[833] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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| 7 | // * conditions of the Geant4 Software License, included in the file * |
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| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
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| 9 | // * include a list of copyright holders. * |
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| 10 | // * * |
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| 11 | // * Neither the authors of this software system, nor their employing * |
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| 12 | // * institutes,nor the agencies providing financial support for this * |
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| 13 | // * work make any representation or warranty, express or implied, * |
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| 14 | // * regarding this software system or assume any liability for its * |
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| 15 | // * use. Please see the license in the file LICENSE and URL above * |
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| 16 | // * for the full disclaimer and the limitation of liability. * |
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| 17 | // * * |
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| 18 | // * This code implementation is the result of the scientific and * |
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| 19 | // * technical work of the GEANT4 collaboration. * |
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| 20 | // * By using, copying, modifying or distributing the software (or * |
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| 21 | // * any work based on the software) you agree to acknowledge its * |
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| 22 | // * use in resulting scientific publications, and indicate your * |
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| 23 | // * acceptance of all terms of the Geant4 Software license. * |
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| 24 | // ******************************************************************** |
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| 25 | // |
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| 26 | // |
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| 27 | // $Id: G4SimpleIntegration.cc,v 1.7 2006/06/29 19:00:21 gunter Exp $ |
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[850] | 28 | // GEANT4 tag $Name: HEAD $ |
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[833] | 29 | // |
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| 30 | // Implementation file for simple integration methods |
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| 31 | // |
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| 32 | |
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| 33 | #include "globals.hh" |
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| 34 | #include "G4SimpleIntegration.hh" |
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| 35 | |
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| 36 | |
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| 37 | G4int G4SimpleIntegration::fMaxDepth = 100 ; |
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| 38 | |
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| 39 | |
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| 40 | G4SimpleIntegration::G4SimpleIntegration( function pFunction ) |
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| 41 | : fFunction(pFunction), |
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| 42 | fTolerance(.0001) |
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| 43 | { |
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| 44 | } |
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| 45 | |
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| 46 | G4SimpleIntegration::G4SimpleIntegration( function pFunction, |
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| 47 | G4double pTolerance) |
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| 48 | : fFunction(pFunction), |
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| 49 | fTolerance(pTolerance) |
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| 50 | { |
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| 51 | } |
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| 52 | |
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| 53 | |
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| 54 | G4SimpleIntegration::~G4SimpleIntegration() |
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| 55 | { |
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| 56 | } |
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| 57 | |
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| 58 | // Simple integration methods |
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| 59 | |
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| 60 | G4double |
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| 61 | G4SimpleIntegration::Trapezoidal(G4double xInitial, |
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| 62 | G4double xFinal, |
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| 63 | G4int iterationNumber ) |
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| 64 | { |
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| 65 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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| 66 | G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; |
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| 67 | G4double x = xInitial ; |
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| 68 | for(G4int i=1;i<iterationNumber;i++) |
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| 69 | { |
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| 70 | x += Step ; |
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| 71 | mean += fFunction(x) ; |
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| 72 | } |
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| 73 | return mean*Step ; |
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| 74 | } |
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| 75 | |
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| 76 | G4double |
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| 77 | G4SimpleIntegration::MidPoint(G4double xInitial, |
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| 78 | G4double xFinal, |
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| 79 | G4int iterationNumber ) |
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| 80 | { |
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| 81 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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| 82 | G4double x = xInitial + 0.5*Step; |
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| 83 | G4double mean = fFunction(x) ; |
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| 84 | for(G4int i=1;i<iterationNumber;i++) |
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| 85 | { |
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| 86 | x += Step ; |
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| 87 | mean += fFunction(x) ; |
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| 88 | } |
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| 89 | return mean*Step ; |
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| 90 | } |
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| 91 | |
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| 92 | G4double |
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| 93 | G4SimpleIntegration::Gauss(G4double xInitial, |
