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// File: TwoPointsNumericalDerivative.h
// Created by: Julien Dutheil
// Created on: Mon May 28 10:33 2007
//
/*
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 _TWOPOINTSNUMERICALDERIVATIVE_H_
#define _TWOPOINTSNUMERICALDERIVATIVE_H_
#include "Functions.h"
#include "AbstractNumericalDerivative.h"
//From the STL:
#include <map>
#include <vector>
#include <string>
namespace bpp
{
/**
* @brief Two points numerical derivative function wrapper.
*
* Numerical derivatives use two points to compute the (first order) derivatives.
* @f$x_0@f$ is the focus point and @f$x_{+1} = x_0+h@f$ (or @f$x_0-h@f$, if constrained on the right).
* Corresponding function values are @f$f_0@f$, @f$f_{-1}@f$ and @f$f_{+1/-1}@f$ respectively.
* The derivatives are then computed using the central formulas:
* @f{eqnarray*}
* \dfrac{\partial f}{\partial x } &=& \dfrac{f_{+1}-f_{0}}{h}\mathrm{\ or}\\
* \dfrac{\partial f}{\partial x } &=& \dfrac{f_{0}-f_{-1}}{h}\\
* @f}
* This class does not allow computation of second order derivatives.
*
* 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, ThreePointsNumericalDerivative, FivePointsNumericalDerivative
*/
class TwoPointsNumericalDerivative:
public AbstractNumericalDerivative
{
private:
double f1_, f2_;
public:
TwoPointsNumericalDerivative(Function* function) :
AbstractNumericalDerivative(function), f1_(), f2_() {}
TwoPointsNumericalDerivative(DerivableFirstOrder* function) :
AbstractNumericalDerivative(function), f1_(), f2_() {}
virtual ~TwoPointsNumericalDerivative() {}
TwoPointsNumericalDerivative* clone() const { return new TwoPointsNumericalDerivative(*this); }
public:
double getValue() const throw (Exception) { return f1_; }
/**
* @name The DerivableSecondOrder interface
*
* @{
*/
double getSecondOrderDerivative(const std::string & variable) const
throw (Exception)
{
throw Exception("Second order derivative not avalaible with two points method.");
}
double getSecondOrderDerivative(const std::string & variable1, const std::string & variable2) const
throw (Exception)
{
throw Exception("Unimplemented cross derivative.");
}
/** @} */
protected:
void updateDerivatives(const ParameterList parameters)
throw (ParameterNotFoundException, ConstraintException);
};
} //end of namespace bpp.
#endif //_TWOPOINTSNUMERICALDERIVATIVE_H_
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