m_lorenz_a.h

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/////////////////////////////////////////////////////////////////////////////
///
/// @file m_lorenz_a.h
///
/// An approximate time-t map for the Lorenz equations.
/// This map defines a sample time-t map for an ODE.
///
/// @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 June 26, 2012. Last revision: June 26, 2012.
 
 
#ifndef _CMGRAPHS_LORENZAPPR_H_
#define _CMGRAPHS_LORENZAPPR_H_
 
 
// include local header files
#include "maptype.h"
#include "odeapprox.h"
 
 
// --------------------------------------------------
// ------------ the Lorenz time-t map ------------
// --------------------------------------------------
 
/// An approximate time-t map for the Lorenz equations.
class MapLorenzApprox: public MapOdeApprox
{
public:
        /// The constructor of a Lorenz map object.
        MapLorenzApprox ();
 
private:
        /// The vector field.
        void vectorField (double, const double *x, double *y, int dim) const;
 
}; /* class MapLorenzApprox */
 
// --------------------------------------------------
 
inline MapLorenzApprox::MapLorenzApprox ():
        MapOdeApprox (0.05/20, 20, 4)
{
        return;
} /* MapLorenzApprox::MapLorenzApprox */
 
inline void MapLorenzApprox::vectorField (double,
        const double *x, double *y, int dim) const
{
        if (dim != 3)
                throw "This model is valid in dimension 3 only.";
 
        // is this the Lorenz equation with reversed time?
        const bool reversed = false;
 
        // retrieve the parameters (the left bound only)
        double sigma = getLeftParam (0);
        double rho = getLeftParam (1);
        double beta = getLeftParam (2);
 
        // compute the vector field
        y [0] = sigma * (x [1] - x [0]);
        y [1] = x [0] * (rho - x [2]) - x [1];
        y [2] = x [0] * x [1] - beta * x [2];
 
        // reverse the vector field if requested to
        if (reversed)
        {
                for (int i = 0; i < dim; ++ i)
                        y [i] = -y [i];
        }
 
        return;
} /* MapLorenzApprox::vectorField */
 
 
#endif // _CMGRAPHS_LORENZAPPR_H_