odeint/stepper/runge_kutta_cash_karp54_classic.hpp

0001 /*
0002  [auto_generated]
0003  boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp
0004
0005  [begin_description]
0006  Classical implementation of the Runge-Kutta Cash-Karp 5(4) method.
0007  [end_description]
0008
0009  Copyright 2010-2013 Mario Mulansky
0010  Copyright 2010-2013 Karsten Ahnert
0011  Copyright 2012 Christoph Koke
0012
0013  Distributed under the Boost Software License, Version 1.0.
0014  (See accompanying file LICENSE_1_0.txt or
0015  copy at http://www.boost.org/LICENSE_1_0.txt)
0016  */
0017
0018
0019 #ifndef BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
0020 #define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED
0021
0022
0023 #include <boost/numeric/odeint/util/bind.hpp>
0024
0025 #include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp>
0026 #include <boost/numeric/odeint/algebra/range_algebra.hpp>
0027 #include <boost/numeric/odeint/algebra/default_operations.hpp>
0028 #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
0029 #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
0030 #include <boost/numeric/odeint/stepper/stepper_categories.hpp>
0031 #include <boost/numeric/odeint/util/state_wrapper.hpp>
0032 #include <boost/numeric/odeint/util/is_resizeable.hpp>
0033 #include <boost/numeric/odeint/util/resizer.hpp>
0034
0035 namespace boost {
0036 namespace numeric {
0037 namespace odeint {
0038
0039
0040
0041
0042 template<
0043 class State ,
0044 class Value = double ,
0045 class Deriv = State ,
0046 class Time = Value ,
0047 class Algebra = typename algebra_dispatcher< State >::algebra_type ,
0048 class Operations = typename operations_dispatcher< State >::operations_type ,
0049 class Resizer = initially_resizer
0050 >
0051 #ifndef DOXYGEN_SKIP
0052 class runge_kutta_cash_karp54_classic
0053 : public explicit_error_stepper_base<
0054   runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
0055   5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
0056 #else
0057 class runge_kutta_cash_karp54_classic : public explicit_error_stepper_base
0058 #endif
0059 {
0060
0061
0062 public :
0063
0064     #ifndef DOXYGEN_SKIP
0065     typedef explicit_error_stepper_base<
0066     runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
0067     5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
0068     #else
0069     typedef explicit_error_stepper_base< runge_kutta_cash_karp54_classic< ... > , ... > stepper_base_type;
0070     #endif
0071
0072     typedef typename stepper_base_type::state_type state_type;
0073     typedef typename stepper_base_type::value_type value_type;
0074     typedef typename stepper_base_type::deriv_type deriv_type;
0075     typedef typename stepper_base_type::time_type time_type;
0076     typedef typename stepper_base_type::algebra_type algebra_type;
0077     typedef typename stepper_base_type::operations_type operations_type;
0078     typedef typename stepper_base_type::resizer_type resizer_type;
0079
0080     #ifndef DOXYGEN_SKIP
0081     typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
0082     typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
0083     typedef typename stepper_base_type::stepper_type stepper_type;
0084     #endif
0085
0086
0087     runge_kutta_cash_karp54_classic( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra )
0088     { }
0089
0090
0091
0092     template< class System , class StateIn , class DerivIn , class StateOut , class Err >
0093     void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
0094     {
0095         const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 );
0096         const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 );
0097         const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 );
0098         const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 );
0099
0100         const value_type dc1 = c1 - static_cast<value_type> ( 2825 ) / static_cast<value_type>( 27648 );
0101         const value_type dc3 = c3 - static_cast<value_type> ( 18575 ) / static_cast<value_type>( 48384 );
0102         const value_type dc4 = c4 - static_cast<value_type> ( 13525 ) / static_cast<value_type>( 55296 );
0103         const value_type dc5 = static_cast<value_type> ( -277 ) / static_cast<value_type>( 14336 );
0104         const value_type dc6 = c6 - static_cast<value_type> ( 1 ) / static_cast<value_type> ( 4 );
0105
0106         do_step_impl( system , in , dxdt , t , out , dt );
0107
0108         //error estimate
0109         stepper_base_type::m_algebra.for_each6( xerr , dxdt , m_k3.m_v , m_k4.m_v , m_k5.m_v , m_k6.m_v ,
