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25 // 7 //
26 // G4SimpleIntegration class implementation << 8 // $Id: G4SimpleIntegration.cc,v 1.2 1999/11/16 17:31:11 gcosmo Exp $
>> 9 // GEANT4 tag $Name: geant4-02-00 $
>> 10 //
>> 11 // Implementation file for simple integration methods
27 // 12 //
28 // Author: V.Grichine, 26.03.1997 <<
29 // ------------------------------------------- <<
30 13
31 #include "G4SimpleIntegration.hh" 14 #include "G4SimpleIntegration.hh"
32 #include "globals.hh" <<
33 15
34 G4SimpleIntegration::G4SimpleIntegration(funct << 16
35 : fFunction(pFunction) << 17 G4int G4SimpleIntegration::fMaxDepth = 100 ;
36 {} << 18
37 << 19
38 G4SimpleIntegration::G4SimpleIntegration(funct << 20 G4SimpleIntegration::G4SimpleIntegration( function pFunction )
39 G4dou << 21 {
40 : fFunction(pFunction) << 22 fFunction = pFunction ;
41 , fTolerance(pTolerance) << 23 }
42 {} << 24
43 << 25 G4SimpleIntegration::G4SimpleIntegration( function pFunction,
44 // Simple integration methods << 26 G4double pTolerance)
45 << 27 {
46 G4double G4SimpleIntegration::Trapezoidal(G4do << 28 fFunction = pFunction ;
47 G4in << 29 fTolerance = pTolerance ;
48 { << 30 }
49 G4double Step = (xFinal - xInitial) / iterat << 31
50 G4double mean = (fFunction(xInitial) + fFunc << 32
51 G4double x = xInitial; << 33 G4SimpleIntegration::~G4SimpleIntegration()
52 for(G4int i = 1; i < iterationNumber; ++i) << 34 {
53 { << 35 ;
54 x += Step; << 36 }
55 mean += fFunction(x); << 37
56 } << 38 // Simple integration methods
57 return mean * Step; << 39
58 } << 40 G4double
59 << 41 G4SimpleIntegration::Trapezoidal(G4double xInitial,
60 G4double G4SimpleIntegration::MidPoint(G4doubl << 42 G4double xFinal,
61 G4int i << 43 G4int iterationNumber )
62 { << 44 {
63 G4double Step = (xFinal - xInitial) / iterat << 45 G4int i ;
64 G4double x = xInitial + 0.5 * Step; << 46 G4double Step = (xFinal - xInitial)/iterationNumber ;
65 G4double mean = fFunction(x); << 47 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
66 for(G4int i = 1; i < iterationNumber; ++i) << 48 G4double x = xInitial ;
67 { << 49 for(i=1;i<iterationNumber;i++)
68 x += Step; << 50 {
69 mean += fFunction(x); << 51 x += Step ;
70 } << 52 mean += fFunction(x) ;
71 return mean * Step; << 53 }
72 } << 54 return mean*Step ;
73 << 55 }
74 G4double G4SimpleIntegration::Gauss(G4double x << 56
75 G4int iter << 57 G4double
76 { << 58 G4SimpleIntegration::MidPoint(G4double xInitial,
77 G4double x = 0.; << 59 G4double xFinal,
78 static const G4double root = 1.0 / std::sqrt << 60 G4int iterationNumber )
79 G4double Step = (xFinal - xInit << 61 {
80 G4double delta = Step * root; << 62 G4int i ;
81 G4double mean = 0.0; << 63 G4double Step = (xFinal - xInitial)/iterationNumber ;
82 for(G4int i = 0; i < iterationNumber; ++i) << 64 G4double x = xInitial + 0.5*Step;
83 { << 65 G4double mean = fFunction(x) ;
84 x = (2 * i + 1) * Step; << 66 for(i=1;i<iterationNumber;i++)
85 mean += (fFunction(x + delta) + fFunction( << 67 {
86 } << 68 x += Step ;
87 return mean * Step; << 69 mean += fFunction(x) ;
88 } << 70 }
89 << 71 return mean*Step ;
90 G4double G4SimpleIntegration::Simpson(G4double << 72 }
91 G4int it << 73
92 { << 74 G4double
93 G4double Step = (xFinal - xInitial) / itera << 75 G4SimpleIntegration::Gauss(G4double xInitial,
94 G4double x = xInitial; << 76 G4double xFinal,
95 G4double xPlus = xInitial + 0.5 * Step; << 77 G4int iterationNumber )
96 G4double mean = (fFunction(xInitial) + fFun << 78 {
97 G4double sum = fFunction(xPlus); << 79 G4int i ;
98 for(G4int i = 1; i < iterationNumber; ++i) << 80 G4double x ;
99 { << 81 static G4double root = 1.0/sqrt(3.0) ;
