diff options
| -rw-r--r-- | src/Makefile.am | 2 | ||||
| -rw-r--r-- | src/vZ.hpp | 2 | ||||
| -rw-r--r-- | src/vZ/Adaptive.hpp | 109 | ||||
| -rw-r--r-- | src/vZ/Euler.hpp | 6 | ||||
| -rw-r--r-- | src/vZ/HE12.hpp | 107 | ||||
| -rw-r--r-- | src/vZ/Heun.hpp | 2 | ||||
| -rw-r--r-- | src/vZ/Midpoint.hpp | 8 | ||||
| -rw-r--r-- | src/vZ/RK4.hpp | 12 | ||||
| -rw-r--r-- | src/vZ/Simple.hpp | 2 | ||||
| -rw-r--r-- | tests/HE12.cpp | 39 | ||||
| -rw-r--r-- | tests/Makefile.am | 4 |
11 files changed, 276 insertions, 17 deletions
diff --git a/src/Makefile.am b/src/Makefile.am index 9ad815b..04dabb8 100644 --- a/src/Makefile.am +++ b/src/Makefile.am @@ -18,7 +18,9 @@ ########################################################################### nobase_include_HEADERS = vZ.hpp \ + vZ/Adaptive.hpp \ vZ/Euler.hpp \ + vZ/HE12.hpp \ vZ/Heun.hpp \ vZ/Integrator.hpp \ vZ/Midpoint.hpp \ @@ -31,5 +31,7 @@ #include <vZ/Midpoint.hpp> #include <vZ/Heun.hpp> #include <vZ/RK4.hpp> +#include <vZ/Adaptive.hpp> +#include <vZ/HE12.hpp> #endif // VZ_HPP diff --git a/src/vZ/Adaptive.hpp b/src/vZ/Adaptive.hpp new file mode 100644 index 0000000..864b038 --- /dev/null +++ b/src/vZ/Adaptive.hpp @@ -0,0 +1,109 @@ +/************************************************************************* + * 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_ADAPTIVE_HPP +#define VZ_ADAPTIVE_HPP + +#include <cmath> + +namespace vZ +{ + // Base class for adaptive RK-style algorithms + template <typename Y> + class GenericAdaptiveIntegrator : public GenericRKIntegrator<Y> + { + public: + typedef typename GenericRKIntegrator<Y>::Scalar Scalar; + typedef typename GenericRKIntegrator<Y>::Function Function; + + GenericAdaptiveIntegrator& atol(Scalar tol) { m_atol = tol; return *this; } + GenericAdaptiveIntegrator& rtol(Scalar tol) { m_rtol = tol; return *this; } + + Scalar atol() const { return m_atol; } + Scalar rtol() const { return m_rtol; } + + protected: + typedef typename GenericRKIntegrator<Y>::ACoefficients ACoefficients; + typedef typename GenericRKIntegrator<Y>::BCoefficients BCoefficients; + typedef typename GenericRKIntegrator<Y>::KVector KVector; + + GenericAdaptiveIntegrator(Function f, unsigned int order, + ACoefficients a, BCoefficients b, + BCoefficients bStar) + : GenericRKIntegrator<Y>(f), m_order(order), + m_a(a), m_b(b), m_bStar(bStar) + { } + virtual ~GenericAdaptiveIntegrator() { } + + void step(); + + private: + Scalar m_atol, m_rtol; + unsigned int m_order; + ACoefficients m_a; + BCoefficients m_b, m_bStar; + }; + + // Type alias + typedef GenericAdaptiveIntegrator<double> AdaptiveIntegrator; + + // Implementations + + template <typename Y> + void + GenericAdaptiveIntegrator<Y>::step() + { + static const Scalar S = Scalar(19)/Scalar(20); // Arbitrary saftey factor + Scalar newH; + Y y; + + // Attempt the integration step in a loop + bool rejected = true; + while (rejected) { + KVector k = calculateK(m_a); + y = calculateY(k, m_b); + Y yStar = calculateY(k, m_bStar); + + // Get an error estimate + using std::abs; + using std::pow; + Scalar delta = abs(y - yStar); + Scalar scale = m_atol + std::max(abs(y), abs(this->y()))*m_rtol; + + newH = S*this->h()*pow(scale/delta, Scalar(1)/m_order); + + if (delta > scale) { + // Reject the step + this->h(newH); + } else { + rejected = false; + } + } + + // Update x and y + this->y(y); + this->x(this->x() + this->h()); + + // Adjust the stepsize for the next iteration + this->h(newH); + } +} + +#endif // VZ_ADAPTIVE_HPP diff --git a/src/vZ/Euler.hpp b/src/vZ/Euler.hpp index 56c5678..033da2e 100644 --- a/src/vZ/Euler.hpp +++ b/src/vZ/Euler.hpp @@ -29,9 +29,9 @@ namespace vZ // First order // Its tableau is: // - // 0| - // -+- - // |1 + // 0 | + // --+-- + // | 1 // // y[n + 1] = y[n] + dt*f(y[n]) template <typename Y> diff --git a/src/vZ/HE12.hpp b/src/vZ/HE12.hpp new file mode 100644 index 0000000..0f7a299 --- /dev/null +++ b/src/vZ/HE12.hpp @@ -0,0 +1,107 @@ +/************************************************************************* + * 