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