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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 ridder.cpp
\brief Ridder 1-D solver
\fullpath
ql/Solvers1D/%ridder.cpp
*/
// $Id: ridder.cpp,v 1.5 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/ridder.hpp>
namespace QuantLib {
namespace Solvers1D {
#define SIGN(a,b) ((b) >= 0.0 ? QL_FABS(a) : -QL_FABS(a))
double Ridder::solve_(const ObjectiveFunction& f, double xAcc) const {
double fxMid, froot, s, xMid, nextRoot;
// test on black scholes implied vol show that Ridder solver
// algorythm actually provides an accuracy 100 times below promised
double xAccuracy = xAcc/100.0;
// Any highly unlikely value, to simplify logic below
root_=QL_MIN_DOUBLE;
while (evaluationNumber_<=maxEvaluations_) {
xMid=0.5*(xMin_+xMax_);
// First of two function evaluations per iteraton
fxMid=f(xMid);
evaluationNumber_++;
s=QL_SQRT(fxMid*fxMid-fxMin_*fxMax_);
if (s == 0.0)
return root_;
// Updating formula
nextRoot = xMid + (xMid - xMin_) *
((fxMin_ >= fxMax_ ? 1.0 : -1.0) * fxMid / s);
if (QL_FABS(nextRoot-root_) <= xAccuracy)
return root_;
root_=nextRoot;
// Second of two function evaluations per iteration
froot=f(root_);
evaluationNumber_++;
if (froot == 0.0)
return root_;
// Bookkeeping to keep the root bracketed on next iteration
if (SIGN(fxMid,froot) != fxMid) {
xMin_=xMid;
fxMin_=fxMid;
xMax_=root_;
fxMax_=froot;
} else if (SIGN(fxMin_,froot) != fxMin_) {
xMax_=root_;
fxMax_=froot;
} else if (SIGN(fxMax_,froot) != fxMax_) {
xMin_=root_;
fxMin_=froot;
} else
throw Error("Ridder: never get here.");
if (QL_FABS(xMax_-xMin_) <= xAccuracy) return root_;
}
throw Error("Ridder: maximum number of function evaluations (" +
IntegerFormatter::toString(maxEvaluations_) + ") exceeded");
QL_DUMMY_RETURN(0.0);
}
}
}
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