[833] | 1 | // |
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| 2 | // ******************************************************************** |
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| 3 | // * License and Disclaimer * |
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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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| 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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| 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: G4GaussLaguerreQ.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 "G4GaussLaguerreQ.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 | // |
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| 36 | // Constructor for Gauss-Laguerre quadrature method: integral from zero to |
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| 37 | // infinity of std::pow(x,alpha)*std::exp(-x)*f(x). |
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| 38 | // The value of nLaguerre sets the accuracy. |
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| 39 | // The constructor creates arrays fAbscissa[0,..,nLaguerre-1] and |
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| 40 | // fWeight[0,..,nLaguerre-1] . |
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| 41 | // |
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| 42 | |
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| 43 | G4GaussLaguerreQ::G4GaussLaguerreQ( function pFunction, |
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| 44 | G4double alpha, |
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| 45 | G4int nLaguerre ) |
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| 46 | : G4VGaussianQuadrature(pFunction) |
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| 47 | { |
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| 48 | const G4double tolerance = 1.0e-10 ; |
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| 49 | const G4int maxNumber = 12 ; |
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| 50 | G4int i=1, k=1 ; |
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| 51 | G4double newton0=0.0, newton1=0.0, |
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| 52 | temp1=0.0, temp2=0.0, temp3=0.0, temp=0.0, cofi=0.0 ; |
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| 53 | |
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| 54 | fNumber = nLaguerre ; |
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| 55 | fAbscissa = new G4double[fNumber] ; |
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| 56 | fWeight = new G4double[fNumber] ; |
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| 57 | |
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| 58 | for(i=1;i<=fNumber;i++) // Loop over the desired roots |
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| 59 | { |
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| 60 | if(i == 1) |
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| 61 | { |
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| 62 | newton0 = (1.0 + alpha)*(3.0 + 0.92*alpha) |
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| 63 | / (1.0 + 2.4*fNumber + 1.8*alpha) ; |
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| 64 | } |
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| 65 | else if(i == 2) |
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| 66 | { |
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| 67 | newton0 += (15.0 + 6.25*alpha)/(1.0 + 0.9*alpha + 2.5*fNumber) ; |
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| 68 | } |
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| 69 | else |
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| 70 | { |
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| 71 | cofi = i - 2 ; |
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| 72 | newton0 += ((1.0+2.55*cofi)/(1.9*cofi) |
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| 73 | + 1.26*cofi*alpha/(1.0+3.5*cofi)) |
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| 74 | * (newton0 - fAbscissa[i-3])/(1.0 + 0.3*alpha) ; |
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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 = 1.0 ; |
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| 79 | temp2 = 0.0 ; |
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| 80 | for(G4int j=1;j<=fNumber;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 = ((2*j - 1 + alpha - newton0)*temp2 |
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| 85 | - (j - 1 + alpha)*temp3)/j ; |
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| 86 | } |
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| 87 | temp = (fNumber*temp1 - (fNumber +alpha)*temp2)/newton0 ; |
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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("G4GaussLaguerreQ::G4GaussLaguerreQ()", |
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| 98 | "OutOfRange", FatalException, |
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| 99 | "Too many iterations in Gauss-Laguerre constructor") ; |
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| 100 | } |
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| 101 | |
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| 102 | fAbscissa[i-1] = newton0 ; |
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| 103 | fWeight[i-1] = -std::exp(GammaLogarithm(alpha + fNumber) |
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| 104 | - GammaLogarithm((G4double)fNumber))/(temp*fNumber*temp2) ; |
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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 | // |
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| 110 | // Gauss-Laguerre method for integration of |
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| 111 | // std::pow(x,alpha)*std::exp(-x)*pFunction(x) |
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| 112 | // from zero up to infinity. pFunction is evaluated in fNumber points |
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| 113 | // for which fAbscissa[i] and fWeight[i] arrays were created in |
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| 114 | // G4VGaussianQuadrature(double,int) constructor |
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| 115 | |
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| 116 | G4double |
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| 117 | G4GaussLaguerreQ::Integral() const |
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| 118 | { |
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| 119 | G4double integral = 0.0 ; |
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| 120 | for(G4int i=0;i<fNumber;i++) |
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| 121 | { |
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| 122 | integral += fWeight[i]*fFunction(fAbscissa[i]) ; |
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| 123 | } |
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| 124 | return integral ; |
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| 125 | } |
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