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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012 Klaus Spanderen
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 richardsonextrapolation.cpp
*/
#include <ql/errors.hpp>
#include <ql/math/solvers1d/brent.hpp>
#include <ql/math/richardsonextrapolation.hpp>
#include <cmath>
namespace QuantLib {
namespace {
class RichardsonEqn {
public:
RichardsonEqn(Real fh, Real ft, Real fs, Real t, Real s)
: fdelta_h_(fh), ft_(ft), fs_(fs), t_(t), s_(s) { }
Real operator()(Real k) const {
return ft_ + (ft_-fdelta_h_)/(std::pow(t_, k)-1.0)
- ( fs_ + (fs_-fdelta_h_)/(std::pow(s_, k)-1.0));
}
private:
const Real fdelta_h_, ft_, fs_, t_, s_;
};
}
RichardsonExtrapolation::RichardsonExtrapolation(
const ext::function<Real (Real)>& f, Real delta_h, Real n)
: delta_h_(delta_h),
fdelta_h_(f(delta_h)),
n_(n),
f_(f) {
}
Real RichardsonExtrapolation::operator()(Real t) const {
QL_REQUIRE(t > 1, "scaling factor must be greater than 1");
QL_REQUIRE(n_ != Null<Real>(), "order of convergence must be known");
const Real tk = std::pow(t, n_);
return (tk*f_(delta_h_/t)-fdelta_h_)/(tk-1.0);
}
Real RichardsonExtrapolation::operator()(Real t, Real s)
const {
QL_REQUIRE(t > 1 && s > 1, "scaling factors must be greater than 1");
QL_REQUIRE(t > s, "t must be greater than s");
const Real ft = f_(delta_h_/t);
const Real fs = f_(delta_h_/s);
const RichardsonEqn eqn(fdelta_h_, ft, fs, t, s);
const Real step = 0.1;
Real left = 0.05;
Real fr = eqn(left + step), fl = eqn(left);
while (fr*fl > 0.0 && left < 15.1) {
left+=step;
fl = fr;
fr = eqn(left + step);
}
QL_REQUIRE(left < 15.1,"could not estimate the order of convergence");
const Real k = Brent().solve(eqn, 1e-8, left+0.5*step, left, left+step);
const Real ts = std::pow(s, k);
return (ts*fs-fdelta_h_)/(ts-1.0);
}
}
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