From 180d804d9199b79bcad951638105250c77a002bc Mon Sep 17 00:00:00 2001
From: Tavian Barnes <tavianator@gmail.com>
Date: Thu, 7 Oct 2010 01:54:17 -0400
Subject: Add CK45 method.
---
src/vZ/CK45.hpp | 154 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 154 insertions(+)
create mode 100644 src/vZ/CK45.hpp
(limited to 'src/vZ')
diff --git a/src/vZ/CK45.hpp b/src/vZ/CK45.hpp
new file mode 100644
index 0000000..333e451
--- /dev/null
+++ b/src/vZ/CK45.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_CK45_HPP
+#define VZ_CK45_HPP
+
+namespace vZ
+{
+ // Cash-Karp method
+ //
+ // Fifth-order with embedded fourth-order
+ // Its tableau is:
+ //
+ // 0 |
+ // 1/5 | 1/5
+ // 3/10 | 3/40 9/40
+ // 3/5 | 3/10 -9/10 6/5
+ // 1 | -11/54 5/2 -70/27 35/27
+ // 7/8 | 1631/55296 175/512 575/13824 44275/110592 253/4096
+ // ------+-----------------------------------------------------------------
+ // b | 37/378 0 250/621 125/594 0 512/1771
+ // b* | 2825/27648 0 18575/48384 13525/55296 277/14336 1/4
+ template <typename Y>
+ class GenericCK45Integrator : public GenericAdaptiveIntegrator<Y>
+ {
+ public:
+ typedef typename GenericAdaptiveIntegrator<Y>::Scalar Scalar;
+ typedef typename GenericAdaptiveIntegrator<Y>::Function Function;
+
+ GenericCK45Integrator(Function f)
+ : GenericAdaptiveIntegrator<Y>(f, 5, s_a, s_b, s_bStar) { }
+ ~GenericCK45Integrator() { }
+
+ 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 GenericCK45Integrator<double> CK45Integrator;
+
+ // Implementation
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a2Arr[1] = {
+ Scalar(1)/Scalar(5)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a3Arr[2] = {
+ Scalar(3)/Scalar(40), Scalar(9)/Scalar(40)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a4Arr[3] = {
+ Scalar(3)/Scalar(10),
+ -Scalar(9)/Scalar(10),
+ Scalar(6)/Scalar(5)
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a5Arr[4] = {
+ -Scalar(11)/Scalar(54),
+ Scalar(5)/Scalar(2),
+ -Scalar(70)/Scalar(27),
+ Scalar(35)/Scalar(27),
+ };
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_a6Arr[5] = {
+ Scalar(1631)/Scalar(55296),
+ Scalar(175)/Scalar(512),
+ Scalar(575)/Scalar(13824),
+ Scalar(44275)/Scalar(110592),
+ Scalar(253)/Scalar(4096)
+ };
+
+ template <typename Y>
+ std::vector<typename GenericCK45Integrator<Y>::Scalar>
+ GenericCK45Integrator<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 GenericCK45Integrator<Y>::ACoefficients
+ GenericCK45Integrator<Y>::s_a(s_aArr, s_aArr + 5);
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_bArr[6] = {
+ Scalar(37)/Scalar(378),
+ Scalar(0),
+ Scalar(250)/Scalar(621),
+ Scalar(125)/Scalar(594),
+ Scalar(0),
+ Scalar(512)/Scalar(1771),
+ };
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::BCoefficients
+ GenericCK45Integrator<Y>::s_b(s_bArr, s_bArr + 6);
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::Scalar
+ GenericCK45Integrator<Y>::s_bStarArr[6] = {
+ Scalar(2825)/Scalar(27648),
+ Scalar(0),
+ Scalar(18575)/Scalar(48384),
+ Scalar(13525)/Scalar(55296),
+ Scalar(277)/Scalar(14336),
+ Scalar(1)/Scalar(4)
+ };
+
+ template <typename Y>
+ typename GenericCK45Integrator<Y>::BCoefficients
+ GenericCK45Integrator<Y>::s_bStar(s_bStarArr, s_bStarArr + 6);
+}
+
+#endif // VZ_CK45_HPP
--
cgit v1.2.3