http://quantlib.414.s1.nabble.com/Re-QuantLib-svn-SF-net-SVN-quantlib-18270-trunk-QuantLib-tp13412.html
order of convergence. Just a thought, no big deal anyway---it's just
> Revision: 18270
>
http://quantlib.svn.sourceforge.net/quantlib/?rev=18270&view=rev> Author: klausspanderen
> Date: 2012-06-10 08:56:09 +0000 (Sun, 10 Jun 2012)
> Log Message:
> -----------
> added Richardson extrapolation
>
> Modified Paths:
> --------------
> trunk/QuantLib/ql/math/Makefile.am
> trunk/QuantLib/ql/math/all.hpp
> trunk/QuantLib/test-suite/interpolations.cpp
> trunk/QuantLib/test-suite/interpolations.hpp
>
> Added Paths:
> -----------
> trunk/QuantLib/ql/math/richardsonextrapolation.cpp
> trunk/QuantLib/ql/math/richardsonextrapolation.hpp
>
> Added: trunk/QuantLib/ql/math/richardsonextrapolation.cpp
> ===================================================================
> --- trunk/QuantLib/ql/math/richardsonextrapolation.cpp (rev 0)
> +++ trunk/QuantLib/ql/math/richardsonextrapolation.cpp 2012-06-10 08:56:09 UTC (rev 18270)
> @@ -0,0 +1,73 @@
> +/* -*- 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
> + <
[hidden email]>. 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)
> + : fh_(fh), ft_(ft), fs_(fs), t_(t), s_(s) { }
> +
> + Real operator()(Real k) const {
> + return ft_ + (ft_-fh_)/(std::pow(t_, k)-1.0)
> + - ( fs_ + (fs_-fh_)/(std::pow(s_, k)-1.0));
> + }
> + private:
> + const Real fh_, ft_, fs_, t_, s_;
> + };
> +
> + }
> +
> + RichardsonExtrapolation::RichardsonExtrapolation(
> + Real h, const boost::function<Real (Real)>& f)
> + : h_(h), fh_(f(h)), f_(f) { }
> +
> +
> + Real RichardsonExtrapolation::formula(Real t, Real k) const {
> +
> + QL_REQUIRE(t > 1, "scaling factor must be greater than 1");
> + const Real tk = std::pow(t,k);
> +
> + return (tk*f_(h_/t)-fh_)/(tk-1.0);
> + }
> +
> + Real RichardsonExtrapolation::formulaUnknownConvergence(Real t, Real s)
> + const {
> + QL_REQUIRE(t > 1 && s > 1, "scaling factors must be greater than 1");
> +
> + const Real ft = f_(h_/t);
> + const Real fs = f_(h_/s);
> +
> + const Real k = Brent().solve(RichardsonEqn(fh_, ft, fs, t, s),
> + 1e-8, 0.05, 10);
> +
> + const Real ts = std::pow(s,k);
> +
> + return (ts*fs-fh_)/(ts-1.0);
> + }
> +}
>
>
> Property changes on: trunk/QuantLib/ql/math/richardsonextrapolation.cpp
> ___________________________________________________________________
> Added: svn:mime-type
> + text/plain
>
> Added: trunk/QuantLib/ql/math/richardsonextrapolation.hpp
> ===================================================================
> --- trunk/QuantLib/ql/math/richardsonextrapolation.hpp (rev 0)
> +++ trunk/QuantLib/ql/math/richardsonextrapolation.hpp 2012-06-10 08:56:09 UTC (rev 18270)
> @@ -0,0 +1,62 @@
> +/* -*- 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
> + <
[hidden email]>. 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.hpp
> +*/
> +
> +#ifndef quantlib_richardson_extrapolation_hpp
> +#define quantlib_richardson_extrapolation_hpp
> +
> +#include <ql/types.hpp>
> +
> +#include <boost/function.hpp>
> +
> +namespace QuantLib {
> +
> + //! Richardson Extrapolatio
> + /*! References:
> +
> +
http://en.wikipedia.org/wiki/Richardson_extrapolation> + */
> +
> + class RichardsonExtrapolation {
> + public:
> + RichardsonExtrapolation(Real h,
> + const boost::function<Real (Real)>& f);
> +
> + /*! Extrapolation for known order of convergence
> + \param step size for extrapolation. Is often 2
> + \param k order of convergence
> + */
> + Real formula(Real t, Real k) const;
> +
> + /*! Extrapolation for unknown order of convergence
> + \param t first step size for the extrapolation.