0110                 typename operations_type::template scale_sum5< time_type , time_type , time_type , time_type , time_type >( dt*dc1 , dt*dc3 , dt*dc4 , dt*dc5 , dt*dc6 ));
0111
0112     }
0113
0114
0115
0116     template< class System , class StateIn , class DerivIn , class StateOut >
0117     void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
0118     {
0119         const value_type a2 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 );
0120         const value_type a3 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 );
0121         const value_type a4 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 5 );
0122         const value_type a5 = static_cast<value_type> ( 1 );
0123         const value_type a6 = static_cast<value_type> ( 7 ) / static_cast<value_type> ( 8 );
0124
0125         const value_type b21 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 );
0126         const value_type b31 = static_cast<value_type> ( 3 ) / static_cast<value_type>( 40 );
0127         const value_type b32 = static_cast<value_type> ( 9 ) / static_cast<value_type>( 40 );
0128         const value_type b41 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 );
0129         const value_type b42 = static_cast<value_type> ( -9 ) / static_cast<value_type> ( 10 );
0130         const value_type b43 = static_cast<value_type> ( 6 ) / static_cast<value_type> ( 5 );
0131         const value_type b51 = static_cast<value_type> ( -11 ) / static_cast<value_type>( 54 );
0132         const value_type b52 = static_cast<value_type> ( 5 ) / static_cast<value_type> ( 2 );
0133         const value_type b53 = static_cast<value_type> ( -70 ) / static_cast<value_type>( 27 );
0134         const value_type b54 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 27 );
0135         const value_type b61 = static_cast<value_type> ( 1631 ) / static_cast<value_type>( 55296 );
0136         const value_type b62 = static_cast<value_type> ( 175 ) / static_cast<value_type>( 512 );
0137         const value_type b63 = static_cast<value_type> ( 575 ) / static_cast<value_type>( 13824 );
0138         const value_type b64 = static_cast<value_type> ( 44275 ) / static_cast<value_type>( 110592 );
0139         const value_type b65 = static_cast<value_type> ( 253 ) / static_cast<value_type>( 4096 );
0140
0141         const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 );
0142         const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 );
0143         const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 );
0144         const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 );
0145
0146         typename odeint::unwrap_reference< System >::type &sys = system;
0147
0148         m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
0149
0150         //m_x1 = x + dt*b21*dxdt
0151         stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , dxdt ,
0152                 typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , dt*b21 ) );
0153
0154         sys( m_x_tmp.m_v , m_k2.m_v , t + dt*a2 );
0155         // m_x_tmp = x + dt*b31*dxdt + dt*b32*m_x2
0156         stepper_base_type::m_algebra.for_each4( m_x_tmp.m_v , in , dxdt , m_k2.m_v ,
0157                 typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt*b31 , dt*b32 ));
0158
0159         sys( m_x_tmp.m_v , m_k3.m_v , t + dt*a3 );
0160         // m_x_tmp = x + dt * (b41*dxdt + b42*m_x2 + b43*m_x3)
0161         stepper_base_type::m_algebra.for_each5( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v ,
0162                 typename operations_type::template scale_sum4< value_type , time_type , time_type , time_type >( 1.0 , dt*b41 , dt*b42 , dt*b43 ));
0163
0164         sys( m_x_tmp.m_v, m_k4.m_v , t + dt*a4 );
0165         stepper_base_type::m_algebra.for_each6( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v , m_k4.m_v ,
0166                 typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b51 , dt*b52 , dt*b53 , dt*b54 ));
0167
0168         sys( m_x_tmp.m_v , m_k5.m_v , t + dt*a5 );
0169         stepper_base_type::m_algebra.for_each7( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v , m_k4.m_v , m_k5.m_v ,
0170                 typename operations_type::template scale_sum6< value_type , time_type , time_type , time_type , time_type , time_type >( 1.0 , dt*b61 , dt*b62 , dt*b63 , dt*b64 , dt*b65 ));
0171
0172         sys( m_x_tmp.m_v , m_k6.m_v , t + dt*a6 );
0173         stepper_base_type::m_algebra.for_each6( out , in , dxdt , m_k3.m_v , m_k4.m_v , m_k6.m_v ,
0174                 typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt*c1 , dt*c3 , dt*c4 , dt*c6 ));
0175
0176     }
0177
0178     /**
0179      * \brief Adjust the size of all temporaries in the stepper manually.
