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/*
Copyright (C) 2000, 2001, 2002 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 ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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.cpp
\brief Safe (braketed) Newton 1-D solver
\fullpath
ql/Solvers1D/%newtonsafe.cpp
*/
// $Id: newtonsafe.cpp,v 1.6 2002/01/16 14:41:17 nando Exp $
/* The implementation of the algorithm was inspired by
* "Numerical Recipes in C", 2nd edition, Press, Teukolsky, Vetterling, Flannery
* Chapter 9
*/
#include <ql/Solvers1D/newtonsafe.hpp>
namespace QuantLib {
namespace Solvers1D {
double NewtonSafe::solve_(const ObjectiveFunction& f,
double xAccuracy) const {
double froot, dfroot, dx, dxold;
double 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=QL_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<double>(),
"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)
|| (QL_FABS(2.0*froot) > QL_FABS(dxold*dfroot))) {
dxold = dx;
dx = (xh-xl)/2.0;
root_=xl+dx;
} else {
dxold=dx;
dx=froot/dfroot;
root_ -= dx;
}
// Convergence criterion
if (QL_FABS(dx) < xAccuracy)
return root_;
froot = f(root_);
dfroot = f.derivative(root_);
evaluationNumber_++;
if (froot < 0.0)
xl=root_;
else
xh=root_;
}
throw Error("NewtonSafe: maximum number of function evaluations (" +
IntegerFormatter::toString(maxEvaluations_) +
") exceeded");
QL_DUMMY_RETURN(0.0);
} // double NewtonSafe::solve_
} // namespace Solvers1D
} // namespace QuantLib
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