| 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: G4GaussJacobiQ.cc,v 1.8 2007/11/13 17:35:06 gcosmo Exp $
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| 28 | // GEANT4 tag $Name: geant4-09-04-beta-01 $
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| 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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