G4TDormandPrince45< T_Equation, N > Class Template Reference

G4TDormandPrince45 is a templated version of G4DormandPrince745 5th order Runge-Kutta stepper. More...

#include <G4TDormandPrince45.hh>

Inheritance diagram for G4TDormandPrince45< T_Equation, N >:

Public Member Functions
	G4TDormandPrince45 (T_Equation *equation)
	G4TDormandPrince45 (T_Equation *equation, G4int numVar)
void	StepWithError (const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[])
void	Stepper (const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[]) final
void	StepWithFinalDerivate (const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[], G4double dydxOutput[])
void	SetupInterpolation ()
void	Interpolate (G4double tau, G4double yOut[]) const
G4double	DistChord () const final
G4int	IntegratorOrder () const override
G4StepperType	StepperType () const override
const field_utils::ShortState< N > &	GetYOut () const
void	Interpolate4thOrder (G4double yOut[], G4double tau) const
void	SetupInterpolation5thOrder ()
void	Interpolate5thOrder (G4double yOut[], G4double tau) const
void	RightHandSideInl (const G4double y[], G4double dydx[])
void	Stepper (const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[], G4double dydxOutput[])
T_Equation *	GetSpecificEquation ()
Public Member Functions inherited from G4MagIntegratorStepper
	G4MagIntegratorStepper (G4EquationOfMotion *Equation, G4int numIntegrationVariables, G4int numStateVariables=12, G4bool isFSAL=false)
virtual	~G4MagIntegratorStepper ()=default
	G4MagIntegratorStepper (const G4MagIntegratorStepper &)=delete
G4MagIntegratorStepper &	operator= (const G4MagIntegratorStepper &)=delete
void	NormaliseTangentVector (G4double vec[6])
void	NormalisePolarizationVector (G4double vec[12])
void	RightHandSide (const G4double y[], G4double dydx[]) const
void	RightHandSide (const G4double y[], G4double dydx[], G4double field[]) const
G4int	GetNumberOfVariables () const
G4int	GetNumberOfStateVariables () const
G4int	IntegrationOrder ()
G4EquationOfMotion *	GetEquationOfMotion ()
const G4EquationOfMotion *	GetEquationOfMotion () const
void	SetEquationOfMotion (G4EquationOfMotion *newEquation)
unsigned long	GetfNoRHSCalls ()
void	ResetfNORHSCalls ()
G4bool	IsFSAL () const
G4bool	isQSS () const
void	SetIsQSS (G4bool val)

Static Public Attributes
static constexpr G4int	N8 = N > 8 ? N : 8

Additional Inherited Members
Protected Member Functions inherited from G4MagIntegratorStepper
void	SetIntegrationOrder (G4int order)
void	SetFSAL (G4bool flag=true)

Detailed Description

template<class T_Equation, unsigned int N = 6>
class G4TDormandPrince45< T_Equation, N >

G4TDormandPrince45 is a templated version of G4DormandPrince745 5th order Runge-Kutta stepper.

Definition at line 55 of file G4TDormandPrince45.hh.

Constructor & Destructor Documentation

G4TDormandPrince45() [1/2]

template<class T_Equation, unsigned int N>

G4TDormandPrince45< T_Equation, N >::G4TDormandPrince45

(

T_Equation *

equation

)

Definition at line 164 of file G4TDormandPrince45.hh.

    : G4MagIntegratorStepper(dynamic_cast<G4EquationOfMotion*>(equation), N )
    , fEquation_Rhs(equation)
{
  // assert( dynamic_cast<G4EquationOfMotion*>(equation) != nullptr );
  if( dynamic_cast<G4EquationOfMotion*>(equation) == nullptr )
  {
    G4Exception("G4TDormandPrince745: constructor", "GeomField0001",
                FatalException, "T_Equation is not an G4EquationOfMotion.");
  }
 
  /***
  assert( equation->GetNumberOfVariables == N );
  if( equation->GetNumberOfVariables != N ){
    G4ExceptionDescription msg;
    msg << "Equation has an incompatible number of variables." ;
    msg << "   template N = " << N << " equation-Nvar= "
        << equation->GetNumberOfVariables;
    G4Exception("G4TCashKarpRKF45: constructor", "GeomField0001",
                FatalException, msg );
   } ****/
}

Referenced by G4TDormandPrince45().

G4TDormandPrince45() [2/2]

template<class T_Equation, unsigned int N>

G4TDormandPrince45< T_Equation, N >::G4TDormandPrince45 ( T_Equation * equation, G4int numVar )

inline

Definition at line 188 of file G4TDormandPrince45.hh.

