Add RKF45 method.

4 files changed, 197 insertions, 1 deletions

diff --git a/src/vZ.hpp b/src/vZ.hpp
index 5aabd1c..7f72407 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -34,5 +34,6 @@
 #include <vZ/Adaptive.hpp>
 #include <vZ/HE12.hpp>
 #include <vZ/BS23.hpp>
+#include <vZ/RKF45.hpp>
 
 #endif // VZ_HPP
diff --git a/src/vZ/RKF45.hpp b/src/vZ/RKF45.hpp
new file mode 100644
index 0000000..5d40b88
--- /dev/null
+++ b/src/vZ/RKF45.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_RKF45_HPP
+#define VZ_RKF45_HPP
+
+namespace vZ
+{
+  // Runge-Kutta-Fehlberg method
+  //
+  // Fifth-order with embedded fourth-order
+  // Its tableau is:
+  //
+  //   0     |
+  //   1/4   |  1/4
+  //   3/8   |  3/32       9/34
+  //   12/13 |  1932/2197 -7200/2197  7296/2197
+  //   1     |  439/216   -8          3680/513   -845/4104
+  //   1/2   | -8/27       2         -3544/2565   1859/4104   -11/40
+  //   ------+-----------------------------------------------------------
+  //   b     | 25/216      0          1408/2565   2197/4104   -1/5   0
+  //   b*    | 16/135      0          6656/12825  28561/56430 -9/50  2/55
+  template <typename Y>
+  class GenericRKF45Integrator : public GenericAdaptiveIntegrator<Y>
+  {
+  public:
+    typedef typename GenericAdaptiveIntegrator<Y>::Scalar   Scalar;
+    typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+    GenericRKF45Integrator(Function f)
+      : GenericAdaptiveIntegrator<Y>(f, 3, s_a, s_b, s_bStar) { }
+    ~GenericRKF45Integrator() { }
+
+  private:
+    typedef typename GenericAdaptiveIntegrator<Y>::ACoefficients ACoefficients;
+    typedef typename GenericAdaptiveIntegrator<Y>::BCoefficients BCoefficients;
+
+    static ACoefficients s_a;
+    static BCoefficients s_b;
+    static BCoefficients s_bStar;
+
+    static Scalar s_a2Arr[1];
+    static Scalar s_a3Arr[2];
+    static Scalar s_a4Arr[3];
+    static Scalar s_a5Arr[4];
+    static Scalar s_a6Arr[5];
+    static std::vector<Scalar> s_aArr[5];
+    static Scalar s_bArr[6];
+    static Scalar s_bStarArr[6];
+  };
+
+  // Type alias
+  typedef GenericRKF45Integrator<double> RKF45Integrator;
+
+  // Implementation
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_a2Arr[1] = {
+    Scalar(1)/Scalar(4)
+  };
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_a3Arr[2] = {
+    Scalar(3)/Scalar(32), Scalar(9)/Scalar(32)
+  };
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_a4Arr[3] = {
+     Scalar(1932)/Scalar(2197),
+    -Scalar(7200)/Scalar(2197),
+     Scalar(7296)/Scalar(2197)
+  };
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_a5Arr[4] = {
+     Scalar(439)/Scalar(216),
+    -Scalar(8),
+     Scalar(3680)/Scalar(513),
+    -Scalar(845)/Scalar(4104),
+  };
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_a6Arr[5] = {
+    -Scalar(8)/Scalar(27),
+     Scalar(2),
+    -Scalar(3544)/Scalar(2565),
+     Scalar(1859)/Scalar(4104),
+    -Scalar(11)/Scalar(40)
+  };
+
+  template <typename Y>
+  std::vector<typename GenericRKF45Integrator<Y>::Scalar>
+  GenericRKF45Integrator<Y>::s_aArr[5] = {
+    std::vector<Scalar>(s_a2Arr, s_a2Arr + 1),
+    std::vector<Scalar>(s_a3Arr, s_a3Arr + 2),
+    std::vector<Scalar>(s_a4Arr, s_a4Arr + 3),
+    std::vector<Scalar>(s_a5Arr, s_a5Arr + 4),
+    std::vector<Scalar>(s_a6Arr, s_a6Arr + 5)
+  };
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::ACoefficients
+  GenericRKF45Integrator<Y>::s_a(s_aArr, s_aArr + 5);
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_bArr[6] = {
+     Scalar(16)/Scalar(135),
+     Scalar(0),
+     Scalar(6656)/Scalar(12825),
+     Scalar(28561)/Scalar(56430),
+    -Scalar(9)/Scalar(50),
+     Scalar(2)/Scalar(55),
+  };
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::BCoefficients
+  GenericRKF45Integrator<Y>::s_b(s_bArr, s_bArr + 6);
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::Scalar
+  GenericRKF45Integrator<Y>::s_bStarArr[6] = {
+     Scalar(25)/Scalar(216),
+     Scalar(0),
+     Scalar(1408)/Scalar(2565),
+     Scalar(2197)/Scalar(4104),
+    -Scalar(1)/Scalar(5),
+     Scalar(0)
+  };
+
+  template <typename Y>
+  typename GenericRKF45Integrator<Y>::BCoefficients
+  GenericRKF45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 6);
+}
+
+#endif // VZ_RKF45_HPP
diff --git a/tests/Makefile.am b/tests/Makefile.am
index cab6d98..f6ad25e 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -24,7 +24,8 @@ check_PROGRAMS = Euler-test                                                    \
                  Heun-test                                                     \
                  RK4-test                                                      \
                  HE12-test                                                     \
-                 BS23-test
+                 BS23-test                                                     \
+                 RKF45-test
 TESTS          = $(check_PROGRAMS)
 
 Euler_test_SOURCES    = Euler.cpp
@@ -33,3 +34,4 @@ 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
diff --git a/tests/RKF45.cpp b/tests/RKF45.cpp
new file mode 100644
index 0000000..8b87216
--- /dev/null
+++ b/tests/RKF45.cpp
@@ -0,0 +1,39 @@
+#include "vZ.hpp"
+#include <cmath>
+#include <cstdlib>
+#include <iostream>
+#include <iomanip>
+
+// y' = y (y == C*exp(t))
+double
+f(double t, double y)
+{
+  return y;
+}
+
+int
+main()
+{
+  vZ::RKF45Integrator integrator(f);
+  integrator.tol(1e-6).y(1.0).x(0.0).h(0.06);
+
+  integrator.integrate(2.0);
+
+  double actual   = integrator.y();
+  double expected = std::exp(2.0);
+
+  std::cout << std::setprecision(10)
+            << "Numerical:  " << actual << std::endl
+            << "Expected:   " << expected  << std::endl
+            << "h:          " << integrator.h() << 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;
+  }
+}