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/*************************************************************************
* 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
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