100 x += Step; << 82 G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ;
101 xPlus += Step; << 83 G4double delta = Step*root ;
102 mean += fFunction(x); << 84 G4double mean = 0.0 ;
103 sum += fFunction(xPlus); << 85 for(i=0;i<iterationNumber;i++)
104 } << 86 {
105 mean += 2.0 * sum; << 87 x = (2*i + 1)*Step ;
106 return mean * Step / 3.0; << 88 mean += (fFunction(x+delta) + fFunction(x-delta)) ;
107 } << 89 }
108 << 90 return mean*Step ;
109 // Adaptive Gauss integration << 91 }
110 << 92
111 G4double G4SimpleIntegration::AdaptGaussIntegr << 93 G4double
112 << 94 G4SimpleIntegration::Simpson(G4double xInitial,
113 { << 95 G4double xFinal,
114 G4int depth = 0; << 96 G4int iterationNumber )
115 G4double sum = 0.0; << 97 {
116 AdaptGauss(xInitial, xFinal, sum, depth); << 98 G4int i ;
117 return sum; << 99 G4double Step = (xFinal - xInitial)/iterationNumber ;
118 } << 100 G4double x = xInitial ;
119 << 101 G4double xPlus = xInitial + 0.5*Step ;
120 G4double G4SimpleIntegration::Gauss(G4double x << 102 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
121 { << 103 G4double sum = fFunction(xPlus) ;
122 static const G4double root = 1.0 / std::sqrt << 104 for(i=1;i<iterationNumber;i++)
123 << 105 {
124 G4double xMean = (xInitial + xFinal) / 2.0; << 106 x += Step ;
125 G4double Step = (xFinal - xInitial) / 2.0; << 107 xPlus += Step ;
126 G4double delta = Step * root; << 108 mean += fFunction(x) ;
127 G4double sum = (fFunction(xMean + delta) + << 109 sum += fFunction(xPlus) ;
128 << 110 }
129 return sum * Step; << 111 mean += 2.0*sum ;
130 } << 112 return mean*Step/3.0 ;
131 << 113 }
132 void G4SimpleIntegration::AdaptGauss(G4double << 114
133 G4double& << 115
134 { << 116
135 if(depth > fMaxDepth) << 117 // Adaptive Gauss integration
136 { << 118
137 G4Exception("G4SimpleIntegration::AdaptGau << 119 G4double
138 "Function varies too rapidly ! << 120 G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial,
139 } << 121 G4double xFinal )
140 G4double xMean = (xInitial + xFinal) / 2 << 122 {
141 G4double leftHalf = Gauss(xInitial, xMean); << 123 G4int depth = 0 ;
142 G4double rightHalf = Gauss(xMean, xFinal); << 124 G4double sum = 0.0 ;
143 G4double full = Gauss(xInitial, xFinal) << 125 AdaptGauss(xInitial,xFinal,sum,depth) ;
144 if(std::fabs(leftHalf + rightHalf - full) < << 126 return sum ;
145 { << 127 }
146 sum += full; << 128
147 } << 129
148 else << 130 G4double
149 { << 131 G4SimpleIntegration::Gauss( G4double xInitial,
150 ++depth; << 132 G4double xFinal )
151 AdaptGauss(xInitial, xMean, sum, depth); << 133 {
152 AdaptGauss(xMean, xFinal, sum, depth); << 134 static G4double root = 1.0/sqrt(3.0) ;
153 } << 135
>> 136 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 137 G4double Step = (xFinal - xInitial)/2.0 ;
>> 138 G4double delta = Step*root ;
>> 139 G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ;
>> 140
>> 141 return sum*Step ;
>> 142 }
>> 143
>> 144
>> 145 void
>> 146 G4SimpleIntegration::AdaptGauss( G4double xInitial,
>> 147 G4double xFinal,
>> 148 G4double& sum,
>> 149 G4int& depth )
>> 150 {
>> 151 if(depth >fMaxDepth)
>> 152 {
>> 153 G4Exception("Function varies too rapidly in G4SimpleIntegration::AdaptGauss") ;
>> 154 }
>> 155 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 156 G4double leftHalf = Gauss(xInitial,xMean) ;
>> 157 G4double rightHalf = Gauss(xMean,xFinal) ;
>> 158 G4double full = Gauss(xInitial,xFinal) ;
>> 159 if(fabs(leftHalf+rightHalf-full) < fTolerance)
>> 160 {
>> 161 sum += full ;
>> 162 }
>> 163 else
>> 164 {
>> 165 depth++ ;
>> 166 AdaptGauss(xInitial,xMean,sum,depth) ;
>> 167 AdaptGauss(xMean,xFinal,sum,depth) ;
>> 168 }
154 } 169 }
155 170