boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp
/* [auto_generated] boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp [begin_description] Classical implementation of the Runge-Kutta Cash-Karp 5(4) method. [end_description] Copyright 2009-2011 Karsten Ahnert Copyright 2009-2011 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_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED #define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED #include <boost/numeric/odeint/util/bind.hpp> #include <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp> #include <boost/numeric/odeint/algebra/range_algebra.hpp> #include <boost/numeric/odeint/algebra/default_operations.hpp> #include <boost/numeric/odeint/stepper/stepper_categories.hpp> #include <boost/numeric/odeint/util/state_wrapper.hpp> #include <boost/numeric/odeint/util/is_resizeable.hpp> #include <boost/numeric/odeint/util/resizer.hpp> namespace boost { namespace numeric { namespace odeint { template< class State , class Value = double , class Deriv = State , class Time = double , class Algebra = range_algebra , class Operations = default_operations , class Resizer = initially_resizer > #ifndef DOXYGEN_SKIP class runge_kutta_cash_karp54_classic : public explicit_error_stepper_base< runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > #else class runge_kutta_cash_karp54_classic : public explicit_error_stepper_base #endif { public : #ifndef DOXYGEN_SKIP typedef explicit_error_stepper_base< runge_kutta_cash_karp54_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 5 , 5 , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type; #else typedef explicit_error_stepper_base< runge_kutta_cash_karp54_classic< ... > , ... > stepper_base_type; #endif typedef typename stepper_base_type::state_type state_type; typedef typename stepper_base_type::value_type value_type; typedef typename stepper_base_type::deriv_type deriv_type; typedef typename stepper_base_type::time_type time_type; typedef typename stepper_base_type::algebra_type algebra_type; typedef typename stepper_base_type::operations_type operations_type; typedef typename stepper_base_type::resizer_type resizer_type; #ifndef DOXYGEN_SKIP typedef typename stepper_base_type::wrapped_state_type wrapped_state_type; typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type; typedef typename stepper_base_type::stepper_type stepper_type; #endif runge_kutta_cash_karp54_classic( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra ) { } template< class System , class StateIn , class DerivIn , class StateOut , class Err > void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , Err &xerr ) { const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 ); const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 ); const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 ); const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 ); const value_type dc1 = c1 - static_cast<value_type> ( 2825 ) / static_cast<value_type>( 27648 ); const value_type dc3 = c3 - static_cast<value_type> ( 18575 ) / static_cast<value_type>( 48384 ); const value_type dc4 = c4 - static_cast<value_type> ( 13525 ) / static_cast<value_type>( 55296 ); const value_type dc5 = static_cast<value_type> ( -277 ) / static_cast<value_type>( 14336 ); const value_type dc6 = c6 - static_cast<value_type> ( 1 ) / static_cast<value_type> ( 4 ); do_step_impl( system , in , dxdt , t , out , dt ); //error estimate 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 , 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 )); } template< class System , class StateIn , class DerivIn , class StateOut > void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt ) { const value_type a2 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 ); const value_type a3 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 ); const value_type a4 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 5 ); const value_type a5 = static_cast<value_type> ( 1 ); const value_type a6 = static_cast<value_type> ( 7 ) / static_cast<value_type> ( 8 ); const value_type b21 = static_cast<value_type> ( 1 ) / static_cast<value_type> ( 5 ); const value_type b31 = static_cast<value_type> ( 3 ) / static_cast<value_type>( 40 ); const value_type b32 = static_cast<value_type> ( 9 ) / static_cast<value_type>( 40 ); const value_type b41 = static_cast<value_type> ( 3 ) / static_cast<value_type> ( 10 ); const value_type b42 = static_cast<value_type> ( -9 ) / static_cast<value_type> ( 10 ); const value_type b43 = static_cast<value_type> ( 6 ) / static_cast<value_type> ( 5 ); const value_type b51 = static_cast<value_type> ( -11 ) / static_cast<value_type>( 54 ); const value_type b52 = static_cast<value_type> ( 5 ) / static_cast<value_type> ( 2 ); const value_type b53 = static_cast<value_type> ( -70 ) / static_cast<value_type>( 27 ); const value_type b54 = static_cast<value_type> ( 35 ) / static_cast<value_type>( 27 ); const value_type b61 = static_cast<value_type> ( 1631 ) / static_cast<value_type>( 55296 ); const value_type b62 = static_cast<value_type> ( 175 ) / static_cast<value_type>( 512 ); const value_type b63 = static_cast<value_type> ( 575 ) / static_cast<value_type>( 13824 ); const value_type b64 = static_cast<value_type> ( 44275 ) / static_cast<value_type>( 110592 ); const value_type b65 = static_cast<value_type> ( 253 ) / static_cast<value_type>( 4096 ); const