/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */

/*

 Copyright (C) 2015 Klaus Spanderen

 This file is part of QuantLib, a free-software/open-source library

 for financial quantitative analysts and developers - http://quantlib.org/

 QuantLib is free software: you can redistribute it and/or modify it

 under the terms of the QuantLib license.  You should have received a

 copy of the license along with this program; if not, please email

 <quantlib-dev@lists.sf.net>. The license is also available online at

 <http://quantlib.org/license.shtml>.

 This program 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 license for more details.

*/

/*! \file numericaldifferentiation.hpp

    \brief numerical differentiation of arbitrary order

           and on irregular grids

*/

#ifndef quantlib_numerical_differentiation_hpp

#define quantlib_numerical_differentiation_hpp

#include <ql/math/array.hpp>

#include <ql/functional.hpp>

namespace QuantLib {

    //! Numerical Differentiation on arbitrarily spaced grids

    /*! References:

        B. Fornberg, 1988. Generation of Finite Difference Formulas

        on Arbitrarily Spaced Grids,

        http://amath.colorado.edu/faculty/fornberg/Docs/MathComp_88_FD_formulas.pdf

    */

    class NumericalDifferentiation {

      public:

        enum Scheme { Central, Backward, Forward };

        NumericalDifferentiation(std::function<Real(Real)> f,

                                 Size orderOfDerivative,

                                 Array x_offsets);

        NumericalDifferentiation(std::function<Real(Real)> f,

                                 Size orderOfDerivative,

                                 Real stepSize,

                                 Size steps,

                                 Scheme scheme);

        Real operator()(Real x) const;

        const Array& offsets() const;

        const Array& weights() const;

      private:

        const Array offsets_, w_;

        const std::function<Real(Real)> f_;

    };

    inline Real NumericalDifferentiation::operator()(Real x) const {

        Real s = 0.0;

        for (Size i=0; i < w_.size(); ++i) {

            if (std::fabs(w_[i]) > QL_EPSILON*QL_EPSILON) {

                s += w_[i] * f_(x+offsets_[i]);

            }

        }

        return s;

    }

    inline const Array& NumericalDifferentiation::weights() const {

        return w_;

    }

    inline const Array& NumericalDifferentiation::offsets() const {

        return offsets_;

    }

}

#endif