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// -*- coding: utf-8
// vim: set fileencoding=utf-8
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NUMERICAL_DIFF_H
#define EIGEN_NUMERICAL_DIFF_H
namespace Eigen {
enum NumericalDiffMode {
Forward,
Central
};
/**
* This class allows you to add a method df() to your functor, which will
* use numerical differentiation to compute an approximate of the
* derivative for the functor. Of course, if you have an analytical form
* for the derivative, you should rather implement df() by yourself.
*
* More information on
* http://en.wikipedia.org/wiki/Numerical_differentiation
*
* Currently only "Forward" and "Central" scheme are implemented.
*/
template<typename _Functor, NumericalDiffMode mode=Forward>
class NumericalDiff : public _Functor
{
public:
typedef _Functor Functor;
typedef typename Functor::Scalar Scalar;
typedef typename Functor::InputType InputType;
typedef typename Functor::ValueType ValueType;
typedef typename Functor::JacobianType JacobianType;
NumericalDiff(Scalar _epsfcn=0.) : Functor(), epsfcn(_epsfcn) {}
NumericalDiff(const Functor& f, Scalar _epsfcn=0.) : Functor(f), epsfcn(_epsfcn) {}
// forward constructors
template<typename T0>
NumericalDiff(const T0& a0) : Functor(a0), epsfcn(0) {}
template<typename T0, typename T1>
NumericalDiff(const T0& a0, const T1& a1) : Functor(a0, a1), epsfcn(0) {}
template<typename T0, typename T1, typename T2>
NumericalDiff(const T0& a0, const T1& a1, const T2& a2) : Functor(a0, a1, a2), epsfcn(0) {}
enum {
InputsAtCompileTime = Functor::InputsAtCompileTime,
ValuesAtCompileTime = Functor::ValuesAtCompileTime
};
/**
* return the number of evaluation of functor
*/
int df(const InputType& _x, JacobianType &jac) const
{
/* Local variables */
Scalar h;
int nfev=0;
const typename InputType::Index n = _x.size();
const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
ValueType val1, val2;
InputType x = _x;
// TODO : we should do this only if the size is not already known
val1.resize(Functor::values());
val2.resize(Functor::values());
// initialization
switch(mode) {
case Forward:
// compute f(x)
Functor::operator()(x, val1); nfev++;
break;
case Central:
// do nothing
break;
default:
assert(false);
};
// Function Body
for (int j = 0; j < n; ++j) {
h = eps * internal::abs(x[j]);
if (h == 0.) {
h = eps;
}
switch(mode) {
case Forward:
x[j] += h;
Functor::operator()(x, val2);
nfev++;
x[j] = _x[j];
jac.col(j) = (val2-val1)/h;
break;
case Central:
x[j] += h;
Functor::operator()(x, val2); nfev++;
x[j] -= 2*h;
Functor::operator()(x, val1); nfev++;
x[j] = _x[j];
jac.col(j) = (val2-val1)/(2*h);
break;
default:
assert(false);
};
}
return nfev;
}
private:
Scalar epsfcn;
NumericalDiff& operator=(const NumericalDiff&);
};
} // end namespace Eigen
//vim: ai ts=4 sts=4 et sw=4
#endif // EIGEN_NUMERICAL_DIFF_H
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