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 | // $Id: G4ConstRK4.cc,v 1.2 2008/10/29 14:17:42 gcosmo Exp $ |
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28 | // GEANT4 tag $Name: geant4-09-02-cand-01 $ |
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29 | // |
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30 | // |
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31 | // - 18.09.2008 - J.Apostolakis, T.Nikitina - Created |
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32 | // ------------------------------------------------------------------- |
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33 | |
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34 | #include "G4ConstRK4.hh" |
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35 | #include "G4ThreeVector.hh" |
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36 | #include "G4LineSection.hh" |
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37 | |
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38 | ////////////////////////////////////////////////////////////////// |
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39 | // |
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40 | // Constructor sets the number of variables (default = 8) |
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41 | |
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42 | G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4int numberOfVariables) |
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43 | : G4MagErrorStepper(EqRhs, numberOfVariables) |
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44 | { |
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45 | if(numberOfVariables !=8 ) |
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46 | { |
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47 | G4Exception("G4ConstRK4::G4ConstRK4()", "InvalidSetup", FatalException, |
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48 | "Valid only for number of variables=8. Use another Stepper!"); |
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49 | } |
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50 | else |
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51 | { |
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52 | fEq=EqRhs; |
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53 | yMiddle= new G4double[8]; |
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54 | dydxMid= new G4double[8]; |
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55 | yInitial= new G4double[8]; |
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56 | yOneStep= new G4double[8]; |
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57 | |
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58 | dydxm = new G4double[8]; |
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59 | dydxt = new G4double[8]; |
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60 | yt = new G4double[8]; |
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61 | Field[0]=0.;Field[1]=0.;Field[2]=0.; |
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62 | } |
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63 | } |
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64 | |
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65 | //////////////////////////////////////////////////////////////// |
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66 | // |
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67 | // Destructor |
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68 | |
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69 | G4ConstRK4::~G4ConstRK4() |
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70 | { |
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71 | delete [] yMiddle; |
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72 | delete [] dydxMid; |
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73 | delete [] yInitial; |
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74 | delete [] yOneStep; |
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75 | delete [] dydxm; |
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76 | delete [] dydxt; |
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77 | delete [] yt; |
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78 | } |
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79 | |
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80 | ////////////////////////////////////////////////////////////////////// |
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81 | // |
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82 | // Given values for the variables y[0,..,n-1] and their derivatives |
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83 | // dydx[0,...,n-1] known at x, use the classical 4th Runge-Kutta |
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84 | // method to advance the solution over an interval h and return the |
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85 | // incremented variables as yout[0,...,n-1], which is not a distinct |
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86 | // array from y. The user supplies the routine RightHandSide(x,y,dydx), |
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87 | // which returns derivatives dydx at x. The source is routine rk4 from |
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88 | // NRC p. 712-713 . |
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89 | |
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90 | void G4ConstRK4::DumbStepper( const G4double yIn[], |
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91 | const G4double dydx[], |
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92 | G4double h, |
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93 | G4double yOut[]) |
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94 | { |
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95 | G4double hh = h*0.5 , h6 = h/6.0 ; |
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96 | |
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97 | // 1st Step K1=h*dydx |
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98 | yt[5] = yIn[5] + hh*dydx[5] ; |
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99 | yt[4] = yIn[4] + hh*dydx[4] ; |
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100 | yt[3] = yIn[3] + hh*dydx[3] ; |
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101 | yt[2] = yIn[2] + hh*dydx[2] ; |
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102 | yt[1] = yIn[1] + hh*dydx[1] ; |
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103 | yt[0] = yIn[0] + hh*dydx[0] ; |
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104 | RightHandSideConst(yt,dydxt) ; |
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105 | |
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106 | // 2nd Step K2=h*dydxt |
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107 | yt[5] = yIn[5] + hh*dydxt[5] ; |
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108 | yt[4] = yIn[4] + hh*dydxt[4] ; |
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109 | yt[3] = yIn[3] + hh*dydxt[3] ; |
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110 | yt[2] = yIn[2] + hh*dydxt[2] ; |
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111 | yt[1] = yIn[1] + hh*dydxt[1] ; |
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112 | yt[0] = yIn[0] + hh*dydxt[0] ; |
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113 | RightHandSideConst(yt,dydxm) ; |
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114 | |
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115 | // 3rd Step K3=h*dydxm |
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116 | // now dydxm=(K2+K3)/h |
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117 | yt[5] = yIn[5] + h*dydxm[5] ; |
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118 | dydxm[5] += dydxt[5] ; |
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119 | yt[4] = yIn[4] + h*dydxm[4] ; |
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120 | dydxm[4] += dydxt[4] ; |
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121 | yt[3] = yIn[3] + h*dydxm[3] ; |
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122 | dydxm[3] += dydxt[3] ; |
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123 | yt[2] = yIn[2] + h*dydxm[2] ; |
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124 | dydxm[2] += dydxt[2] ; |
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125 | yt[1] = yIn[1] + h*dydxm[1] ; |
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126 | dydxm[1] += dydxt[1] ; |
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127 | yt[0] = yIn[0] + h*dydxm[0] ; |
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128 | dydxm[0] += dydxt[0] ; |
