G4TsitourasRK45.cc

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// G4TsitourasRK45 implementation
//
// Author: Somnath Banerjee, Google Summer of Code 2015, 11.06.2015
// Supervision: John Apostolakis, CERN
// -------------------------------------------------------------------
 
#include "G4TsitourasRK45.hh"
#include "G4LineSection.hh"
 
/////////////////////////////////////////////////////////////////////
//
// Constructor
//
G4TsitourasRK45::G4TsitourasRK45(G4EquationOfMotion *EqRhs, 
                                 G4int noIntegrationVariables, 
                                 G4bool primary)
  : G4MagIntegratorStepper(EqRhs, noIntegrationVariables)
{
  const G4int numberOfVariables = noIntegrationVariables;
  
  ak2 = new G4double[numberOfVariables] ;  
  ak3 = new G4double[numberOfVariables] ; 
  ak4 = new G4double[numberOfVariables] ; 
  ak5 = new G4double[numberOfVariables] ; 
  ak6 = new G4double[numberOfVariables] ; 
  ak7 = new G4double[numberOfVariables] ;
  ak8 = new G4double[numberOfVariables] ;
 
  // 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 );
                                      
  yTemp = new G4double[numStateVars] ;
  yIn = new G4double[numStateVars] ;
 
  fLastInitialVector = new G4double[numberOfVariables] ;
  fLastFinalVector = new G4double[numberOfVariables] ;
 
  fLastDyDx = new G4double[numberOfVariables];
 
  fMidVector = new G4double[numberOfVariables];
  fMidError =  new G4double[numberOfVariables];
 
  if( primary )
  { 
    fAuxStepper = new G4TsitourasRK45(EqRhs, numberOfVariables, !primary);
  }
}
 
/////////////////////////////////////////////////////////////////////
//
// Destructor
//
G4TsitourasRK45::~G4TsitourasRK45()
{
  delete [] ak2;
  delete [] ak3;
  delete [] ak4;
  delete [] ak5;
  delete [] ak6;
  delete [] ak7;
  delete [] ak8;
 
  delete [] yTemp;
  delete [] yIn;
 
  delete [] fLastInitialVector;
  delete [] fLastFinalVector;
  delete [] fLastDyDx;
  delete [] fMidVector;
  delete [] fMidError; 
 
  delete fAuxStepper;
}
 
// The following coefficients have been obtained from
// Table 1: The Coefficients of the new pair
//
// C. Tsitouras, "Runge–Kutta pairs of order 5(4) satisfying only
//                the first column simplifying assumption"
// Computers & Mathematics with Applications, vol.62, no.2, pp.770-775, 2011.
//
// A corresponding matlab code was also found at:
//   http://users.ntua.gr/tsitoura/new54.m
//
// Doing a step
//
void
G4TsitourasRK45::Stepper( const G4double yInput[],
                          const G4double dydx[],
                                G4double Step,
                                G4double yOut[],
                                G4double yErr[] )
{
    const G4double b21 = 0.161 ,
                   b31 = -0.00848065549235698854 ,
                   b32 = 0.335480655492356989 ,
    
                   b41 =  2.89715305710549343 ,
                   b42 = -6.35944848997507484 ,
                   b43 = 4.36229543286958141 ,
 
                   b51 = 5.325864828439257,
                   b52 = -11.748883564062828,
                   b53 = 7.49553934288983621 ,
                   b54 = -0.09249506636175525,
 
                   b61 = 5.8614554429464200,
                   b62 = -12.9209693178471093 ,
                   b63 = 8.1593678985761586 ,
                   b64 = -0.071584973281400997,
                   b65 = -0.0282690503940683829,
 
                   b71 = 0.0964607668180652295 ,
                   b72 = 0.01, 
                   b73 = 0.479889650414499575,
                   b74 = 1.37900857410374189,
                   b75 = -3.2900695154360807,
                   b76 = 2.32471052409977398,
    
             //    c1 = 0.001780011052226 ,
             //    c2 = 0.000816434459657 ,
             //    c3 = -0.007880878010262 ,
             //    c4 = 0.144711007173263 ,
             //    c5 = -0.582357165452555 ,
             //    c6 = 0.458082105929187 ,
             //    c7 = 1.0/66.0 ;
 
                   dc1 = 0.0935237485818927066 - b71 , // - 0.001780011052226,
                   dc2 = 0.00865288314156636761 - b72, // - 0.000816434459657,
                   dc3 = 0.492893099131431868 - b73 ,  // + 0.007880878010262,
                   dc4 = 1.14023541226785810 - b74 ,   //   0.144711007173263,
                   dc5 = - 2.3291801924393646 - b75,   // + 0.582357165452555,
                   dc6 = 1.56887504931661552 - b76 ,   // - 0.458082105929187,
                   dc7 = 0.025; //- 1.0/66.0 ;
    
