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// G4RK547FEq3
//
// Class description:
//
// An implementation of the 7 stage embedded Runge-Kutta 4,5 pair (RK547FEq3)
// from the paper:
//    D. J. Higham and G. Hall,
//    "Embedded Runge-Kutta formulae with stable equilibrium states",
//    J. Comput. Appl. Math., vol. 29, no. 1, pp. 25-33, 1990.

// Author: Dmitry Sorokin (CERN, Google Summer of Code 2017), 02.11.2017
// Supervision: John Apostolakis (CERN)
// --------------------------------------------------------------------
#ifndef G4RK547FEq3_HH
#define G4RK547FEq3_HH

#include "G4MagIntegratorStepper.hh"
#include "G4FieldTrack.hh"

/**
 * @brief G4RK547FEq3 is an implementation of the 7 stage embedded
 * Runge-Kutta 4,5 pair.
 */

class G4RK547FEq3 : public G4MagIntegratorStepper
{
  public:

    /**
     * Constructor for G4RK547FEq1.
     *  @param[in] EqRhs Pointer to the provided equation of motion.
     *  @param[in] integrationVariables The number of integration variables.
     */
    G4RK547FEq3(G4EquationOfMotion* EqRhs,
                G4int integrationVariables = 6);

    /**
     * Default Destructor.
     */
    ~G4RK547FEq3() override = default;

    /**
     * Copy constructor and assignment operator not allowed.
     */
    G4RK547FEq3(const G4RK547FEq3&) = delete;
    G4RK547FEq3& operator = (const G4RK547FEq3&) = delete;

    /**
     * The stepper for the Runge Kutta integration.
     * The stepsize is fixed, with the step size given by 'hstep'.
     * Integrates ODE starting values yInput[0 to 6].
     * Outputs yOutput[] and its estimated error yError[].
     *  @param[in] yInput Starting values array of integration variables.
     *  @param[in] dydx Derivatives array.
     *  @param[in] hstep The given step size.
     *  @param[out] yOutput Integration output.
     *  @param[out] yError The estimated error.
     */
    void Stepper( const G4double yInput[],
                  const G4double dydx[],
                        G4double hstep,
                        G4double yOutput[],
                        G4double yError[] ) override;

    /**
     * Same as the Stepper() function above, with dydx also in ouput.
     *  @param[in] yInput Starting values array of integration variables.
     *  @param[in] dydx Derivatives array.
     *  @param[in] hstep The given step size.
     *  @param[out] yOutput Integration output.
     *  @param[out] yError The estimated error.
     *  @param[out] dydxOutput dydx in output.
     */
    void Stepper( const G4double yInput[],
                  const G4double dydx[],
                        G4double hstep,
                        G4double yOutput[],
                        G4double yError[],
                        G4double dydxOutput[] );

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

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

    /**
     * Returns the stepper type-ID, "kRK547FEq3".
     */
    G4StepperType StepperType() const override { return kRK547FEq3; }

  private:

    /**
     * Utility method used in Stepper() for computing the actual step.
     */
    void makeStep( const G4double yInput[],
                   const G4double dydx[],
                   const G4double hstep,
                         G4double yOutput[],
                         G4double* dydxOutput = nullptr,
                         G4double* yError = nullptr) const;
  private:

    G4double fyIn[G4FieldTrack::ncompSVEC],
             fdydx[G4FieldTrack::ncompSVEC],
             fyOut[G4FieldTrack::ncompSVEC],
             fdydxOut[G4FieldTrack::ncompSVEC];

    G4double fhstep = -1.0;
};

#endif