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25 // 22 //
26 // G4SimpleIntegration class implementation <<
27 // 23 //
28 // Author: V.Grichine, 26.03.1997 << 24 // $Id: G4SimpleIntegration.cc,v 1.3 2001/07/11 10:00:42 gunter Exp $
29 // ------------------------------------------- << 25 // GEANT4 tag $Name: geant4-05-02-patch-01 $
>> 26 //
>> 27 // Implementation file for simple integration methods
>> 28 //
30 29
31 #include "G4SimpleIntegration.hh" 30 #include "G4SimpleIntegration.hh"
32 #include "globals.hh" <<
33 31
34 G4SimpleIntegration::G4SimpleIntegration(funct << 32
35 : fFunction(pFunction) << 33 G4int G4SimpleIntegration::fMaxDepth = 100 ;
36 {} << 34
37 << 35
38 G4SimpleIntegration::G4SimpleIntegration(funct << 36 G4SimpleIntegration::G4SimpleIntegration( function pFunction )
39 G4dou << 37 {
40 : fFunction(pFunction) << 38 fFunction = pFunction ;
41 , fTolerance(pTolerance) << 39 }
42 {} << 40
43 << 41 G4SimpleIntegration::G4SimpleIntegration( function pFunction,
44 // Simple integration methods << 42 G4double pTolerance)
45 << 43 {
46 G4double G4SimpleIntegration::Trapezoidal(G4do << 44 fFunction = pFunction ;
47 G4in << 45 fTolerance = pTolerance ;
48 { << 46 }
49 G4double Step = (xFinal - xInitial) / iterat << 47
50 G4double mean = (fFunction(xInitial) + fFunc << 48
51 G4double x = xInitial; << 49 G4SimpleIntegration::~G4SimpleIntegration()
52 for(G4int i = 1; i < iterationNumber; ++i) << 50 {
53 { << 51 ;
54 x += Step; << 52 }
55 mean += fFunction(x); << 53
56 } << 54 // Simple integration methods
57 return mean * Step; << 55
58 } << 56 G4double
59 << 57 G4SimpleIntegration::Trapezoidal(G4double xInitial,
60 G4double G4SimpleIntegration::MidPoint(G4doubl << 58 G4double xFinal,
61 G4int i << 59 G4int iterationNumber )
62 { << 60 {
63 G4double Step = (xFinal - xInitial) / iterat << 61 G4int i ;
64 G4double x = xInitial + 0.5 * Step; << 62 G4double Step = (xFinal - xInitial)/iterationNumber ;
65 G4double mean = fFunction(x); << 63 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
66 for(G4int i = 1; i < iterationNumber; ++i) << 64 G4double x = xInitial ;
67 { << 65 for(i=1;i<iterationNumber;i++)
68 x += Step; << 66 {
69 mean += fFunction(x); << 67 x += Step ;
70 } << 68 mean += fFunction(x) ;
71 return mean * Step; << 69 }
72 } << 70 return mean*Step ;
73 << 71 }
74 G4double G4SimpleIntegration::Gauss(G4double x << 72
75 G4int iter << 73 G4double
76 { << 74 G4SimpleIntegration::MidPoint(G4double xInitial,
77 G4double x = 0.; << 75 G4double xFinal,
78 static const G4double root = 1.0 / std::sqrt << 76 G4int iterationNumber )
79 G4double Step = (xFinal - xInit << 77 {
80 G4double delta = Step * root; << 78 G4int i ;
81 G4double mean = 0.0; << 79 G4double Step = (xFinal - xInitial)/iterationNumber ;
82 for(G4int i = 0; i < iterationNumber; ++i) << 80 G4double x = xInitial + 0.5*Step;
83 { << 81 G4double mean = fFunction(x) ;
84 x = (2 * i + 1) * Step; << 82 for(i=1;i<iterationNumber;i++)
85 mean += (fFunction(x + delta) + fFunction( << 83 {
86 } << 84 x += Step ;
87 return mean * Step; << 85 mean += fFunction(x) ;
88 } << 86 }
89 << 87 return mean*Step ;
90 G4double G4SimpleIntegration::Simpson(G4double << 88 }
91 G4int it << 89
92 { << 90 G4double
93 G4double Step = (xFinal - xInitial) / itera << 91 G4SimpleIntegration::Gauss(G4double xInitial,
94 G4double x = xInitial; << 92 G4double xFinal,
95 G4double xPlus = xInitial + 0.5 * Step; << 93 G4int iterationNumber )
96 G4double mean = (fFunction(xInitial) + fFun << 94 {
97 G4double sum = fFunction(xPlus); << 95 G4int i ;
98 for(G4int i = 1; i < iterationNumber; ++i) << 96 G4double x ;
99 { << 97 static G4double root = 1.0/sqrt(3.0) ;
