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// G4TsitourasRK45
//
// Class description:
//
// Tsitouras - 5(4) RK stepper (non-FSAL version)
// Implements RK tableau from 'Table 1' of:
//    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.

// Author: Somnath Banerjee (CERN, Google Summer of Code 2015), 11.06.2015
// Supervision: John Apostolakis (CERN)
// --------------------------------------------------------------------
#ifndef TSITOURAS_RK45_HH
#define TSITOURAS_RK45_HH

#include "G4MagIntegratorStepper.hh"

/**
 * @brief G4TsitourasRK45 is an implementation of the 5(4) Runge-Kutta
 * stepper (non-FSAL version).
 */

class G4TsitourasRK45 : public G4MagIntegratorStepper
{
  public:

    /**
     * Constructor for G4TsitourasRK45.
     *  @param[in] EqRhs Pointer to the provided equation of motion.
     *  @param[in] numberOfVariables The number of integration variables.
     *  @param[in] primary Flag for initialisation of the auxiliary stepper.
     */
    G4TsitourasRK45(G4EquationOfMotion* EqRhs,
                    G4int numberOfVariables = 6,
                    G4bool primary = true);
    /**
     * Destructor.
     */
    ~G4TsitourasRK45() override;

    /**
     * Copy constructor and assignment operator not allowed.
     */
    G4TsitourasRK45(const G4TsitourasRK45&) = delete;
    G4TsitourasRK45& operator=(const G4TsitourasRK45&) = delete;
    
    /**
     * 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[].
     *  @param[in] y Starting values array of integration variables.
     *  @param[in] dydx Derivatives array.
     *  @param[in] h The given step size.
     *  @param[out] yout Integration output.
     *  @param[out] yerr The estimated error.
     */
    void Stepper( const G4double y[],
                  const G4double dydx[],
                        G4double h,
                        G4double yout[],
                        G4double yerr[] ) override;
    
    /**
     * Setup all coefficients for interpolation.
     */
    void SetupInterpolation( /* const G4double yInput[],
                              const G4double dydx[],
                              const G4double Step */  );
    
    /**
     * Calculates the output at the tau fraction of step.
     *  @param[in] yInput Starting values array of integration variables.
     *  @param[in] dydx Derivatives array.
     *  @param[in] Step The given step size.
     *  @param[out] yOut Interpolation output.
     *  @param[in] tau The tau fraction of the step.
     */
    void Interpolate( const G4double yInput[],
                      const G4double dydx[],
                      const G4double Step,
                            G4double yOut[],
                            G4double tau );
    void interpolate( const G4double yInput[],
                      const G4double dydx[],
                            G4double yOut[],
                            G4double Step,
                            G4double tau);

    /**
     * Returns the distance from chord line.
     */
    G4double DistChord() const override;

    /**
     * Returns the order, 4, of integration.
     */
    inline G4int IntegratorOrder() const override { return 4; }

    /**
     * Returns the stepper type-ID, "kTsitourasRK45".
     */
    inline G4StepperType StepperType() const override { return kTsitourasRK45; }
    
  private :
    
    G4double *ak2, *ak3, *ak4, *ak5, *ak6, *ak7, *ak8, *yTemp, *yIn;
    
    G4double fLastStepLength = 0.0;
    G4double *fLastInitialVector, *fLastFinalVector,
             *fLastDyDx, *fMidVector, *fMidError;
      // For DistChord calculations
    
    G4TsitourasRK45* fAuxStepper = nullptr;
};

#endif