Add DP45 method.

1 files changed, 167 insertions, 0 deletions

diff --git a/src/vZ/DP45.hpp b/src/vZ/DP45.hpp
new file mode 100644
index 0000000..343bd72
--- /dev/null
+++ b/src/vZ/DP45.hpp
@@ -0,0 +1,167 @@
+/*************************************************************************
+ * 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_DP45_HPP
+#define VZ_DP45_HPP
+
+namespace vZ
+{
+  // Dormand-Prince method
+  //
+  // Fifth-order with embedded fourth-order
+  // Its tableau is:
+  //
+  //   0    |
+  //   1/5  | 1/5
+  //   3/10 | 3/40        9/40
+  //   4/5  | 44/45      -56/15      32/9
+  //   8/9  | 19372/6561 -25360/2186 64448/6561 -212/729
+  //   1    | 9017/3168  -355/33     46732/5247  49/176   -5103/18656
+  //   1    | 35/384      0          500/1113    125/192  -2187/6784    11/84
+  //   -----+------------------------------------------------------------------------
+  //   b    | 35/384      0          500/1113    125/192  -2187/6784    11/84    0
+  //   b*   | 5179/57600  0          7571/16695  393/640  -92097/339200 172/2100 1/40
+  template <typename Y>
+  class GenericDP45Integrator : public GenericAdaptiveIntegrator<Y>
+  {
+  public:
+    typedef typename GenericAdaptiveIntegrator<Y>::Scalar   Scalar;
+    typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+    GenericDP45Integrator(Function f)
+      : GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { }
+    ~GenericDP45Integrator() { }
+
+  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 Scalar s_a7Arr[6];
+    static std::vector<Scalar> s_aArr[6];
+    static Scalar s_bArr[7];
+    static Scalar s_bStarArr[7];
+  };
+
+  // Type alias
+  typedef GenericDP45Integrator<double> DP45Integrator;
+
+  // Implementation
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a2Arr[1] = {
+    Scalar(1)/Scalar(5)
+  };
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a3Arr[2] = {
+    Scalar(3)/Scalar(40), Scalar(9)/Scalar(40)
+  };
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a4Arr[3] = {
+     Scalar(44)/Scalar(45), -Scalar(56)/Scalar(15), Scalar(32)/Scalar(9)
+  };
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a5Arr[4] = {
+     Scalar(19372)/Scalar(6561),
+    -Scalar(25360)/Scalar(2187),
+     Scalar(64448)/Scalar(6561),
+    -Scalar(212)/Scalar(729),
+  };
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a6Arr[5] = {
+     Scalar(9017)/Scalar(3168),
+    -Scalar(355)/Scalar(33),
+     Scalar(46732)/Scalar(5247),
+     Scalar(49)/Scalar(176),
+    -Scalar(5103)/Scalar(18656)
+  };
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_a7Arr[6] = {
+     Scalar(35)/Scalar(384),
+     Scalar(0),
+     Scalar(500)/Scalar(1113),
+     Scalar(125)/Scalar(192),
+    -Scalar(2187)/Scalar(6784),
+     Scalar(11)/Scalar(84)
+  };
+
+  template <typename Y>
+  std::vector<typename GenericDP45Integrator<Y>::Scalar>
+  GenericDP45Integrator<Y>::s_aArr[6] = {
+    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),
+    std::vector<Scalar>(s_a7Arr, s_a7Arr + 6)
+  };
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::ACoefficients
+  GenericDP45Integrator<Y>::s_a(s_aArr, s_aArr + 6);
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_bArr[7] = {
+     Scalar(35)/Scalar(384),
+     Scalar(0),
+     Scalar(500)/Scalar(1113),
+     Scalar(125)/Scalar(192),
+    -Scalar(2187)/Scalar(6784),
+     Scalar(11)/Scalar(84),
+     Scalar(0)
+  };
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::BCoefficients
+  GenericDP45Integrator<Y>::s_b(s_bArr, s_bArr + 7);
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::Scalar
+  GenericDP45Integrator<Y>::s_bStarArr[7] = {
+     Scalar(5179)/Scalar(57600),
+     Scalar(0),
+     Scalar(7571)/Scalar(16695),
+     Scalar(393)/Scalar(640),
+    -Scalar(92097)/Scalar(339200),
+     Scalar(187)/Scalar(2100),
+     Scalar(1)/Scalar(40)
+  };
+
+  template <typename Y>
+  typename GenericDP45Integrator<Y>::BCoefficients
+  GenericDP45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 7);
+}
+
+#endif // VZ_DP45_HPP