m_henon.h

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/////////////////////////////////////////////////////////////////////////////
///
/// @file m_henon.h
///
/// The Henon map.
///
/// @author Pawel Pilarczyk
///
/////////////////////////////////////////////////////////////////////////////
 
// Copyright (C) 1997-2014 by Pawel Pilarczyk.
//
// This file is part of my research software package. This is free software:
// you can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// This software is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this software; see the file "license.txt". If not,
// please, see <https://www.gnu.org/licenses/>.
 
// Started on January 18, 2010. Last revision: January 18, 2010.
 
 
#ifndef _CMGRAPHS_HENON_H_
#define _CMGRAPHS_HENON_H_
 
 
// the generic class for the type of a map
#include "maptype.h"
 
// the interval arithmetic data types
#include "typeintv.h"
 
 
// --------------------------------------------------
// -------- a sample difference equation map --------
// --------------------------------------------------
 
/// This class defines the Henon map.
/// There are only two parameters of this map: 'a' and 'b'.
class MapHenon: public MapType
{
public:
        /// The default constructor.
        MapHenon ();
 
        /// Computes the image of a box whose left and right coordinates
        /// are given. Fills in the images with the left and right
        /// coordinates of the image box.
        void compute (const double *xleft, const double *xright,
                double *yleft, double *yright, int dim,
                const spcCoord *coord, int subdiv) const;
 
}; /* class MapHenon */
 
// --------------------------------------------------
 
inline MapHenon::MapHenon ()
{
        testIntervals ();
        return;
} /* MapHenon::MapHenon */
 
inline void MapHenon::compute (const double *xleft, const double *xright,
        double *yleft, double *yright, int dim, const spcCoord *, int) const
{
        if (dim != 2)
                throw "Wrong phase space dim for the Henon map.";
        IntervalType a (getLeftParam (0), getRightParam (0));
        IntervalType b (getLeftParam (1), getRightParam (1));
        IntervalType x (xleft [0], xright [0]);
        IntervalType x2;
        if ((xleft [0] >= 0) || (xright [0] <= 0))
        {
                x2 = x * x;
        }
        else
        {
                IntervalType half (0, (-xleft [0] >= xright [0]) ?
                        (-xleft [0]) : xright [0]);
                x2 = half * half;
        }
        IntervalType y (xleft [1], xright [1]);
        IntervalType one (1.0, 1.0);
        IntervalType xNew (y + one - a * x2);
        IntervalType yNew (b * x);
        yleft [0] = xNew. leftBound ();
        yright [0] = xNew. rightBound ();
        yleft [1] = yNew. leftBound ();
        yright [1] = yNew. rightBound ();
 
        // swich the rounding direction to the neutral one
        resetRounding ();
        return;
} /* MapHenon::compute */
 
 
#endif // _CMGRAPHS_HENON_H_