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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
<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
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