Add a simple vector class.

6 files changed, 304 insertions, 13 deletions

diff --git a/TODO b/TODO
index 1df2c69..432b231 100644
--- a/TODO
+++ b/TODO
@@ -1,2 +1,2 @@
-- Implement vector class
 - Implement FSAL
+- Add C++0x API extensions
diff --git a/src/vZ.hpp b/src/vZ.hpp
index c6efc80..1b2ba29 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -24,6 +24,7 @@
 #define VZ_HPP
 
 #include <vZ/Traits.hpp>
+#include <vZ/Vector.hpp>
 #include <vZ/EquationSystem.hpp>
 #include <vZ/Integrator.hpp>
 #include <vZ/RK.hpp>
diff --git a/src/vZ/EquationSystem.hpp b/src/vZ/EquationSystem.hpp
index 790676c..5a50f6d 100644
--- a/src/vZ/EquationSystem.hpp
+++ b/src/vZ/EquationSystem.hpp
@@ -64,6 +64,38 @@ namespace vZ
     Traits();
   };
 
+  // Unary operators
+
+  template <std::size_t N, typename T>
+  inline EquationSystem<N, T>
+  operator+(const EquationSystem<N, T>& rhs)
+  {
+    return rhs;
+  }
+
+  template <std::size_t N, typename T>
+  inline EquationSystem<N, T>
+  operator-(const EquationSystem<N, T>& rhs)
+  {
+    EquationSystem<N, T> res;
+    for (std::size_t i = 0; i < N; ++i) {
+      res[i] = -rhs[i];
+    }
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  typename EquationSystem<N, T>::Scalar
+  abs(const EquationSystem<N, T>& es)
+  {
+    typename EquationSystem<N, T>::Scalar ret(0);
+    for (std::size_t i = 0; i < N; ++i) {
+      using std::abs;
+      ret = std::max(ret, abs(es[i]));
+    }
+    return ret;
+  }
+
   // Binary operators
 
   template <std::size_t N, typename T>
@@ -155,18 +187,6 @@ namespace vZ
     }
     return *this;
   }
-
-  template <std::size_t N, typename T>
-  typename EquationSystem<N, T>::Scalar
-  abs(const EquationSystem<N, T>& es)
-  {
-    typename EquationSystem<N, T>::Scalar ret(0);
-    for (std::size_t i = 0; i < N; ++i) {
-      using std::abs;
-      ret = std::max(ret, abs(es[i]));
-    }
-    return ret;
-  }
 }
 
