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/*************************************************************************
* Copyright (C) 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
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