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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 ridder.hpp
\brief Ridder 1-D solver
*/
#ifndef quantlib_solver1d_ridder_h
#define quantlib_solver1d_ridder_h
#include <ql/math/solver1d.hpp>
namespace QuantLib {
//! %Ridder 1-D solver
/*! \test the correctness of the returned values is tested by
checking them against known good results.
*/
class Ridder : public Solver1D<Ridder> {
public:
template <class F>
Real solveImpl(const F& f,
Real xAcc) const {
/* The implementation of the algorithm was inspired by
Press, Teukolsky, Vetterling, and Flannery,
"Numerical Recipes in C", 2nd edition,
Cambridge University Press
*/
Real fxMid, froot, s, xMid, nextRoot;
// test on Black-Scholes implied volatility show that
// Ridder solver algorithm actually provides an
// accuracy 100 times below promised
Real xAccuracy = xAcc/100.0;
// Any highly unlikely value, to simplify logic below
root_ = QL_MIN_REAL;
while (evaluationNumber_<=maxEvaluations_) {
xMid = 0.5*(xMin_+xMax_);
// First of two function evaluations per iteraton
fxMid = f(xMid);
++evaluationNumber_;
s = std::sqrt(fxMid*fxMid-fxMin_*fxMax_);
if (close(s, 0.0)) {
f(root_);
++evaluationNumber_;
return root_;
}
// Updating formula
nextRoot = xMid + (xMid - xMin_) *
((fxMin_ >= fxMax_ ? 1.0 : -1.0) * fxMid / s);
if (std::fabs(nextRoot-root_) <= xAccuracy) {
f(root_);
++evaluationNumber_;
return root_;
}
root_ = nextRoot;
// Second of two function evaluations per iteration
froot = f(root_);
++evaluationNumber_;
if (close(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 {
QL_FAIL("never get here.");
}
if (std::fabs(xMax_-xMin_) <= xAccuracy) {
f(root_);
++evaluationNumber_;
return root_;
}
}
QL_FAIL("maximum number of function evaluations ("
<< maxEvaluations_ << ") exceeded");
}
private:
Real sign(Real a, Real b) const {
return b >= 0.0 ? std::fabs(a) : -std::fabs(a);
}
};
}
#endif
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