// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Thomas Capricelli <orzel@freehackers.org>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, 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 2 of
// the License, or (at your option) any later version.
//
// Eigen 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 Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.

#ifndef EIGEN_NUMERICAL_DIFF_H
#define EIGEN_NUMERICAL_DIFF_H

enum NumericalDiffMode {
    Forward,
    Central
};


/**
  * \brief asdf 
  *
  * 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() using it.
  *
  * More information on
  * http://en.wikipedia.org/wiki/Numerical_differentiation
  *
  * Currently only "Forward" and "Central" scheme are implemented. Those
  * are basic methods, and there exist some more elaborated way of
  * computing such approximates. They are implemented using both
  * proprietary and free software, and usually requires linking to an
  * external library. It is very easy for you to write a functor
  * using such software, and the purpose is quite orthogonal to what we
  * want to achieve with Eigen.
  *
  * This is why we will not provide wrappers for every great numerical
  * differenciation software that exist, but should rather stick with those
  * basic ones, that still are useful for testing.
  *
  * Also, the module "Non linear optimization" needs this in order to
  * provide full features compatibility with the original (c)minpack
  * package.
  *
  */
template<typename Functor, NumericalDiffMode mode=Forward>
class NumericalDiff : public Functor
{
public:
    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 T1& 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 int n = _x.size();
        const Scalar eps = ei_sqrt((std::max(epsfcn,epsilon<Scalar>() )));
        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 * ei_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;
};

#endif // EIGEN_NUMERICAL_DIFF_H