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diff --git a/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp b/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp new file mode 100644 index 0000000000..80f1a3c030 --- /dev/null +++ b/boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp @@ -0,0 +1,289 @@ +/* + [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 2010-2013 Mario Mulansky + Copyright 2010-2013 Karsten Ahnert + 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_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/algebra/algebra_dispatcher.hpp> +#include <boost/numeric/odeint/algebra/operations_dispatcher.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 = 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_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 |