Add RK4.

7 files changed, 148 insertions, 3 deletions

diff --git a/src/Makefile.am b/src/Makefile.am
index 6cd2924..ff03023 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -22,5 +22,6 @@ nobase_include_HEADERS = vZ.hpp                                                \
                          vZ/Integrator.hpp                                     \
                          vZ/Midpoint.hpp                                       \
                          vZ/RK.hpp                                             \
+                         vZ/RK4.hpp                                            \
                          vZ/Simple.hpp                                         \
                          vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index b25e615..9d47b33 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -29,5 +29,6 @@
 #include <vZ/Simple.hpp>
 #include <vZ/Euler.hpp>
 #include <vZ/Midpoint.hpp>
+#include <vZ/RK4.hpp>
 
 #endif // VZ_HPP
diff --git a/src/vZ/Midpoint.hpp b/src/vZ/Midpoint.hpp
index 3d7ce2c..2329457 100644
--- a/src/vZ/Midpoint.hpp
+++ b/src/vZ/Midpoint.hpp
@@ -68,7 +68,7 @@ namespace vZ
   template <typename Y>
   typename GenericMidpointIntegrator<Y>::Scalar
   GenericMidpointIntegrator<Y>::s_a2Arr[1] = {
-    Scalar(1)/2
+    Scalar(1)/Scalar(2)
   };
 
   template <typename Y>
diff --git a/src/vZ/RK.hpp b/src/vZ/RK.hpp
index df608ff..a832779 100644
--- a/src/vZ/RK.hpp
+++ b/src/vZ/RK.hpp
@@ -69,7 +69,7 @@ namespace vZ
          i != a.end();
          ++i)
     {
-      Scalar c = 0;
+      Scalar c(0);
       Y y = this->y();
       for (typename std::vector<Scalar>::size_type j = 0; j < i->size(); ++j) {
         Scalar aij = i->at(j);
diff --git a/src/vZ/RK4.hpp b/src/vZ/RK4.hpp
new file mode 100644
index 0000000..fa50461
--- /dev/null
+++ b/src/vZ/RK4.hpp
@@ -0,0 +1,116 @@
+/*************************************************************************
+ * 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_RK4_HPP
+#define VZ_RK4_HPP
+
+namespace vZ
+{
+  // RK4 method
+  //
+  // Fourth order Runge-Kutta method
+  // Four function evaluations per step
+  // Its tableau is:
+  //
+  //   0  |
+  //   1/2|1/2
+  //   1/2|0   1/2
+  //   1  |0   0   1
+  //   ---+---------------
+  //      |1/6 1/3 1/3 1/6
+  //
+  //    k1    = dt*f(y[n])
+  //    k2    = dt*f(y[n] + (dt/2)*k1)
+  //    k3    = dt*f(y[n] + (dt/2)*k2)
+  //    k4    = dt*f(y[n] + dt*k3)
+  // y[n + 1] = y[n] + (k1 + 2*k2 + 2*k3 + k4)/6
+  template <typename Y>
+  class GenericRK4Integrator : public GenericSimpleIntegrator<Y>
+  {
+  public:
+    typedef typename GenericSimpleIntegrator<Y>::Scalar   Scalar;
+    typedef typename GenericSimpleIntegrator<Y>::Function Function;
+
+    GenericRK4Integrator(Function f)
+      : GenericSimpleIntegrator<Y>(f, s_a, s_b) { }
+    ~GenericRK4Integrator() { }
+
+  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 Scalar s_a3Arr[2];
+    static Scalar s_a4Arr[3];
+    static std::vector<Scalar> s_aArr[3];
+    static Scalar s_bArr[4];
+  };
+
+  // Type alias
+  typedef GenericRK4Integrator<double> RK4Integrator;
+
+  // Implementation
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a2Arr[1] = {
+    Scalar(1)/Scalar(2)
+  };
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a3Arr[2] = {
+    Scalar(0), Scalar(1)/Scalar(2)
+  };
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_a4Arr[3] = {
+    Scalar(0), Scalar(0), Scalar(1)
+  };
+
+  template <typename Y>
+  std::vector<typename GenericRK4Integrator<Y>::Scalar>
+  GenericRK4Integrator<Y>::s_aArr[3] = {
+    std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
+    std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
+    std::vector<Scalar>(s_a4Arr, s_a4Arr + 3)
+  };
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::ACoefficients
+  GenericRK4Integrator<Y>::s_a(s_aArr, s_aArr + 3);
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::Scalar
+  GenericRK4Integrator<Y>::s_bArr[4] = {
+    Scalar(1)/Scalar(6),
+    Scalar(1)/Scalar(3),
+    Scalar(1)/Scalar(3),
+    Scalar(1)/Scalar(6)
+  };
+
+  template <typename Y>
+  typename GenericRK4Integrator<Y>::BCoefficients
+  GenericRK4Integrator<Y>::s_b(s_bArr, s_bArr + 4);
+}
+
+#endif // VZ_RK4_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 5f94aab..edef1ae 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -20,8 +20,10 @@
 INCLUDES = -I$(top_srcdir)/src
 
 check_PROGRAMS = Euler-test                                                    \
-                 Midpoint-test
+                 Midpoint-test                                                 \
+                 RK4-test
 TESTS          = $(check_PROGRAMS)
 
 Euler_test_SOURCES    = Euler.cpp
 Midpoint_test_SOURCES = Midpoint.cpp
+RK4_test_SOURCES      = RK4.cpp
diff --git a/tests/RK4.cpp b/tests/RK4.cpp
new file mode 100644
index 0000000..8e0ca0a
--- /dev/null
+++ b/tests/RK4.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::RK4Integrator integrator(f);
+  integrator.y(1.0).x(0.0).h(0.04);
+
+  integrator.integrate(2.0);
+
+  std::cout << integrator.y() << std::endl
+            << std::exp(2.0)  << std::endl;
+
+  return EXIT_SUCCESS;
+}