  : G4TDormandPrince45<T_Equation,N>(equation )
{
  if( numVar != G4int(N))
  {
    G4ExceptionDescription msg;
    msg << "Equation has an incompatible number of variables." ;
    msg << "   template N = " << N
        << "   argument numVar = " << numVar ;
    //    << " equation-Nvar= " << equation->GetNumberOfVariables(); // --> Expected later
    G4Exception("G4TCashKarpRKF45: constructor", "GeomField0001",
                   FatalErrorInArgument, msg );
  }
  assert( numVar == N );
}

Member Function Documentation

DistChord()

template<class T_Equation, unsigned int N>

G4double G4TDormandPrince45< T_Equation, N >::DistChord ( ) const

inlinefinalvirtual

Estimates the maximum distance of a chord from the true path over the segment last integrated.

Implements G4MagIntegratorStepper.

Definition at line 352 of file G4TDormandPrince45.hh.

{
  // Coefficients were taken from Some Practical Runge-Kutta Formulas
  // by Lawrence F. Shampine, page 149, c*
  //
  const G4double hf1 = 6025192743.0 / 30085553152.0,
                 hf3 = 51252292925.0 / 65400821598.0,
                 hf4 = - 2691868925.0 / 45128329728.0,
                 hf5 = 187940372067.0 / 1594534317056.0,
                 hf6 = - 1776094331.0 / 19743644256.0,
                 hf7 = 11237099.0 / 235043384.0;
 
  G4ThreeVector mid;
 
  for(unsigned int i = 0; i < 3; ++i) 
  {
    mid[i] = fyIn[i] + 0.5 * fLastStepLength * (
        hf1 * fdydxIn[i] + hf3 * ak3[i] + 
        hf4 * ak4[i] + hf5 * ak5[i] + hf6 * ak6[i] + hf7 * ak7[i]);
  }
 
  const G4ThreeVector begin = makeVector(fyIn, field_utils::Value3D::Position);
  const G4ThreeVector end = makeVector(fyOut,  field_utils::Value3D::Position);
 
  return G4LineSection::Distline(mid, begin, end);
}

GetSpecificEquation()

template<class T_Equation, unsigned int N = 6>

T_Equation * G4TDormandPrince45< T_Equation, N >::GetSpecificEquation ( )

inline

Definition at line 117 of file G4TDormandPrince45.hh.

{ return fEquation_Rhs; }

GetYOut()

template<class T_Equation, unsigned int N = 6>

const field_utils::ShortState< N > & G4TDormandPrince45< T_Equation, N >::GetYOut ( ) const

inline

Definition at line 95 of file G4TDormandPrince45.hh.

{ return fyOut; }

IntegratorOrder()

template<class T_Equation, unsigned int N = 6>

G4int G4TDormandPrince45< T_Equation, N >::IntegratorOrder ( ) const

inlineoverridevirtual

Returns the order of the integrator, i.e. its error behaviour is of the order O(h^order).

Implements G4MagIntegratorStepper.

Definition at line 91 of file G4TDormandPrince45.hh.

{ return 4; }

Referenced by IntegratorOrder().

Interpolate()

template<class T_Equation, unsigned int N = 6>

void G4TDormandPrince45< T_Equation, N >::Interpolate ( G4double tau, G4double yOut[] ) const

inline

Definition at line 83 of file G4TDormandPrince45.hh.

    {
      Interpolate4thOrder(yOut, tau);
    }

Interpolate4thOrder()

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::Interpolate4thOrder ( G4double yOut[], G4double tau ) const

inline

Definition at line 386 of file G4TDormandPrince45.hh.

{    
  const G4double tau2 = tau * tau,
                 tau3 = tau * tau2,
                 tau4 = tau2 * tau2;
 
  const G4double bf1 = 1.0 / 11282082432.0 * (
      157015080.0 * tau4 - 13107642775.0 * tau3 + 34969693132.0 * tau2 - 
      32272833064.0 * tau + 11282082432.0);
 
  const G4double bf3 = - 100.0 / 32700410799.0 * tau * (
      15701508.0 * tau3 - 914128567.0 * tau2 + 2074956840.0 * tau - 
      1323431896.0);
    
  const G4double bf4 = 25.0 / 5641041216.0 * tau * (
      94209048.0 * tau3 - 1518414297.0 * tau2 + 2460397220.0 * tau - 
      889289856.0);
    
  const G4double bf5 = - 2187.0 / 199316789632.0 * tau * (
      52338360.0 * tau3 - 451824525.0 * tau2 + 687873124.0 * tau - 
      259006536.0);
 
