Support systems of ODEs.

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