/usr/include/ql/math/solvers1d/brent.hpp is in libquantlib0-dev 1.1-2build1.
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/*
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 brent.hpp
\brief Brent 1-D solver
*/
#ifndef quantlib_solver1d_brent_h
#define quantlib_solver1d_brent_h
#include <ql/math/solver1d.hpp>
namespace QuantLib {
//! %Brent 1-D solver
/*! \test the correctness of the returned values is tested by
checking them against known good results.
*/
class Brent : public Solver1D<Brent> {
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 min1, min2;
Real froot, p, q, r, s, xAcc1, xMid;
// dummy assignements to avoid compiler warning
Real d = 0.0, e = 0.0;
root_ = xMax_;
froot = fxMax_;
while (evaluationNumber_<=maxEvaluations_) {
if ((froot > 0.0 && fxMax_ > 0.0) ||
(froot < 0.0 && fxMax_ < 0.0)) {
// Rename xMin_, root_, xMax_ and adjust bounds
xMax_=xMin_;
fxMax_=fxMin_;
e=d=root_-xMin_;
}
if (std::fabs(fxMax_) < std::fabs(froot)) {
xMin_=root_;
root_=xMax_;
xMax_=xMin_;
fxMin_=froot;
froot=fxMax_;
fxMax_=fxMin_;
}
// Convergence check
xAcc1=2.0*QL_EPSILON*std::fabs(root_)+0.5*xAccuracy;
xMid=(xMax_-root_)/2.0;
if (std::fabs(xMid) <= xAcc1 || (close(froot, 0.0)))
return root_;
if (std::fabs(e) >= xAcc1 &&
std::fabs(fxMin_) > std::fabs(froot)) {
// Attempt inverse quadratic interpolation
s=froot/fxMin_;
if (close(xMin_,xMax_)) {
p=2.0*xMid*s;
q=1.0-s;
} else {
q=fxMin_/fxMax_;
r=froot/fxMax_;
p=s*(2.0*xMid*q*(q-r)-(root_-xMin_)*(r-1.0));
q=(q-1.0)*(r-1.0)*(s-1.0);
}
if (p > 0.0) q = -q; // Check whether in bounds
p=std::fabs(p);
min1=3.0*xMid*q-std::fabs(xAcc1*q);
min2=std::fabs(e*q);
if (2.0*p < (min1 < min2 ? min1 : min2)) {
e=d; // Accept interpolation
d=p/q;
} else {
d=xMid; // Interpolation failed, use bisection
e=d;
}
} else {
// Bounds decreasing too slowly, use bisection
d=xMid;
e=d;
}
xMin_=root_;
fxMin_=froot;
if (std::fabs(d) > xAcc1)
root_ += d;
else
root_ += sign(xAcc1,xMid);
froot=f(root_);
++evaluationNumber_;
}
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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