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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2000, 2001, 2002, 2003 RiskMap srl
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 newtonsafe.hpp
\brief Safe (bracketed) Newton 1-D solver
*/
#ifndef quantlib_solver1d_newtonsafe_h
#define quantlib_solver1d_newtonsafe_h
#include <ql/math/solver1d.hpp>
namespace QuantLib {
//! safe %Newton 1-D solver
/*! \note This solver requires that the passed function object
implement a method <tt>Real derivative(Real)</tt>.
\test the correctness of the returned values is tested by
checking them against known good results.
*/
class NewtonSafe : public Solver1D<NewtonSafe> {
public:
template <class F>
Real solveImpl(const F& f,
Real xAccuracy) const {
/* The implementation of the algorithm was inspired by
Press, Teukolsky, Vetterling, and Flannery,
"Numerical Recipes in C", 2nd edition,
Cambridge University Press
*/
Real froot, dfroot, dx, dxold;
Real xh, xl;
// Orient the search so that f(xl) < 0
if (fxMin_ < 0.0) {
xl = xMin_;
xh = xMax_;
} else {
xh = xMin_;
xl = xMax_;
}
// the "stepsize before last"
dxold = xMax_-xMin_;
// it was dxold=std::fabs(xMax_-xMin_); in Numerical Recipes
// here (xMax_-xMin_ > 0) is verified in the constructor
// and the last step
dx = dxold;
froot = f(root_);
dfroot = f.derivative(root_);
QL_REQUIRE(dfroot != Null<Real>(),
"NewtonSafe requires function's derivative");
++evaluationNumber_;
while (evaluationNumber_<=maxEvaluations_) {
// Bisect if (out of range || not decreasing fast enough)
if ((((root_-xh)*dfroot-froot)*
((root_-xl)*dfroot-froot) > 0.0)
|| (std::fabs(2.0*froot) > std::fabs(dxold*dfroot))) {
dxold = dx;
dx = (xh-xl)/2.0;
root_=xl+dx;
} else {
dxold = dx;
dx = froot/dfroot;
root_ -= dx;
}
// Convergence criterion
if (std::fabs(dx) < xAccuracy)
return root_;
froot = f(root_);
dfroot = f.derivative(root_);
++evaluationNumber_;
if (froot < 0.0)
xl=root_;
else
xh=root_;
}
QL_FAIL("maximum number of function evaluations ("
<< maxEvaluations_ << ") exceeded");
}
};
}
#endif
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