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

   1 /*
   2  [auto_generated]
   3  boost/numeric/odeint/stepper/modified_midpoint.hpp
   4
   5  [begin_description]
   6  Modified midpoint method for the use in Burlish-Stoer stepper.
   7  [end_description]
   8
   9  Copyright 2011-2013 Mario Mulansky
  10  Copyright 2011-2013 Karsten Ahnert
  11  Copyright 2012 Christoph Koke
  12
  13  Distributed under the Boost Software License, Version 1.0.
  14  (See accompanying file LICENSE_1_0.txt or
  15  copy at http://www.boost.org/LICENSE_1_0.txt)
  16  */
  17
  18
  19 #ifndef BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
  20 #define BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
  21
  22 #include <vector>
  23
  24 #include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
  25 #include <boost/numeric/odeint/util/resizer.hpp>
  26 #include <boost/numeric/odeint/util/is_resizeable.hpp>
  27 #include <boost/numeric/odeint/algebra/range_algebra.hpp>
  28 #include <boost/numeric/odeint/algebra/default_operations.hpp>
  29 #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
  30 #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
  31 #include <boost/numeric/odeint/util/copy.hpp>
  32
  33 namespace boost {
  34 namespace numeric {
  35 namespace odeint {
  36
  37 template<
  38 class State ,
  39 class Value = double ,
  40 class Deriv = State ,
  41 class Time = Value ,
  42 class Algebra = typename algebra_dispatcher< State >::algebra_type ,
  43 class Operations = typename operations_dispatcher< State >::operations_type ,
  44 class Resizer = initially_resizer
  45 >
  46 #ifndef DOXYGEN_SKIP
  47 class modified_midpoint
  48 : public explicit_stepper_base<
  49   modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
  50   2 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
  51 #else
  52 class modified_midpoint : public explicit_stepper_base
  53 #endif
  54 {
  55
  56 public :
  57
  58     typedef explicit_stepper_base<
  59     modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
  60     2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
  61
  62     typedef typename stepper_base_type::state_type state_type;
  63     typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
  64     typedef typename stepper_base_type::value_type value_type;
  65     typedef typename stepper_base_type::deriv_type deriv_type;
  66     typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
  67     typedef typename stepper_base_type::time_type time_type;
  68     typedef typename stepper_base_type::algebra_type algebra_type;
  69     typedef typename stepper_base_type::operations_type operations_type;
  70     typedef typename stepper_base_type::resizer_type resizer_type;
  71     typedef typename stepper_base_type::stepper_type stepper_type;
  72
  73
  74     modified_midpoint( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
  75     : stepper_base_type( algebra ) , m_steps( steps )
  76     { }
  77
  78     template< class System , class StateIn , class DerivIn , class StateOut >
  79     void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
  80     {
  81         static const value_type val1 = static_cast< value_type >( 1 );
  82         static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
  83
  84         m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
  85
  86         const time_type h = dt /  static_cast<value_type>( m_steps );
  87         const time_type h2 = static_cast<value_type>(2) * h;
  88
  89         typename odeint::unwrap_reference< System >::type &sys = system;
  90
  91         time_type th = t + h;
  92
  93         // m_x1 = x + h*dxdt
  94         stepper_base_type::m_algebra.for_each3( m_x1.m_v , in , dxdt ,
  95                 typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
  96
  97         sys( m_x1.m_v , m_dxdt.m_v , th );
  98
  99         boost::numeric::odeint::copy( in , m_x0.m_v );
 100
 101         unsigned short i = 1;
 102         while( i != m_steps )
 103         {
 104             // general step
 105             //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
 106             stepper_base_type::m_algebra.for_each3( m_x1.m_v , m_x0.m_v , m_dxdt.m_v ,
 107                     typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
 108             th += h;
 109             sys( m_x1.m_v , m_dxdt.m_v , th);
 110             i++;
 111         }
 112
 113         // last step
 114         // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
 115         stepper_base_type::m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , m_dxdt.m_v ,
 116                 typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
 117     }
 118
 119
 120     void set_steps( unsigned short steps )
 121     {   m_steps = steps; }
 122
 123
 124     unsigned short steps( void ) const
 125     {   return m_steps; }
 126
 127
 128     template< class StateIn >
 129     void adjust_size( const StateIn &x )
 130     {
 131         resize_impl( x );
 132         stepper_base_type::adjust_size( x );
 133     }
 134
 135 private:
 136
 137     template< class StateIn >
 138     bool resize_impl( const StateIn &x )
 139     {
 140         bool resized( false );
 141         resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
 142         resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
 143         resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
 144         return resized;
 145     }
 146
 147
 148     unsigned short m_steps;
 149
 150     resizer_type m_resizer;
 151
 152     wrapped_state_type m_x0;
 153     wrapped_state_type m_x1;
 154     wrapped_deriv_type m_dxdt;
 155
 156 };
 157
 158
 159 /* Modified midpoint which stores derivatives and state at dt/2 in some external storage for later usage in dense output calculation
 160  * This Stepper is for use in Bulirsch Stoer only. It DOES NOT meet any stepper concept.
