G4CashKarpRKF45.cc

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//
// G4CashKarpRKF45 implementation
//
// The Cash-Karp Runge-Kutta-Fehlberg 4/5 method is an embedded fourth
// order method (giving fifth-order accuracy) for the solution of an ODE.
// Two different fourth order estimates are calculated; their difference
// gives an error estimate. [ref. Numerical Recipes in C, 2nd Edition]
// It is used to integrate the equations of the motion of a particle 
// in a magnetic field.
//
// [ref. Numerical Recipes in C, 2nd Edition]
//
// Authors: J.Apostolakis, V.Grichine - 30.01.1997
// -------------------------------------------------------------------

#include "G4CashKarpRKF45.hh"
#include "G4LineSection.hh"

//
// Constructor
//
G4CashKarpRKF45::G4CashKarpRKF45(G4EquationOfMotion *EqRhs, 
                                 G4int noIntegrationVariables, 
                                 G4bool primary)
  : G4MagIntegratorStepper(EqRhs, noIntegrationVariables)
{
  const G4int numberOfVariables =
      std::max( noIntegrationVariables,
               ( ( (noIntegrationVariables-1)/4 + 1 ) * 4 ) );
  // For better alignment with cache-line
  
  ak2 = new G4double[numberOfVariables] ;
  ak3 = new G4double[numberOfVariables] ;
  ak4 = new G4double[numberOfVariables] ;
  ak5 = new G4double[numberOfVariables] ;
  ak6 = new G4double[numberOfVariables] ;
  // ak7 = 0;

  // Must ensure space extra 'state' variables exists - i.e. yIn[7]
  const G4int numStateMax  = std::max(GetNumberOfStateVariables(), 8);  
  const G4int numStateVars = std::max(noIntegrationVariables,
                                      numStateMax );
                                   // GetNumberOfStateVariables() ); 
                                      
  yTemp = new G4double[numStateVars] ;
  yIn = new G4double[numStateVars] ;

  fLastInitialVector = new G4double[numStateVars] ;
  fLastFinalVector = new G4double[numStateVars] ;
  fLastDyDx = new G4double[numberOfVariables];

  fMidVector = new G4double[numStateVars];
  fMidError =  new G4double[numStateVars];
  if( primary )
  { 
    fAuxStepper = new G4CashKarpRKF45(EqRhs, numberOfVariables, !primary);
  }
}

//
// Destructor
//
G4CashKarpRKF45::~G4CashKarpRKF45()
{
  delete [] ak2;
  delete [] ak3;
  delete [] ak4;
  delete [] ak5;
  delete [] ak6;
  // delete [] ak7;
  delete [] yTemp;
  delete [] yIn;

  delete [] fLastInitialVector;
  delete [] fLastFinalVector;
  delete [] fLastDyDx;
  delete [] fMidVector;
  delete [] fMidError; 

  delete fAuxStepper;
}

//
// Given values for n = 6 variables yIn[0,...,n-1] 
// known  at x, use the fifth-order Cash-Karp Runge-
// Kutta-Fehlberg-4-5 method to advance the solution over an interval
// Step and return the incremented variables as yOut[0,...,n-1]. Also
// return an estimate of the local truncation error yErr[] using the
// embedded 4th-order method. The user supplies routine
// RightHandSide(y,dydx), which returns derivatives dydx for y .
//
void
G4CashKarpRKF45::Stepper(const G4double yInput[],
                         const G4double dydx[],
                               G4double Step,
                               G4double yOut[],
                               G4double yErr[])
{
  // const G4int nvar = 6 ;
  // const G4double a2 = 0.2 , a3 = 0.3 , a4 = 0.6 , a5 = 1.0 , a6 = 0.875;
  G4int i;

  const G4double  b21 = 0.2 ,
                  b31 = 3.0/40.0 , b32 = 9.0/40.0 ,
                  b41 = 0.3 , b42 = -0.9 , b43 = 1.2 ,

                  b51 = -11.0/54.0 , b52 = 2.5 , b53 = -70.0/27.0 ,
                  b54 = 35.0/27.0 ,

                  b61 = 1631.0/55296.0 , b62 =   175.0/512.0 ,
                  b63 =  575.0/13824.0 , b64 = 44275.0/110592.0 ,
                  b65 =  253.0/4096.0 ,

                  c1 = 37.0/378.0 , c3 = 250.0/621.0 , c4 = 125.0/594.0 ,
                  c6 = 512.0/1771.0 , dc5 = -277.0/14336.0 ;

  const G4double dc1 = c1 - 2825.0/27648.0 ,  dc3 = c3 - 18575.0/48384.0 ,
                 dc4 = c4 - 13525.0/55296.0 , dc6 = c6 - 0.25 ;

