diff options
| -rw-r--r-- | src/vZ.hpp | 1 | ||||
| -rw-r--r-- | src/vZ/CK45.hpp | 154 | ||||
| -rw-r--r-- | tests/CK45.cpp | 40 | ||||
| -rw-r--r-- | tests/Makefile.am | 4 |
4 files changed, 198 insertions, 1 deletions
@@ -35,5 +35,6 @@ #include <vZ/HE12.hpp> #include <vZ/BS23.hpp> #include <vZ/RKF45.hpp> +#include <vZ/CK45.hpp> #endif // VZ_HPP diff --git a/src/vZ/CK45.hpp b/src/vZ/CK45.hpp new file mode 100644 index 0000000..333e451 --- /dev/null +++ b/src/vZ/CK45.hpp @@ -0,0 +1,154 @@ +/************************************************************************* + * Copyright (C) 2009-2010 Tavian Barnes <tavianator@gmail.com> * + * * + * This file is part of The vZ Library. * + * * + * The vZ Library is free software; you can redistribute it and/or * + * modify it under the terms of the GNU Lesser General Public License as * + * published by the Free Software Foundation; either version 3 of the * + * License, or (at your option) any later version. * + * * + * The vZ Library 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 GNU * + * Lesser General Public License for more details. * + * * + * You should have received a copy of the GNU Lesser General Public * + * License along with this program. If not, see * + * <http://www.gnu.org/licenses/>. * + *************************************************************************/ + +#ifndef VZ_CK45_HPP +#define VZ_CK45_HPP + +namespace vZ +{ + // Cash-Karp method + // + // Fifth-order with embedded fourth-order + // Its tableau is: + // + // 0 | + // 1/5 | 1/5 + // 3/10 | 3/40 9/40 + // 3/5 | 3/10 -9/10 6/5 + // 1 | -11/54 5/2 -70/27 35/27 + // 7/8 | 1631/55296 175/512 575/13824 44275/110592 253/4096 + // ------+----------------------------------------------------------------- + // b | 37/378 0 250/621 125/594 0 512/1771 + // b* | 2825/27648 0 18575/48384 13525/55296 277/14336 1/4 + template <typename Y> + class GenericCK45Integrator : public GenericAdaptiveIntegrator<Y> + { + public: + typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar; + typedef typename GenericAdaptiveIntegrator<Y>::Function Function; + + GenericCK45Integrator(Function f) + : GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { } + ~GenericCK45Integrator() { } + + private: + typedef typename GenericAdaptiveIntegrator<Y>::ACoefficients ACoefficients; + typedef typename GenericAdaptiveIntegrator<Y>::BCoefficients BCoefficients; + + static ACoefficients s_a; + static BCoefficients s_b; + static BCoefficients s_bStar; + + static Scalar s_a2Arr[1]; + static Scalar s_a3Arr[2]; + static Scalar s_a4Arr[3]; + static Scalar s_a5Arr[4]; + static Scalar s_a6Arr[5]; + static std::vector<Scalar> s_aArr[5]; + static Scalar s_bArr[6]; + static Scalar s_bStarArr[6]; + }; + + // Type alias + typedef GenericCK45Integrator<double> CK45Integrator; + + // Implementation + + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_a2Arr[1] = { + Scalar(1)/Scalar(5) + }; + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_a3Arr[2] = { + Scalar(3)/Scalar(40), Scalar(9)/Scalar(40) + }; + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_a4Arr[3] = { + Scalar(3)/Scalar(10), + -Scalar(9)/Scalar(10), + Scalar(6)/Scalar(5) + }; + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_a5Arr[4] = { + -Scalar(11)/Scalar(54), + Scalar(5)/Scalar(2), + -Scalar(70)/Scalar(27), + Scalar(35)/Scalar(27), + }; + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_a6Arr[5] = { + Scalar(1631)/Scalar(55296), + Scalar(175)/Scalar(512), + Scalar(575)/Scalar(13824), + Scalar(44275)/Scalar(110592), + Scalar(253)/Scalar(4096) + }; + + template <typename Y> + std::vector<typename GenericCK45Integrator<Y>::Scalar> + GenericCK45Integrator<Y>::s_aArr[5] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1), + std::vector<Scalar>(s_a3Arr, s_a3Arr + 2), + std::vector<Scalar>(s_a4Arr, s_a4Arr + 3), + std::vector<Scalar>(s_a5Arr, s_a5Arr + 4), + std::vector<Scalar>(s_a6Arr, s_a6Arr + 5) + }; + + template <typename Y> + typename GenericCK45Integrator<Y>::ACoefficients + GenericCK45Integrator<Y>::s_a(s_aArr, s_aArr + 5); + + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_bArr[6] = { + Scalar(37)/Scalar(378), + Scalar(0), + Scalar(250)/Scalar(621), + Scalar(125)/Scalar(594), + Scalar(0), + Scalar(512)/Scalar(1771), + }; + + template <typename Y> + typename GenericCK45Integrator<Y>::BCoefficients + GenericCK45Integrator<Y>::s_b(s_bArr, s_bArr + 6); + + template <typename Y> + typename GenericCK45Integrator<Y>::Scalar + GenericCK45Integrator<Y>::s_bStarArr[6] = { + Scalar(2825)/Scalar(27648), + Scalar(0), + Scalar(18575)/Scalar(48384), + Scalar(13525)/Scalar(55296), + Scalar(277)/Scalar(14336), + Scalar(1)/Scalar(4) + }; + + template <typename Y> + typename GenericCK45Integrator<Y>::BCoefficients + GenericCK45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 6); +} + +#endif // VZ_CK45_HPP diff --git a/tests/CK45.cpp b/tests/CK45.cpp new file mode 100644 index 0000000..e726bc6 --- /dev/null +++ b/tests/CK45.cpp @@ -0,0 +1,40 @@ +#include "vZ.hpp" +#include <cmath> +#include <cstdlib> +#include <iostream> +#include <iomanip> + +// y' = y (y == C*exp(t)) +double +f(double t, double y) +{ + return y; +} + +int +main() +{ + vZ::CK45Integrator integrator(f); + integrator.tol(1e-6).y(1.0).x(0.0).h(0.06); + + integrator.integrate(2.0); + + double actual = integrator.y(); + double expected = std::exp(2.0); + + std::cout << std::setprecision(10) + << "Numerical: " << actual << std::endl + << "Expected: " << expected << std::endl + << "h: " << integrator.h() << std::endl + << "Iterations: " << integrator.iterations() << std::endl + << "Rejections: " << integrator.rejections() << std::endl; + + double error = std::fabs(expected - actual)/expected; + if (error > 2.7e-6) { + std::cerr << "Error: " << 100.0*error << "%" << std::endl; + return EXIT_FAILURE; + } else { + std::cout << "Error: " << 100.0*error << "%" << std::endl; + return EXIT_SUCCESS; + } +} diff --git a/tests/Makefile.am b/tests/Makefile.am index f6ad25e..60e5cf3 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -25,7 +25,8 @@ check_PROGRAMS = Euler-test \ RK4-test \ HE12-test \ BS23-test \ - RKF45-test + RKF45-test \ + CK45-test TESTS = $(check_PROGRAMS) Euler_test_SOURCES = Euler.cpp @@ -35,3 +36,4 @@ RK4_test_SOURCES = RK4.cpp HE12_test_SOURCES = HE12.cpp BS23_test_SOURCES = BS23.cpp RKF45_test_SOURCES = RKF45.cpp +CK45_test_SOURCES = CK45.cpp |