 161  */
 162 template<
 163 class State ,
 164 class Value = double ,
 165 class Deriv = State ,
 166 class Time = Value ,
 167 class Algebra = typename algebra_dispatcher< State >::algebra_type ,
 168 class Operations = typename operations_dispatcher< State >::operations_type ,
 169 class Resizer = initially_resizer
 170 >
 171 class modified_midpoint_dense_out
 172 {
 173
 174 public :
 175
 176     typedef State state_type;
 177     typedef Value value_type;
 178     typedef Deriv deriv_type;
 179     typedef Time time_type;
 180     typedef Algebra algebra_type;
 181     typedef Operations operations_type;
 182     typedef Resizer resizer_type;
 183     typedef state_wrapper< state_type > wrapped_state_type;
 184     typedef state_wrapper< deriv_type > wrapped_deriv_type;
 185
 186     typedef modified_midpoint_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
 187     typedef std::vector< wrapped_deriv_type > deriv_table_type;
 188
 189     modified_midpoint_dense_out( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
 190     : m_algebra( algebra ) , m_steps( steps )
 191     { }
 192
 193     /*
 194      * performs a modified midpoint step with m_steps intermediate points
 195      * stores approximation for x(t+dt/2) in x_mp and all evaluated function results in derivs
 196      *
 197      */
 198
 199     template< class System , class StateIn , class DerivIn , class StateOut >
 200     void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt ,
 201             state_type &x_mp , deriv_table_type &derivs )
 202     {
 203
 204         static const value_type val1 = static_cast< value_type >( 1 );
 205         static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
 206
 207         m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize< StateIn > , detail::ref( *this ) , detail::_1 ) );
 208
 209         const time_type h = dt / static_cast<value_type>( m_steps );
 210         const time_type h2 = static_cast<value_type>( 2 ) * h;
 211
 212         typename odeint::unwrap_reference< System >::type &sys = system;
 213
 214         time_type th = t + h;
 215
 216         // m_x1 = x + h*dxdt
 217         m_algebra.for_each3( m_x1.m_v , in , dxdt ,
 218                 typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
 219
 220         if( m_steps == 2 )
 221             // result of first step already gives approximation at the center of the interval
 222             boost::numeric::odeint::copy( m_x1.m_v , x_mp );
 223
 224         sys( m_x1.m_v , derivs[0].m_v , th );
 225
 226         boost::numeric::odeint::copy( in , m_x0.m_v );
 227
 228         unsigned short i = 1;
 229         while( i != m_steps )
 230         {
 231             // general step
 232             //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
 233             m_algebra.for_each3( m_x1.m_v , m_x0.m_v , derivs[i-1].m_v ,
 234                     typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
 235             if( i == m_steps/2-1 )
 236                 // save approximation at the center of the interval
 237                 boost::numeric::odeint::copy( m_x1.m_v , x_mp );
 238
 239             th += h;
 240             sys( m_x1.m_v , derivs[i].m_v , th);
 241             i++;
 242         }
 243
 244         // last step
 245         // x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
 246         m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , derivs[m_steps-1].m_v ,
 247                 typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
 248     }
 249
 250
 251     void set_steps( unsigned short steps )
 252     {   m_steps = steps; }
 253
 254
 255     unsigned short steps( void ) const
 256     {   return m_steps; }
 257
 258
 259     template< class StateIn >
 260     bool resize( const StateIn &x )
 261     {
 262         bool resized( false );
 263         resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
 264         resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
 265         return resized;
 266     }
 267
 268     template< class StateIn >
 269     void adjust_size( const StateIn &x )
 270     {
 271         resize( x );
 272     }
 273
 274 private:
 275
 276     algebra_type m_algebra;
 277
 278     unsigned short m_steps;
 279
 280     resizer_type m_resizer;
 281
 282     wrapped_state_type m_x0;
 283     wrapped_state_type m_x1;
 284
 285 };
 286
 287
 288
 289 /********** DOXYGEN ***********/
 290
 291 /**
 292  * \class modified_midpoint
 293  *
 294  * Implementation of the modified midpoint method with a configurable
 295  * number of intermediate steps. This class is used by the Bulirsch-Stoer
 296  * algorithm and is not meant for direct usage.
 297  */
 298
 299
 300 /**
 301  * \class modified_midpoint_dense_out
 302  *
 303  * Implementation of the modified midpoint method with a configurable
 304  * number of intermediate steps. This class is used by the dense output
 305  * Bulirsch-Stoer algorithm and is not meant for direct usage.
 306  * \note This stepper is for internal use only and does not meet
 307  * any stepper concept.
 308  */
 309
 310
 311 }
 312 }
 313 }
 314
 315 #endif // BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED