codac2_CtcLohner.h

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#pragma once
 
#include "codac2_TimePropag.h"
#include "codac2_AnalyticFunction.h"
#include "codac2_TDomain.h"
#include "codac2_SlicedTube.h"
 
namespace codac2
{ 

  struct GlobalEnclosureError : public std::runtime_error {
    GlobalEnclosureError() : std::runtime_error(
        "Exceeded loop maximum range while looking for a global enclosure for the system.") {}
  };

  class LohnerAlgorithm {
  public:
    constexpr static const double FWD = 1., BWD = -1.;

    LohnerAlgorithm(const AnalyticFunction<VectorType> *f,
                    double h,
                    bool forward,
                    const IntervalVector &u0,
                    int contractions = 1,
                    double eps = 0.1);
    const IntervalVector &integrate(unsigned int steps, double H = -1);

    void contractStep(const IntervalVector &x);

    const IntervalVector &getLocalEnclosure() const;

    const IntervalVector &getGlobalEnclosure() const;
  private:
    IntervalVector globalEnclosure(const IntervalVector &initialGuess, double dir);
 
    unsigned int _dim; 
    double _h; 
    double _direction; 
    double _eps; 
    int _contractions; 
    IntervalVector _u; 
    IntervalVector _z; 
    IntervalVector _r; 
    IntervalVector _u_tilde; 
    Matrix _B, _Binv;
    Vector _u_hat; 
    const AnalyticFunction<VectorType> *_f; 
  };

  class CtcLohner
  {
    public:

      CtcLohner(const AnalyticFunction<VectorType>& f, int contractions = 5, double eps = 0.1);

      void contract(SlicedTube<IntervalVector> &tube, TimePropag t_propa = TimePropag::FWD_BWD) const;
 
 
    protected:
 
      AnalyticFunction<VectorType> _f; 
      int _contractions; 
      int _dim; 
      double _eps; 
  };
}