  const G4double bf6 = 11.0 / 2467955532.0 * tau * (
      106151040.0 * tau3 - 661884105.0 * tau2 + 
      946554244.0 * tau - 361440756.0);
    
  const G4double bf7 = 1.0 / 29380423.0 * tau * (1.0 - tau) * (
      8293050.0 * tau2 - 82437520.0 * tau + 44764047.0);
 
  for(unsigned int i = 0; i < N; ++i)
  {
      yOut[i] = fyIn[i] + fLastStepLength * tau * (
          bf1 * fdydxIn[i] + bf3 * ak3[i] + bf4 * ak4[i] + 
          bf5 * ak5[i] + bf6 * ak6[i] + bf7 * ak7[i]);
  }
}

Referenced by Interpolate().

Interpolate5thOrder()

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::Interpolate5thOrder ( G4double yOut[], G4double tau ) const

inline

Definition at line 481 of file G4TDormandPrince45.hh.

{
  // Define the coefficients for the polynomials
  //
  G4double bi[10][5];
    
  //  COEFFICIENTS OF   bi[1]
  bi[1][0] = 1.0,
  bi[1][1] = -38039.0 / 7040.0,
  bi[1][2] = 125923.0 / 10560.0,
  bi[1][3] = -19683.0 / 1760.0,
  bi[1][4] = 3303.0 / 880.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[2]
  bi[2][0] = 0.0,
  bi[2][1] = 0.0,
  bi[2][2] = 0.0,
  bi[2][3] = 0.0,
  bi[2][4] = 0.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[3]
  bi[3][0] = 0.0,
  bi[3][1] = -12500.0 / 4081.0,
  bi[3][2] = 205000.0 / 12243.0,
  bi[3][3] = -90000.0 / 4081.0,
  bi[3][4] = 36000.0 / 4081.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[4]
  bi[4][0] = 0.0,
  bi[4][1] = -3125.0 / 704.0,
  bi[4][2] = 25625.0 / 1056.0,
  bi[4][3] = -5625.0 / 176.0,
  bi[4][4] = 1125.0 / 88.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[5]
  bi[5][0] = 0.0,
  bi[5][1] = 164025.0 / 74624.0,
  bi[5][2] = -448335.0 / 37312.0,
  bi[5][3] = 295245.0 / 18656.0,
  bi[5][4] = -59049.0 / 9328.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[6]
  bi[6][0] = 0.0,
  bi[6][1] = -25.0 / 28.0,
  bi[6][2] = 205.0 / 42.0,
  bi[6][3] = -45.0 / 7.0,
  bi[6][4] = 18.0 / 7.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[7]
  bi[7][0] = 0.0,
  bi[7][1] = -2.0 / 11.0,
  bi[7][2] = 73.0 / 55.0,
  bi[7][3] = -171.0 / 55.0,
  bi[7][4] = 108.0 / 55.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[8]
  bi[8][0] = 0.0,
  bi[8][1] = 189.0 / 22.0,
  bi[8][2] = -1593.0 / 55.0,
  bi[8][3] = 3537.0 / 110.0,
  bi[8][4] = -648.0 / 55.0,
  //  --------------------------------------------------------
  //
  //  COEFFICIENTS OF  bi[9]
  bi[9][0] = 0.0,
  bi[9][1] = 351.0 / 110.0,
  bi[9][2] = -999.0 / 55.0,
  bi[9][3] = 2943.0 / 110.0,
  bi[9][4] = -648.0 / 55.0;
  //  --------------------------------------------------------
        
  // Calculating the polynomials
 
  G4double b[10];
  std::memset(b, 0.0, sizeof(b));
 
  G4double tauPower = 1.0;
  for(G4int j = 0; j <= 4; ++j)
  {       
    for(G4int iStage = 1; iStage <= 9; ++iStage)
    {
      b[iStage] += bi[iStage][j] * tauPower;
    }
    tauPower *= tau;       
  }
 
  const G4double stepLen = fLastStepLength * tau;
  for(G4int i = 0; i < N; ++i)
  {
    yOut[i] = fyIn[i] + stepLen * (
       b[1] * fdydxIn[i] + b[2] * ak2[i] + b[3] * ak3[i] +
       b[4] * ak4[i] + b[5] * ak5[i] + b[6] * ak6[i] +
       b[7] * ak7[i] + b[8] * ak8[i] + b[9] * ak9[i]
    );
  }
}

RightHandSideInl()

template<class T_Equation, unsigned int N = 6>

void G4TDormandPrince45< T_Equation, N >::RightHandSideInl ( const G4double y[], G4double dydx[] )

inline

Definition at line 103 of file G4TDormandPrince45.hh.

