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Please see the license in the file LICENSE and URL above * 16 // * for the full disclaimer and the limitatio 16 // * for the full disclaimer and the limitation of liability. * 17 // * 17 // * * 18 // * This code implementation is the result 18 // * This code implementation is the result of the scientific and * 19 // * technical work of the GEANT4 collaboratio 19 // * technical work of the GEANT4 collaboration. * 20 // * By using, copying, modifying or distri 20 // * By using, copying, modifying or distributing the software (or * 21 // * any work based on the software) you ag 21 // * any work based on the software) you agree to acknowledge its * 22 // * use in resulting scientific publicati 22 // * use in resulting scientific publications, and indicate your * 23 // * acceptance of all terms of the Geant4 Sof 23 // * acceptance of all terms of the Geant4 Software license. * 24 // ******************************************* 24 // ******************************************************************** 25 // 25 // 26 // G4SimpleIntegration class implementation << 27 // 26 // 28 // Author: V.Grichine, 26.03.1997 << 27 // 29 // ------------------------------------------- << 28 // Implementation file for simple integration methods >> 29 // 30 30 31 #include "G4SimpleIntegration.hh" << 32 #include "globals.hh" 31 #include "globals.hh" >> 32 #include "G4SimpleIntegration.hh" >> 33 33 34 34 G4SimpleIntegration::G4SimpleIntegration(funct << 35 G4SimpleIntegration::G4SimpleIntegration( function pFunction ) 35 : fFunction(pFunction) << 36 : fFunction(pFunction), 36 {} << 37 fTolerance(.0001), 37 << 38 fMaxDepth(100) 38 G4SimpleIntegration::G4SimpleIntegration(funct << 39 { 39 G4dou << 40 } 40 : fFunction(pFunction) << 41 41 , fTolerance(pTolerance) << 42 G4SimpleIntegration::G4SimpleIntegration( function pFunction, 42 {} << 43 G4double pTolerance) 43 << 44 : fFunction(pFunction), 44 // Simple integration methods << 45 fTolerance(pTolerance), 45 << 46 fMaxDepth(100) 46 G4double G4SimpleIntegration::Trapezoidal(G4do << 47 { 47 G4in << 48 } 48 { << 49 49 G4double Step = (xFinal - xInitial) / iterat << 50 50 G4double mean = (fFunction(xInitial) + fFunc << 51 G4SimpleIntegration::~G4SimpleIntegration() 51 G4double x = xInitial; << 52 { 52 for(G4int i = 1; i < iterationNumber; ++i) << 53 } 53 { << 54 54 x += Step; << 55 // Simple integration methods 55 mean += fFunction(x); << 56 56 } << 57 G4double 57 return mean * Step; << 58 G4SimpleIntegration::Trapezoidal(G4double xInitial, 58 } << 59 G4double xFinal, 59 << 60 G4int iterationNumber ) 60 G4double G4SimpleIntegration::MidPoint(G4doubl << 61 { 61 G4int i << 62 G4double Step = (xFinal - xInitial)/iterationNumber ; 62 { << 63 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; 63 G4double Step = (xFinal - xInitial) / iterat << 64 G4double x = xInitial ; 64 G4double x = xInitial + 0.5 * Step; << 65 for(G4int i=1;i<iterationNumber;i++) 65 G4double mean = fFunction(x); << 66 { 66 for(G4int i = 1; i < iterationNumber; ++i) << 67 x += Step ; 67 { << 68 mean += fFunction(x) ; 68 x += Step; << 69 } 69 mean += fFunction(x); << 70 return mean*Step ; 70 } << 71 } 71 return mean * Step; << 72 72 } << 73 G4double 73 << 74 G4SimpleIntegration::MidPoint(G4double xInitial, 74 G4double G4SimpleIntegration::Gauss(G4double x << 75 G4double xFinal, 75 G4int iter << 76 G4int iterationNumber ) 76 { << 77 { 77 G4double x = 0.; << 78 G4double Step = (xFinal - xInitial)/iterationNumber ; 78 static const G4double root = 1.0 / std::sqrt << 79 G4double x = xInitial + 0.5*Step; 79 G4double Step = (xFinal - xInit << 80 G4double mean = fFunction(x) ; 80 G4double delta = Step * root; << 81 for(G4int i=1;i<iterationNumber;i++) 81 G4double mean = 0.0; << 82 { 82 for(G4int i = 0; i < iterationNumber; ++i) << 83 x += Step ; 83 { << 84 mean += fFunction(x) ; 84 x = (2 * i + 1) * Step; << 85 } 85 mean += (fFunction(x + delta) + fFunction( << 86 return mean*Step ; 86 } << 87 } 87 return mean * Step; << 88 88 } << 89 G4double 89 << 90 G4SimpleIntegration::Gauss(G4double xInitial, 90 G4double G4SimpleIntegration::Simpson(G4double << 91 G4double xFinal, 91 G4int it << 92 G4int iterationNumber ) 92 { << 93 { 93 G4double Step = (xFinal - xInitial) / itera << 94 G4double x=0.; 94 G4double x = xInitial; << 95 static const G4double root = 1.0/std::sqrt(3.0) ; 95 G4double xPlus = xInitial + 0.5 * Step; << 96 G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ; 96 G4double mean = (fFunction(xInitial) + fFun << 97 G4double delta = Step*root ; 97 G4double sum = fFunction(xPlus); << 98 G4double mean = 0.0 ; 98 for(G4int i = 1; i < iterationNumber; ++i) << 99 for(G4int i=0;i<iterationNumber;i++) 99 { << 100 { 100 x += Step; << 101 x = (2*i + 1)*Step ; 101 xPlus += Step; << 102 mean += (fFunction(x+delta) + fFunction(x-delta)) ; 102 mean += fFunction(x); << 103 } 103 sum += fFunction(xPlus); << 104 return mean*Step ; 104 } << 105 } 105 mean += 2.0 * sum; << 106 106 return mean * Step / 3.0; << 107 G4double 107 } << 108 G4SimpleIntegration::Simpson(G4double xInitial, 108 << 109 G4double xFinal, 109 // Adaptive Gauss integration << 110 G4int iterationNumber ) 110 << 111 { 111 G4double G4SimpleIntegration::AdaptGaussIntegr << 112 G4double Step = (xFinal - xInitial)/iterationNumber ; 112 << 113 G4double x = xInitial ; 113 { << 114 G4double xPlus = xInitial + 0.5*Step ; 114 G4int depth = 0; << 115 G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; 115 G4double sum = 0.0; << 116 G4double sum = fFunction(xPlus) ; 116 AdaptGauss(xInitial, xFinal, sum, depth); << 117 for(G4int i=1;i<iterationNumber;i++) 117 return sum; << 118 { 118 } << 119 x += Step ; 119 << 120 xPlus += Step ; 120 G4double G4SimpleIntegration::Gauss(G4double x << 121 mean += fFunction(x) ; 121 { << 122 sum += fFunction(xPlus) ; 122 static const G4double root = 1.0 / std::sqrt << 123 } 123 << 124 mean += 2.0*sum ; 124 G4double xMean = (xInitial + xFinal) / 2.0; << 125 return mean*Step/3.0 ; 125 G4double Step = (xFinal - xInitial) / 2.0; << 126 } 126 G4double delta = Step * root; << 127 127 G4double sum = (fFunction(xMean + delta) + << 128 128 << 129 129 return sum * Step; << 130 // Adaptive Gauss integration 130 } << 131 131 << 132 G4double 132 void G4SimpleIntegration::AdaptGauss(G4double << 133 G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial, 133 G4double& << 134 G4double xFinal ) 134 { << 135 { 135 if(depth > fMaxDepth) << 136 G4int depth = 0 ; 136 { << 137 G4double sum = 0.0 ; 137 G4Exception("G4SimpleIntegration::AdaptGau << 138 AdaptGauss(xInitial,xFinal,sum,depth) ; 138 "Function varies too rapidly ! << 139 return sum ; 139 } << 140 } 140 G4double xMean = (xInitial + xFinal) / 2 << 141 141 G4double leftHalf = Gauss(xInitial, xMean); << 142 142 G4double rightHalf = Gauss(xMean, xFinal); << 143 G4double 143 G4double full = Gauss(xInitial, xFinal) << 144 G4SimpleIntegration::Gauss( G4double xInitial, 144 if(std::fabs(leftHalf + rightHalf - full) < << 145 G4double xFinal ) 145 { << 146 { 146 sum += full; << 147 static const G4double root = 1.0/std::sqrt(3.0) ; 147 } << 148 148 else << 149 G4double xMean = (xInitial + xFinal)/2.0 ; 149 { << 150 G4double Step = (xFinal - xInitial)/2.0 ; 150 ++depth; << 151 G4double delta = Step*root ; 151 AdaptGauss(xInitial, xMean, sum, depth); << 152 G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ; 152 AdaptGauss(xMean, xFinal, sum, depth); << 153 153 } << 154 return sum*Step ; >> 155 } >> 156 >> 157 >> 158 void >> 159 G4SimpleIntegration::AdaptGauss( G4double xInitial, >> 160 G4double xFinal, >> 161 G4double& sum, >> 162 G4int& depth ) >> 163 { >> 164 if(depth >fMaxDepth) >> 165 { >> 166 G4Exception("G4SimpleIntegration::AdaptGauss()", "Error", >> 167 FatalException, "Function varies too rapidly !") ; >> 168 } >> 169 G4double xMean = (xInitial + xFinal)/2.0 ; >> 170 G4double leftHalf = Gauss(xInitial,xMean) ; >> 171 G4double rightHalf = Gauss(xMean,xFinal) ; >> 172 G4double full = Gauss(xInitial,xFinal) ; >> 173 if(std::fabs(leftHalf+rightHalf-full) < fTolerance) >> 174 { >> 175 sum += full ; >> 176 } >> 177 else >> 178 { >> 179 depth++ ; >> 180 AdaptGauss(xInitial,xMean,sum,depth) ; >> 181 AdaptGauss(xMean,xFinal,sum,depth) ; >> 182 } 154 } 183 } 155 184