iterationNumber; ++i)
 99   {                                               101   {
100     x += Step;                                    102     x += Step;
101     xPlus += Step;                                103     xPlus += Step;
102     mean += fFunction(x);                         104     mean += fFunction(x);
103     sum += fFunction(xPlus);                      105     sum += fFunction(xPlus);
104   }                                               106   }
105   mean += 2.0 * sum;                              107   mean += 2.0 * sum;
106   return mean * Step / 3.0;                       108   return mean * Step / 3.0;
107 }                                                 109 }
108                                                   110 
109 // Adaptive Gauss integration                     111 // Adaptive Gauss integration
110                                                   112 
111 G4double G4SimpleIntegration::AdaptGaussIntegr    113 G4double G4SimpleIntegration::AdaptGaussIntegration(G4double xInitial,
112                                                   114                                                     G4double xFinal)
113 {                                                 115 {
114   G4int depth  = 0;                               116   G4int depth  = 0;
115   G4double sum = 0.0;                             117   G4double sum = 0.0;
116   AdaptGauss(xInitial, xFinal, sum, depth);       118   AdaptGauss(xInitial, xFinal, sum, depth);
117   return sum;                                     119   return sum;
118 }                                                 120 }
119                                                   121 
120 G4double G4SimpleIntegration::Gauss(G4double x    122 G4double G4SimpleIntegration::Gauss(G4double xInitial, G4double xFinal)
121 {                                                 123 {
122   static const G4double root = 1.0 / std::sqrt    124   static const G4double root = 1.0 / std::sqrt(3.0);
123                                                   125 
124   G4double xMean = (xInitial + xFinal) / 2.0;     126   G4double xMean = (xInitial + xFinal) / 2.0;
125   G4double Step  = (xFinal - xInitial) / 2.0;     127   G4double Step  = (xFinal - xInitial) / 2.0;
126   G4double delta = Step * root;                   128   G4double delta = Step * root;
127   G4double sum   = (fFunction(xMean + delta) +    129   G4double sum   = (fFunction(xMean + delta) + fFunction(xMean - delta));
128                                                   130 
129   return sum * Step;                              131   return sum * Step;
130 }                                                 132 }
131                                                   133 
132 void G4SimpleIntegration::AdaptGauss(G4double     134 void G4SimpleIntegration::AdaptGauss(G4double xInitial, G4double xFinal,
133                                      G4double&    135                                      G4double& sum, G4int& depth)
134 {                                                 136 {
135   if(depth > fMaxDepth)                           137   if(depth > fMaxDepth)
136   {                                               138   {
137     G4Exception("G4SimpleIntegration::AdaptGau    139     G4Exception("G4SimpleIntegration::AdaptGauss()", "Error", FatalException,
138                 "Function varies too rapidly !    140                 "Function varies too rapidly !");
139   }                                               141   }
140   G4double xMean     = (xInitial + xFinal) / 2    142   G4double xMean     = (xInitial + xFinal) / 2.0;
141   G4double leftHalf  = Gauss(xInitial, xMean);    143   G4double leftHalf  = Gauss(xInitial, xMean);
142   G4double rightHalf = Gauss(xMean, xFinal);      144   G4double rightHalf = Gauss(xMean, xFinal);
143   G4double full      = Gauss(xInitial, xFinal)    145   G4double full      = Gauss(xInitial, xFinal);
144   if(std::fabs(leftHalf + rightHalf - full) <     146   if(std::fabs(leftHalf + rightHalf - full) < fTolerance)
145   {                                               147   {
146     sum += full;                                  148     sum += full;
147   }                                               149   }
148   else                                            150   else
149   {                                               151   {
150     ++depth;                                      152     ++depth;
151     AdaptGauss(xInitial, xMean, sum, depth);      153     AdaptGauss(xInitial, xMean, sum, depth);
152     AdaptGauss(xMean, xFinal, sum, depth);        154     AdaptGauss(xMean, xFinal, sum, depth);
153   }                                               155   }
154 }                                                 156 }
155                                                   157