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_HE12_HPP +#define VZ_HE12_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 GenericHE12Integrator : public GenericAdaptiveIntegrator<Y> + { + public: + typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar; + typedef typename GenericAdaptiveIntegrator<Y>::Function Function; + + GenericHE12Integrator(Function f) + : GenericAdaptiveIntegrator<Y>(f, 2, s_a, s_b, s_bStar) { } + ~GenericHE12Integrator() { } + + 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 std::vector<Scalar> s_aArr[1]; + static Scalar s_bArr[2]; + static Scalar s_bStarArr[2]; + }; + + // Type alias + typedef GenericHE12Integrator<double> HE12Integrator; + + // Implementation + + template <typename Y> + typename GenericHE12Integrator<Y>::Scalar + GenericHE12Integrator<Y>::s_a2Arr[1] = { + Scalar(1) + }; + + template <typename Y> + std::vector<typename GenericHE12Integrator<Y>::Scalar> + GenericHE12Integrator<Y>::s_aArr[1] = { + std::vector<Scalar>(s_a2Arr, s_a2Arr + 1) + }; + + template <typename Y> + typename GenericHE12Integrator<Y>::ACoefficients + GenericHE12Integrator<Y>::s_a(s_aArr, s_aArr + 1); + + template <typename Y> + typename GenericHE12Integrator<Y>::Scalar + GenericHE12Integrator<Y>::s_bArr[2] = { + Scalar(1)/Scalar(2), Scalar(1)/Scalar(2) + }; + + template <typename Y> + typename GenericHE12Integrator<Y>::BCoefficients + GenericHE12Integrator<Y>::s_b(s_bArr, s_bArr + 2); + + template <typename Y> + typename GenericHE12Integrator<Y>::Scalar + GenericHE12Integrator<Y>::s_bStarArr[2] = { + Scalar(1), Scalar(0) + }; + + template <typename Y> + typename GenericHE12Integrator<Y>::BCoefficients + GenericHE12Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 2); +} + +#endif // VZ_HE12_HPP diff --git a/src/vZ/Heun.hpp b/src/vZ/Heun.hpp index b70df9e..5e697af 100644 --- a/src/vZ/Heun.hpp +++ b/src/vZ/Heun.hpp @@ -32,7 +32,7 @@ namespace vZ // 0 | // 1 | 1 // --+--------- - // | 1/2 1/2 + // | 1/2 1/2 // // k1 = dt*f(y[n]) // k2 = dt*f(y[n] + dt*k1) diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp index 2329457..a4bb906 100644 --- a/src/vZ/Midpoint.hpp +++ b/src/vZ/Midpoint.hpp @@ -29,10 +29,10 @@ namespace vZ // Two function evaluations per step // Its tableau is: // - // 0 | - // 1/2|1/2 - // ---+----- - // |0 1 + // 0 | + // 1/2 | 1/2 + // ----+------ + // | 0 1 // // k1 = dt*f(y[n]) // k2 = dt*f(y[n] + (dt/2)*k1) diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp index fa50461..39fa306 100644 --- a/src/vZ/RK4.hpp +++ b/src/vZ/RK4.hpp @@ -29,12 +29,12 @@ namespace vZ // Four function evaluations per step // Its tableau is: // - // 0 | - // 1/2|1/2 - // 1/2|0 1/2 - // 1 |0 0 1 - // ---+--------------- - // |1/6 1/3 1/3 1/6 + // 0 | + // 1/2 | 1/2 + // 1/2 | 0 1/2 + // 1 | 0 0 1 + // ----+---------------- + // | 1/6 1/3 1/3 1/6 // // k1 = dt*f(y[n]) // k2 = dt*f(y[n] + (dt/2)*k1) diff --git a/src/vZ/Simple.hpp b/src/vZ/Simple.hpp index 9d9be46..5e4f7f8 100644 --- a/src/vZ/Simple.hpp +++ b/src/vZ/Simple.hpp @@ -21,8 +21,6 @@ #ifndef VZ_SIMPLE_HPP #define VZ_SIMPLE_HPP -#include <vector> - namespace vZ { // Base class for non-adaptive RK-style algorithms diff --git a/tests/HE12.cpp b/tests/HE12.cpp new file mode 100644 index 0000000..9a556ef --- /dev/null +++ b/tests/HE12.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() +{ + double tol = 1e-6; + vZ::HE12Integrator integrator(f); + integrator.atol(tol).rtol(tol).y(1.0).x(0.0).h(0.02); + + 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; + + double error = std::fabs(expected - actual)/expected; + if (error > 8.7e-7) { + 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 0baa463..e3c7601 100644 --- a/tests/Makefile.am +++ b/tests/Makefile.am @@ -22,10 +22,12 @@ INCLUDES = -I$(top_srcdir)/src check_PROGRAMS = Euler-test \ Midpoint-test \ Heun-test \ - RK4-test + RK4-test \ + HE12-test TESTS = $(check_PROGRAMS) Euler_test_SOURCES = Euler.cpp Midpoint_test_SOURCES = Midpoint.cpp Heun_test_SOURCES = Heun.cpp RK4_test_SOURCES = RK4.cpp +HE12_test_SOURCES = HE12.cpp |