| 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: G4GaussHermiteQ.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 "G4GaussHermiteQ.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-Hermite
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| 36 |
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| 37 | G4GaussHermiteQ::G4GaussHermiteQ ( function pFunction,
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| 38 | G4int nHermite )
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| 39 | : G4VGaussianQuadrature(pFunction)
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| 40 | {
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| 41 | const G4double tolerance = 1.0e-12 ;
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| 42 | const G4int maxNumber = 12 ;
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| 43 |
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| 44 | G4int i=1, j=1, k=1 ;
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| 45 | G4double newton0=0.;
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| 46 | G4double newton1=0.0, temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0 ;
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| 47 | G4double piInMinusQ = std::pow(pi,-0.25) ; // 1.0/std::sqrt(std::sqrt(pi)) ??
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| 48 |
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| 49 | fNumber = (nHermite +1)/2 ;
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| 50 | fAbscissa = new G4double[fNumber] ;
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| 51 | fWeight = new G4double[fNumber] ;
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| 52 |
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| 53 | for(i=1;i<=fNumber;i++)
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| 54 | {
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| 55 | if(i == 1)
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| 56 | {
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| 57 | newton0 = std::sqrt((G4double)(2*nHermite + 1)) -
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| 58 | 1.85575001*std::pow((G4double)(2*nHermite + 1),-0.16666999) ;
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| 59 | }
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| 60 | else if(i == 2)
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| 61 | {
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| 62 | newton0 -= 1.14001*std::pow((G4double)nHermite,0.425999)/newton0 ;
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| 63 | }
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| 64 | else if(i == 3)
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| 65 | {
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| 66 | newton0 = 1.86002*newton0 - 0.86002*fAbscissa[0] ;
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| 67 | }
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| 68 | else if(i == 4)
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| 69 | {
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| 70 | newton0 = 1.91001*newton0 - 0.91001*fAbscissa[1] ;
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| 71 | }
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| 72 | else
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| 73 | {
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| 74 | newton0 = 2.0*newton0 - fAbscissa[i - 3] ;
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| 75 | }
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| 76 | for(k=1;k<=maxNumber;k++)
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| 77 | {
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| 78 | temp1 = piInMinusQ ;
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| 79 | temp2 = 0.0 ;
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| 80 | for(j=1;j<=nHermite;j++)
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| 81 | {
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| 82 | temp3 = temp2 ;
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| 83 | temp2 = temp1 ;
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| 84 | temp1 = newton0*std::sqrt(2.0/j)*temp2
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| 85 | - std::sqrt(((G4double)(j - 1))/j)*temp3 ;
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| 86 | }
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| 87 | temp = std::sqrt((G4double)2*nHermite)*temp2 ;
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| 88 | newton1 = newton0 ;
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| 89 | newton0 = newton1 - temp1/temp ;
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| 90 | if(std::fabs(newton0 - newton1) <= tolerance)
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| 91 | {
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| 92 | break ;
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| 93 | }
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| 94 | }
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| 95 | if(k > maxNumber)
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| 96 | {
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| 97 | G4Exception("G4GaussHermiteQ::G4GaussHermiteQ()",
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| 98 | "OutOfRange", FatalException,
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| 99 | "Too many iterations in Gauss-Hermite constructor.") ;
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| 100 | }
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| 101 | fAbscissa[i-1] = newton0 ;
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| 102 | fWeight[i-1] = 2.0/(temp*temp) ;
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| 103 | }
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| 104 | }
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| 105 |
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| 106 |
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| 107 | // ----------------------------------------------------------
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| 108 | //
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| 109 | // Gauss-Hermite method for integration of std::exp(-x*x)*nFunction(x)
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| 110 | // from minus infinity to plus infinity .
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| 111 |
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| 112 | G4double G4GaussHermiteQ::Integral() const
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| 113 | {
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| 114 | G4double integral = 0.0 ;
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| 115 | for(G4int i=0;i<fNumber;i++)
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| 116 | {
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| 117 | integral += fWeight[i]*(fFunction(fAbscissa[i])
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| 118 | + fFunction(-fAbscissa[i])) ;
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| 119 | }
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| 120 | return integral ;
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| 121 | }
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