    {
      fEquation_Rhs->T_Equation::RightHandSide(y, dydx);
    }

Referenced by SetupInterpolation5thOrder(), and StepWithError().

SetupInterpolation()

template<class T_Equation, unsigned int N = 6>

void G4TDormandPrince45< T_Equation, N >::SetupInterpolation ( )

inline

Definition at line 81 of file G4TDormandPrince45.hh.

{}

SetupInterpolation5thOrder()

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::SetupInterpolation5thOrder ( )

inline

Definition at line 432 of file G4TDormandPrince45.hh.

{
  // Coefficients for the additional stages
  //
  const G4double b81 = 6245.0 / 62208.0,
                 b82 = 0.0,
                 b83 = 8875.0 / 103032.0,
                 b84 = -125.0 / 1728.0,
                 b85 = 801.0 / 13568.0,
                 b86 = -13519.0 / 368064.0,
                 b87 = 11105.0 / 368064.0,
 
                 b91 = 632855.0 / 4478976.0,
                 b92 = 0.0,
                 b93 = 4146875.0 / 6491016.0,
                 b94 = 5490625.0 /14183424.0,
                 b95 = -15975.0 / 108544.0,
                 b96 = 8295925.0 / 220286304.0,
                 b97 = -1779595.0 / 62938944.0,
                 b98 = -805.0 / 4104.0;
 
  field_utils::ShortState<N> yTemp;
 
  // Evaluate the extra stages
  //
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + fLastStepLength * (
        b81 * fdydxIn[i] + b82 * ak2[i] + b83 * ak3[i] +
        b84 * ak4[i] + b85 * ak5[i] + b86 * ak6[i] +
        b87 * ak7[i]
    );
  }
  RightHandSideInl(yTemp, ak8);          // 8th Stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + fLastStepLength * (
        b91 * fdydxIn[i] + b92 * ak2[i] + b93 * ak3[i] +
        b94 * ak4[i] + b95 * ak5[i] + b96 * ak6[i] +
        b97 * ak7[i] + b98 * ak8[i]
    );
  }
  RightHandSideInl(yTemp, ak9);          // 9th Stage
}

Stepper() [1/2]

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::Stepper ( const G4double y[], const G4double dydx[], G4double h, G4double yout[], G4double yerr[] )

inlinefinalvirtual

The stepper for the Runge Kutta integration. The stepsize is fixed, with the step size given by 'h'. Integrates ODE starting values y[0 to 6]. Outputs yout[] and its estimated error yerr[].

Parameters

[in]	y	Starting values array of integration variables.
[in]	dydx	Derivatives array.
[in]	h	The given step size.
[out]	yout	Integration output.
[out]	yerr	The estimated error.

Implements G4MagIntegratorStepper.

Definition at line 339 of file G4TDormandPrince45.hh.

{
  assert( yOutput != yInput );
  assert( yError  != yInput );
  
  StepWithError( yInput, dydx, Step, yOutput, yError);
}

Stepper() [2/2]

template<class T_Equation, unsigned int N = 6>

void G4TDormandPrince45< T_Equation, N >::Stepper ( const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[], G4double dydxOutput[] )

inline

Definition at line 109 of file G4TDormandPrince45.hh.

    {
      StepWithFinalDerivate(yInput, dydx, hstep, yOutput, yError, dydxOutput);
    }

StepperType()

template<class T_Equation, unsigned int N = 6>

G4StepperType G4TDormandPrince45< T_Equation, N >::StepperType ( ) const

inlineoverridevirtual

Returns the stepper type ID ('kUserStepper'). This function should be overriden in derived classes.

Reimplemented from G4MagIntegratorStepper.

Definition at line 93 of file G4TDormandPrince45.hh.

{ return kTDormandPrince45; }

StepWithError()

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::StepWithError ( const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[] )

inline

Definition at line 226 of file G4TDormandPrince45.hh.

