1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
|
/*
[auto_generated]
boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp
[begin_description]
Implementation of the symplectic MacLachlan stepper for separable Hamiltonian system.
[end_description]
Copyright 2011-2013 Karsten Ahnert
Copyright 2011-2013 Mario Mulansky
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or
copy at http://www.boost.org/LICENSE_1_0.txt)
*/
#ifndef BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
#include <boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp>
#include <boost/numeric/odeint/algebra/range_algebra.hpp>
#include <boost/numeric/odeint/algebra/default_operations.hpp>
#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
#include <boost/numeric/odeint/util/resizer.hpp>
#include <boost/array.hpp>
namespace boost {
namespace numeric {
namespace odeint {
#ifndef DOXYGEN_SKIP
namespace detail {
namespace symplectic_rkn_sb3a_mclachlan {
/*
exp( a1 t A ) exp( b1 t B )
exp( a2 t A ) exp( b2 t B )
exp( a3 t A ) exp( b3 t B ) exp( a3 t A )
exp( b2 t B ) exp( a2 t A )
exp( b1 t B ) exp( a1 t A )
*/
template< class Value >
struct coef_a_type : public boost::array< Value , 6 >
{
coef_a_type( void )
{
(*this)[0] = static_cast< Value >( 0.40518861839525227722 );
(*this)[1] = static_cast< Value >( -0.28714404081652408900 );
(*this)[2] = static_cast< Value >( 1 ) / static_cast< Value >( 2 ) - ( (*this)[0] + (*this)[1] );
(*this)[3] = (*this)[2];
(*this)[4] = (*this)[1];
(*this)[5] = (*this)[0];
}
};
template< class Value >
struct coef_b_type : public boost::array< Value , 6 >
{
coef_b_type( void )
{
(*this)[0] = static_cast< Value >( -3 ) / static_cast< Value >( 73 );
(*this)[1] = static_cast< Value >( 17 ) / static_cast< Value >( 59 );
(*this)[2] = static_cast< Value >( 1 ) - static_cast< Value >( 2 ) * ( (*this)[0] + (*this)[1] );
(*this)[3] = (*this)[1];
(*this)[4] = (*this)[0];
(*this)[5] = static_cast< Value >( 0 );
}
};
} // namespace symplectic_rkn_sb3a_mclachlan
} // namespace detail
#endif // DOXYGEN_SKIP
template<
class Coor ,
class Momentum = Coor ,
class Value = double ,
class CoorDeriv = Coor ,
class MomentumDeriv = Coor ,
class Time = Value ,
class Algebra = typename algebra_dispatcher< Coor >::algebra_type ,
class Operations = typename operations_dispatcher< Coor >::operations_type ,
class Resizer = initially_resizer
>
#ifndef DOXYGEN_SKIP
class symplectic_rkn_sb3a_mclachlan :
public symplectic_nystroem_stepper_base
<
6 , 4 ,
Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
>
#else
class symplectic_rkn_sb3a_mclachlan : public symplectic_nystroem_stepper_base
#endif
{
public:
#ifndef DOXYGEN_SKIP
typedef symplectic_nystroem_stepper_base
<
6 , 4 ,
Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer
> stepper_base_type;
#endif
typedef typename stepper_base_type::algebra_type algebra_type;
typedef typename stepper_base_type::value_type value_type;
symplectic_rkn_sb3a_mclachlan( const algebra_type &algebra = algebra_type() )
: stepper_base_type(
detail::symplectic_rkn_sb3a_mclachlan::coef_a_type< value_type >() ,
detail::symplectic_rkn_sb3a_mclachlan::coef_b_type< value_type >() ,
algebra )
{ }
};
/************* DOXYGEN ***********/
/**
* \class symplectic_rkn_sb3a_mclachlan
* \brief Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order.
*
* The method is of fourth order and has six stages. It is described HERE. This method cannot be used
* with multiprecision types since the coefficients are not defined analytically.
*
* ToDo Add reference to the paper.
*
* \tparam Order The order of the stepper.
* \tparam Coor The type representing the coordinates q.
* \tparam Momentum The type representing the coordinates p.
* \tparam Value The basic value type. Should be something like float, double or a high-precision type.
* \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt.
* \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt.
* \tparam Time The type representing the time t.
* \tparam Algebra The algebra.
* \tparam Operations The operations.
* \tparam Resizer The resizer policy.
*/
/**
* \fn symplectic_rkn_sb3a_mclachlan::symplectic_rkn_sb3a_mclachlan( const algebra_type &algebra )
* \brief Constructs the symplectic_rkn_sb3a_mclachlan. This constructor can be used as a default
* constructor if the algebra has a default constructor.
* \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
*/
} // namespace odeint
} // namespace numeric
} // namespace boost
#endif // BOOST_NUMERIC_ODEINT_STEPPER_SYMPLECTIC_RKN_SB3A_MCLACHLAN_HPP_INCLUDED
|
