From fa85e866aa876a50e735e6d84f5fa32e52fb2f0b Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@gmail.com>
Date: Wed, 6 Oct 2010 17:26:06 -0400
Subject: Add the midpoint method.

---
 src/Makefile.am     |  1 +
 src/vZ.hpp          |  1 +
 src/vZ/Midpoint.hpp | 95 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 tests/Makefile.am   |  6 ++--
 tests/Midpoint.cpp  | 25 ++++++++++++++
 5 files changed, 126 insertions(+), 2 deletions(-)
 create mode 100644 src/vZ/Midpoint.hpp
 create mode 100644 tests/Midpoint.cpp

diff --git a/src/Makefile.am b/src/Makefile.am
index 76c30b1..6cd2924 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -20,6 +20,7 @@
 nobase_include_HEADERS = vZ.hpp                                                \
                          vZ/Euler.hpp                                          \
                          vZ/Integrator.hpp                                     \
+                         vZ/Midpoint.hpp                                       \
                          vZ/RK.hpp                                             \
                          vZ/Simple.hpp                                         \
                          vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index 12e4cbc..b25e615 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -28,5 +28,6 @@
 #include <vZ/RK.hpp>
 #include <vZ/Simple.hpp>
 #include <vZ/Euler.hpp>
+#include <vZ/Midpoint.hpp>
 
 #endif // VZ_HPP
diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp
new file mode 100644
index 0000000..3d7ce2c
--- /dev/null
+++ b/src/vZ/Midpoint.hpp
@@ -0,0 +1,95 @@
+/*************************************************************************
+ * 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_MIDPOINT_HPP
+#define VZ_MIDPOINT_HPP
+
+namespace vZ
+{
+  // Midpoint method
+  //
+  // Second order Runge-Kutta method
+  // Two function evaluations per step
+  // Its tableau is:
+  //
+  //   0  |
+  //   1/2|1/2
+  //   ---+-----
+  //      |0   1
+  //
+  //    k1    = dt*f(y[n])
+  //    k2    = dt*f(y[n] + (dt/2)*k1)
+  // y[n + 1] = y[n] + k2
+  template <typename Y>
+  class GenericMidpointIntegrator : public GenericSimpleIntegrator<Y>
+  {
+  public:
+    typedef typename GenericSimpleIntegrator<Y>::Scalar   Scalar;
+    typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+    GenericMidpointIntegrator(Function f)
+      : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+    ~GenericMidpointIntegrator() { }
+
+  private:
+    typedef typename GenericSimpleIntegrator<Y>::ACoefficients ACoefficients;
+    typedef typename GenericSimpleIntegrator<Y>::BCoefficients BCoefficients;
+
+    static ACoefficients s_a;
+    static BCoefficients s_b;
+
+    static Scalar s_a2Arr[1];
+    static std::vector<Scalar> s_aArr[1];
+    static Scalar s_bArr[2];
+  };
+
+  // Type alias
+  typedef GenericMidpointIntegrator<double> MidpointIntegrator;
+
+  // Implementation
+
+  template <typename Y>
+  typename GenericMidpointIntegrator<Y>::Scalar
+  GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
+    Scalar(1)/2
+  };
+
+  template <typename Y>
+  std::vector<typename GenericMidpointIntegrator<Y>::Scalar>
+  GenericMidpointIntegrator<Y>::s_aArr[1] = {
+    std::vector<Scalar>(s_a2Arr, s_a2Arr + 1)
+  };
+
+  template <typename Y>
+  typename GenericMidpointIntegrator<Y>::ACoefficients
+  GenericMidpointIntegrator<Y>::s_a(s_aArr, s_aArr + 1);
+
+  template <typename Y>
+  typename GenericMidpointIntegrator<Y>::Scalar
+  GenericMidpointIntegrator<Y>::s_bArr[2] = {
+    Scalar(0), Scalar(1)
+  };
+
+  template <typename Y>
+  typename GenericMidpointIntegrator<Y>::BCoefficients
+  GenericMidpointIntegrator<Y>::s_b(s_bArr, s_bArr + 2);
+}
+
+#endif // VZ_MIDPOINT_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index a3d5a77..5f94aab 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -19,7 +19,9 @@
 
 INCLUDES = -I$(top_srcdir)/src
 
-check_PROGRAMS = Euler-test
+check_PROGRAMS = Euler-test                                                    \
+                 Midpoint-test
 TESTS          = $(check_PROGRAMS)
 
-Euler_test_SOURCES = Euler.cpp
+Euler_test_SOURCES    = Euler.cpp
+Midpoint_test_SOURCES = Midpoint.cpp
diff --git a/tests/Midpoint.cpp b/tests/Midpoint.cpp
new file mode 100644
index 0000000..aea1885
--- /dev/null
+++ b/tests/Midpoint.cpp
@@ -0,0 +1,25 @@
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+
+// y' = y (y == C*exp(t))
+double
+f(double t, double y)
+{
+  return y;
+}
+
+int
+main()
+{
+  vZ::MidpointIntegrator integrator(f);
+  integrator.y(1.0).x(0.0).h(0.02);
+
+  integrator.integrate(2.0);
+
+  std::cout << integrator.y() << std::endl
+            << std::exp(2.0)  << std::endl;
+
+  return EXIT_SUCCESS;
+}
-- 
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