boost/numeric/odeint/stepper/runge_kutta4_classic.hpp
/* [auto_generated] boost/numeric/odeint/stepper/runge_kutta4_classic.hpp [begin_description] Implementation for the classical Runge Kutta stepper. [end_description] Copyright 2010-2013 Karsten Ahnert Copyright 2010-2013 Mario Mulansky Copyright 2012 Christoph Koke 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_KUTTA4_CLASSIC_HPP_INCLUDED #define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_CLASSIC_HPP_INCLUDED #include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp> #include <boost/numeric/odeint/algebra/range_algebra.hpp> #include <boost/numeric/odeint/algebra/default_operations.hpp> #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp> #include <boost/numeric/odeint/algebra/operations_dispatcher.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 = Value , class Algebra = typename algebra_dispatcher< State >::algebra_type , class Operations = typename operations_dispatcher< State >::operations_type , class Resizer = initially_resizer > #ifndef DOXYGEN_SKIP class runge_kutta4_classic : public explicit_stepper_base< runge_kutta4_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > #else class runge_kutta4_classic : public explicit_stepper_base #endif { public : #ifndef DOXYGEN_SKIP typedef explicit_stepper_base< runge_kutta4_classic< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 4 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type; #else typedef explicit_stepper_base< runge_kutta4_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::stepper_type stepper_type; typedef typename stepper_base_type::wrapped_state_type wrapped_state_type; typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type; #endif // DOXYGEN_SKIP runge_kutta4_classic( const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra ) { } 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 ) { // ToDo : check if size of in,dxdt,out are equal? static const value_type val1 = static_cast< value_type >( 1 ); m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ); typename odeint::unwrap_reference< System >::type &sys = system; const time_type dh = dt / static_cast< value_type >( 2 ); const time_type th = t + dh; // dt * dxdt = k1 // m_x_tmp = x + dh*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 >( val1 , dh ) ); // dt * m_dxt = k2 sys( m_x_tmp.m_v , m_dxt.m_v , th ); // m_x_tmp = x + dh*m_dxt stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , m_dxt.m_v , typename operations_type::template scale_sum2< value_type , time_type >( val1 , dh ) ); // dt * m_dxm = k3 sys( m_x_tmp.m_v , m_dxm.m_v , th ); //m_x_tmp = x + dt*m_dxm stepper_base_type::m_algebra.for_each3( m_x_tmp.m_v , in , m_dxm.m_v , typename operations_type::template scale_sum2< value_type , time_type >( val1 , dt ) ); // dt * m_dxh = k4 sys( m_x_tmp.m_v , m_dxh.m_v , t + dt ); //x += dt/6 * ( m_dxdt + m_dxt + val2*m_dxm ) time_type dt6 = dt / static_cast< value_type >( 6 ); time_type dt3 = dt / static_cast< value_type >( 3 ); stepper_base_type::m_algebra.for_each6( out , in , dxdt , m_dxt.m_v , m_dxm.m_v , m_dxh.m_v , typename operations_type::template scale_sum5< value_type , time_type , time_type , time_type , time_type >( 1.0 , dt6 , dt3 , dt3 , dt6 ) ); // x += dt/6 * m_dxdt + dt/3 * m_dxt ) // stepper_base_type::m_algebra.for_each4( out , in , dxdt , m_dxt.m_v , // typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt6 , dt3 ) ); // // x += dt/3 * m_dxm + dt/6 * m_dxh ) // stepper_base_type::m_algebra.for_each4( out , out , m_dxm.m_v , m_dxh.m_v , // typename operations_type::template scale_sum3< value_type , time_type , time_type >( 1.0 , dt3 , dt6 ) ); } template< class StateType > void adjust_size( const StateType &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_dxm , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_dxt , x , typename is_resizeable<deriv_type>::type() ); resized |= adjust_size_by_resizeability( m_dxh , x , typename is_resizeable<deriv_type>::type() ); return resized; } resizer_type m_resizer; wrapped_deriv_type m_dxt; wrapped_deriv_type m_dxm; wrapped_deriv_type m_dxh; wrapped_state_type m_x_tmp; }; /********* DOXYGEN *********/ /** * \class runge_kutta4_classic * \brief The classical Runge-Kutta stepper of fourth order. * * The Runge-Kutta method of fourth order is one standard method for * solving ordinary differential equations and is widely used, see also * <a href="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods">en.wikipedia.org/wiki/Runge-Kutta_methods</a> * The method is explicit and fulfills the Stepper concept. Step size control * or continuous output are not provided. This class implements the method directly, hence the * generic Runge-Kutta algorithm is not used. * * This class derives from explicit_stepper_base and inherits its interface via * CRTP (current recurring template pattern). For more details see * explicit_stepper_base. * * \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_kutta4_classic::runge_kutta4_classic( const algebra_type &algebra ) * \brief Constructs the runge_kutta4_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_kutta4_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_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. */ /** * \fn runge_kutta4_classic::adjust_size( const StateType &x ) * \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. */ } // odeint } // numeric } // boost #endif // BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA4_CLASSIC_HPP_INCLUDED