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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: geant4-09-03 $ |
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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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