1 | // |
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2 | // ******************************************************************** |
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3 | // * License and Disclaimer * |
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4 | // * * |
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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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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: G4CashKarpRKF45.cc,v 1.15 2008/01/11 18:11:44 japost Exp $ |
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28 | // GEANT4 tag $Name: $ |
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29 | // |
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30 | // The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth |
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31 | // order method (giving fifth-order accuracy) for the solution of an ODE. |
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32 | // Two different fourth order estimates are calculated; their difference |
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33 | // gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition] |
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34 | // It is used to integrate the equations of the motion of a particle |
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35 | // in a magnetic field. |
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36 | // |
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37 | // [ref. Numerical Recipes in C, 2nd Edition] |
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38 | // |
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39 | // ------------------------------------------------------------------- |
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40 | |
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41 | #include "G4CashKarpRKF45.hh" |
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42 | #include "G4LineSection.hh" |
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43 | |
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44 | ///////////////////////////////////////////////////////////////////// |
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45 | // |
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46 | // Constructor |
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47 | |
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48 | G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfMotion *EqRhs, |
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49 | G4int noIntegrationVariables, |
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50 | G4bool primary) |
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51 | : G4MagIntegratorStepper(EqRhs, noIntegrationVariables) |
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52 | { |
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53 | // unsigned int noVariables= std::max(numberOfVariables,8); // For Time .. 7+1 |
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54 | const G4int numberOfVariables = noIntegrationVariables; |
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55 | |
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56 | ak2 = new G4double[numberOfVariables] ; |
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57 | ak3 = new G4double[numberOfVariables] ; |
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58 | ak4 = new G4double[numberOfVariables] ; |
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59 | ak5 = new G4double[numberOfVariables] ; |
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60 | ak6 = new G4double[numberOfVariables] ; |
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61 | ak7 = 0; |
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62 | yTemp = new G4double[numberOfVariables] ; |
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63 | yIn = new G4double[numberOfVariables] ; |
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64 | |
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65 | fLastInitialVector = new G4double[numberOfVariables] ; |
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66 | fLastFinalVector = new G4double[numberOfVariables] ; |
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67 | fLastDyDx = new G4double[numberOfVariables]; |
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68 | |
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69 | fMidVector = new G4double[numberOfVariables]; |
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70 | fMidError = new G4double[numberOfVariables]; |
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71 | fAuxStepper = 0; |
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72 | if( primary ) |
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73 | fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary); |
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74 | |
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75 | } |
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76 | |
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77 | ///////////////////////////////////////////////////////////////////// |
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78 | // |
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79 | // Destructor |
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80 | |
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81 | G4CashKarpRKF45::~G4CashKarpRKF45() |
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82 | { |
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83 | delete[] ak2; |
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84 | delete[] ak3; |
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85 | delete[] ak4; |
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86 | delete[] ak5; |
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87 | delete[] ak6; |
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88 | // delete[] ak7; |
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89 | delete[] yTemp; |
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90 | delete[] yIn; |
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91 | |
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92 | delete[] fLastInitialVector; |
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93 | delete[] fLastFinalVector; |
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94 | delete[] fLastDyDx; |
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95 | delete[] fMidVector; |
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96 | delete[] fMidError; |
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97 | |
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98 | delete fAuxStepper; |
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99 | } |
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100 | |
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101 | ////////////////////////////////////////////////////////////////////// |
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102 | // |
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103 | // Given values for n = 6 variables yIn[0,...,n-1] |
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104 | // known at x, use the fifth-order Cash-Karp Runge- |
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105 | // Kutta-Fehlberg-4-5 method to advance the solution over an interval |
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106 | // Step and return the incremented variables as yOut[0,...,n-1]. Also |
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107 | // return an estimate of the local truncation error yErr[] using the |
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108 | // embedded 4th-order method. The user supplies routine |
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109 | // RightHandSide(y,dydx), which returns derivatives dydx for y . |
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110 | |
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111 | void |
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112 | G4CashKarpRKF45::Stepper(const G4double yInput[], |
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113 | const G4double dydx[], |
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114 | G4double Step, |
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115 | G4double yOut[], |
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116 | G4double yErr[]) |
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117 | { |
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118 | // const G4int nvar = 6 ; |
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119 | // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875; |
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120 | G4int i; |
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121 | |
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122 | const G4double b21 = 0.2 , |
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123 | b31 = 3.0/40.0 , b32 = 9.0/40.0 , |
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124 | b41 = 0.3 , b42 = -0.9 , b43 = 1.2 , |
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125 | |
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126 | b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 , |
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127 | b54 = 35.0/27.0 , |
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128 | |
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129 | b61 = 1631.0/55296.0 , b62 = 175.0/512.0 , |
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130 | b63 = 575.0/13824.0 , b64 = 44275.0/110592.0 , |
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131 | b65 = 253.0/4096.0 , |
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132 | |
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133 | c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 , |
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134 | c6 = 512.0/1771.0 , |
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135 | dc5 = -277.0/14336.0 ; |
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136 | |
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137 | const G4double dc1 = c1 - 2825.0/27648.0 , dc3 = c3 - 18575.0/48384.0 , |
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138 | dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ; |
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139 | |
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140 | // Initialise time to t0, needed when it is not updated by the integration. |
