halley.hpp

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/* -*- 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
 <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 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