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| 94 | G4double xFinal, |
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| 95 | G4int iterationNumber ) |
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| 96 | { |
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| 97 | G4double x=0.; |
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| 98 | static G4double root = 1.0/std::sqrt(3.0) ; |
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| 99 | G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ; |
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| 100 | G4double delta = Step*root ; |
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| 101 | G4double mean = 0.0 ; |
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| 102 | for(G4int i=0;i<iterationNumber;i++) |
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| 103 | { |
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| 104 | x = (2*i + 1)*Step ; |
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| 105 | mean += (fFunction(x+delta) + fFunction(x-delta)) ; |
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| 106 | } |
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| 107 | return mean*Step ; |
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| 108 | } |
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| 109 | |
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| 110 | G4double |
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| 111 | G4SimpleIntegration::Simpson(G4double xInitial, |
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| 112 | G4double xFinal, |
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| 113 | G4int iterationNumber ) |
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| 114 | { |
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| 115 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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| 116 | G4double x = xInitial ; |
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| 117 | G4double xPlus = xInitial + 0.5*Step ; |
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| 118 | G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; |
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| 119 | G4double sum = fFunction(xPlus) ; |
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| 120 | for(G4int i=1;i<iterationNumber;i++) |
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| 121 | { |
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| 122 | x += Step ; |
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| 123 | xPlus += Step ; |
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| 124 | mean += fFunction(x) ; |
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| 125 | sum += fFunction(xPlus) ; |
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| 126 | } |
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| 127 | mean += 2.0*sum ; |
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| 128 | return mean*Step/3.0 ; |
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| 129 | } |
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| 130 | |
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| 131 | |
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| 132 | |
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| 133 | // Adaptive Gauss integration |
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| 134 | |
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| 135 | G4double |
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| 136 | G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial, |
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| 137 | G4double xFinal ) |
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| 138 | { |
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| 139 | G4int depth = 0 ; |
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| 140 | G4double sum = 0.0 ; |
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| 141 | AdaptGauss(xInitial,xFinal,sum,depth) ; |
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| 142 | return sum ; |
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| 143 | } |
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| 144 | |
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| 145 | |
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| 146 | G4double |
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| 147 | G4SimpleIntegration::Gauss( G4double xInitial, |
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| 148 | G4double xFinal ) |
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| 149 | { |
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| 150 | static G4double root = 1.0/std::sqrt(3.0) ; |
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| 151 | |
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| 152 | G4double xMean = (xInitial + xFinal)/2.0 ; |
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| 153 | G4double Step = (xFinal - xInitial)/2.0 ; |
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| 154 | G4double delta = Step*root ; |
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| 155 | G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ; |
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| 156 | |
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| 157 | return sum*Step ; |
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| 158 | } |
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| 159 | |
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| 160 | |
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| 161 | void |
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| 162 | G4SimpleIntegration::AdaptGauss( G4double xInitial, |
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| 163 | G4double xFinal, |
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| 164 | G4double& sum, |
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| 165 | G4int& depth ) |
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| 166 | { |
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| 167 | if(depth >fMaxDepth) |
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| 168 | { |
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| 169 | G4Exception("G4SimpleIntegration::AdaptGauss()", "Error", |
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| 170 | FatalException, "Function varies too rapidly !") ; |
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| 171 | } |
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| 172 | G4double xMean = (xInitial + xFinal)/2.0 ; |
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| 173 | G4double leftHalf = Gauss(xInitial,xMean) ; |
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| 174 | G4double rightHalf = Gauss(xMean,xFinal) ; |
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| 175 | G4double full = Gauss(xInitial,xFinal) ; |
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| 176 | if(std::fabs(leftHalf+rightHalf-full) < fTolerance) |
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| 177 | { |
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| 178 | sum += full ; |
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| 179 | } |
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| 180 | else |
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| 181 | { |
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| 182 | depth++ ; |
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| 183 | AdaptGauss(xInitial,xMean,sum,depth) ; |
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| 184 | AdaptGauss(xMean,xFinal,sum,depth) ; |
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| 185 | } |
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| 186 | } |
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