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authorTavian Barnes <tavianator@gmail.com>2010-10-11 02:38:46 -0400
committerTavian Barnes <tavianator@gmail.com>2010-10-11 02:38:46 -0400
commit2c2b69e1df183f118c45d74c18c7e84934aaff1f (patch)
tree20b71268a0024c751c7075fbb7ac7210f827c4d7
parentc9d71b99d4bf8c7eef40c043c8d7726962847667 (diff)
downloadvz-2c2b69e1df183f118c45d74c18c7e84934aaff1f.tar.xz
Support systems of ODEs.
-rw-r--r--TODO2
-rw-r--r--src/Makefile.am1
-rw-r--r--src/vZ.hpp1
-rw-r--r--src/vZ/EquationSystem.hpp154
-rw-r--r--src/vZ/Integrator.hpp4
-rw-r--r--tests/EquationSystem.cpp46
-rw-r--r--tests/Makefile.am22
7 files changed, 217 insertions, 13 deletions
diff --git a/TODO b/TODO
index 6eded45..1df2c69 100644
--- a/TODO
+++ b/TODO
@@ -1,2 +1,2 @@
-- Support systems of ODEs
+- Implement vector class
- Implement FSAL
diff --git a/src/Makefile.am b/src/Makefile.am
index bf2b10c..7db29dc 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -23,6 +23,7 @@ nobase_include_HEADERS = vZ.hpp \
vZ/CK45.hpp \
vZ/DP45.hpp \
vZ/Euler.hpp \
+ vZ/EquationSystem.hpp \
vZ/HE12.hpp \
vZ/Heun.hpp \
vZ/Integrator.hpp \
diff --git a/src/vZ.hpp b/src/vZ.hpp
index ab7b3c2..c6efc80 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -24,6 +24,7 @@
#define VZ_HPP
#include <vZ/Traits.hpp>
+#include <vZ/EquationSystem.hpp>
#include <vZ/Integrator.hpp>
#include <vZ/RK.hpp>
#include <vZ/Simple.hpp>
diff --git a/src/vZ/EquationSystem.hpp b/src/vZ/EquationSystem.hpp
new file mode 100644
index 0000000..0963baf
--- /dev/null
+++ b/src/vZ/EquationSystem.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_EQUATIONSYSTEM_HPP
+#define VZ_EQUATIONSYSTEM_HPP
+
+#include <cstddef>
+
+namespace vZ
+{
+ // A class to easily represent a system of ODEs
+ template <std::size_t N, typename T = double>
+ class EquationSystem
+ {
+ public:
+ typedef typename Traits<T>::Scalar Scalar;
+
+ // EquationSystem();
+ // ~EquationSystem();
+
+ T& operator[](std::size_t i) { return m_values[0]; }
+ const T& operator[](std::size_t i) const { return m_values[0]; }
+
+ EquationSystem& operator+=(const EquationSystem& rhs);
+ EquationSystem& operator-=(const EquationSystem& rhs);
+ EquationSystem& operator*=(Scalar rhs);
+ EquationSystem& operator/=(Scalar rhs);
+
+ private:
+ T m_values[N];
+ };
+
+ // Traits specialization
+ template <std::size_t N, typename T>
+ class Traits<EquationSystem<N, T> >
+ {
+ public:
+ typedef typename Traits<T>::Scalar Scalar;
+
+ private:
+ Traits();
+ };
+
+ // Binary operators
+
+ template <std::size_t N, typename T>
+ inline EquationSystem<N, T>
+ operator+(const EquationSystem<N, T>& lhs, const EquationSystem<N, T>& rhs)
+ {
+ EquationSystem<N, T> res = lhs;
+ res += rhs;
+ return res;
+ }
+
+ template <std::size_t N, typename T>
+ inline EquationSystem<N, T>
+ operator-(const EquationSystem<N, T>& lhs, const EquationSystem<N, T>& rhs)
+ {
+ EquationSystem<N, T> res = lhs;
+ res -= rhs;
+ return res;
+ }
+
+ template <std::size_t N, typename T>
+ inline EquationSystem<N, T>
+ operator*(typename EquationSystem<N, T>::Scalar lhs,
+ const EquationSystem<N, T>& rhs)
+ {
+ EquationSystem<N, T> res = rhs;
+ res *= lhs;
+ return res;
+ }
+
+ template <std::size_t N, typename T>
+ inline EquationSystem<N, T>
+ operator*(const EquationSystem<N, T>& lhs,
+ typename EquationSystem<N, T>::Scalar rhs)
+ {
+ EquationSystem<N, T> res = lhs;
