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// File: ThreePointsNumericalDerivative.h
// Created by: Julien Dutheil
// Created on: Thu Aug 17 15:00 2006
//
/*
Copyright or © or Copr. CNRS, (November 17, 2004)
This software is a computer program whose purpose is to provide classes
for numerical calculus.
This software is governed by the CeCILL license under French law and
abiding by the rules of distribution of free software. You can use,
modify and/ or redistribute the software under the terms of the CeCILL
license as circulated by CEA, CNRS and INRIA at the following URL
"http://www.cecill.info".
As a counterpart to the access to the source code and rights to copy,
modify and redistribute granted by the license, users are provided only
with a limited warranty and the software's author, the holder of the
economic rights, and the successive licensors have only limited
liability.
In this respect, the user's attention is drawn to the risks associated
with loading, using, modifying and/or developing or reproducing the
software by the user in light of its specific status of free software,
that may mean that it is complicated to manipulate, and that also
therefore means that it is reserved for developers and experienced
professionals having in-depth computer knowledge. Users are therefore
encouraged to load and test the software's suitability as regards their
requirements in conditions enabling the security of their systems and/or
data to be ensured and, more generally, to use and operate it in the
same conditions as regards security.
The fact that you are presently reading this means that you have had
knowledge of the CeCILL license and that you accept its terms.
*/
#ifndef _THREEPOINTSNUMERICALDERIVATIVE_H_
#define _THREEPOINTSNUMERICALDERIVATIVE_H_
#include "Functions.h"
#include "AbstractNumericalDerivative.h"
// From the STL:
#include <map>
#include <vector>
#include <string>
namespace bpp
{
/**
* @brief Three points numerical derivative function wrapper.
*
* Numerical derivatives use three points to compute the derivatives.
* @f$x_0@f$ is the focus point, @f$x_{-1} = x_0-h@f$ and @f$x_{+1} = x_0+h@f$
* are other points, with function values @f$f_0@f$, @f$f_{-1}@f$ and @f$f_{+1}@f$ respectively.
* The derivatives are then computed using the central formulas:
* @f{eqnarray*}
* \dfrac{\partial f}{\partial x } &=& \dfrac{f_{+1}-f_{-1}}{2h}\\
* \dfrac{\partial^2 f}{\partial x^2} &=& \dfrac{f_{+1}-2f_0+f_{-1}}{h^2}\\
* @f}
* In case of border limit (when @f$x_{-1}@f$ or @f$x_{+1}@f$ are not computable),
* the foreward and backward computations are performed, respectively:
* @f{eqnarray*}
* \dfrac{\partial f}{\partial x } &=& \dfrac{f_{+1}-f_0}{h}\\
* \dfrac{\partial^2 f}{\partial x^2} &=& \dfrac{f_{+2}-2f_{+1}+f_0}{h^2}\\
* @f}
* and
* @f{eqnarray*}
* \dfrac{\partial f}{\partial x } &=& \dfrac{f_0-f_{-1}}{h}\\
* \dfrac{\partial^2 f}{\partial x^2} &=& \dfrac{f_0-2f_{-1}+f_{-2}}{h^2}\\
* @f}
*
* The @f$h@f$ parameter is computed in a parameter dependent manner:
* @f$ h = x \times e@f$, with @f$x \neq 0@f$ being the current parameter value.
* If @f$x = 0@f$, @f$h = e@f$.
* Default value is provided for @f$e@f$ and corresponds to the _h field.
* The default value works fine in most cases, but you may want to change it using the setInterval method.
*
* @see AbstractNumericalDerivative
*/
class ThreePointsNumericalDerivative :
public AbstractNumericalDerivative
{
private:
double f1_, f2_, f3_, f11_, f22_, f12_, f21_;
public:
ThreePointsNumericalDerivative (Function* function) :
AbstractNumericalDerivative(function),
f1_(),
f2_(),
f3_(),
f11_(),
f22_(),
f12_(),
f21_() {}
ThreePointsNumericalDerivative (DerivableFirstOrder* function) :
AbstractNumericalDerivative(function),
f1_(),
f2_(),
f3_(),
f11_(),
f22_(),
f12_(),
f21_() {}
ThreePointsNumericalDerivative (DerivableSecondOrder* function) :
AbstractNumericalDerivative(function),
f1_(),
f2_(),
f3_(),
f11_(),
f22_(),
f12_(),
f21_() {}
virtual ~ThreePointsNumericalDerivative() {}
ThreePointsNumericalDerivative* clone() const { return new ThreePointsNumericalDerivative(*this); }
public:
double getValue() const
{
return f2_;
}
protected:
void updateDerivatives(const ParameterList parameters);
};
} // end of namespace bpp.
#endif // _THREEPOINTSNUMERICALDERIVATIVE_H_
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