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 | // |
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28 | // Author: Luciano Pandola (Luciano.Pandola@cern.ch) |
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29 | // |
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30 | // History: |
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31 | // ----------- |
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32 | // 30 Nov 2002 LP Created |
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33 | // 14 Feb 2003 MGP Corrected compilation errors from SUN |
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34 | // |
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35 | // ------------------------------------------------------------------- |
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36 | |
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37 | template <class T,class F> |
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38 | G4double G4PenelopeIntegrator<T,F>::Calculate(T& typeT, F f, |
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39 | G4double LowPoint,G4double HighPoint, |
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40 | G4double MaxError) |
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41 | { |
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42 | const G4int npoints=10; |
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43 | const G4int ncallsmax=20000; |
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44 | const G4int nst=256; |
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45 | static G4double Abscissas[10] = {7.652651133497334e-02,2.2778585114164508e-01,3.7370608871541956e-01, |
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46 | 5.1086700195082710e-01,6.3605368072651503e-01,7.4633190646015079e-01, |
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47 | 8.3911697182221882e-01,9.1223442825132591e-01,9.6397192727791379e-01, |
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48 | 9.9312859918509492e-01}; |
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49 | static G4double Weights[10] = {1.5275338713072585e-01,1.4917298647260375e-01,1.4209610931838205e-01, |
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50 | 1.3168863844917663e-01,1.1819453196151842e-01,1.0193011981724044e-01, |
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51 | 8.3276741576704749e-02,6.2672048334109064e-02,4.0601429800386941e-02, |
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52 | 1.7614007139152118e-02}; |
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53 | |
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54 | //Error control |
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55 | G4double Ctol = std::min(std::max(MaxError,1e-13),1e-02); |
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56 | G4double Ptol = 0.01*Ctol; |
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57 | G4double Err=1e35; |
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58 | //Gauss integration from LowPoint to HighPoint |
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59 | G4double h,sumga,a,b,c,d; |
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60 | h=HighPoint-LowPoint; |
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61 | sumga=0.0; |
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62 | a=0.5*(HighPoint-LowPoint); |
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63 | b=0.5*(HighPoint+LowPoint); |
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64 | c=a*Abscissas[0]; |
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65 | d=Weights[0]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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66 | G4int i; |
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67 | for (i=2;i<=npoints;i++){ |
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68 | c=a*Abscissas[i-1]; |
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69 | d=d+Weights[i-1]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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70 | } |
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71 | G4int icall = 2*npoints; |
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72 | G4int LH=1; |
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73 | G4double S[nst],x[nst],sn[nst],xrn[nst]; |
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74 | S[0]=d*a; |
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75 | x[0]=LowPoint; |
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76 | |
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77 | //Adaptive bipartition scheme |
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78 | do{ |
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79 | G4double h0=h; |
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80 | h=0.5*h; //bipartition |
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81 | G4double sumr=0; |
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82 | G4int LHN=0; |
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83 | G4double si,xa,xb,xc; |
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84 | for (i=1;i<=LH;i++){ |
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85 | si=S[i-1]; |
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86 | xa=x[i-1]; |
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87 | xb=xa+h; |
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88 | xc=xa+h0; |
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89 | a=0.5*(xb-xa); |
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90 | b=0.5*(xb+xa); |
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91 | c=a*Abscissas[0]; |
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92 | d=Weights[0]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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93 | G4int j; |
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94 | for (j=1;j<npoints;j++){ |
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95 | c=a*Abscissas[j]; |
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96 | d=d+Weights[j]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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97 | } |
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98 | G4double s1,s2,s12; |
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99 | s1=d*a; |
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100 | a=0.5*(xc-xb); |
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101 | b=0.5*(xc+xb); |
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102 | c=a*Abscissas[0]; |
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103 | d=Weights[0]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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104 | for (j=1;j<npoints;j++){ |
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105 | c=a*Abscissas[j]; |
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106 | d=d+Weights[j]*((typeT.*f)(b+c)+(typeT.*f)(b-c)); |
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107 | } |
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108 | s2=d*a; |
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109 | icall=icall+4*npoints; |
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110 | s12=s1+s2; |
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111 | if (std::abs(s12-si)<std::max(Ptol*std::abs(s12),1e-35)){ |
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112 | sumga=sumga+s12; |
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113 | } |
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114 | else |
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115 | { |
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116 | sumr=sumr+s12; |
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117 | LHN=LHN+2; |
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118 | sn[LHN-1]=s2; |
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119 | xrn[LHN-1]=xb; |
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120 | sn[LHN-2]=s1; |
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121 | xrn[LHN-2]=xa; |
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122 | } |
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123 | if (icall>ncallsmax || LHN>nst) |
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124 | { |
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125 | G4cout << "G4PenelopeIntegrator: " << G4endl; |
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126 | G4cout << "LowPoint: " << LowPoint << ", High Point: " << HighPoint << G4endl; |
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127 | G4cout << "Tolerance: " << MaxError << G4endl; |
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128 | G4cout << "Calls: " << icall << ", Integral: " << sumga << ", Error: " << Err << G4cout; |
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129 | G4cout << "Number of open subintervals: " << LHN << G4endl; |
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130 | G4cout << "WARNING: the required accuracy has not been attained" << G4endl; |
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131 | return sumga; |
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132 | } |
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133 | } |
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134 | Err=std::abs(sumr)/std::max(std::abs(sumr+sumga),1e-35); |
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135 | if (Err < Ctol || LHN == 0) return sumga; //end of cycle |
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136 | LH=LHN; |
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137 | for (G4int i=0;i<LH;i++){ |
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138 | S[i]=sn[i]; |
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139 | x[i]=xrn[i]; |
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140 | } |
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141 | }while(Ctol < 1.0); //infinite loop |
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142 | return 0; //It should never get here |
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143 | } |
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144 | |
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145 | template <class T,class F> |
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146 | G4double G4PenelopeIntegrator<T,F>::Calculate(T* ptrT, F f, |
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147 | G4double LowPoint,G4double HighPoint, |
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148 | G4double MaxError) |
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149 | { |
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150 | return Calculate(*ptrT,f,LowPoint,HighPoint,MaxError); |
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151 | } |
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152 | |
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153 | |
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