[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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| 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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[1058] | 28 | // GEANT4 tag $Name: geant4-09-02-ref-02 $ |
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[833] | 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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