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25 // 25 //
26 // G4SimpleIntegration class implementation <<
27 // 26 //
28 // Author: V.Grichine, 26.03.1997 << 27 // $Id: G4SimpleIntegration.cc,v 1.7 2006-06-29 19:00:21 gunter Exp $
29 // ------------------------------------------- << 28 // GEANT4 tag $Name: not supported by cvs2svn $
>> 29 //
>> 30 // Implementation file for simple integration methods
>> 31 //
30 32
31 #include "G4SimpleIntegration.hh" <<
32 #include "globals.hh" 33 #include "globals.hh"
>> 34 #include "G4SimpleIntegration.hh"
>> 35
>> 36
>> 37 G4int G4SimpleIntegration::fMaxDepth = 100 ;
>> 38
33 39
34 G4SimpleIntegration::G4SimpleIntegration(funct << 40 G4SimpleIntegration::G4SimpleIntegration( function pFunction )
35 : fFunction(pFunction) << 41 : fFunction(pFunction),
36 {} << 42 fTolerance(.0001)
37 << 43 {
38 G4SimpleIntegration::G4SimpleIntegration(funct << 44 }
39 G4dou << 45
40 : fFunction(pFunction) << 46 G4SimpleIntegration::G4SimpleIntegration( function pFunction,
41 , fTolerance(pTolerance) << 47 G4double pTolerance)
42 {} << 48 : fFunction(pFunction),
43 << 49 fTolerance(pTolerance)
44 // Simple integration methods << 50 {
45 << 51 }
46 G4double G4SimpleIntegration::Trapezoidal(G4do << 52
47 G4in << 53
48 { << 54 G4SimpleIntegration::~G4SimpleIntegration()
49 G4double Step = (xFinal - xInitial) / iterat << 55 {
50 G4double mean = (fFunction(xInitial) + fFunc << 56 }
51 G4double x = xInitial; << 57
52 for(G4int i = 1; i < iterationNumber; ++i) << 58 // Simple integration methods
53 { << 59
54 x += Step; << 60 G4double
55 mean += fFunction(x); << 61 G4SimpleIntegration::Trapezoidal(G4double xInitial,
56 } << 62 G4double xFinal,
57 return mean * Step; << 63 G4int iterationNumber )
58 } << 64 {
59 << 65 G4double Step = (xFinal - xInitial)/iterationNumber ;
60 G4double G4SimpleIntegration::MidPoint(G4doubl << 66 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
61 G4int i << 67 G4double x = xInitial ;
62 { << 68 for(G4int i=1;i<iterationNumber;i++)
63 G4double Step = (xFinal - xInitial) / iterat << 69 {
64 G4double x = xInitial + 0.5 * Step; << 70 x += Step ;
65 G4double mean = fFunction(x); << 71 mean += fFunction(x) ;
66 for(G4int i = 1; i < iterationNumber; ++i) << 72 }
67 { << 73 return mean*Step ;
68 x += Step; << 74 }
69 mean += fFunction(x); << 75
70 } << 76 G4double
71 return mean * Step; << 77 G4SimpleIntegration::MidPoint(G4double xInitial,
72 } << 78 G4double xFinal,
73 << 79 G4int iterationNumber )
74 G4double G4SimpleIntegration::Gauss(G4double x << 80 {
75 G4int iter << 81 G4double Step = (xFinal - xInitial)/iterationNumber ;
76 { << 82 G4double x = xInitial + 0.5*Step;
77 G4double x = 0.; << 83 G4double mean = fFunction(x) ;
78 static const G4double root = 1.0 / std::sqrt << 84 for(G4int i=1;i<iterationNumber;i++)
79 G4double Step = (xFinal - xInit << 85 {
80 G4double delta = Step * root; << 86 x += Step ;
81 G4double mean = 0.0; << 87 mean += fFunction(x) ;
82 for(G4int i = 0; i < iterationNumber; ++i) << 88 }
83 { << 89 return mean*Step ;
84 x = (2 * i + 1) * Step; << 90 }
85 mean += (fFunction(x + delta) + fFunction( << 91
86 } << 92 G4double
87 return mean * Step; << 93 G4SimpleIntegration::Gauss(G4double xInitial,
88 } << 94 G4double xFinal,
89 << 95 G4int iterationNumber )
90 G4double G4SimpleIntegration::Simpson(G4double << 96 {
91 G4int it << 97 G4double x=0.;
92 { << 98 static G4double root = 1.0/std::sqrt(3.0) ;
93 G4double Step = (xFinal - xInitial) / itera << 99 G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ;
94 G4double x = xInitial; << 100 G4double delta = Step*root ;
