boost/numeric/odeint/stepper/modified_midpoint.hpp
/* [auto_generated] boost/numeric/odeint/stepper/modified_midpoint.hpp [begin_description] Modified midpoint method for the use in Burlish-Stoer stepper. [end_description] Copyright 2011-2013 Mario Mulansky Copyright 2011-2013 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_MODIFIED_MIDPOINT_HPP_INCLUDED #define BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED #include <vector> #include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp> #include <boost/numeric/odeint/util/resizer.hpp> #include <boost/numeric/odeint/util/is_resizeable.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/copy.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 modified_midpoint : public explicit_stepper_base< modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > #else class modified_midpoint : public explicit_stepper_base #endif { public : typedef explicit_stepper_base< modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type; typedef typename stepper_base_type::state_type state_type; typedef typename stepper_base_type::wrapped_state_type wrapped_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::wrapped_deriv_type wrapped_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; typedef typename stepper_base_type::stepper_type stepper_type; modified_midpoint( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() ) : stepper_base_type( algebra ) , m_steps( steps ) { } 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 ) { static const value_type val1 = static_cast< value_type >( 1 ); static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 ); m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ); const time_type h = dt / static_cast<value_type>( m_steps ); const time_type h2 = static_cast<value_type>(2) * h; typename odeint::unwrap_reference< System >::type &sys = system; time_type th = t + h; // m_x1 = x + h*dxdt stepper_base_type::m_algebra.for_each3( m_x1.m_v , in , dxdt , typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) ); sys( m_x1.m_v , m_dxdt.m_v , th ); boost::numeric::odeint::copy( in , m_x0.m_v ); unsigned short i = 1; while( i != m_steps ) { // general step //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp stepper_base_type::m_algebra.for_each3( m_x1.m_v , m_x0.m_v , m_dxdt.m_v , typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) ); th += h; sys( m_x1.m_v , m_dxdt.m_v , th); i++; } // last step // x = 0.5*( m_x0 + m_x1 + h*m_dxdt ) stepper_base_type::m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , m_dxdt.m_v , typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) ); } void set_steps( unsigned short steps ) { m_steps = steps; } unsigned short steps( void ) const { return m_steps; } 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_x0 , x , typename is_resizeable<state_type>::type() ); resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() ); resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() ); return resized; } unsigned short m_steps; resizer_type m_resizer; wrapped_state_type m_x0; wrapped_state_type m_x1; wrapped_deriv_type m_dxdt; }; /* Modified midpoint which stores derivatives and state at dt/2 in some external storage for later usage in dense output calculation * This Stepper is for use in Bulirsch Stoer only. It DOES NOT meet any stepper concept. */ 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 > class modified_midpoint_dense_out { public : typedef State state_type; typedef Value value_type; typedef Deriv deriv_type; typedef Time time_type; typedef Algebra algebra_type; typedef Operations operations_type; typedef Resizer resizer_type; typedef state_wrapper< state_type > wrapped_state_type; typedef state_wrapper< deriv_type > wrapped_deriv_type; typedef modified_midpoint_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type; typedef std::vector< wrapped_deriv_type > deriv_table_type; modified_midpoint_dense_out( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() ) : m_algebra( algebra ) , m_steps( steps ) { } /* * performs a modified midpoint step with m_steps intermediate points * stores approximation for x(t+dt/2) in x_mp and all evaluated function results in derivs * */ template< class System , class StateIn , class DerivIn , class StateOut > void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt , state_type &x_mp , deriv_table_type &derivs ) { static const value_type val1 = static_cast< value_type >( 1 ); static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 ); m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize< StateIn > , detail::ref( *this ) , detail::_1 ) ); const time_type h = dt / static_cast<value_type>( m_steps ); const time_type h2 = static_cast<value_type>( 2 ) * h; typename odeint::unwrap_reference< System >::type &sys = system; time_type th = t + h; // m_x1 = x + h*dxdt m_algebra.for_each3( m_x1.m_v , in , dxdt , typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) ); if( m_steps == 2 ) // result of first step already gives approximation at the center of the interval boost::numeric::odeint::copy( m_x1.m_v , x_mp ); sys( m_x1.m_v , derivs[0].m_v , th ); boost::numeric::odeint::copy( in , m_x0.m_v ); unsigned short i = 1; while( i != m_steps ) { // general step //tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp m_algebra.for_each3( m_x1.m_v , m_x0.m_v , derivs[i-1].m_v , typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) ); if( i == m_steps/2-1 ) // save approximation at the center of the interval boost::numeric::odeint::copy( m_x1.m_v , x_mp ); th += h; sys( m_x1.m_v , derivs[i].m_v , th); i++; } // last step // x = 0.5*( m_x0 + m_x1 + h*m_dxdt ) m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , derivs[m_steps-1].m_v , typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) ); } void set_steps( unsigned short steps ) { m_steps = steps; } unsigned short steps( void ) const { return m_steps; } template< class StateIn > bool resize( const StateIn &x ) { bool resized( false ); resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() ); resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() ); return resized; } template< class StateIn > void adjust_size( const StateIn &x ) { resize( x ); } private: algebra_type m_algebra; unsigned short m_steps; resizer_type m_resizer; wrapped_state_type m_x0; wrapped_state_type m_x1; }; /********** DOXYGEN ***********/ /** * \class modified_midpoint * * Implementation of the modified midpoint method with a configurable * number of intermediate steps. This class is used by the Bulirsch-Stoer * algorithm and is not meant for direct usage. */ /** * \class modified_midpoint_dense_out * * Implementation of the modified midpoint method with a configurable * number of intermediate steps. This class is used by the dense output * Bulirsch-Stoer algorithm and is not meant for direct usage. * \note This stepper is for internal use only and does not meet * any stepper concept. */ } } } #endif // BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED