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2 | // ******************************************************************** |
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24 | // ******************************************************************** |
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25 | // |
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26 | // |
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27 | // $Id: G4SimpleIntegration.cc,v 1.7 2006/06/29 19:00:21 gunter Exp $ |
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28 | // GEANT4 tag $Name: $ |
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29 | // |
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30 | // Implementation file for simple integration methods |
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31 | // |
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32 | |
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33 | #include "globals.hh" |
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34 | #include "G4SimpleIntegration.hh" |
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35 | |
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36 | |
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37 | G4int G4SimpleIntegration::fMaxDepth = 100 ; |
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38 | |
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39 | |
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40 | G4SimpleIntegration::G4SimpleIntegration( function pFunction ) |
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41 | : fFunction(pFunction), |
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42 | fTolerance(.0001) |
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43 | { |
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44 | } |
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45 | |
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46 | G4SimpleIntegration::G4SimpleIntegration( function pFunction, |
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47 | G4double pTolerance) |
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48 | : fFunction(pFunction), |
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49 | fTolerance(pTolerance) |
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50 | { |
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51 | } |
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52 | |
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53 | |
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54 | G4SimpleIntegration::~G4SimpleIntegration() |
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55 | { |
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56 | } |
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57 | |
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58 | // Simple integration methods |
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59 | |
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60 | G4double |
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61 | G4SimpleIntegration::Trapezoidal(G4double xInitial, |
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62 | G4double xFinal, |
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63 | G4int iterationNumber ) |
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64 | { |
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65 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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66 | G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; |
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67 | G4double x = xInitial ; |
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68 | for(G4int i=1;i<iterationNumber;i++) |
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69 | { |
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70 | x += Step ; |
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71 | mean += fFunction(x) ; |
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72 | } |
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73 | return mean*Step ; |
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74 | } |
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75 | |
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76 | G4double |
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77 | G4SimpleIntegration::MidPoint(G4double xInitial, |
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78 | G4double xFinal, |
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79 | G4int iterationNumber ) |
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80 | { |
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81 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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82 | G4double x = xInitial + 0.5*Step; |
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83 | G4double mean = fFunction(x) ; |
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84 | for(G4int i=1;i<iterationNumber;i++) |
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85 | { |
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86 | x += Step ; |
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87 | mean += fFunction(x) ; |
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88 | } |
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89 | return mean*Step ; |
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90 | } |
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91 | |
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92 | G4double |
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93 | G4SimpleIntegration::Gauss(G4double xInitial, |
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94 | G4double xFinal, |
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95 | G4int iterationNumber ) |
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96 | { |
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97 | G4double x=0.; |
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98 | static G4double root = 1.0/std::sqrt(3.0) ; |
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99 | G4double Step = (xFinal - xInitial)/(2.0*iterationNumber) ; |
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100 | G4double delta = Step*root ; |
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101 | G4double mean = 0.0 ; |
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102 | for(G4int i=0;i<iterationNumber;i++) |
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103 | { |
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104 | x = (2*i + 1)*Step ; |
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105 | mean += (fFunction(x+delta) + fFunction(x-delta)) ; |
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106 | } |
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107 | return mean*Step ; |
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108 | } |
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109 | |
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110 | G4double |
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111 | G4SimpleIntegration::Simpson(G4double xInitial, |
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112 | G4double xFinal, |
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113 | G4int iterationNumber ) |
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114 | { |
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115 | G4double Step = (xFinal - xInitial)/iterationNumber ; |
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116 | G4double x = xInitial ; |
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117 | G4double xPlus = xInitial + 0.5*Step ; |
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118 | G4double mean = (fFunction(xInitial) + fFunction(xFinal))*0.5 ; |
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119 | G4double sum = fFunction(xPlus) ; |
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120 | for(G4int i=1;i<iterationNumber;i++) |
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121 | { |
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122 | x += Step ; |
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123 | xPlus += Step ; |
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124 | mean += fFunction(x) ; |
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125 | sum += fFunction(xPlus) ; |
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126 | } |
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127 | mean += 2.0*sum ; |
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128 | return mean*Step/3.0 ; |
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129 | } |
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130 | |
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131 | |
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132 | |
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133 | // Adaptive Gauss integration |
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134 | |
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135 | G4double |
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136 | G4SimpleIntegration::AdaptGaussIntegration( G4double xInitial, |
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137 | G4double xFinal ) |
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138 | { |
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139 | G4int depth = 0 ; |
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140 | G4double sum = 0.0 ; |
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141 | AdaptGauss(xInitial,xFinal,sum,depth) ; |
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142 | return sum ; |
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143 | } |
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144 | |
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145 | |
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146 | G4double |
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147 | G4SimpleIntegration::Gauss( G4double xInitial, |
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148 | G4double xFinal ) |
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149 | { |
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150 | static G4double root = 1.0/std::sqrt(3.0) ; |
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151 | |
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152 | G4double xMean = (xInitial + xFinal)/2.0 ; |
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153 | G4double Step = (xFinal - xInitial)/2.0 ; |
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154 | G4double delta = Step*root ; |
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155 | G4double sum = (fFunction(xMean + delta) + fFunction(xMean - delta)) ; |
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156 | |
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157 | return sum*Step ; |
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158 | } |
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159 | |
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160 | |
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161 | void |
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162 | G4SimpleIntegration::AdaptGauss( G4double xInitial, |
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163 | G4double xFinal, |
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164 | G4double& sum, |
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165 | G4int& depth ) |
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166 | { |
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167 | if(depth >fMaxDepth) |
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168 | { |
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169 | G4Exception("G4SimpleIntegration::AdaptGauss()", "Error", |
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170 | FatalException, "Function varies too rapidly !") ; |
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171 | } |
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172 | G4double xMean = (xInitial + xFinal)/2.0 ; |
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173 | G4double leftHalf = Gauss(xInitial,xMean) ; |
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174 | G4double rightHalf = Gauss(xMean,xFinal) ; |
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175 | G4double full = Gauss(xInitial,xFinal) ; |
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176 | if(std::fabs(leftHalf+rightHalf-full) < fTolerance) |
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177 | { |
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178 | sum += full ; |
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179 | } |
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180 | else |
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181 | { |
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182 | depth++ ; |
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183 | AdaptGauss(xInitial,xMean,sum,depth) ; |
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184 | AdaptGauss(xMean,xFinal,sum,depth) ; |
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185 | } |
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186 | } |
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