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129 | RightHandSideConst(yt,dydxt) ; |
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130 | |
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131 | // 4th Step K4=h*dydxt |
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132 | yOut[5] = yIn[5]+h6*(dydx[5]+dydxt[5]+2.0*dydxm[5]); |
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133 | yOut[4] = yIn[4]+h6*(dydx[4]+dydxt[4]+2.0*dydxm[4]); |
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134 | yOut[3] = yIn[3]+h6*(dydx[3]+dydxt[3]+2.0*dydxm[3]); |
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135 | yOut[2] = yIn[2]+h6*(dydx[2]+dydxt[2]+2.0*dydxm[2]); |
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136 | yOut[1] = yIn[1]+h6*(dydx[1]+dydxt[1]+2.0*dydxm[1]); |
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137 | yOut[0] = yIn[0]+h6*(dydx[0]+dydxt[0]+2.0*dydxm[0]); |
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138 | |
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139 | } // end of DumbStepper .................................................... |
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140 | |
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141 | //////////////////////////////////////////////////////////////// |
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142 | // |
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143 | // Stepper |
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144 | |
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145 | void |
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146 | G4ConstRK4::Stepper( const G4double yInput[], |
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147 | const G4double dydx[], |
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148 | G4double hstep, |
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149 | G4double yOutput[], |
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150 | G4double yError [] ) |
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151 | { |
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152 | const G4int nvar = 8 ; |
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153 | const G4int maxvar= 8; |
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154 | |
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155 | G4int i; |
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156 | |
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157 | // Correction for Richardson extrapolation |
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158 | // |
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159 | G4double correction = 1. / ( (1 << IntegratorOrder()) -1 ); |
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160 | |
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161 | // Saving yInput because yInput and yOutput can be aliases for same array |
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162 | |
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163 | for (i=0;i<nvar;i++) { yInitial[i]=yInput[i]; } |
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164 | |
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165 | yInitial[7]= yInput[7]; // Copy the time in case...even if not really needed |
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166 | yMiddle[7] = yInput[7]; // Copy the time from initial value |
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167 | yOneStep[7] = yInput[7]; // As it contributes to final value of yOutput ? |
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168 | yOutput[7] = yInput[7]; // -> dumb stepper does it too for RK4 |
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169 | for (i=nvar;i<maxvar;i++) { yOutput[i]=yInput[i]; } |
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170 | yError[7] = 0.0; |
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171 | |
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172 | G4double halfStep = hstep * 0.5; |
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173 | |
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174 | // Do two half steps |
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175 | // |
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176 | GetConstField(yInitial,Field); |
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177 | DumbStepper (yInitial, dydx, halfStep, yMiddle); |
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178 | RightHandSideConst(yMiddle, dydxMid); |
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179 | DumbStepper (yMiddle, dydxMid, halfStep, yOutput); |
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180 | |
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181 | // Store midpoint, chord calculation |
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182 | // |
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183 | fMidPoint = G4ThreeVector( yMiddle[0], yMiddle[1], yMiddle[2]); |
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184 | |
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185 | // Do a full Step |
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186 | // |
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187 | DumbStepper(yInitial, dydx, hstep, yOneStep); |
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188 | for(i=0;i<nvar;i++) |
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189 | { |
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190 | yError [i] = yOutput[i] - yOneStep[i] ; |
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191 | yOutput[i] += yError[i]*correction ; |
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192 | // Provides accuracy increased by 1 order via the |
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193 | // Richardson extrapolation |
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194 | } |
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195 | |
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196 | fInitialPoint = G4ThreeVector( yInitial[0], yInitial[1], yInitial[2]); |
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197 | fFinalPoint = G4ThreeVector( yOutput[0], yOutput[1], yOutput[2]); |
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198 | |
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199 | return; |
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200 | } |
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201 | |
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202 | //////////////////////////////////////////////////////////////// |
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203 | // |
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204 | // Estimate the maximum distance from the curve to the chord |
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205 | // |
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206 | // We estimate this using the distance of the midpoint to chord. |
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207 | // The method below is good only for angle deviations < 2 pi; |
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208 | // this restriction should not be a problem for the Runge Kutta methods, |
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209 | // which generally cannot integrate accurately for large angle deviations |
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210 | |
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211 | G4double G4ConstRK4::DistChord() const |
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212 | { |
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213 | G4double distLine, distChord; |
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214 | |
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215 | if (fInitialPoint != fFinalPoint) |
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216 | { |
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217 | distLine= G4LineSection::Distline( fMidPoint, fInitialPoint, fFinalPoint ); |
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218 | // This is a class method that gives distance of Mid |
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219 | // from the Chord between the Initial and Final points |
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220 | distChord = distLine; |
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221 | } |
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222 | else |
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223 | { |
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224 | distChord = (fMidPoint-fInitialPoint).mag(); |
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225 | } |
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226 | return distChord; |
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227 | } |
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