diff options
| -rw-r--r-- | src/Makefile.am | 1 | ||||
| -rw-r--r-- | src/vZ.hpp | 1 | ||||
| -rw-r--r-- | src/vZ/Adaptive.hpp | 6 | ||||
| -rw-r--r-- | src/vZ/BS23.hpp | 127 | ||||
| -rw-r--r-- | tests/BS23.cpp | 39 | ||||
| -rw-r--r-- | tests/HE12.cpp | 11 | ||||
| -rw-r--r-- | tests/Makefile.am | 4 |
7 files changed, 182 insertions, 7 deletions
diff --git a/src/Makefile.am b/src/Makefile.am index 04dabb8..42c9279 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -19,6 +19,7 @@ nobase_include_HEADERS = vZ.hpp \ vZ/Adaptive.hpp \ + vZ/BS23.hpp \ vZ/Euler.hpp \ vZ/HE12.hpp \ vZ/Heun.hpp \ @@ -33,5 +33,6 @@ #include <vZ/RK4.hpp> #include <vZ/Adaptive.hpp> #include <vZ/HE12.hpp> +#include <vZ/BS23.hpp> #endif // VZ_HPP diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp index 74de0db..256bda6 100644 --- a/src/vZ/Adaptive.hpp +++ b/src/vZ/Adaptive.hpp @@ -41,6 +41,8 @@ namespace vZ Scalar atol() const { return m_atol; } Scalar rtol() const { return m_rtol; } + unsigned int rejections() const { return m_rejections; } + protected: typedef typename GenericRKIntegrator<Y>::ACoefficients ACoefficients; typedef typename GenericRKIntegrator<Y>::BCoefficients BCoefficients; @@ -49,7 +51,7 @@ namespace vZ GenericAdaptiveIntegrator(Function f, unsigned int order, ACoefficients a, BCoefficients b, BCoefficients bStar) - : GenericRKIntegrator<Y>(f), m_order(order), + : GenericRKIntegrator<Y>(f), m_order(order), m_rejections(0), m_a(a), m_b(b), m_bStar(bStar) { } virtual ~GenericAdaptiveIntegrator() { } @@ -59,6 +61,7 @@ namespace vZ private: Scalar m_atol, m_rtol; unsigned int m_order; + unsigned int m_rejections; ACoefficients m_a; BCoefficients m_b, m_bStar; }; @@ -94,6 +97,7 @@ namespace vZ if (delta > scale) { // Reject the step this->h(newH); + ++m_rejections; } else { rejected = false; } diff --git a/src/vZ/BS23.hpp b/src/vZ/BS23.hpp new file mode 100644 index 0000000..1092d81 --- /dev/null +++ b/src/vZ/BS23.hpp @@ -0,0 +1,127 @@ +/************************************************************************* + * 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_BS23_HPP +#define VZ_BS23_HPP + +namespace vZ +{ + // Heun-Euler method + // + // Second-order with embedded first-order + // Its tableau is: + // + // 0 | + // 1 | 1 + // --+--------- + // | 1/2 1/2 + // | 1 0 + // + // k1 = dt*f(y[n]) + // k2 = dt*f(y[n] + dt*k1) + // y[n + 1] = y[n] + 1/2*(k1 + k2) + template <typename Y> + class GenericBS23Integrator : public GenericAdaptiveIntegrator<Y> + { + public: + typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar; + typedef typename GenericAdaptiveIntegrator<Y>::Function Function; + + GenericBS23Integrator(Function f) + : GenericAdaptiveIntegrator<Y>(f, 3, s_a, s_b, s_bStar) { } + ~GenericBS23Integrator() { } + + 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 std::vector<Scalar> s_aArr[3]; + static Scalar s_bArr[4]; + static Scalar s_bStarArr[4]; + }; + + // Type alias + typedef GenericBS23Integrator<double> BS23Integrator; + + // Implementation + + template <typename Y> + typename GenericBS23Integrator<Y>::Scalar + GenericBS23Integrator<Y>::s_a2Arr[1] = { + Scalar(1)/Scalar(2) + }; + template <typename Y> + typename GenericBS23Integrator<Y>::Scalar + GenericBS23Integrator<Y>::s_a3Arr[2] = { + Scalar(0), Scalar(3)/Scalar(4) + }; + template <typename Y> + typename GenericBS23Integrator<Y>::Scalar + GenericBS23Integrator<Y>::s_a4Arr[3] = { + Scalar(2)/Scalar(9), Scalar(1)/Scalar(3), Scalar(4)/Scalar(9) + }; + + template <typename Y> + std::vector<typename GenericBS23Integrator<Y>::Scalar> + GenericBS23Integrator<Y>::s_aArr[3] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1), + std::vector<Scalar>(s_a3Arr, s_a3Arr + 2), + std::vector<Scalar>(s_a4Arr, s_a4Arr + 3) + }; + + template <typename Y> + typename GenericBS23Integrator<Y>::ACoefficients + GenericBS23Integrator<Y>::s_a(s_aArr, s_aArr + 3); + + template <typename Y> + typename GenericBS23Integrator<Y>::Scalar + GenericBS23Integrator<Y>::s_bArr[4] = { + Scalar(2)/Scalar(9), + Scalar(1)/Scalar(3), + Scalar(4)/Scalar(9), + Scalar(0) + }; + + template <typename Y> + typename GenericBS23Integrator<Y>::BCoefficients + GenericBS23Integrator<Y>::s_b(s_bArr, s_bArr + 4); + + template <typename Y> + typename GenericBS23Integrator<Y>::Scalar + GenericBS23Integrator<Y>::s_bStarArr[4] = { + Scalar(7)/Scalar(24), + Scalar(1)/Scalar(4), + Scalar(1)/Scalar(3), + Scalar(1)/Scalar(8) + }; + + template <typename Y> + typename GenericBS23Integrator<Y>::BCoefficients + GenericBS23Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 4); +} + +#endif // VZ_BS23_HPP diff --git a/tests/BS23.cpp b/tests/BS23.cpp new file mode 100644 index 0000000..15abd0c --- /dev/null +++ b/tests/BS23.cpp @@ -0,0 +1,39 @@ +#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::BS23Integrator integrator(f); + integrator.tol(1e-6).y(1.0).x(0.0).h(0.03); + + 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 + << "rejections: " << integrator.rejections() << std::endl; + + double error = std::fabs(expected - actual)/expected; + if (error > 4.8e-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/HE12.cpp b/tests/HE12.cpp index 44d6943..511a8e0 100644 --- a/tests/HE12.cpp +++ b/tests/HE12.cpp @@ -23,16 +23,17 @@ main() double expected = std::exp(2.0); std::cout << std::setprecision(10) - << "Numerical: " << actual << std::endl - << "Expected: " << expected << std::endl - << "h: " << integrator.h() << std::endl; + << "Numerical: " << actual << std::endl + << "Expected: " << expected << std::endl + << "h: " << integrator.h() << std::endl + << "rejections: " << integrator.rejections() << std::endl; double error = std::fabs(expected - actual)/expected; if (error > 8.7e-7) { - std::cerr << "Error: " << 100.0*error << "%" << std::endl; + std::cerr << "Error: " << 100.0*error << "%" << std::endl; return EXIT_FAILURE; } else { - std::cout << "Error: " << 100.0*error << "%" << std::endl; + std::cout << "Error: " << 100.0*error << "%" << std::endl; return EXIT_SUCCESS; } } diff --git a/tests/Makefile.am b/tests/Makefile.am index e3c7601..cab6d98 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -23,7 +23,8 @@ check_PROGRAMS = Euler-test \ Midpoint-test \ Heun-test \ RK4-test \ - HE12-test + HE12-test \ + BS23-test TESTS = $(check_PROGRAMS) Euler_test_SOURCES = Euler.cpp @@ -31,3 +32,4 @@ Midpoint_test_SOURCES = Midpoint.cpp Heun_test_SOURCES = Heun.cpp RK4_test_SOURCES = RK4.cpp HE12_test_SOURCES = HE12.cpp +BS23_test_SOURCES = BS23.cpp |