95 G4double xPlus = xInitial + 0.5 * Step; << 101 G4double mean = 0.0 ;
96 G4double mean = (fFunction(xInitial) + fFun << 102 for(G4int i=0;i<iterationNumber;i++)
97 G4double sum = fFunction(xPlus); << 103 {
98 for(G4int i = 1; i < iterationNumber; ++i) << 104 x = (2*i + 1)*Step ;
99 { << 105 mean += (fFunction(x+delta) + fFunction(x-delta)) ;
100 x += Step; << 106 }
101 xPlus += Step; << 107 return mean*Step ;
102 mean += fFunction(x); << 108 }
103 sum += fFunction(xPlus); << 109
104 } << 110 G4double
105 mean += 2.0 * sum; << 111 G4SimpleIntegration::Simpson(G4double xInitial,
106 return mean * Step / 3.0; << 112 G4double xFinal,
107 } << 113 G4int iterationNumber )
108 << 114 {
109 // Adaptive Gauss integration << 115 G4double Step = (xFinal - xInitial)/iterationNumber ;
110 << 116 G4double x = xInitial ;
111 G4double G4SimpleIntegration::AdaptGaussIntegr << 117 G4double xPlus = xInitial + 0.5*Step ;
112 << 118 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
113 { << 119 G4double sum = fFunction(xPlus) ;
114 G4int depth = 0; << 120 for(G4int i=1;i<iterationNumber;i++)
115 G4double sum = 0.0; << 121 {
116 AdaptGauss(xInitial, xFinal, sum, depth); << 122 x += Step ;
117 return sum; << 123 xPlus += Step ;
118 } << 124 mean += fFunction(x) ;
119 << 125 sum += fFunction(xPlus) ;
120 G4double G4SimpleIntegration::Gauss(G4double x << 126 }
121 { << 127 mean += 2.0*sum ;
122 static const G4double root = 1.0 / std::sqrt << 128 return mean*Step/3.0 ;
123 << 129 }
124 G4double xMean = (xInitial + xFinal) / 2.0; << 130
125 G4double Step = (xFinal - xInitial) / 2.0; << 131
126 G4double delta = Step * root; << 132
127 G4double sum = (fFunction(xMean + delta) + << 133 // Adaptive Gauss integration
128 << 134
129 return sum * Step; << 135 G4double
130 } << 136 G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial,
131 << 137 G4double xFinal )
132 void G4SimpleIntegration::AdaptGauss(G4double << 138 {
133 G4double& << 139 G4int depth = 0 ;
134 { << 140 G4double sum = 0.0 ;
135 if(depth > fMaxDepth) << 141 AdaptGauss(xInitial,xFinal,sum,depth) ;
136 { << 142 return sum ;
137 G4Exception("G4SimpleIntegration::AdaptGau << 143 }
138 "Function varies too rapidly ! << 144
139 } << 145
140 G4double xMean = (xInitial + xFinal) / 2 << 146 G4double
141 G4double leftHalf = Gauss(xInitial, xMean); << 147 G4SimpleIntegration::Gauss( G4double xInitial,
142 G4double rightHalf = Gauss(xMean, xFinal); << 148 G4double xFinal )
143 G4double full = Gauss(xInitial, xFinal) << 149 {
144 if(std::fabs(leftHalf + rightHalf - full) < << 150 static G4double root = 1.0/std::sqrt(3.0) ;
145 { << 151
146 sum += full; << 152 G4double xMean = (xInitial + xFinal)/2.0 ;
147 } << 153 G4double Step = (xFinal - xInitial)/2.0 ;
148 else << 154 G4double delta = Step*root ;
149 { << 155 G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ;
150 ++depth; << 156
151 AdaptGauss(xInitial, xMean, sum, depth); << 157 return sum*Step ;
152 AdaptGauss(xMean, xFinal, sum, depth); << 158 }
153 } << 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("G4SimpleIntegration::AdaptGauss()", "Error",
>> 170 FatalException, "Function varies too rapidly !") ;
>> 171 }
>> 172 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 173 G4double leftHalf = Gauss(xInitial,xMean) ;
>> 174 G4double rightHalf = Gauss(xMean,xFinal) ;
>> 175 G4double full = Gauss(xInitial,xFinal) ;
>> 176 if(std::fabs(leftHalf+rightHalf-full) < fTolerance)
>> 177 {
>> 178 sum += full ;
>> 179 }
>> 180 else
>> 181 {
>> 182 depth++ ;
>> 183 AdaptGauss(xInitial,xMean,sum,depth) ;
>> 184 AdaptGauss(xMean,xFinal,sum,depth) ;
>> 185 }
154 } 186 }
155 187