0180      * \param x A state from which the size of the temporaries to be resized is deduced.
0181      */
0182     template< class StateIn >
0183     void adjust_size( const StateIn &x )
0184     {
0185         resize_impl( x );
0186         stepper_base_type::adjust_size( x );
0187     }
0188
0189 private:
0190
0191     template< class StateIn >
0192     bool resize_impl( const StateIn &x )
0193     {
0194         bool resized = false;
0195         resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() );
0196         resized |= adjust_size_by_resizeability( m_k2 , x , typename is_resizeable<deriv_type>::type() );
0197         resized |= adjust_size_by_resizeability( m_k3 , x , typename is_resizeable<deriv_type>::type() );
0198         resized |= adjust_size_by_resizeability( m_k4 , x , typename is_resizeable<deriv_type>::type() );
0199         resized |= adjust_size_by_resizeability( m_k5 , x , typename is_resizeable<deriv_type>::type() );
0200         resized |= adjust_size_by_resizeability( m_k6 , x , typename is_resizeable<deriv_type>::type() );
0201         return resized;
0202     }
0203
0204
0205     wrapped_state_type m_x_tmp;
0206     wrapped_deriv_type m_k2, m_k3, m_k4, m_k5, m_k6;
0207     resizer_type m_resizer;
0208
0209 };
0210
0211
0212
0213 /************ DOXYGEN *************/
0214
0215 /**
0216  * \class runge_kutta_cash_karp54_classic
0217  * \brief The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm.
0218  *
0219  * The Runge-Kutta Cash-Karp method is one of the standard methods for
0220  * solving ordinary differential equations, see
0221  * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method">en.wikipedia.org/wiki/Cash-Karp_method</a>.
0222  * The method is explicit and fulfills the Error Stepper concept. Step size control
0223  * is provided but continuous output is not available for this method.
0224  *
0225  * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring
0226  * template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.
0227  *
0228  * \tparam State The state type.
0229  * \tparam Value The value type.
0230  * \tparam Deriv The type representing the time derivative of the state.
0231  * \tparam Time The time representing the independent variable - the time.
0232  * \tparam Algebra The algebra type.
0233  * \tparam Operations The operations type.
0234  * \tparam Resizer The resizer policy type.
0235  */
0236
0237
0238     /**
0239      * \fn runge_kutta_cash_karp54_classic::runge_kutta_cash_karp54_classic( const algebra_type &algebra )
0240      * \brief Constructs the runge_kutta_cash_karp54_classic class. This constructor can be used as a default
0241      * constructor if the algebra has a default constructor.
0242      * \param algebra A copy of algebra is made and stored inside explicit_stepper_base.
0243      */
0244
0245
0246     /**
0247      * \fn runge_kutta_cash_karp54_classic::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr )
0248      * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
0249      *
0250      * The result is updated out-of-place, hence the input is in `in` and the output in `out`. Futhermore, an
0251      * estimation of the error is stored in `xerr`.
0252      * Access to this step functionality is provided by explicit_error_stepper_base and
0253      * `do_step_impl` should not be called directly.
0254
0255      *
0256      * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
0257      *               Simple System concept.
0258      * \param in The state of the ODE which should be solved. in is not modified in this method
0259      * \param dxdt The derivative of x at t.
0260      * \param t The value of the time, at which the step should be performed.
0261      * \param out The result of the step is written in out.
0262      * \param dt The step size.
0263      * \param xerr The result of the error estimation is written in xerr.
0264      */
0265
0266     /**
0267      * \fn runge_kutta_cash_karp54_classic::do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
0268      * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method.
0269      * The result is updated out-of-place, hence the input is in `in` and the output in `out`.
0270      * Access to this step functionality is provided by explicit_error_stepper_base and
0271      * `do_step_impl` should not be called directly.
0272      *
0273      * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
0274      *               Simple System concept.
0275      * \param in The state of the ODE which should be solved. in is not modified in this method
0276      * \param dxdt The derivative of x at t.
0277      * \param t The value of the time, at which the step should be performed.
0278      * \param out The result of the step is written in out.
0279      * \param dt The step size.
0280      */
0281
0282 } // odeint
0283 } // numeric
0284 } // boost
0285
0286
0287
0288
0289 #endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED