[833] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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| 4 | // * * |
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| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
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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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| 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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| 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: G4GaussJacobiQ.cc,v 1.8 2007/11/13 17:35:06 gcosmo Exp $ |
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[1228] | 28 | // GEANT4 tag $Name: geant4-09-03 $ |
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[833] | 29 | // |
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| 30 | #include "G4GaussJacobiQ.hh" |
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| 31 | |
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| 32 | |
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| 33 | // ------------------------------------------------------------- |
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| 34 | // |
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| 35 | // Constructor for Gauss-Jacobi integration method. |
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| 36 | // |
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| 37 | |
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| 38 | G4GaussJacobiQ::G4GaussJacobiQ( function pFunction, |
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| 39 | G4double alpha, |
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| 40 | G4double beta, |
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| 41 | G4int nJacobi ) |
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| 42 | : G4VGaussianQuadrature(pFunction) |
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| 43 | |
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| 44 | { |
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| 45 | const G4double tolerance = 1.0e-12 ; |
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| 46 | const G4double maxNumber = 12 ; |
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| 47 | G4int i=1, k=1 ; |
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| 48 | G4double root=0.; |
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| 49 | G4double alphaBeta=0.0, alphaReduced=0.0, betaReduced=0.0, |
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| 50 | root1=0.0, root2=0.0, root3=0.0 ; |
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| 51 | G4double a=0.0, b=0.0, c=0.0, |
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| 52 | newton1=0.0, newton2=0.0, newton3=0.0, newton0=0.0, |
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| 53 | temp=0.0, rootTemp=0.0 ; |
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| 54 | |
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| 55 | fNumber = nJacobi ; |
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| 56 | fAbscissa = new G4double[fNumber] ; |
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| 57 | fWeight = new G4double[fNumber] ; |
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| 58 | |
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| 59 | for (i=1;i<=nJacobi;i++) |
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| 60 | { |
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| 61 | if (i == 1) |
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| 62 | { |
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| 63 | alphaReduced = alpha/nJacobi ; |
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| 64 | betaReduced = beta/nJacobi ; |
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| 65 | root1 = (1.0+alpha)*(2.78002/(4.0+nJacobi*nJacobi)+ |
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| 66 | 0.767999*alphaReduced/nJacobi) ; |
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| 67 | root2 = 1.0+1.48*alphaReduced+0.96002*betaReduced |
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| 68 | + 0.451998*alphaReduced*alphaReduced |
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| 69 | + 0.83001*alphaReduced*betaReduced ; |
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| 70 | root = 1.0-root1/root2 ; |
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| 71 | } |
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| 72 | else if (i == 2) |
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| 73 | { |
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| 74 | root1=(4.1002+alpha)/((1.0+alpha)*(1.0+0.155998*alpha)) ; |
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| 75 | root2=1.0+0.06*(nJacobi-8.0)*(1.0+0.12*alpha)/nJacobi ; |
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| 76 | root3=1.0+0.012002*beta*(1.0+0.24997*std::fabs(alpha))/nJacobi ; |
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| 77 | root -= (1.0-root)*root1*root2*root3 ; |
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| 78 | } |
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| 79 | else if (i == 3) |
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| 80 | { |
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| 81 | root1=(1.67001+0.27998*alpha)/(1.0+0.37002*alpha) ; |
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| 82 | root2=1.0+0.22*(nJacobi-8.0)/nJacobi ; |
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| 83 | root3=1.0+8.0*beta/((6.28001+beta)*nJacobi*nJacobi) ; |
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| 84 | root -= (fAbscissa[0]-root)*root1*root2*root3 ; |
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| 85 | } |
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| 86 | else if (i == nJacobi-1) |
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| 87 | { |
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| 88 | root1=(1.0+0.235002*beta)/(0.766001+0.118998*beta) ; |
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| 89 | root2=1.0/(1.0+0.639002*(nJacobi-4.0)/(1.0+0.71001*(nJacobi-4.0))) ; |
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| 90 | root3=1.0/(1.0+20.0*alpha/((7.5+alpha)*nJacobi*nJacobi)) ; |
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| 91 | root += (root-fAbscissa[nJacobi-4])*root1*root2*root3 ; |
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| 92 | } |
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| 93 | else if (i == nJacobi) |
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| 94 | { |
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| 95 | root1 = (1.0+0.37002*beta)/(1.67001+0.27998*beta) ; |
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| 96 | root2 = 1.0/(1.0+0.22*(nJacobi-8.0)/nJacobi) ; |
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| 97 | root3 = 1.0/(1.0+8.0*alpha/((6.28002+alpha)*nJacobi*nJacobi)) ; |
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| 98 | root += (root-fAbscissa[nJacobi-3])*root1*root2*root3 ; |
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| 99 | } |
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| 100 | else |
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| 101 | { |
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| 102 | root = 3.0*fAbscissa[i-2]-3.0*fAbscissa[i-3]+fAbscissa[i-4] ; |
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| 103 | } |
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| 104 | alphaBeta = alpha + beta ; |
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| 105 | for (k=1;k<=maxNumber;k++) |
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| 106 | { |
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| 107 | temp = 2.0 + alphaBeta ; |
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| 108 | newton1 = (alpha-beta+temp*root)/2.0 ; |
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| 109 | newton2 = 1.0 ; |
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| 110 | for (G4int j=2;j<=nJacobi;j++) |
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| 111 | { |
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| 112 | newton3 = newton2 ; |
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| 113 | newton2 = newton1 ; |
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| 114 | temp = 2*j+alphaBeta ; |
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| 115 | a = 2*j*(j+alphaBeta)*(temp-2.0) ; |
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| 116 | b = (temp-1.0)*(alpha*alpha-beta*beta+temp*(temp-2.0)*root) ; |
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| 117 | c = 2.0*(j-1+alpha)*(j-1+beta)*temp ; |
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| 118 | newton1 = (b*newton2-c*newton3)/a ; |
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| 119 | } |
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| 120 | newton0 = (nJacobi*(alpha - beta - temp*root)*newton1 + |
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| 121 | 2.0*(nJacobi + alpha)*(nJacobi + beta)*newton2)/ |
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| 122 | (temp*(1.0 - root*root)) ; |
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| 123 | rootTemp = root ; |
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| 124 | root = rootTemp - newton1/newton0 ; |
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| 125 | if (std::fabs(root-rootTemp) <= tolerance) |
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| 126 | { |
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| 127 | break ; |
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| 128 | } |
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| 129 | } |
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| 130 | if (k > maxNumber) |
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| 131 | { |
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| 132 | G4Exception("G4GaussJacobiQ::G4GaussJacobiQ()", "OutOfRange", |
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| 133 | FatalException, "Too many iterations in constructor.") ; |
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| 134 | } |
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| 135 | fAbscissa[i-1] = root ; |
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| 136 | fWeight[i-1] = std::exp(GammaLogarithm((G4double)(alpha+nJacobi)) + |
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| 137 | GammaLogarithm((G4double)(beta+nJacobi)) - |
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| 138 | GammaLogarithm((G4double)(nJacobi+1.0)) - |
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| 139 | GammaLogarithm((G4double)(nJacobi + alphaBeta + 1.0))) |
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| 140 | *temp*std::pow(2.0,alphaBeta)/(newton0*newton2) ; |
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| 141 | } |
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| 142 | } |
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| 143 | |
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| 144 | |
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| 145 | // ---------------------------------------------------------- |
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| 146 | // |
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| 147 | // Gauss-Jacobi method for integration of |
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| 148 | // ((1-x)^alpha)*((1+x)^beta)*pFunction(x) |
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| 149 | // from minus unit to plus unit . |
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| 150 | |
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| 151 | |
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| 152 | G4double |
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| 153 | G4GaussJacobiQ::Integral() const |
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| 154 | { |
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| 155 | G4double integral = 0.0 ; |
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| 156 | for(G4int i=0;i<fNumber;i++) |
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| 157 | { |
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| 158 | integral += fWeight[i]*fFunction(fAbscissa[i]) ; |
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| 159 | } |
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| 160 | return integral ; |
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| 161 | } |
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| 162 | |
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