| 1 | /* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */ |
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| 2 | |
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| 3 | /* |
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| 4 | Copyright (C) 2012 Klaus Spanderen |
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| 5 | |
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| 6 | This file is part of QuantLib, a free-software/open-source library |
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| 7 | for financial quantitative analysts and developers - http://quantlib.org/ |
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| 8 | |
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| 9 | QuantLib is free software: you can redistribute it and/or modify it |
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| 10 | under the terms of the QuantLib license. You should have received a |
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| 11 | copy of the license along with this program; if not, please email |
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| 12 | <quantlib-dev@lists.sf.net>. The license is also available online at |
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| 13 | <http://quantlib.org/license.shtml>. |
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| 14 | |
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| 15 | This program is distributed in the hope that it will be useful, but WITHOUT |
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| 16 | ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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| 17 | FOR A PARTICULAR PURPOSE. See the license for more details. |
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| 18 | */ |
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| 19 | |
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| 20 | /*! \file richardsonextrapolation.cpp |
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| 21 | */ |
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| 22 | |
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| 23 | #include <ql/errors.hpp> |
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| 24 | #include <ql/math/solvers1d/brent.hpp> |
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| 25 | #include <ql/math/richardsonextrapolation.hpp> |
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| 26 | |
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| 27 | #include <cmath> |
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| 28 | |
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| 29 | namespace QuantLib { |
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| 30 | namespace { |
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| 31 | class RichardsonEqn { |
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| 32 | public: |
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| 33 | RichardsonEqn(Real fh, Real ft, Real fs, Real t, Real s) |
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| 34 | : fdelta_h_(fh), ft_(ft), fs_(fs), t_(t), s_(s) { } |
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| 35 | |
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| 36 | Real operator()(Real k) const { |
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| 37 | return ft_ + (ft_-fdelta_h_)/(std::pow(x: t_, y: k)-1.0) |
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| 38 | - ( fs_ + (fs_-fdelta_h_)/(std::pow(x: s_, y: k)-1.0)); |
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| 39 | } |
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| 40 | private: |
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| 41 | const Real fdelta_h_, ft_, fs_, t_, s_; |
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| 42 | }; |
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| 43 | |
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| 44 | } |
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| 45 | |
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| 46 | RichardsonExtrapolation::( |
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| 47 | const ext::function<Real (Real)>& f, Real delta_h, Real n) |
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| 48 | : delta_h_(delta_h), |
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| 49 | fdelta_h_(f(delta_h)), |
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| 50 | n_(n), |
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| 51 | f_(f) { |
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| 52 | } |
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| 53 | |
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| 54 | |
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| 55 | Real RichardsonExtrapolation::(Real t) const { |
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| 56 | |
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| 57 | QL_REQUIRE(t > 1, "scaling factor must be greater than 1" ); |
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| 58 | QL_REQUIRE(n_ != Null<Real>(), "order of convergence must be known" ); |
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| 59 | |
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| 60 | const Real tk = std::pow(x: t, y: n_); |
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| 61 | |
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| 62 | return (tk*f_(delta_h_/t)-fdelta_h_)/(tk-1.0); |
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| 63 | } |
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| 64 | |
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| 65 | Real RichardsonExtrapolation::(Real t, Real s) |
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| 66 | const { |
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| 67 | QL_REQUIRE(t > 1 && s > 1, "scaling factors must be greater than 1" ); |
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| 68 | QL_REQUIRE(t > s, "t must be greater than s" ); |
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| 69 | |
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| 70 | const Real ft = f_(delta_h_/t); |
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| 71 | const Real fs = f_(delta_h_/s); |
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| 72 | |
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| 73 | const RichardsonEqn eqn(fdelta_h_, ft, fs, t, s); |
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| 74 | |
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| 75 | const Real step = 0.1; |
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| 76 | Real left = 0.05; |
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| 77 | Real fr = eqn(left + step), fl = eqn(left); |
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| 78 | while (fr*fl > 0.0 && left < 15.1) { |
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| 79 | left+=step; |
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| 80 | fl = fr; |
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| 81 | fr = eqn(left + step); |
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| 82 | } |
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| 83 | |
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| 84 | QL_REQUIRE(left < 15.1,"could not estimate the order of convergence" ); |
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| 85 | |
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| 86 | const Real k = Brent().solve(f: eqn, accuracy: 1e-8, guess: left+0.5*step, xMin: left, xMax: left+step); |
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| 87 | |
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| 88 | const Real ts = std::pow(x: s, y: k); |
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| 89 | |
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| 90 | return (ts*fs-fdelta_h_)/(ts-1.0); |
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| 91 | } |
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| 92 | } |
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| 93 | |
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