316 lines
11 KiB
Plaintext
316 lines
11 KiB
Plaintext
/*
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[auto_generated]
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boost/numeric/odeint/stepper/modified_midpoint.hpp
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[begin_description]
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Modified midpoint method for the use in Burlish-Stoer stepper.
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[end_description]
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Copyright 2011-2013 Mario Mulansky
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Copyright 2011-2013 Karsten Ahnert
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Copyright 2012 Christoph Koke
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
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#define BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
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#include <vector>
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#include <boost/numeric/odeint/stepper/base/explicit_stepper_base.hpp>
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#include <boost/numeric/odeint/util/resizer.hpp>
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#include <boost/numeric/odeint/util/is_resizeable.hpp>
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#include <boost/numeric/odeint/algebra/range_algebra.hpp>
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#include <boost/numeric/odeint/algebra/default_operations.hpp>
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#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
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#include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
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#include <boost/numeric/odeint/util/copy.hpp>
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namespace boost {
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namespace numeric {
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namespace odeint {
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template<
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class State ,
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class Value = double ,
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class Deriv = State ,
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class Time = Value ,
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class Algebra = typename algebra_dispatcher< State >::algebra_type ,
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class Operations = typename operations_dispatcher< State >::operations_type ,
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class Resizer = initially_resizer
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>
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#ifndef DOXYGEN_SKIP
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class modified_midpoint
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: public explicit_stepper_base<
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modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
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2 , State , Value , Deriv , Time , Algebra , Operations , Resizer >
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#else
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class modified_midpoint : public explicit_stepper_base
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#endif
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{
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public :
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typedef explicit_stepper_base<
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modified_midpoint< State , Value , Deriv , Time , Algebra , Operations , Resizer > ,
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2 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type;
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typedef typename stepper_base_type::state_type state_type;
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typedef typename stepper_base_type::wrapped_state_type wrapped_state_type;
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typedef typename stepper_base_type::value_type value_type;
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typedef typename stepper_base_type::deriv_type deriv_type;
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typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type;
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typedef typename stepper_base_type::time_type time_type;
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typedef typename stepper_base_type::algebra_type algebra_type;
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typedef typename stepper_base_type::operations_type operations_type;
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typedef typename stepper_base_type::resizer_type resizer_type;
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typedef typename stepper_base_type::stepper_type stepper_type;
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modified_midpoint( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
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: stepper_base_type( algebra ) , m_steps( steps )
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{ }
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template< class System , class StateIn , class DerivIn , class StateOut >
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void do_step_impl( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt )
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{
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static const value_type val1 = static_cast< value_type >( 1 );
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static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
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m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
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const time_type h = dt / static_cast<value_type>( m_steps );
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const time_type h2 = static_cast<value_type>(2) * h;
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typename odeint::unwrap_reference< System >::type &sys = system;
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time_type th = t + h;
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// m_x1 = x + h*dxdt
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stepper_base_type::m_algebra.for_each3( m_x1.m_v , in , dxdt ,
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typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
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sys( m_x1.m_v , m_dxdt.m_v , th );
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boost::numeric::odeint::copy( in , m_x0.m_v );
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unsigned short i = 1;
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while( i != m_steps )
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{
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// general step
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//tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
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stepper_base_type::m_algebra.for_each3( m_x1.m_v , m_x0.m_v , m_dxdt.m_v ,
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typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
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th += h;
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sys( m_x1.m_v , m_dxdt.m_v , th);
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i++;
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}
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// last step
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// x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
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stepper_base_type::m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , m_dxdt.m_v ,
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typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
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}
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void set_steps( unsigned short steps )
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{ m_steps = steps; }
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unsigned short steps( void ) const
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{ return m_steps; }
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template< class StateIn >
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void adjust_size( const StateIn &x )
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{
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resize_impl( x );
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stepper_base_type::adjust_size( x );
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}
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private:
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template< class StateIn >
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bool resize_impl( const StateIn &x )
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{
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bool resized( false );
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resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
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resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
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resized |= adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
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return resized;
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}
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unsigned short m_steps;
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resizer_type m_resizer;
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wrapped_state_type m_x0;
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wrapped_state_type m_x1;
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wrapped_deriv_type m_dxdt;
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};
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/* Modified midpoint which stores derivatives and state at dt/2 in some external storage for later usage in dense output calculation
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* This Stepper is for use in Bulirsch Stoer only. It DOES NOT meet any stepper concept.
