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1 | /* |
2 | [auto_generated] | |
3 | boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp | |
4 | ||
5 | [begin_description] | |
6 | tba. | |
7 | [end_description] | |
8 | ||
9 | Copyright 2012-2013 Karsten Ahnert | |
10 | Copyright 2012-2013 Mario Mulansky | |
11 | ||
12 | Distributed under the Boost Software License, Version 1.0. | |
13 | (See accompanying file LICENSE_1_0.txt or | |
14 | copy at http://www.boost.org/LICENSE_1_0.txt) | |
15 | */ | |
16 | ||
17 | ||
18 | #ifndef BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED | |
19 | #define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED | |
20 | ||
21 | #include <boost/numeric/odeint/algebra/default_operations.hpp> | |
22 | #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp> | |
23 | #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp> | |
24 | ||
25 | #include <boost/numeric/odeint/util/resizer.hpp> | |
26 | ||
27 | ||
28 | namespace boost { | |
29 | namespace numeric { | |
30 | namespace odeint { | |
31 | ||
32 | #ifndef DOXYGEN_SKIP | |
33 | namespace detail { | |
34 | namespace symplectic_rkn_sb3a_m4_mclachlan { | |
35 | ||
36 | /* | |
37 | exp( a1 t A ) exp( b1 t B ) | |
38 | exp( a2 t A ) exp( b2 t B ) | |
39 | exp( a3 t A ) | |
40 | exp( b2 t B ) exp( a2 t A ) | |
41 | exp( b1 t B ) exp( a1 t A ) | |
42 | */ | |
43 | ||
44 | ||
45 | ||
46 | template< class Value > | |
47 | struct coef_a_type : public boost::array< Value , 5 > | |
48 | { | |
49 | coef_a_type( void ) | |
50 | { | |
51 | using std::sqrt; | |
52 | ||
53 | Value z = sqrt( static_cast< Value >( 7 ) / static_cast< Value >( 8 ) ) / static_cast< Value >( 3 ); | |
54 | (*this)[0] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - z ; | |
55 | (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 3 ) + z ; | |
56 | (*this)[2] = static_cast< Value >( 2 ) / static_cast< Value >( 3 ); | |
57 | (*this)[3] = (*this)[1]; | |
58 | (*this)[4] = (*this)[0]; | |
59 | } | |
60 | }; | |
61 | ||
62 | template< class Value > | |
63 | struct coef_b_type : public boost::array< Value , 5 > | |
64 | { | |
65 | coef_b_type( void ) | |
66 | { | |
67 | (*this)[0] = static_cast< Value >( 1 ); | |
68 | (*this)[1] = static_cast< Value >( -1 ) / static_cast< Value >( 2 ); | |
69 | (*this)[2] = (*this)[1]; | |
70 | (*this)[3] = (*this)[0]; | |
71 | (*this)[4] = static_cast< Value >( 0 ); | |
72 | } | |
73 | }; | |
74 | ||
75 | } // namespace symplectic_rkn_sb3a_m4_mclachlan | |
76 | } // namespace detail | |
77 | #endif // DOXYGEN_SKIP | |
78 | ||
79 | ||
80 | ||
81 | ||
82 | template< | |
83 | class Coor , | |
84 | class Momentum = Coor , | |
85 | class Value = double , | |
86 | class CoorDeriv = Coor , | |
87 | class MomentumDeriv = Coor , | |
88 | class Time = Value , | |
89 | class Algebra = typename algebra_dispatcher< Coor >::algebra_type , | |
90 | class Operations = typename operations_dispatcher< Coor >::operations_type , | |
91 | class Resizer = initially_resizer | |
92 | > | |
93 | #ifndef DOXYGEN_SKIP | |
94 | class symplectic_rkn_sb3a_m4_mclachlan : | |
95 | public symplectic_nystroem_stepper_base | |
96 | < | |
97 | 5 , 4 , | |
98 | Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer | |
99 | > | |
100 | #else | |
101 | class symplectic_rkn_sb3a_m4_mclachlan : public symplectic_nystroem_stepper_base | |
102 | #endif | |
103 | { | |
104 | public: | |
105 | #ifndef DOXYGEN_SKIP | |
106 | typedef symplectic_nystroem_stepper_base | |
107 | < | |
108 | 5 , 4 , | |
109 | Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer | |
110 | > stepper_base_type; | |
111 | #endif | |
112 | typedef typename stepper_base_type::algebra_type algebra_type; | |
113 | typedef typename stepper_base_type::value_type value_type; | |
114 | ||
115 | ||
116 | symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra = algebra_type() ) | |
117 | : stepper_base_type( | |
118 | detail::symplectic_rkn_sb3a_m4_mclachlan::coef_a_type< value_type >() , | |
119 | detail::symplectic_rkn_sb3a_m4_mclachlan::coef_b_type< value_type >() , | |
120 | algebra ) | |
121 | { } | |
122 | }; | |
123 | ||
124 | ||
125 | /***************** DOXYGEN ***************/ | |
126 | ||
127 | /** | |
128 | * \class symplectic_rkn_sb3a_m4_mclachlan | |
129 | * \brief Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order. | |
130 | * | |
131 | * The method is of fourth order and has five stages. It is described HERE. This method can be used | |
132 | * with multiprecision types since the coefficients are defined analytically. | |
133 | * | |
134 | * ToDo: add reference to paper. | |
135 | * | |
136 | * \tparam Order The order of the stepper. | |
137 | * \tparam Coor The type representing the coordinates q. | |
138 | * \tparam Momentum The type representing the coordinates p. | |
139 | * \tparam Value The basic value type. Should be something like float, double or a high-precision type. | |
140 | * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt. | |
141 | * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt. | |
142 | * \tparam Time The type representing the time t. | |
143 | * \tparam Algebra The algebra. | |
144 | * \tparam Operations The operations. | |
145 | * \tparam Resizer The resizer policy. | |
146 | */ | |
147 | ||
148 | /** | |
149 | * \fn symplectic_rkn_sb3a_m4_mclachlan::symplectic_rkn_sb3a_m4_mclachlan( const algebra_type &algebra ) | |
150 | * \brief Constructs the symplectic_rkn_sb3a_m4_mclachlan. This constructor can be used as a default | |
151 | * constructor if the algebra has a default constructor. | |
152 | * \param algebra A copy of algebra is made and stored inside explicit_stepper_base. | |
153 | */ | |
154 | ||
155 | } // namespace odeint | |
156 | } // namespace numeric | |
157 | } // namespace boost | |
158 | ||
159 | ||
160 | #endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_M4_MCLACHLAN_HPP_DEFINED |