{
  // The parameters of the Butcher tableu
  //
  constexpr G4double b21 = 0.2,
                 b31 = 3.0 / 40.0, b32 = 9.0 / 40.0,
                 b41 = 44.0 / 45.0, b42 = -56.0 / 15.0, b43 = 32.0/9.0,
 
  b51 = 19372.0 / 6561.0, b52 = -25360.0 / 2187.0, b53 = 64448.0 / 6561.0,
  b54 = -212.0 / 729.0,
        
  b61 = 9017.0 / 3168.0 , b62 =   -355.0 / 33.0,
  b63 = 46732.0 / 5247.0, b64 = 49.0 / 176.0,
  b65 = -5103.0 / 18656.0,
        
  b71 = 35.0 / 384.0, b72 = 0.,
  b73 = 500.0 / 1113.0, b74 = 125.0 / 192.0,
  b75 = -2187.0 / 6784.0, b76 = 11.0 / 84.0,
    
  // Sum of columns, sum(bij) = ei
  //    e1 = 0. ,
  //    e2 = 1.0/5.0 ,
  //    e3 = 3.0/10.0 ,
  //    e4 = 4.0/5.0 ,
  //    e5 = 8.0/9.0 ,
  //    e6 = 1.0 ,
  //    e7 = 1.0 ,
  
  // Difference between the higher and the lower order method coeff. :
  // b7j are the coefficients of higher order
    
  dc1 = -(b71 - 5179.0 / 57600.0),
  dc2 = -(b72 - .0),
  dc3 = -(b73 - 7571.0 / 16695.0),
  dc4 = -(b74 - 393.0 / 640.0),
  dc5 = -(b75 + 92097.0 / 339200.0),
  dc6 = -(b76 - 187.0 / 2100.0),
  dc7 = -(- 1.0 / 40.0);
    
  // const G4int numberOfVariables = GetNumberOfVariables();
  //   The number of variables to be integrated over    
  field_utils::ShortState<N8> yTemp;
    
  yOut[7] = yTemp[7]  = fyIn[7] = yInput[7];  // Pass along the time - used in RightHandSide
    
  //  Saving yInput because yInput and yOut can be aliases for same array
  //
  for(unsigned int i = 0; i < N; ++i)
  {
    fyIn[i]  = yInput[i];
    yTemp[i] = yInput[i] + b21 * hstep * dydx[i];
  }
  RightHandSideInl(yTemp, ak2);              // 2nd stage
 
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + hstep * (b31 * dydx[i] + b32 * ak2[i]);
  }
  RightHandSideInl(yTemp, ak3);              // 3rd stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + hstep * (
        b41 * dydx[i] + b42 * ak2[i] + b43 * ak3[i]);
  }
  RightHandSideInl(yTemp, ak4);              // 4th stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + hstep * (
        b51 * dydx[i] + b52 * ak2[i] + b53 * ak3[i] + b54 * ak4[i]);
  }
  RightHandSideInl(yTemp, ak5);              // 5th stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yTemp[i] = fyIn[i] + hstep * (
        b61 * dydx[i] + b62 * ak2[i] + 
        b63 * ak3[i] + b64 * ak4[i] + b65 * ak5[i]);
  }
  RightHandSideInl(yTemp, ak6);              // 6th stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yOut[i] = fyIn[i] + hstep * (
        b71 * dydx[i] + b72 * ak2[i] + b73 * ak3[i] +
        b74 * ak4[i] + b75 * ak5[i] + b76 * ak6[i]);
  }
  RightHandSideInl(yOut, ak7);               // 7th and Final stage
    
  for(unsigned int i = 0; i < N; ++i)
  {
    yErr[i] = hstep * (
        dc1 * dydx[i] + dc2 * ak2[i] + 
        dc3 * ak3[i] + dc4 * ak4[i] +
        dc5 * ak5[i] + dc6 * ak6[i] + dc7 * ak7[i]
    ) + 1.5e-18;
 
    // Store Input and Final values, for possible use in calculating chord
    //
    fyOut[i] = yOut[i];
    fdydxIn[i] = dydx[i];        
  }
    
  fLastStepLength = hstep;
}

Referenced by Stepper(), and StepWithFinalDerivate().

StepWithFinalDerivate()

template<class T_Equation, unsigned int N>

void G4TDormandPrince45< T_Equation, N >::StepWithFinalDerivate ( const G4double yInput[], const G4double dydx[], G4double hstep, G4double yOutput[], G4double yError[], G4double dydxOutput[] )

inline

Definition at line 207 of file G4TDormandPrince45.hh.

{
  StepWithError(yInput, dydx, hstep, yOutput, yError);
  field_utils::copy(dydxOutput, ak7, N);
}

Referenced by Stepper().

Member Data Documentation

N8

template<class T_Equation, unsigned int N = 6>

G4int G4TDormandPrince45< T_Equation, N >::N8 = N > 8 ? N : 8

staticconstexpr

Definition at line 119 of file G4TDormandPrince45.hh.

---

The documentation for this class was generated from the following file:

• G4TDormandPrince45.hh