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// G4ImplicitEuler
//
// Class description:
//
// Implicit Euler stepper for magnetic field:
//      x_1 = x_0 + h/2 * ( dx(t_0,x_0) + dx(t_0+h,x_0+h*dx(t_0,x_0) ) )
//
// Second order solver.
// Takes the current derivative and add it to the current position.
// Takes the output and its derivative. Adds the mean of both
// derivatives to form the final output.

// Author: W.Wander (MIT), 12.09.1997
// -------------------------------------------------------------------
#ifndef G4IMPLICITEULER_HH
#define G4IMPLICITEULER_HH

#include "G4MagErrorStepper.hh"

/**
 * @brief G4ImplicitEuler implements a Euler stepper for magnetic field
 * with 2nd order solver.
 */

class G4ImplicitEuler : public G4MagErrorStepper
{
  public:

    /**
     * Constructor for G4HelixSimpleRunge.
     *  @param[in] EqRhs Pointer to the provided equation of motion.
     *  @param[in] numberOfVariables The number of integration variables.
     */
    G4ImplicitEuler(G4EquationOfMotion* EqRhs,
                    G4int numberOfVariables = 6);

    /**
     * Destructor.
     */
    ~G4ImplicitEuler() override;

    /**
     * The stepper function for the integration.
     *  @param[in] y Starting values array of integration variables.
     *  @param[in] dydx The derivates array.
     *  @param[in] h The given step size.
     *  @param[out] yout Integration output.
     */
    void DumbStepper( const G4double y[] ,
                      const G4double dydx[] ,
                            G4double h ,
                            G4double yout[] ) override;

    /**
     * Returns the order, 2, of integration.
     */
    inline G4int IntegratorOrder() const override { return 2; }
    /**
     * Returns the stepper type-ID, "kImplicitEuler".
     */
    inline G4StepperType StepperType() const override { return kImplicitEuler; }

  private:

    /** Temporaries, created to avoid new/delete on every call. */
    G4double* dydxTemp = nullptr;
    G4double* yTemp = nullptr;    
};

#endif