G4RKG3_Stepper.cc

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//
// G4RKG3_Stepper implementation
//
// Authors: John Apostolakis & Vladimir Grichine (CERN), 30.01.1997
// -------------------------------------------------------------------
 
#include "G4RKG3_Stepper.hh"
#include "G4LineSection.hh"
#include "G4Mag_EqRhs.hh"
 
G4RKG3_Stepper::G4RKG3_Stepper(G4Mag_EqRhs* EqRhs)
  : G4MagIntegratorStepper(EqRhs,6)
{
}
 
void G4RKG3_Stepper::Stepper( const G4double yInput[], // [8]
                              const G4double dydx[],   // [6]
                                    G4double Step,
                                    G4double yOut[],   // [8]
                                    G4double yErr[] )
{
   G4double  B[3];
   G4int nvar = 6 ;
   G4double  by15 = 1. / 15. ; // was  0.066666666 ;
 
   G4double yTemp[8], dydxTemp[6], yIn[8];
 
   // Saving yInput because yInput and yOut can be aliases for same array
   //
   for(G4int i=0; i<nvar; ++i)
   {
     yIn[i]=yInput[i];
   }
   yIn[6] = yInput[6];
   yIn[7] = yInput[7];
   G4double h = Step * 0.5; 
   hStep = Step;
     // Do two half steps
 
   StepNoErr(yIn, dydx,h, yTemp,B) ;
   
   // Store Bfld for DistChord Calculation
   //
   for(auto i=0; i<3; ++i)
   {
     BfldIn[i] = B[i];
   }
   // RightHandSide(yTemp,dydxTemp) ;
 
   GetEquationOfMotion()->EvaluateRhsGivenB(yTemp,B,dydxTemp) ;  
   StepNoErr(yTemp,dydxTemp,h,yOut,B);      
        
   // Store midpoint, chord calculation
                                 
   fyMidPoint = G4ThreeVector(yTemp[0],  yTemp[1],  yTemp[2]); 
 
   // Do a full Step
  //
   h *= 2 ;
   StepNoErr(yIn,dydx,h,yTemp,B); 
   for(G4int i=0; i<nvar; ++i)
   {
      yErr[i] = yOut[i] - yTemp[i] ;
      yOut[i] += yErr[i]*by15 ;          // Provides 5th order of accuracy
   }
 
   // Store values for DistChord method
   //
   fyInitial = G4ThreeVector( yIn[0],   yIn[1],   yIn[2]);
   fpInitial = G4ThreeVector( yIn[3],   yIn[4],   yIn[5]);
   fyFinal   = G4ThreeVector( yOut[0],  yOut[1],  yOut[2]); 
}
 
// ---------------------------------------------------------------------------
 
// Integrator for RK from G3 with evaluation of error in solution and delta
// geometry based on naive similarity with the case of uniform magnetic field.
// B1[3] is input  and is the first magnetic field values
// B2[3] is output and is the final magnetic field values.
//
void G4RKG3_Stepper::StepWithEst( const G4double*,
                                  const G4double*,
                                        G4double,
                                        G4double*,
                                        G4double&,
                                        G4double&,
                                  const G4double*,
                                        G4double* )
   
{
  G4Exception("G4RKG3_Stepper::StepWithEst()", "GeomField0001",
              FatalException, "Method no longer used.");
}
 
// -----------------------------------------------------------------
 
// Integrator RK Stepper from G3 with only two field evaluation per Step. 
// It is used in propagation initial Step by small substeps after solution 
// error and delta geometry considerations. B[3] is magnetic field which 
// is passed from substep to substep.
//
void G4RKG3_Stepper::StepNoErr(const G4double tIn[8],
                               const G4double dydx[6],
                                     G4double Step,
                                     G4double tOut[8],
                                     G4double B[3] )
   
{ 
  
   // Copy and edit the routine above, to delete alpha2, beta2, ...
   //
   G4double K1[7], K2[7], K3[7], K4[7];
   G4double tTemp[8]={0.0}, yderiv[6]={0.0};
 
   // Need Momentum value to give correct values to the coefficients in
   // equation. Integration on unit velocity, but tIn[3,4,5] is momentum
 
   G4double mom, inverse_mom;
   const G4double c1=0.5, c2=0.125, c3=1./6.;
  
   // Correction for momentum not a velocity
   // Need the protection !!! must be not zero
   //
   mom = std::sqrt(tIn[3]*tIn[3]+tIn[4]*tIn[4]+tIn[5]*tIn[5]); 
   inverse_mom = 1./mom;    
   for(auto i=0; i<3; ++i)
   {
      K1[i] = Step * dydx[i+3]*inverse_mom;
      tTemp[i] = tIn[i] + Step*(c1*tIn[i+3]*inverse_mom + c2*K1[i]) ;
      tTemp[i+3] = tIn[i+3] + c1*K1[i]*mom ;
   }
    
   GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;
      
   for(auto i=0; i<3; ++i)
   {
      K2[i] = Step * yderiv[i+3]*inverse_mom;
      tTemp[i+3] = tIn[i+3] + c1*K2[i]*mom ;
   }
   
   // Given B, calculate yderiv !
   //
   GetEquationOfMotion()->EvaluateRhsGivenB(tTemp,B,yderiv) ;  
 
   for(auto i=0; i<3; ++i)
   {
      K3[i] = Step * yderiv[i+3]*inverse_mom;
      tTemp[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom + c1*K3[i]) ;
      tTemp[i+3] = tIn[i+3] + K3[i]*mom ;
   }
 
   // Calculates y-deriv(atives) & returns B too!
   //
   GetEquationOfMotion()->EvaluateRhsReturnB(tTemp,yderiv,B) ;  
 
   for(auto i=0; i<3; ++i)        // Output trajectory vector
   {
      K4[i] = Step * yderiv[i+3]*inverse_mom;
      tOut[i] = tIn[i] + Step*(tIn[i+3]*inverse_mom+ (K1[i]+K2[i]+K3[i])*c3) ;
      tOut[i+3] = tIn[i+3] + mom*(K1[i] + 2*K2[i] + 2*K3[i] +K4[i])*c3 ;
   }
   tOut[6] = tIn[6];
   tOut[7] = tIn[7];
}
 
// ---------------------------------------------------------------------------
 
G4double G4RKG3_Stepper::DistChord() const 
{
   // Soon: must check whether h/R > 2 pi  !!
   // Method below is good only for < 2 pi
 
   G4double distChord,distLine;
   
   if (fyInitial != fyFinal)
   {
      distLine = G4LineSection::Distline(fyMidPoint,fyInitial,fyFinal);
      distChord = distLine;
   }
   else
   {
      distChord = (fyMidPoint-fyInitial).mag();
   }
 
   return distChord;
}