From dbd081ad1808d4e8550dd23971b60b862c7904e0 Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@gmail.com>
Date: Mon, 11 Oct 2010 19:01:41 -0400
Subject: Add a test for a system of vector equations.

---
 src/vZ/Vector.hpp               | 14 +++++++++
 tests/EquationSystem-Vector.cpp | 70 +++++++++++++++++++++++++++++++++++++++++
 tests/Makefile.am               | 26 ++++++++-------
 3 files changed, 98 insertions(+), 12 deletions(-)
 create mode 100644 tests/EquationSystem-Vector.cpp

diff --git a/src/vZ/Vector.hpp b/src/vZ/Vector.hpp
index 66b9a68..0f5cf49 100644
--- a/src/vZ/Vector.hpp
+++ b/src/vZ/Vector.hpp
@@ -24,6 +24,7 @@
 #include <algorithm>
 #include <cmath>
 #include <cstddef>
+#include <ostream>
 
 namespace vZ
 {
@@ -182,6 +183,19 @@ namespace vZ
                         lhs.x()*rhs.y() - lhs.y()*rhs.x());
   }
 
+  // Stream output
+
+  template <std::size_t N, typename T>
+  std::ostream&
+  operator<<(std::ostream& ostr, const Vector<N, T>& v)
+  {
+    ostr << "(" << v[0];
+    for (std::size_t i = 1; i < N; ++i) {
+      ostr << ", " << v[i];
+    }
+    return ostr << ")";
+  }
+
   // Implementation
 
   template <std::size_t N, typename T>
diff --git a/tests/EquationSystem-Vector.cpp b/tests/EquationSystem-Vector.cpp
new file mode 100644
index 0000000..b121026
--- /dev/null
+++ b/tests/EquationSystem-Vector.cpp
@@ -0,0 +1,70 @@
+/*************************************************************************
+ * Copyright (C) 2010 Tavian Barnes <tavianator@gmail.com>               *
+ *                                                                       *
+ * This file is part of The vZ Test Suite.                               *
+ *                                                                       *
+ * The vZ Test Suite is free software; you can redistribute it and/or    *
+ * modify it under the terms of the GNU 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 Test Suite 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     *
+ * General Public License for more details.                              *
+ *                                                                       *
+ * You should have received a copy of the GNU General Public License     *
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>. *
+ *************************************************************************/
+
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <iomanip>
+
+typedef vZ::EquationSystem<2, vZ::Vector<2> > Y;
+
+// y'' = -(|y'|^2/|y|)*(y/|y|) (circular motion)
+Y
+f(double t, Y y)
+{
+  Y r;
+  r[0] = y[1];
+  r[1] = -(dot(y[1], y[1])*y[0])/(dot(y[0], y[0]));
+  return r;
+}
+
+int
+main()
+{
+  Y y;
+  y[0] = vZ::Vector<2>(0.0, 1.0);
+  y[1] = vZ::Vector<2>(8*std::atan(1.0), 0.0);
+  vZ::GenericDP45Integrator<Y> integrator(f);
+  integrator.tol(1e-6)
+            .y(y)
+            .x(0.0)
+            .h(0.06);
+
+  integrator.integrate(2.0);
+
+  vZ::Vector<2> actual = integrator.y()[0];
+  vZ::Vector<2> expected(0.0, 1.0);
+
+  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 = norm(expected - actual)/norm(expected);
+  if (error > 4.0e-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/Makefile.am b/tests/Makefile.am
index d072e35..2091b15 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -29,17 +29,19 @@ check_PROGRAMS = Euler-test                                                    \
                  CK45-test                                                     \
                  DP45-test                                                     \
                  Vector-test                                                   \
-                 EquationSystem-test
+                 EquationSystem-test                                           \
+                 EquationSystem-Vector-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
-Vector_test_SOURCES         = Vector.cpp
-EquationSystem_test_SOURCES = EquationSystem.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
+Vector_test_SOURCES                = Vector.cpp
+EquationSystem_test_SOURCES        = EquationSystem.cpp
+EquationSystem_Vector_test_SOURCES = EquationSystem-Vector.cpp
-- 
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