/* -*- 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

 <https://www.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.cpp */

#include <ql/methods/finitedifferences/operators/numericaldifferentiation.hpp>

#pragma push_macro("BOOST_DISABLE_ASSERTS")

#ifndef BOOST_DISABLE_ASSERTS

#define BOOST_DISABLE_ASSERTS

#endif

#include <boost/multi_array.hpp>

#pragma pop_macro("BOOST_DISABLE_ASSERTS")

#include <utility>

namespace QuantLib {

    namespace {

        Array calcOffsets(

            Real h, Size n, NumericalDifferentiation::Scheme scheme) {

            QL_REQUIRE(n > 1, "number of steps must be greater than one");

            Array retVal(n);

            switch (scheme) {

              case NumericalDifferentiation::Central:

                QL_REQUIRE(n > 2 && (n % 2),

                    "number of steps must be an odd number greater than two");

                for (Integer i=0; i < Integer(n); ++i)

                    retVal[i] = (i-Integer(n/2))*h;

                break;

              case NumericalDifferentiation::Backward:

                for (Size i=0; i < n; ++i)

                    retVal[i]=-(i*h);

                break;

              case NumericalDifferentiation::Forward:

                for (Size i=0; i < n; ++i)

                    retVal[i]=i*h;

                break;

              default:

                QL_FAIL("unknown numerical differentiation scheme");

            }

            return retVal;

        }

        // This is a C++ implementation of the algorithm/pseudo code in

        // B. Fornberg, 1998. Calculation of Weights

        //                    in Finite Difference Formulas

        // https://amath.colorado.edu/faculty/fornberg/Docs/sirev_cl.pdf

        Array calcWeights(const Array& x, Size M) {

            const Size N = x.size();

            QL_REQUIRE(N > M, "number of points must be greater "

                               "than the order of the derivative");

            QL_DEPRECATED_DISABLE_WARNING

            boost::multi_array<Real, 3>  d(boost::extents[M+1][N][N]);

            QL_DEPRECATED_ENABLE_WARNING

            d[0][0][0] = 1.0;

            Real c1 = 1.0;

            for (Size n=1; n < N; ++n) {

                Real c2 = 1.0;

                for (Size nu=0; nu < n; ++nu) {

                    const Real c3 = x[n] - x[nu];

                    c2*=c3;

                    for (Size m=0; m <= std::min(n, M); ++m) {

                        d[m][n][nu] = (x[n]*d[m][n-1][nu]

                             - ((m > 0)? Real(m*d[m-1][n-1][nu]) : 0.0))/c3;

                    }

                }

                for (Size m=0; m <= M; ++m) {

                    d[m][n][n] = c1/c2*( ((m > 0)? Real(m*d[m-1][n-1][n-1]) : 0.0) -

                        x[n-1]*d[m][n-1][n-1] );

                }

                c1=c2;

            }

            Array retVal(N);

            for (Size i=0; i < N; ++i) {

                retVal[i] = d[M][N-1][i];

            }

            return retVal;

        }

    }

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

                                                       Size orderOfDerivative,

                                                       Array x_offsets)

    : offsets_(std::move(x_offsets)), w_(calcWeights(offsets_, orderOfDerivative)),

      f_(std::move(f)) {}

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

                                                       Size orderOfDerivative,

                                                       Real stepSize,

                                                       Size steps,

                                                       Scheme scheme)

    : offsets_(calcOffsets(stepSize, steps, scheme)), w_(calcWeights(offsets_, orderOfDerivative)),

      f_(std::move(f)) {}

}