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141 | // [ Note: Only for time dependent fields (usually electric) |
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142 | // is it neccessary to integrate the time.] |
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143 | yOut[7] = yTemp[7] = yIn[7]; |
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144 | |
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145 | const G4int numberOfVariables= this->GetNumberOfVariables(); |
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146 | // The number of variables to be integrated over |
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147 | |
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148 | // Saving yInput because yInput and yOut can be aliases for same array |
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149 | |
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150 | for(i=0;i<numberOfVariables;i++) |
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151 | { |
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152 | yIn[i]=yInput[i]; |
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153 | } |
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154 | // RightHandSide(yIn, dydx) ; // 1st Step |
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155 | |
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156 | for(i=0;i<numberOfVariables;i++) |
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157 | { |
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158 | yTemp[i] = yIn[i] + b21*Step*dydx[i] ; |
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159 | } |
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160 | RightHandSide(yTemp, ak2) ; // 2nd Step |
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161 | |
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162 | for(i=0;i<numberOfVariables;i++) |
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163 | { |
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164 | yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ; |
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165 | } |
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166 | RightHandSide(yTemp, ak3) ; // 3rd Step |
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167 | |
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168 | for(i=0;i<numberOfVariables;i++) |
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169 | { |
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170 | yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ; |
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171 | } |
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172 | RightHandSide(yTemp, ak4) ; // 4th Step |
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173 | |
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174 | for(i=0;i<numberOfVariables;i++) |
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175 | { |
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176 | yTemp[i] = yIn[i] + Step*(b51*dydx[i] + b52*ak2[i] + b53*ak3[i] + |
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177 | b54*ak4[i]) ; |
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178 | } |
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179 | RightHandSide(yTemp, ak5) ; // 5th Step |
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180 | |
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181 | for(i=0;i<numberOfVariables;i++) |
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182 | { |
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183 | yTemp[i] = yIn[i] + Step*(b61*dydx[i] + b62*ak2[i] + b63*ak3[i] + |
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184 | b64*ak4[i] + b65*ak5[i]) ; |
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185 | } |
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186 | RightHandSide(yTemp, ak6) ; // 6th Step |
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187 | |
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188 | for(i=0;i<numberOfVariables;i++) |
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189 | { |
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190 | // Accumulate increments with proper weights |
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191 | |
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192 | yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ; |
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193 | |
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194 | // Estimate error as difference between 4th and |
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195 | // 5th order methods |
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196 | |
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197 | yErr[i] = Step*(dc1*dydx[i] + dc3*ak3[i] + dc4*ak4[i] + |
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198 | dc5*ak5[i] + dc6*ak6[i]) ; |
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199 | |
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200 | // Store Input and Final values, for possible use in calculating chord |
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201 | fLastInitialVector[i] = yIn[i] ; |
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202 | fLastFinalVector[i] = yOut[i]; |
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203 | fLastDyDx[i] = dydx[i]; |
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204 | } |
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205 | // NormaliseTangentVector( yOut ); // Not wanted |
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206 | |
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207 | fLastStepLength =Step; |
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208 | |
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209 | return ; |
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210 | } |
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211 | |
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212 | /////////////////////////////////////////////////////////////////////////////// |
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213 | |
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214 | void |
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215 | G4CashKarpRKF45::StepWithEst( const G4double*, |
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216 | const G4double*, |
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217 | G4double, |
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218 | G4double*, |
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219 | G4double&, |
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220 | G4double&, |
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221 | const G4double*, |
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222 | G4double* ) |
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223 | { |
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224 | G4Exception("G4CashKarpRKF45::StepWithEst()", "ObsoleteMethod", |
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225 | FatalException, "Method no longer used."); |
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226 | return ; |
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227 | } |
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228 | |
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229 | ///////////////////////////////////////////////////////////////// |
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230 | |
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231 | G4double G4CashKarpRKF45::DistChord() const |
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232 | { |
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233 | G4double distLine, distChord; |
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234 | G4ThreeVector initialPoint, finalPoint, midPoint; |
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235 | |
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236 | // Store last initial and final points (they will be overwritten in self-Stepper call!) |
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237 | initialPoint = G4ThreeVector( fLastInitialVector[0], |
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238 | fLastInitialVector[1], fLastInitialVector[2]); |
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239 | finalPoint = G4ThreeVector( fLastFinalVector[0], |
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240 | fLastFinalVector[1], fLastFinalVector[2]); |
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241 | |
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242 | // Do half a step using StepNoErr |
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243 | |
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244 | fAuxStepper->Stepper( fLastInitialVector, fLastDyDx, 0.5 * fLastStepLength, |
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245 | fMidVector, fMidError ); |
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246 | |
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247 | midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]); |
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248 | |
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249 | // Use stored values of Initial and Endpoint + new Midpoint to evaluate |
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250 | // distance of Chord |
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251 | |
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252 | |
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253 | if (initialPoint != finalPoint) |
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254 | { |
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255 | distLine = G4LineSection::Distline( midPoint, initialPoint, finalPoint ); |
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256 | distChord = distLine; |
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257 | } |
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258 | else |
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259 | { |
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260 | distChord = (midPoint-initialPoint).mag(); |
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261 | } |
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262 | return distChord; |
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263 | } |
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264 | |
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265 | |
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