  // Initialise time to t0, needed when it is not updated by the integration.
  //        [ Note: Only for time dependent fields (usually electric) 
  //                  is it neccessary to integrate the time.] 
  yOut[7] = yTemp[7] = yIn[7] = yInput[7]; 

  const G4int numberOfVariables= this->GetNumberOfVariables(); 
    // The number of variables to be integrated over

  //  Saving yInput because yInput and yOut can be aliases for same array

  for(i=0; i<numberOfVariables; ++i) 
  {
    yIn[i]=yInput[i];
  }
  // RightHandSide(yIn, dydx) ;            // 1st Step

  for(i=0; i<numberOfVariables; ++i) 
  {
    yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
  }
  RightHandSide(yTemp, ak2) ;              // 2nd Step

  for(i=0; i<numberOfVariables; ++i)
  {
    yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
  }
  RightHandSide(yTemp, ak3) ;              // 3rd Step

  for(i=0; i<numberOfVariables; ++i)
  {
    yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
  }
  RightHandSide(yTemp, ak4) ;              // 4th Step

  for(i=0; i<numberOfVariables; ++i)
  {
    yTemp[i] = yIn[i] + Step*(b51*dydx[i]
                      + b52*ak2[i] + b53*ak3[i] + b54*ak4[i]) ;
  }
  RightHandSide(yTemp, ak5) ;              // 5th Step

  for(i=0; i<numberOfVariables; ++i)
  {
    yTemp[i] = yIn[i] + Step*(b61*dydx[i]
                      + b62*ak2[i] + b63*ak3[i] + b64*ak4[i] + b65*ak5[i]) ;
  }
  RightHandSide(yTemp, ak6) ;              // 6th Step

  for(i=0; i<numberOfVariables; ++i)
  {
    // Accumulate increments with proper weights
    //
    yOut[i] = yIn[i] + Step*(c1*dydx[i] + c3*ak3[i] + c4*ak4[i] + c6*ak6[i]) ;

    // Estimate error as difference between 4th and 5th order methods
    //
    yErr[i] = Step*(dc1*dydx[i]
            + dc3*ak3[i] + dc4*ak4[i] + dc5*ak5[i] + dc6*ak6[i]) ;

    // Store Input and Final values, for possible use in calculating chord
    //
    fLastInitialVector[i] = yIn[i] ;
    fLastFinalVector[i]   = yOut[i];
    fLastDyDx[i]          = dydx[i];
  }
  // NormaliseTangentVector( yOut ); // Not wanted

  fLastStepLength = Step;

  return;
} 

//
void
G4CashKarpRKF45::StepWithEst( const G4double*,
                              const G4double*,
                                    G4double,
                                    G4double*,
                                    G4double&,
                                    G4double&,
                              const G4double*,
                                    G4double*  )    
{
  G4Exception("G4CashKarpRKF45::StepWithEst()", "GeomField0001",
              FatalException, "Method no longer used.");
  return ;
}

//
G4double  G4CashKarpRKF45::DistChord() const
{
  G4double distLine, distChord; 
  G4ThreeVector initialPoint, finalPoint, midPoint;

  // Store last initial and final points
  // (they will be overwritten in self-Stepper call!)
  //
  initialPoint = G4ThreeVector( fLastInitialVector[0], 
                                fLastInitialVector[1], fLastInitialVector[2]); 
  finalPoint   = G4ThreeVector( fLastFinalVector[0],  
                                fLastFinalVector[1],  fLastFinalVector[2]); 

  // Do half a step using StepNoErr
  //
  fAuxStepper->Stepper( fLastInitialVector, fLastDyDx,
                        0.5 * fLastStepLength, fMidVector, fMidError );

  midPoint = G4ThreeVector( fMidVector[0], fMidVector[1], fMidVector[2]);       

  // Use stored values of Initial and Endpoint + new Midpoint to evaluate
  // distance of Chord
  //
  if (initialPoint != finalPoint) 
  {
     distLine  = G4LineSection::Distline( midPoint, initialPoint, finalPoint );
     distChord = distLine;
  }
  else
  {
     distChord = (midPoint-initialPoint).mag();
  }
  return distChord;
}