brent.hpp

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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 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.
 
        \ingroup solvers
    */
    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;
 
            // we want to start with root_ (which equals the guess) on
            // one side of the bracket and both xMin_ and xMax_ on the
            // other.
            froot = f(root_);
            ++evaluationNumber_;
            if (froot * fxMin_ < 0) {
                xMax_ = xMin_;
                fxMax_ = fxMin_;
            } else {
                xMin_ = xMax_;
                fxMin_ = fxMax_;
            }
            Real d = root_- xMax_;
            Real e = d;
 
            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))) {
                    f(root_);
                    ++evaluationNumber_;
                    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 ? Real(std::fabs(a)) : Real(-std::fabs(a));
        }
    };
 
}
 
#endif