[831] | 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: G4CashKarpRKF45.cc,v 1.15 2008/01/11 18:11:44 japost Exp $ |
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[1231] | 28 | // GEANT4 tag $Name: $ |
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[831] | 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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