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

/*

 Copyright (C) 2024 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 halley.hpp

    \brief Halley 1-D solver

*/

#ifndef quantlib_solver1d_halley_hpp

#define quantlib_solver1d_halley_hpp

#include <ql/math/solvers1d/newtonsafe.hpp>

namespace QuantLib {

    //! %Halley 1-D solver

    /*! \note This solver requires that the passed function object

              implement a method <tt>Real derivative(Real)</tt>

              and <tt> Real secondDerivative(Real></tt>

        \test the correctness of the returned values is tested by

              checking them against known good results.

        \ingroup solvers

    */

    class Halley : public Solver1D<Halley> {

      public:

        template <class F>

        Real solveImpl(const F& f,

                       Real xAccuracy) const {

            while (++evaluationNumber_ <= maxEvaluations_) {

                const Real fx = f(root_);

                const Real fPrime = f.derivative(root_);

                const Real lf = fx*f.secondDerivative(root_)/(fPrime*fPrime);

                const Real step = 1.0/(1.0 - 0.5*lf)*fx/fPrime;

                root_ -= step;

                // jumped out of brackets, switch to NewtonSafe

                if ((xMin_-root_)*(root_-xMax_) < 0.0) {

                    NewtonSafe s;

                    s.setMaxEvaluations(maxEvaluations_-evaluationNumber_);

                    return s.solve(f, xAccuracy, root_+step, xMin_, xMax_);

                }

                if (std::abs(step) < xAccuracy) {

                    f(root_);

                    ++evaluationNumber_;

                    return root_;

                }

            }

            QL_FAIL("maximum number of function evaluations ("

                    << maxEvaluations_ << ") exceeded");

        }

    };

}

#endif