ridder.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 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.
 
        \ingroup solvers
    */
    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) : Real(-std::fabs(a));
        }
    };
 
}
 
#endif