> + \param s second step size for the extrapolation
> + */
> + Real formulaUnknownConvergence(Real t, Real s) const;
> +
> + private:
> + const Real h_;
> + const Real fh_;
> + const boost::function<Real (Real)> f_;
> + };
> +}
> +
> +#endif
>
>
> Property changes on: trunk/QuantLib/ql/math/richardsonextrapolation.hpp
> ___________________________________________________________________
> Added: svn:mime-type
> + text/plain
>
> Modified: trunk/QuantLib/test-suite/interpolations.cpp
> ===================================================================
> --- trunk/QuantLib/test-suite/interpolations.cpp 2012-05-30 22:32:14 UTC (rev 18269)
> +++ trunk/QuantLib/test-suite/interpolations.cpp 2012-06-10 08:56:09 UTC (rev 18270)
> @@ -36,6 +36,7 @@
> #include <ql/math/integrals/simpsonintegral.hpp>
> #include <ql/math/kernelfunctions.hpp>
> #include <ql/math/functional.hpp>
> +#include <ql/math/richardsonextrapolation.hpp>
> #include <ql/math/randomnumbers/sobolrsg.hpp>
> #include <ql/math/optimization/levenbergmarquardt.hpp>
> #include <boost/assign/std/vector.hpp>
> @@ -1610,6 +1611,35 @@
> }
> }
>
> +namespace {
> + Real f(Real h) {
> + return std::pow( 1.0 + h, 1/h);
> + }
> +}
> +
> +void InterpolationTest::testRichardsonExtrapolation() {
> + BOOST_MESSAGE("Testing Richardson Extrapolation...");
> +
> + /* example taken from
> + *
http://www.ipvs.uni-stuttgart.de/abteilungen/bv/lehre/> + * lehrveranstaltungen/vorlesungen/WS0910/
> + * NSG_termine/dateien/Richardson.pdf
> + */
> +
> + const RichardsonExtrapolation extrap(0.1, f);
> +
> + const Real stepSize = 2.0;
> + const Real orderOfConvergence = 1.0;
> +
> + const Real tol = 0.00001;
> + const Real expected = 2.71285;
> + const Real calculated = extrap.formula(stepSize, orderOfConvergence);
> +
> + if (std::fabs(expected-calculated) > tol) {
> + BOOST_ERROR("failed to reproduce Richardson extrapolation");
> + }
> +}
> +
> test_suite* InterpolationTest::suite() {
> test_suite* suite = BOOST_TEST_SUITE("Interpolation tests");
>
> @@ -1636,6 +1666,8 @@
> suite->add(QUANTLIB_TEST_CASE(
> &InterpolationTest::testKernelInterpolation2D));
> suite->add(QUANTLIB_TEST_CASE(&InterpolationTest::testBicubicDerivatives));
> + suite->add(QUANTLIB_TEST_CASE(
> + &InterpolationTest::testRichardsonExtrapolation));
>
> return suite;
> }
>
> Modified: trunk/QuantLib/test-suite/interpolations.hpp
> ===================================================================
> --- trunk/QuantLib/test-suite/interpolations.hpp 2012-05-30 22:32:14 UTC (rev 18269)
> +++ trunk/QuantLib/test-suite/interpolations.hpp 2012-06-10 08:56:09 UTC (rev 18270)
> @@ -46,6 +46,8 @@
> static void testKernelInterpolation();
> static void testKernelInterpolation2D();
> static void testBicubicDerivatives();
> + static void testRichardsonExtrapolation();
> +
> static boost::unit_test_framework::test_suite* suite();
> };
>
>
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