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25 // 25 //
26 // G4SimpleIntegration class implementation <<
27 // 26 //
28 // Author: V.Grichine, 26.03.1997 << 27 // $Id: G4SimpleIntegration.cc 69546 2013-05-08 09:50:34Z gcosmo $
29 // ------------------------------------------- << 28 //
>> 29 // Implementation file for simple integration methods
>> 30 //
30 31
31 #include "G4SimpleIntegration.hh" <<
32 #include "globals.hh" 32 #include "globals.hh"
>> 33 #include "G4SimpleIntegration.hh"
>> 34
33 35
34 G4SimpleIntegration::G4SimpleIntegration(funct << 36 G4SimpleIntegration::G4SimpleIntegration( function pFunction )
35 : fFunction(pFunction) << 37 : fFunction(pFunction),
36 {} << 38 fTolerance(.0001),
37 << 39 fMaxDepth(100)
38 G4SimpleIntegration::G4SimpleIntegration(funct << 40 {
39 G4dou << 41 }
40 : fFunction(pFunction) << 42
41 , fTolerance(pTolerance) << 43 G4SimpleIntegration::G4SimpleIntegration( function pFunction,
42 {} << 44 G4double pTolerance)
43 << 45 : fFunction(pFunction),
44 // Simple integration methods << 46 fTolerance(pTolerance),
45 << 47 fMaxDepth(100)
46 G4double G4SimpleIntegration::Trapezoidal(G4do << 48 {
47 G4in << 49 }
48 { << 50
49 G4double Step = (xFinal - xInitial) / iterat << 51
50 G4double mean = (fFunction(xInitial) + fFunc << 52 G4SimpleIntegration::~G4SimpleIntegration()
51 G4double x = xInitial; << 53 {
52 for(G4int i = 1; i < iterationNumber; ++i) << 54 }
53 { << 55
54 x += Step; << 56 // Simple integration methods
55 mean += fFunction(x); << 57
56 } << 58 G4double
57 return mean * Step; << 59 G4SimpleIntegration::Trapezoidal(G4double xInitial,
58 } << 60 G4double xFinal,
59 << 61 G4int iterationNumber )
60 G4double G4SimpleIntegration::MidPoint(G4doubl << 62 {
61 G4int i << 63 G4double Step = (xFinal - xInitial)/iterationNumber ;
62 { << 64 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
63 G4double Step = (xFinal - xInitial) / iterat << 65 G4double x = xInitial ;
64 G4double x = xInitial + 0.5 * Step; << 66 for(G4int i=1;i<iterationNumber;i++)
65 G4double mean = fFunction(x); << 67 {
66 for(G4int i = 1; i < iterationNumber; ++i) << 68 x += Step ;
67 { << 69 mean += fFunction(x) ;
68 x += Step; << 70 }
69 mean += fFunction(x); << 71 return mean*Step ;
70 } << 72 }
71 return mean * Step; << 73
72 } << 74 G4double
73 << 75 G4SimpleIntegration::MidPoint(G4double xInitial,
74 G4double G4SimpleIntegration::Gauss(G4double x << 76 G4double xFinal,
75 G4int iter << 77 G4int iterationNumber )
76 { << 78 {
77 G4double x = 0.; << 79 G4double Step = (xFinal - xInitial)/iterationNumber ;
78 static const G4double root = 1.0 / std::sqrt << 80 G4double x = xInitial + 0.5*Step;
79 G4double Step = (xFinal - xInit << 81 G4double mean = fFunction(x) ;
80 G4double delta = Step * root; << 82 for(G4int i=1;i<iterationNumber;i++)
81 G4double mean = 0.0; << 83 {
82 for(G4int i = 0; i < iterationNumber; ++i) << 84 x += Step ;
83 { << 85 mean += fFunction(x) ;
84 x = (2 * i + 1) * Step; << 86 }
85 mean += (fFunction(x + delta) + fFunction( << 87 return mean*Step ;
86 } << 88 }
87 return mean * Step; << 89
88 } << 90 G4double
89 << 91 G4SimpleIntegration::Gauss(G4double xInitial,
90 G4double G4SimpleIntegration::Simpson(G4double << 92 G4double xFinal,
91 G4int it << 93 G4int iterationNumber )
92 { << 94 {
93 G4double Step = (xFinal - xInitial) / itera << 95 G4double x=0.;
94 G4double x = xInitial; << 96 static const G4double root = 1.0/std::sqrt(3.0) ;
95 G4double xPlus = xInitial + 0.5 * Step; << 97 G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ;
96 G4double mean = (fFunction(xInitial) + fFun << 98 G4double delta = Step*root ;
97 G4double sum = fFunction(xPlus); << 99 G4double mean = 0.0 ;