+ res *= rhs;
+ return res;
+ }
+
+ template <std::size_t N, typename T>
+ inline EquationSystem<N, T>
+ operator/(const EquationSystem<N, T>& lhs,
+ typename EquationSystem<N, T>::Scalar rhs)
+ {
+ EquationSystem<N, T> res = lhs;
+ res /= rhs;
+ return res;
+ }
+
+ // Implementation
+
+ template <std::size_t N, typename T>
+ EquationSystem<N, T>&
+ EquationSystem<N, T>::operator+=(const EquationSystem<N, T>& rhs)
+ {
+ for (std::size_t i = 0; i < N; ++i) {
+ m_values[i] += rhs.m_values[i];
+ }
+ return *this;
+ }
+
+ template <std::size_t N, typename T>
+ EquationSystem<N, T>&
+ EquationSystem<N, T>::operator-=(const EquationSystem<N, T>& rhs)
+ {
+ for (std::size_t i = 0; i < N; ++i) {
+ m_values[i] -= rhs.m_values[i];
+ }
+ return *this;
+ }
+
+ template <std::size_t N, typename T>
+ EquationSystem<N, T>&
+ EquationSystem<N, T>::operator*=(typename EquationSystem<N, T>::Scalar rhs)
+ {
+ for (std::size_t i = 0; i < N; ++i) {
+ m_values[i] *= rhs;
+ }
+ return *this;
+ }
+
+ template <std::size_t N, typename T>
+ EquationSystem<N, T>&
+ EquationSystem<N, T>::operator/=(typename EquationSystem<N, T>::Scalar rhs)
+ {
+ for (std::size_t i = 0; i < N; ++i) {
+ m_values[i] /= rhs;
+ }
+ return *this;
+ }
+}
+
+#endif // VZ_EQUATIONSYSTEM_HPP
diff --git a/src/vZ/Integrator.hpp b/src/vZ/Integrator.hpp
index c6d6fbe..cb9649a 100644
--- a/src/vZ/Integrator.hpp
+++ b/src/vZ/Integrator.hpp
@@ -39,9 +39,9 @@ namespace vZ
typedef typename Traits<Y>::Scalar Scalar;
typedef std::tr1::function<Y (Scalar, Y)> Function;
- // By default, y and t start at zero, h starts UNDEFINED
+ // By default, y, t, and h start UNDEFINED
GenericIntegrator(Function f)
- : m_f(f), m_y(0), m_x(0), m_iterations(0) { }
+ : m_f(f),m_iterations(0) { }
virtual ~GenericIntegrator() { }
GenericIntegrator& y(Y y) { m_y = y; return *this; }
diff --git a/tests/EquationSystem.cpp b/tests/EquationSystem.cpp
new file mode 100644
index 0000000..973dd30
--- /dev/null
+++ b/tests/EquationSystem.cpp
@@ -0,0 +1,46 @@
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <iomanip>
+
+typedef vZ::EquationSystem<2> Y;
+
+// y'' = y (y == C*exp(t))
+Y
+f(double t, Y y)
+{
+ Y r;
+ r[0] = y[1];
+ r[1] = y[0];
+ return r;
+}
+
+int
+main()
+{
+ Y y;
+ y[0] = 1.0;
+ y[1] = 1.0;
+ vZ::GenericEulerIntegrator<Y> integrator(f);
+ integrator.y(y).x(0.0).h(0.01);
+
+ integrator.integrate(2.0);
+
+ double actual = integrator.y()[0];
+ double expected = std::exp(2.0);
+
+ std::cout << std::setprecision(10)
+ << "Numerical: " << actual << std::endl
+ << "Expected: " << expected << std::endl
+ << "Iterations: " << integrator.iterations() << std::endl;
+
+ double error = std::fabs(expected - actual)/expected;
+ if (error > 0.01) {
+ 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 5874419..1cd184d 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -27,15 +27,17 @@ check_PROGRAMS = Euler-test \
BS23-test \
RKF45-test \
CK45-test \
- DP45-test
+ DP45-test \
+ EquationSystem-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
-BS23_test_SOURCES = BS23.cpp
-RKF45_test_SOURCES = RKF45.cpp
-CK45_test_SOURCES = CK45.cpp
-DP45_test_SOURCES = DP45.cpp
+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
+BS23_test_SOURCES = BS23.cpp
+RKF45_test_SOURCES = RKF45.cpp
+CK45_test_SOURCES = CK45.cpp
+DP45_test_SOURCES = DP45.cpp
+EquationSystem_test_SOURCES = EquationSystem.cpp