| 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 1.5 2010/09/10 15:51:10 japost Exp $
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| 28 | // GEANT4 tag $Name: field-V09-03-03 $
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| 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 *State* variables (default = 8)
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| 41 | // The number of variables integrated is always 6
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| 42 |
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| 43 | G4ConstRK4::G4ConstRK4(G4Mag_EqRhs* EqRhs, G4int numStateVariables)
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| 44 | : G4MagErrorStepper(EqRhs, 6, numStateVariables)
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| 45 | {
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| 46 | // const G4int numberOfVariables= 6;
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| 47 | if( numStateVariables < 8 )
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| 48 | {
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| 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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| 52 | G4Exception("G4ConstRK4::G4ConstRK4()", "InvalidSetup", FatalException,
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| 53 | "Valid only for number of state variables of 8 or more. Use another Stepper!");
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| 54 | }
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| 55 |
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| 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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| 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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| 155 | const G4int nvar = 6; // number of variables integrated
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| 156 | const G4int maxvar= GetNumberOfStateVariables();
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| 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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| 160 |
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| 161 | G4int i;
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| 162 |
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| 163 | // Saving yInput because yInput and yOutput can be aliases for same array
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| 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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| 168 |
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| 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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| 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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