98 for(G4int i = 1; i < iterationNumber; ++i) << 100 for(G4int i=0;i<iterationNumber;i++)
99 { << 101 {
100 x += Step; << 102 x = (2*i + 1)*Step ;
101 xPlus += Step; << 103 mean += (fFunction(x+delta) + fFunction(x-delta)) ;
102 mean += fFunction(x); << 104 }
103 sum += fFunction(xPlus); << 105 return mean*Step ;
104 } << 106 }
105 mean += 2.0 * sum; << 107
106 return mean * Step / 3.0; << 108 G4double
107 } << 109 G4SimpleIntegration::Simpson(G4double xInitial,
108 << 110 G4double xFinal,
109 // Adaptive Gauss integration << 111 G4int iterationNumber )
110 << 112 {
111 G4double G4SimpleIntegration::AdaptGaussIntegr << 113 G4double Step = (xFinal - xInitial)/iterationNumber ;
112 << 114 G4double x = xInitial ;
113 { << 115 G4double xPlus = xInitial + 0.5*Step ;
114 G4int depth = 0; << 116 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ;
115 G4double sum = 0.0; << 117 G4double sum = fFunction(xPlus) ;
116 AdaptGauss(xInitial, xFinal, sum, depth); << 118 for(G4int i=1;i<iterationNumber;i++)
117 return sum; << 119 {
118 } << 120 x += Step ;
119 << 121 xPlus += Step ;
120 G4double G4SimpleIntegration::Gauss(G4double x << 122 mean += fFunction(x) ;
121 { << 123 sum += fFunction(xPlus) ;
122 static const G4double root = 1.0 / std::sqrt << 124 }
123 << 125 mean += 2.0*sum ;
124 G4double xMean = (xInitial + xFinal) / 2.0; << 126 return mean*Step/3.0 ;
125 G4double Step = (xFinal - xInitial) / 2.0; << 127 }
126 G4double delta = Step * root; << 128
127 G4double sum = (fFunction(xMean + delta) + << 129
128 << 130
129 return sum * Step; << 131 // Adaptive Gauss integration
130 } << 132
131 << 133 G4double
132 void G4SimpleIntegration::AdaptGauss(G4double << 134 G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial,
133 G4double& << 135 G4double xFinal )
134 { << 136 {
135 if(depth > fMaxDepth) << 137 G4int depth = 0 ;
136 { << 138 G4double sum = 0.0 ;
137 G4Exception("G4SimpleIntegration::AdaptGau << 139 AdaptGauss(xInitial,xFinal,sum,depth) ;
138 "Function varies too rapidly ! << 140 return sum ;
139 } << 141 }
140 G4double xMean = (xInitial + xFinal) / 2 << 142
141 G4double leftHalf = Gauss(xInitial, xMean); << 143
142 G4double rightHalf = Gauss(xMean, xFinal); << 144 G4double
143 G4double full = Gauss(xInitial, xFinal) << 145 G4SimpleIntegration::Gauss( G4double xInitial,
144 if(std::fabs(leftHalf + rightHalf - full) < << 146 G4double xFinal )
145 { << 147 {
146 sum += full; << 148 static const G4double root = 1.0/std::sqrt(3.0) ;
147 } << 149
148 else << 150 G4double xMean = (xInitial + xFinal)/2.0 ;
149 { << 151 G4double Step = (xFinal - xInitial)/2.0 ;
150 ++depth; << 152 G4double delta = Step*root ;
151 AdaptGauss(xInitial, xMean, sum, depth); << 153 G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ;
152 AdaptGauss(xMean, xFinal, sum, depth); << 154
153 } << 155 return sum*Step ;
>> 156 }
>> 157
>> 158
>> 159 void
>> 160 G4SimpleIntegration::AdaptGauss( G4double xInitial,
>> 161 G4double xFinal,
>> 162 G4double& sum,
>> 163 G4int& depth )
>> 164 {
>> 165 if(depth >fMaxDepth)
>> 166 {
>> 167 G4Exception("G4SimpleIntegration::AdaptGauss()", "Error",
>> 168 FatalException, "Function varies too rapidly !") ;
>> 169 }
>> 170 G4double xMean = (xInitial + xFinal)/2.0 ;
>> 171 G4double leftHalf = Gauss(xInitial,xMean) ;
>> 172 G4double rightHalf = Gauss(xMean,xFinal) ;
>> 173 G4double full = Gauss(xInitial,xFinal) ;
>> 174 if(std::fabs(leftHalf+rightHalf-full) < fTolerance)
>> 175 {
>> 176 sum += full ;
>> 177 }
>> 178 else
>> 179 {
>> 180 depth++ ;
>> 181 AdaptGauss(xInitial,xMean,sum,depth) ;
>> 182 AdaptGauss(xMean,xFinal,sum,depth) ;
>> 183 }
154 } 184 }
155 185