ceph/src/boost/libs/numeric/odeint/include/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp

   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