[1058] | 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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[1340] | 27 | // $Id: G4ConstRK4.cc,v 1.5 2010/09/10 15:51:10 japost Exp $ |
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| 28 | // GEANT4 tag $Name: field-V09-03-03 $ |
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[1058] | 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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[1340] | 40 | // Constructor sets the number of *State* variables (default = 8) |
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| 41 | // The number of variables integrated is always 6 |
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[1058] | 42 | |
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[1340] | 43 | G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4int numStateVariables) |
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| 44 | : G4MagErrorStepper(EqRhs, 6, numStateVariables) |
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[1058] | 45 | { |
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[1340] | 46 | // const G4int numberOfVariables= 6; |
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| 47 | if( numStateVariables < 8 ) |
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[1058] | 48 | { |
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[1340] | 49 | G4cerr << "ERROR in G4ConstRK4::G4ConstRK4 " |
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| 50 | << " The number of State variables at least 8 " << G4endl; |
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| 51 | G4cerr << " Instead it is numStateVariables= " << numStateVariables << G4endl; |
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[1058] | 52 | G4Exception("G4ConstRK4::G4ConstRK4()", "InvalidSetup", FatalException, |
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[1340] | 53 | "Valid only for number of state variables of 8 or more. Use another Stepper!"); |
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[1058] | 54 | } |
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| 55 | |
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[1340] | 56 | fEq = EqRhs; |
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| 57 | yMiddle = new G4double[8]; |
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| 58 | dydxMid = new G4double[8]; |
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| 59 | yInitial = new G4double[8]; |
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| 60 | yOneStep = new G4double[8]; |
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| 61 | |
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| 62 | dydxm = new G4double[8]; |
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| 63 | dydxt = new G4double[8]; |
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| 64 | yt = new G4double[8]; |
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| 65 | Field[0]=0.; Field[1]=0.; Field[2]=0.; |
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[1058] | 66 | } |
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| 67 | |
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| 68 | //////////////////////////////////////////////////////////////// |
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| 69 | // |
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| 70 | // Destructor |
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| 71 | |
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| 72 | G4ConstRK4::~G4ConstRK4() |
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| 73 | { |
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| 74 | delete [] yMiddle; |
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| 75 | delete [] dydxMid; |
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| 76 | delete [] yInitial; |
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| 77 | delete [] yOneStep; |
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| 78 | delete [] dydxm; |
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| 79 | delete [] dydxt; |
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| 80 | delete [] yt; |
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| 81 | } |
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| 82 | |
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| 83 | ////////////////////////////////////////////////////////////////////// |
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| 84 | // |
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| 85 | // Given values for the variables y[0,..,n-1] and their derivatives |
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| 86 | // dydx[0,...,n-1] known at x, use the classical 4th Runge-Kutta |
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| 87 | // method to advance the solution over an interval h and return the |
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| 88 | // incremented variables as yout[0,...,n-1], which is not a distinct |
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| 89 | // array from y. The user supplies the routine RightHandSide(x,y,dydx), |
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| 90 | // which returns derivatives dydx at x. The source is routine rk4 from |
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| 91 | // NRC p. 712-713 . |
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| 92 | |
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| 93 | void G4ConstRK4::DumbStepper( const G4double yIn[], |
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| 94 | const G4double dydx[], |
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| 95 | G4double h, |
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| 96 | G4double yOut[]) |
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| 97 | { |
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| 98 | G4double hh = h*0.5 , h6 = h/6.0 ; |
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| 99 | |
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| 100 | // 1st Step K1=h*dydx |
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| 101 | yt[5] = yIn[5] + hh*dydx[5] ; |
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| 102 | yt[4] = yIn[4] + hh*dydx[4] ; |
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| 103 | yt[3] = yIn[3] + hh*dydx[3] ; |
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| 104 | yt[2] = yIn[2] + hh*dydx[2] ; |
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| 105 | yt[1] = yIn[1] + hh*dydx[1] ; |
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| 106 | yt[0] = yIn[0] + hh*dydx[0] ; |
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| 107 | RightHandSideConst(yt,dydxt) ; |
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| 108 | |
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| 109 | // 2nd Step K2=h*dydxt |
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| 110 | yt[5] = yIn[5] + hh*dydxt[5] ; |
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| 111 | yt[4] = yIn[4] + hh*dydxt[4] ; |
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| 112 | yt[3] = yIn[3] + hh*dydxt[3] ; |
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| 113 | yt[2] = yIn[2] + hh*dydxt[2] ; |
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| 114 | yt[1] = yIn[1] + hh*dydxt[1] ; |
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| 115 | yt[0] = yIn[0] + hh*dydxt[0] ; |
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| 116 | RightHandSideConst(yt,dydxm) ; |
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| 117 | |
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| 118 | // 3rd Step K3=h*dydxm |
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| 119 | // now dydxm=(K2+K3)/h |
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| 120 | yt[5] = yIn[5] + h*dydxm[5] ; |
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| 121 | dydxm[5] += dydxt[5] ; |
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| 122 | yt[4] = yIn[4] + h*dydxm[4] ; |
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| 123 | dydxm[4] += dydxt[4] ; |
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| 124 | yt[3] = yIn[3] + h*dydxm[3] ; |
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| 125 | dydxm[3] += dydxt[3] ; |
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| 126 | yt[2] = yIn[2] + h*dydxm[2] ; |
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| 127 | dydxm[2] += dydxt[2] ; |
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| 128 | yt[1] = yIn[1] + h*dydxm[1] ; |
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| 129 | dydxm[1] += dydxt[1] ; |
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| 130 | yt[0] = yIn[0] + h*dydxm[0] ; |
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| 131 | dydxm[0] += dydxt[0] ; |
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| 132 | RightHandSideConst(yt,dydxt) ; |
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| 133 | |
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| 134 | // 4th Step K4=h*dydxt |
