Add DP45 method.

6 files changed, 216 insertions, 1 deletions

diff --git a/TODO b/TODO
new file mode 100644
index 0000000..6eded45
--- /dev/null
+++ b/TODO
@@ -0,0 +1,2 @@
+- Support systems of ODEs
+- Implement FSAL
diff --git a/src/Makefile.am b/src/Makefile.am
index 42c9279..bf2b10c 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -20,6 +20,8 @@
 nobase_include_HEADERS = vZ.hpp                                                \
                          vZ/Adaptive.hpp                                       \
                          vZ/BS23.hpp                                           \
+                         vZ/CK45.hpp                                           \
+                         vZ/DP45.hpp                                           \
                          vZ/Euler.hpp                                          \
                          vZ/HE12.hpp                                           \
                          vZ/Heun.hpp                                           \
@@ -27,5 +29,6 @@ nobase_include_HEADERS = vZ.hpp                                                \
                          vZ/Midpoint.hpp                                       \
                          vZ/RK.hpp                                             \
                          vZ/RK4.hpp                                            \
+                         vZ/RKF45.hpp                                          \
                          vZ/Simple.hpp                                         \
                          vZ/Traits.hpp
diff --git a/src/vZ.hpp b/src/vZ.hpp
index afce2d4..ab7b3c2 100644
--- a/src/vZ.hpp
+++ b/src/vZ.hpp
@@ -36,5 +36,6 @@
 #include <vZ/BS23.hpp>
 #include <vZ/RKF45.hpp>
 #include <vZ/CK45.hpp>
+#include <vZ/DP45.hpp>
 
 #endif // VZ_HPP
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
diff --git a/tests/DP45.cpp b/tests/DP45.cpp
new file mode 100644
index 0000000..5faa78a
--- /dev/null
+++ b/tests/DP45.cpp
@@ -0,0 +1,40 @@
+#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::DP45Integrator 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
+            << "Iterations: " << integrator.iterations() << std::endl
+            << "Rejections: " << integrator.rejections() << std::endl;
+
+  double error = std::fabs(expected - actual)/expected;
+  if (error > 6.0e-7) {
+    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 60e5cf3..5874419 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -26,7 +26,8 @@ check_PROGRAMS = Euler-test                                                    \
                  HE12-test                                                     \
                  BS23-test                                                     \
                  RKF45-test                                                    \
-                 CK45-test
+                 CK45-test                                                     \
+                 DP45-test
 TESTS          = $(check_PROGRAMS)
 
 Euler_test_SOURCES    = Euler.cpp
@@ -37,3 +38,4 @@ 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