             //    dc1 = -3.0/1280.0,
             //    dc2 = 0.0,
             //    dc3 = 6561.0/632320.0,
             //    dc4 = -343.0/20800.0,
             //    dc5 = 243.0/12800.0,
             //    dc6 = -1.0/95.0,
             //    dc7 = 0.0   ;
    
    const G4int numberOfVariables = GetNumberOfVariables();
    
    // The number of variables to be integrated over
    //
    yOut[7] = yTemp[7]  = yIn[7] = yInput[7];
 
    //  Saving yInput because yInput and yOut can be aliases for same array
    //
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yIn[i]=yInput[i];
    }
    // RightHandSide(yIn, dydx) ;   // 1st Step - Not doing, getting passed
    
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yTemp[i] = yIn[i] + b21*Step*dydx[i] ;
    }
    RightHandSide(yTemp, ak2) ;              // 2nd Stage
    
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yTemp[i] = yIn[i] + Step*(b31*dydx[i] + b32*ak2[i]) ;
    }
    RightHandSide(yTemp, ak3) ;              // 3rd Stage
    
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yTemp[i] = yIn[i] + Step*(b41*dydx[i] + b42*ak2[i] + b43*ak3[i]) ;
    }
    RightHandSide(yTemp, ak4) ;              // 4th Stage
    
    for(G4int 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 Stage
    
    for(G4int 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 Stage
    
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yOut[i] = yIn[i] + Step*(b71*dydx[i] + b72*ak2[i] + b73*ak3[i] +
                                 b74*ak4[i] + b75*ak5[i] + b76*ak6[i]);
    }
    RightHandSide(yOut, ak7);                // 7th Stage
 
    //Calculate the error in the step:
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yErr[i] = Step*(dc1*dydx[i] + dc2*ak2[i] + dc3*ak3[i] + dc4*ak4[i] +
                        dc5*ak5[i]  + dc6*ak6[i] + dc7*ak7[i] ) ;
        
        // Store Input and Final values, for possible use in calculating chord
        //
        fLastInitialVector[i] = yIn[i] ;
        fLastFinalVector[i]   = yOut[i];
        fLastDyDx[i]          = dydx[i];
    }
    
    fLastStepLength = Step;
    
    return ;
}
 
void G4TsitourasRK45::SetupInterpolation()
  // (const G4double *yInput, const G4double *dydx, const G4double Step)
{
  // Nothing to be done
}
 
void G4TsitourasRK45::Interpolate(const G4double* yInput,
                                  const G4double* dydx,
                                  const G4double Step,
                                        G4double* yOut,
                                        G4double tau)
{
    G4double bf1, bf2, bf3, bf4, bf5, bf6, bf7;
      // Coefficients for all the seven stages.
    
    const G4int numberOfVariables = GetNumberOfVariables();
    
    G4double tau0 = tau;
    
    for(G4int i=0; i<numberOfVariables; ++i)
    {
       yIn[i] = yInput[i];
    }
    
    G4double tau_2 = tau0*tau0 ;
       //    tau_3 = tau0*tau_2,
       //    tau_4 = tau_2*tau_2;
 
    bf1 = -1.0530884977290216*tau*(tau - 1.3299890189751412)*(tau_2 -
                1.4364028541716351*tau + 0.7139816917074209);
    bf2 = 0.1017*tau_2*(tau_2 - 2.1966568338249754*tau +
                        1.2949852507374631);
    bf3 = 2.490627285651252793*tau_2*(tau_2 - 2.38535645472061657*tau
                                      + 1.57803468208092486);
    bf4 = -16.54810288924490272*(tau - 1.21712927295533244)*
                                    (tau - 0.61620406037800089)*tau_2;
    bf5 = 47.37952196281928122*(tau - 1.203071208372362603)*
                                    (tau - 0.658047292653547382)*tau_2;
    bf6 = -34.87065786149660974*(tau - 1.2)*(tau -
                                0.666666666666666667)*tau_2;
    bf7 = 2.5*(tau - 1.0)*(tau - 0.6)*tau_2;
    
    // Putting together the coefficients calculated as the respective
    // stage coefficients
    //
    for(G4int i=0; i<numberOfVariables; ++i)
    {
        yOut[i] = yIn[i] + Step*(  bf1*dydx[i] + bf2*ak2[i] + bf3*ak3[i]
                                 + bf4*ak4[i] + bf5*ak5[i] + bf6*ak6[i]
                                 + bf7*ak7[i]  ) ;
    }
}
 
G4double  G4TsitourasRK45::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;
}