ceph/src/boost/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp

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