value_type c1 = static_cast<value_type> ( 37 ) / static_cast<value_type>( 378 ); const value_type c3 = static_cast<value_type> ( 250 ) / static_cast<value_type>( 621 ); const value_type c4 = static_cast<value_type> ( 125 ) / static_cast<value_type>( 594 ); const value_type c6 = static_cast<value_type> ( 512 ) / static_cast<value_type>( 1771 ); typename odeint::unwrap_reference< System >::type &sys = system; m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) ); //m_x1 = x + dt*b21*dxdt stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , dxdt , typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , dt*b21 ) ); sys( m_x_tmp.m_v , m_k2.m_v , t + dt*a2 ); // m_x_tmp = x + dt*b31*dxdt + dt*b32*m_x2 stepper_base_type::m_algebra.for_each4( m_x_tmp.m_v , in , dxdt , m_k2.m_v , typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt*b31 , dt*b32 )); sys( m_x_tmp.m_v , m_k3.m_v , t + dt*a3 ); // m_x_tmp = x + dt * (b41*dxdt + b42*m_x2 + b43*m_x3) stepper_base_type::m_algebra.for_each5( m_x_tmp.m_v , in , dxdt , m_k2.m_v , m_k3.m_v , typename operations_type::template scale_sum4< value_type , time_type , time_type , time_type >( 1.0 , dt*b41 , dt*b42 , dt*b43 )); sys( m_x_tmp.m_v, m_k4.m_v , t + dt*a4 ); 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 , 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 )); sys( m_x_tmp.m_v , m_k5.m_v , t + dt*a5 ); 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 , 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 )); sys( m_x_tmp.m_v , m_k6.m_v , t + dt*a6 ); stepper_base_type::m_algebra.for_each6( out , in , dxdt , m_k3.m_v , m_k4.m_v , m_k6.m_v , 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 )); } /** * \brief Adjust the size of all temporaries in the stepper manually. * \param x A state from which the size of the temporaries to be resized is deduced. */ template< class StateIn > void adjust_size( const StateIn &x ) { resize_impl( x ); stepper_base_type::adjust_size( x ); } private: template< class StateIn > bool resize_impl( const StateIn &x ) { bool resized = false; resized |= adjust_size_by_resizeability( m_x_tmp , x , typename is_resizeable<state_type>::type() ); resized |= adjust_size_by_resizeability( m_k2 , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_k3 , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_k4 , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_k5 , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_k6 , x , typename is_resizeable<deriv_type>::type() ); return resized; } wrapped_state_type m_x_tmp; wrapped_deriv_type m_k2, m_k3, m_k4, m_k5, m_k6; resizer_type m_resizer; }; /************ DOXYGEN *************/ /** * \class runge_kutta_cash_karp54_classic * \brief The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm. * * The Runge-Kutta Cash-Karp method is one of the standard methods for * solving ordinary differential equations, see * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method">en.wikipedia.org/wiki/Cash-Karp_method</a>. * The method is explicit and fulfills the Error Stepper concept. Step size control * is provided but continuous output is not available for this method. * * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring * template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used. * * \tparam State The state type. * \tparam Value The value type. * \tparam Deriv The type representing the time derivative of the state. * \tparam Time The time representing the independent variable - the time. * \tparam Algebra The algebra type. * \tparam Operations The operations type. * \tparam Resizer The resizer policy type. */ /** * \fn runge_kutta_cash_karp54_classic::runge_kutta_cash_karp54_classic( const algebra_type &algebra ) * \brief Constructs the runge_kutta_cash_karp54_classic class. 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. */ /** * \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 ) * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method. * * The result is updated out-of-place, hence the input is in `in` and the output in `out`. Futhermore, an * estimation of the error is stored in `xerr`. * Access to this step functionality is provided by explicit_error_stepper_base and * `do_step_impl` should not be called directly. * * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the * Simple System concept. * \param in The state of the ODE which should be solved. in is not modified in this method * \param dxdt The derivative of x at t. * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dt The step size. * \param xerr The result of the error estimation is written in xerr. */ /** * \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 ) * \brief This method performs one step. The derivative `dxdt` of `in` at the time `t` is passed to the method. * The result is updated out-of-place, hence the input is in `in` and the output in `out`. * Access to this step functionality is provided by explicit_error_stepper_base and * `do_step_impl` should not be called directly. * * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the * Simple System concept. * \param in The state of the ODE which should be solved. in is not modified in this method * \param dxdt The derivative of x at t. * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dt The step size. */ } // odeint } // numeric } // boost #endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_CLASSIC_HPP_INCLUDED