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| 135 | yOut[5] = yIn[5]+h6*(dydx[5]+dydxt[5]+2.0*dydxm[5]); |
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| 136 | yOut[4] = yIn[4]+h6*(dydx[4]+dydxt[4]+2.0*dydxm[4]); |
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| 137 | yOut[3] = yIn[3]+h6*(dydx[3]+dydxt[3]+2.0*dydxm[3]); |
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| 138 | yOut[2] = yIn[2]+h6*(dydx[2]+dydxt[2]+2.0*dydxm[2]); |
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| 139 | yOut[1] = yIn[1]+h6*(dydx[1]+dydxt[1]+2.0*dydxm[1]); |
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| 140 | yOut[0] = yIn[0]+h6*(dydx[0]+dydxt[0]+2.0*dydxm[0]); |
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| 141 | |
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| 142 | } // end of DumbStepper .................................................... |
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| 143 | |
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| 144 | //////////////////////////////////////////////////////////////// |
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| 145 | // |
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| 146 | // Stepper |
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| 147 | |
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| 148 | void |
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| 149 | G4ConstRK4::Stepper( const G4double yInput[], |
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| 150 | const G4double dydx[], |
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| 151 | G4double hstep, |
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| 152 | G4double yOutput[], |
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| 153 | G4double yError [] ) |
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| 154 | { |
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[1340] | 155 | const G4int nvar = 6; // number of variables integrated |
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| 156 | const G4int maxvar= GetNumberOfStateVariables(); |
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[1058] | 157 | |
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| 158 | // Correction for Richardson extrapolation |
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| 159 | G4double correction = 1. / ( (1 << IntegratorOrder()) -1 ); |
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[1340] | 160 | |
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| 161 | G4int i; |
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[1058] | 162 | |
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| 163 | // Saving yInput because yInput and yOutput can be aliases for same array |
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[1340] | 164 | for (i=0; i<maxvar; i++) { yInitial[i]= yInput[i]; } |
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| 165 | |
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| 166 | // Must copy the part of the state *not* integrated to the output |
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| 167 | for (i=nvar; i<maxvar; i++) { yOutput[i]= yInput[i]; } |
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[1058] | 168 | |
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[1340] | 169 | // yInitial[7]= yInput[7]; // The time is typically needed |
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| 170 | yMiddle[7] = yInput[7]; // Copy the time from initial value |
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| 171 | yOneStep[7] = yInput[7]; // As it contributes to final value of yOutput ? |
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| 172 | // yOutput[7] = yInput[7]; // -> dumb stepper does it too for RK4 |
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[1058] | 173 | yError[7] = 0.0; |
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| 174 | |
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| 175 | G4double halfStep = hstep * 0.5; |
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| 176 | |
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| 177 | // Do two half steps |
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| 178 | // |
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| 179 | GetConstField(yInitial,Field); |
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| 180 | DumbStepper (yInitial, dydx, halfStep, yMiddle); |
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| 181 | RightHandSideConst(yMiddle, dydxMid); |
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| 182 | DumbStepper (yMiddle, dydxMid, halfStep, yOutput); |
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| 183 | |
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| 184 | // Store midpoint, chord calculation |
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| 185 | // |
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| 186 | fMidPoint = G4ThreeVector( yMiddle[0], yMiddle[1], yMiddle[2]); |
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| 187 | |
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| 188 | // Do a full Step |
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| 189 | // |
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| 190 | DumbStepper(yInitial, dydx, hstep, yOneStep); |
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| 191 | for(i=0;i<nvar;i++) |
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| 192 | { |
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| 193 | yError [i] = yOutput[i] - yOneStep[i] ; |
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| 194 | yOutput[i] += yError[i]*correction ; |
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| 195 | // Provides accuracy increased by 1 order via the |
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| 196 | // Richardson extrapolation |
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| 197 | } |
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| 198 | |
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| 199 | fInitialPoint = G4ThreeVector( yInitial[0], yInitial[1], yInitial[2]); |
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| 200 | fFinalPoint = G4ThreeVector( yOutput[0], yOutput[1], yOutput[2]); |
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| 201 | |
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| 202 | return; |
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| 203 | } |
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| 204 | |
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| 205 | //////////////////////////////////////////////////////////////// |
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| 206 | // |
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| 207 | // Estimate the maximum distance from the curve to the chord |
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| 208 | // |
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| 209 | // We estimate this using the distance of the midpoint to chord. |
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| 210 | // The method below is good only for angle deviations < 2 pi; |
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| 211 | // this restriction should not be a problem for the Runge Kutta methods, |
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| 212 | // which generally cannot integrate accurately for large angle deviations |
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| 213 | |
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| 214 | G4double G4ConstRK4::DistChord() const |
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| 215 | { |
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| 216 | G4double distLine, distChord; |
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| 217 | |
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| 218 | if (fInitialPoint != fFinalPoint) |
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| 219 | { |
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| 220 | distLine= G4LineSection::Distline( fMidPoint, fInitialPoint, fFinalPoint ); |
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| 221 | // This is a class method that gives distance of Mid |
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| 222 | // from the Chord between the Initial and Final points |
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| 223 | distChord = distLine; |
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| 224 | } |
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| 225 | else |
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| 226 | { |
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| 227 | distChord = (fMidPoint-fInitialPoint).mag(); |
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| 228 | } |
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| 229 | return distChord; |
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| 230 | } |
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