RDE_lib2/NonLinearSolutionTrajectory.h

/* *************************************************************

Copyright 2010 Terry Lyons, Stephen Buckley, Djalil Chafai, 
Greg Gyurkó and Arend Janssen. 

Distributed under the terms of the GNU General Public License, 
Version 3. (See accompanying file License.txt)

************************************************************* */



#pragma once

#ifndef __NONLINEARSOLUTIONTRAJECTORY__
#define __NONLINEARSOLUTIONTRAJECTORY__


#include "BaseTrajectory.h"
#include "alg_types.h"
#include "NonLinearGroupElement.h"



template <typename my_alg_type_IN, typename my_alg_type_OUT>
class NonLinearSolutionTrajectory :
        public BaseTrajectory<my_alg_type_OUT>
{
private:
        Path<my_alg_type_IN> & theControl;

        const std::vector<POLYLIE<my_alg_type_OUT>> theVectorFields;

        const SCA Inf;

        const AbstractSolutionPoint Ini;

public:
        NonLinearSolutionTrajectory(Path<my_alg_type_IN> & theControlIn, std::vector<POLYLIE<my_alg_type_OUT>> & theVectorFieldsIn, AbstractSolutionPoint & theInitialValue, SCA theStartTime = SCA(0))
                : theControl(theControlIn), theVectorFields(theVectorFieldsIn), Inf(theStartTime), Ini(theInitialValue)
        {
        };

        ~NonLinearSolutionTrajectory(void)
        {
        };

        AbstractSolutionPoint Value(const SCA t, const unsigned int Resolution=11) const
        {
                dyadic_interval Width(t-Inf, Resolution);
                dyadic_interval Begin = dyadic_interval::dyadic_bracket(Inf,Width.n); 
                dyadic_interval End = dyadic_interval::dyadic_bracket(t,Width.n);

                unsigned int NoIncrements = End.k - Begin.k;

                SPB::NonLinearGroupElement<my_alg_type_IN,my_alg_type_OUT> CurrentGroupElt;

                AbstractSolutionPoint CurrentValue;
                CurrentValue = Ini;

                AbstractSolutionPoint temp;

                dyadic_interval CurrentInterval=Begin;

                lietovectorfield<my_alg_type_IN,POLYLIE_OUT> l2vf(theVectorFields);

                for(unsigned int i=1; i <= NoIncrements; i++)
                {
                        CurrentGroupElt = SPB::NonLinearGroupElement<my_alg_type_IN,my_alg_type_OUT>(theControl.DescribePath(CurrentInterval++), l2vf);

                        temp = CurrentGroupElt.evaluate(CurrentValue);
                        CurrentValue = temp;
                }

                return CurrentValue;
        };
};

#endif // __NONLINEARSOLUTIONTRAJECTORY__