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*/
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template<
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class State ,
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class Value = double ,
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class Deriv = State ,
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class Time = Value ,
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class Algebra = typename algebra_dispatcher< State >::algebra_type ,
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class Operations = typename operations_dispatcher< State >::operations_type ,
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class Resizer = initially_resizer
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>
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class modified_midpoint_dense_out
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{
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public :
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typedef State state_type;
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typedef Value value_type;
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typedef Deriv deriv_type;
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typedef Time time_type;
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typedef Algebra algebra_type;
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typedef Operations operations_type;
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typedef Resizer resizer_type;
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typedef state_wrapper< state_type > wrapped_state_type;
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typedef state_wrapper< deriv_type > wrapped_deriv_type;
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typedef modified_midpoint_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_type;
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typedef std::vector< wrapped_deriv_type > deriv_table_type;
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modified_midpoint_dense_out( unsigned short steps = 2 , const algebra_type &algebra = algebra_type() )
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: m_algebra( algebra ) , m_steps( steps )
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{ }
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/*
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* performs a modified midpoint step with m_steps intermediate points
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* stores approximation for x(t+dt/2) in x_mp and all evaluated function results in derivs
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*
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*/
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template< class System , class StateIn , class DerivIn , class StateOut >
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void do_step( System system , const StateIn &in , const DerivIn &dxdt , time_type t , StateOut &out , time_type dt ,
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state_type &x_mp , deriv_table_type &derivs )
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{
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static const value_type val1 = static_cast< value_type >( 1 );
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static const value_type val05 = static_cast< value_type >( 1 ) / static_cast< value_type >( 2 );
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m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize< StateIn > , detail::ref( *this ) , detail::_1 ) );
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const time_type h = dt / static_cast<value_type>( m_steps );
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const time_type h2 = static_cast<value_type>( 2 ) * h;
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typename odeint::unwrap_reference< System >::type &sys = system;
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time_type th = t + h;
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// m_x1 = x + h*dxdt
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m_algebra.for_each3( m_x1.m_v , in , dxdt ,
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typename operations_type::template scale_sum2< value_type , time_type >( val1 , h ) );
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if( m_steps == 2 )
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// result of first step already gives approximation at the center of the interval
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boost::numeric::odeint::copy( m_x1.m_v , x_mp );
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sys( m_x1.m_v , derivs[0].m_v , th );
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boost::numeric::odeint::copy( in , m_x0.m_v );
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unsigned short i = 1;
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while( i != m_steps )
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{
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// general step
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//tmp = m_x1; m_x1 = m_x0 + h2*m_dxdt; m_x0 = tmp
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m_algebra.for_each3( m_x1.m_v , m_x0.m_v , derivs[i-1].m_v ,
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typename operations_type::template scale_sum_swap2< value_type , time_type >( val1 , h2 ) );
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if( i == m_steps/2-1 )
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// save approximation at the center of the interval
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boost::numeric::odeint::copy( m_x1.m_v , x_mp );
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th += h;
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sys( m_x1.m_v , derivs[i].m_v , th);
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i++;
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}
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// last step
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// x = 0.5*( m_x0 + m_x1 + h*m_dxdt )
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m_algebra.for_each4( out , m_x0.m_v , m_x1.m_v , derivs[m_steps-1].m_v ,
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typename operations_type::template scale_sum3< value_type , value_type , time_type >( val05 , val05 , val05*h ) );
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}
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void set_steps( unsigned short steps )
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{ m_steps = steps; }
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unsigned short steps( void ) const
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{ return m_steps; }
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template< class StateIn >
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bool resize( const StateIn &x )
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{
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bool resized( false );
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resized |= adjust_size_by_resizeability( m_x0 , x , typename is_resizeable<state_type>::type() );
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resized |= adjust_size_by_resizeability( m_x1 , x , typename is_resizeable<state_type>::type() );
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return resized;
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}
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template< class StateIn >
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void adjust_size( const StateIn &x )
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{
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resize( x );
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}
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private:
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algebra_type m_algebra;
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unsigned short m_steps;
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resizer_type m_resizer;
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wrapped_state_type m_x0;
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wrapped_state_type m_x1;
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};
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/********** DOXYGEN ***********/
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/**
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* \class modified_midpoint
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*
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* Implementation of the modified midpoint method with a configurable
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* number of intermediate steps. This class is used by the Bulirsch-Stoer
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* algorithm and is not meant for direct usage.
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*/
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/**
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* \class modified_midpoint_dense_out
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*
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* Implementation of the modified midpoint method with a configurable
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* number of intermediate steps. This class is used by the dense output
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* Bulirsch-Stoer algorithm and is not meant for direct usage.
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* \note This stepper is for internal use only and does not meet
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* any stepper concept.
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*/
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}
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}
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}
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#endif // BOOST_NUMERIC_ODEINT_STEPPER_MODIFIED_MIDPOINT_HPP_INCLUDED
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