 #endif // VZ_EQUATIONSYSTEM_HPP
diff --git a/src/vZ/Vector.hpp b/src/vZ/Vector.hpp
new file mode 100644
index 0000000..cf3bf0a
--- /dev/null
+++ b/src/vZ/Vector.hpp
@@ -0,0 +1,228 @@
+/*************************************************************************
+ * 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_VECTOR_HPP
+#define VZ_VECTOR_HPP
+
+#include <algorithm>
+#include <cmath>
+#include <cstddef>
+
+namespace vZ
+{
+  // An N-dimensional vector
+  template <std::size_t N, typename T = double>
+  class Vector
+  {
+  public:
+    typedef typename Traits<T>::Scalar Scalar;
+
+    Vector()              { }
+    explicit Vector(T x)  { m_values[0] = x; }
+    Vector(T x, T y)      { m_values[0] = x; m_values[1] = y; }
+    Vector(T x, T y, T z) { m_values[0] = x; m_values[1] = y; m_values[2] = z; }
+    // Vector(const Vector& v);
+    // ~Vector();
+
+    // Vector& operator=(const Vector& v);
+
+    // Component access
+
+    T&       operator[](std::size_t i)       { return m_values[i]; }
+    const T& operator[](std::size_t i) const { return m_values[i]; }
+
+    T x() const { return m_values[0]; }
+    T y() const { return m_values[1]; }
+    T z() const { return m_values[2]; }
+
+    // Operators
+    inline Vector& operator+=(const Vector& rhs);
+    inline Vector& operator-=(const Vector& rhs);
+    inline Vector& operator*=(Scalar rhs);
+    inline Vector& operator/=(Scalar rhs);
+
+  private:
+    T m_values[N];
+  };
+
+  // Disallow 0-sized Vectors
+  template <typename T>
+  class Vector<0, T>;
+
+  // Traits specialization
+  template <std::size_t N, typename T>
+  class Traits<Vector<N, T> >
+  {
+  public:
+    typedef typename Traits<T>::Scalar Scalar;
+
+  private:
+    Traits();
+  };
+
+  // Unary operators
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator+(const Vector<N, T>& rhs)
+  {
+    return rhs;
+  }
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator-(const Vector<N, T>& rhs)
+  {
+    Vector<N, T> res;
+    for (std::size_t i = 0; i < N; ++i) {
+      res[i] = -rhs[i];
+    }
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline typename Vector<N, T>::Scalar
+  norm(const Vector<N, T>& v)
+  {
+    using std::sqrt;
+    return sqrt(dot(v, v));
+  }
+
+  template <std::size_t N, typename T>
+  inline typename Vector<N, T>::Scalar
+  abs(const Vector<N, T>& v)
+  {
+    return norm(v);
+  }
+
+  // Binary operators
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator+(const Vector<N, T>& lhs, const Vector<N, T>& rhs)
+  {
+    Vector<N, T> res = lhs;
+    res += rhs;
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator-(const Vector<N, T>& lhs, const Vector<N, T>& rhs)
+  {
+    Vector<N, T> res = lhs;
+    res -= rhs;
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator*(typename Vector<N, T>::Scalar lhs,
+            const Vector<N, T>& rhs)
+  {
+    Vector<N, T> res = rhs;
+    res *= lhs;
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator*(const Vector<N, T>& lhs,
+            typename Vector<N, T>::Scalar rhs)
+  {
+    Vector<N, T> res = lhs;
+    res *= rhs;
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>
+  operator/(const Vector<N, T>& lhs,
+            typename Vector<N, T>::Scalar rhs)
+  {
+    Vector<N, T> res = lhs;
+    res /= rhs;
+    return res;
+  }
+
+  template <std::size_t N, typename T>
+  inline typename Vector<N, T>::Scalar
+  dot(const Vector<N, T>& lhs, const Vector<N, T>& rhs)
+  {
+    typename Vector<N, T>::Scalar res(0);
+    for (std::size_t i = 0; i < N; ++i) {
+      res += lhs[i]*rhs[i];
+    }
+    return res;
+  }
+
+  template <typename T>
+  inline Vector<3, T>
+  cross(const Vector<3, T>& lhs, const Vector<3, T>& rhs)
+  {
+    return Vector<3, T>(lhs.y()*rhs.z() - lhs.z()*rhs.y(),
+                        lhs.z()*rhs.x() - lhs.x()*rhs.z(),
+                        lhs.x()*rhs.y() - lhs.y()*rhs.x());
+  }
+
+  // Implementation
+
+  template <std::size_t N, typename T>
+  inline Vector<N, T>&
+  Vector<N, T>::operator+=(const Vector<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>
+  inline Vector<N, T>&
+  Vector<N, T>::operator-=(const Vector<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>
+  inline Vector<N, T>&
+  Vector<N, T>::operator*=(typename Vector<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>
+  inline Vector<N, T>&
+  Vector<N, T>::operator/=(typename Vector<N, T>::Scalar rhs)
+  {
+    for (std::size_t i = 0; i < N; ++i) {
+      m_values[i] /= rhs;
+    }
+    return *this;
+  }
+}
+
+#endif // VZ_VECTOR_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 1cd184d..745562c 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -28,6 +28,7 @@ check_PROGRAMS = Euler-test                                                    \
                  RKF45-test                                                    \
                  CK45-test                                                     \
                  DP45-test                                                     \
+                 Vector-test                                                   \
                  EquationSystem-test
 TESTS          = $(check_PROGRAMS)
 
@@ -40,4 +41,5 @@ BS23_test_SOURCES           = BS23.cpp
 RKF45_test_SOURCES          = RKF45.cpp
 CK45_test_SOURCES           = CK45.cpp
 DP45_test_SOURCES           = DP45.cpp
+Vector_test_SOURCES         = Vector.cpp
 EquationSystem_test_SOURCES = EquationSystem.cpp
diff --git a/tests/Vector.cpp b/tests/Vector.cpp
new file mode 100644
index 0000000..7f53352
--- /dev/null
+++ b/tests/Vector.cpp
@@ -0,0 +1,40 @@
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <iomanip>
+
+// y' = -y (y == C*exp(-t))
+vZ::Vector<3>
+f(double t, vZ::Vector<3> y)
+{
+  return -y;
+}
+
+int
+main()
+{
+  vZ::GenericDP45Integrator<vZ::Vector<3> > integrator(f);
+  integrator.tol(1e-6).y(vZ::Vector<3>(1.0, 1.0, 1.0)).x(0.0).h(0.06);
+
+  integrator.integrate(2.0);
+
+  double actual   = integrator.y().x();
+  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 > 1.5e-6) {
+    std::cerr << "Error:      " << 100.0*error << "%" << std::endl;
+    return EXIT_FAILURE;
+  } else {
+    std::cout << "Error:      " << 100.0*error << "%" << std::endl;
+    return EXIT_SUCCESS;
+  }
+}