100 x += Step; << 98 G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ;
101 xPlus += Step; << 99 G4double delta = Step*root ;
102 mean += fFunction(x); << 100 G4double mean = 0.0 ;
103 sum += fFunction(xPlus); << 101 for(i=0;i<iterationNumber;i++)
104 } << 102 {
105 mean += 2.0 * sum; << 103 x = (2*i + 1)*Step ;
106 return mean * Step / 3.0; << 104 mean += (fFunction(x+delta) + fFunction(x-delta)) ;
107 } << 105 }
108 << 106 return mean*Step ;
109 // Adaptive Gauss integration << 107 }
110 << 108
111 G4double G4SimpleIntegration::AdaptGaussIntegr << 109 G4double
112 << 110 G4SimpleIntegration::Simpson(G4double xInitial,
113 { << 111 G4double xFinal,
114 G4int depth = 0; << 112 G4int iterationNumber )
115 G4double sum = 0.0; << 113 {
116 AdaptGauss(xInitial, xFinal, sum, depth); << 114 G4int i ;
117 return sum; << 115 G4double Step = (xFinal - xInitial)/iterationNumber ;
118 } << 116 G4double x = xInitial ;
119 << 117 G4double xPlus = xInitial + 0.5*Step ;
120 G4double G4SimpleIntegration::Gauss(G4double x << 118 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
121 { << 119 G4double sum = fFunction(xPlus) ;
122 static const G4double root = 1.0 / std::sqrt << 120 for(i=1;i<iterationNumber;i++)
123 << 121 {
124 G4double xMean = (xInitial + xFinal) / 2.0; << 122 x += Step ;
125 G4double Step = (xFinal - xInitial) / 2.0; << 123 xPlus += Step ;
126 G4double delta = Step * root; << 124 mean += fFunction(x) ;
127 G4double sum = (fFunction(xMean + delta) + << 125 sum += fFunction(xPlus) ;
128 << 126 }
129 return sum * Step; << 127 mean += 2.0*sum ;
130 } << 128 return mean*Step/3.0 ;
131 << 129 }
132 void G4SimpleIntegration::AdaptGauss(G4double << 130
133 G4double& << 131
134 { << 132
135 if(depth > fMaxDepth) << 133 // Adaptive Gauss integration
136 { << 134
137 G4Exception("G4SimpleIntegration::AdaptGau << 135 G4double
138 "Function varies too rapidly ! << 136 G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial,
139 } << 137 G4double xFinal )
140 G4double xMean = (xInitial + xFinal) / 2 << 138 {
141 G4double leftHalf = Gauss(xInitial, xMean); << 139 G4int depth = 0 ;
142 G4double rightHalf = Gauss(xMean, xFinal); << 140 G4double sum = 0.0 ;
143 G4double full = Gauss(xInitial, xFinal) << 141 AdaptGauss(xInitial,xFinal,sum,depth) ;
144 if(std::fabs(leftHalf + rightHalf - full) < << 142 return sum ;
145 { << 143 }
146 sum += full; << 144
147 } << 145
148 else << 146 G4double
149 { << 147 G4SimpleIntegration::Gauss( G4double xInitial,
150 ++depth; << 148 G4double xFinal )
151 AdaptGauss(xInitial, xMean, sum, depth); << 149 {
152 AdaptGauss(xMean, xFinal, sum, depth); << 150 static G4double root = 1.0/sqrt(3.0) ;
153 } << 151
>> 152 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 153 G4double Step = (xFinal - xInitial)/2.0 ;
>> 154 G4double delta = Step*root ;
>> 155 G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ;
>> 156
>> 157 return sum*Step ;
>> 158 }
>> 159
>> 160
>> 161 void
>> 162 G4SimpleIntegration::AdaptGauss( G4double xInitial,
>> 163 G4double xFinal,
>> 164 G4double& sum,
>> 165 G4int& depth )
>> 166 {
>> 167 if(depth >fMaxDepth)
>> 168 {
>> 169 G4Exception("Function varies too rapidly in G4SimpleIntegration::AdaptGauss") ;
>> 170 }
>> 171 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 172 G4double leftHalf = Gauss(xInitial,xMean) ;
>> 173 G4double rightHalf = Gauss(xMean,xFinal) ;
>> 174 G4double full = Gauss(xInitial,xFinal) ;
>> 175 if(fabs(leftHalf+rightHalf-full) < fTolerance)
>> 176 {
>> 177 sum += full ;
>> 178 }
>> 179 else
>> 180 {
>> 181 depth++ ;
>> 182 AdaptGauss(xInitial,xMean,sum,depth) ;
>> 183 AdaptGauss(xMean,xFinal,sum,depth) ;
>> 184 }
154 } 185 }
155 186