Chris@16: /*
Chris@16:  [auto_generated]
Chris@16:  boost/numeric/odeint/stepper/adams_bashforth.hpp
Chris@16: 
Chris@16:  [begin_description]
Chris@16:  Implementaton of the Adam-Bashforth method a multistep method used for the predictor step in the
Chris@16:  Adams-Bashforth-Moulton method.
Chris@16:  [end_description]
Chris@16: 
Chris@101:  Copyright 2011-2013 Karsten Ahnert
Chris@101:  Copyright 2011-2013 Mario Mulansky
Chris@101:  Copyright 2012 Christoph Koke
Chris@101:  Copyright 2013 Pascal Germroth
Chris@16: 
Chris@16:  Distributed under the Boost Software License, Version 1.0.
Chris@16:  (See accompanying file LICENSE_1_0.txt or
Chris@16:  copy at http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  */
Chris@16: 
Chris@16: 
Chris@16: #ifndef BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED
Chris@16: #define BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED
Chris@16: 
Chris@16: #include <boost/static_assert.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/bind.hpp>
Chris@16: #include <boost/numeric/odeint/util/unwrap_reference.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/algebra/range_algebra.hpp>
Chris@16: #include <boost/numeric/odeint/algebra/default_operations.hpp>
Chris@101: #include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
Chris@101: #include <boost/numeric/odeint/algebra/operations_dispatcher.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/util/state_wrapper.hpp>
Chris@16: #include <boost/numeric/odeint/util/is_resizeable.hpp>
Chris@16: #include <boost/numeric/odeint/util/resizer.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/stepper/stepper_categories.hpp>
Chris@16: #include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
Chris@101: #include <boost/numeric/odeint/stepper/extrapolation_stepper.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp>
Chris@16: 
Chris@16: #include <boost/numeric/odeint/stepper/detail/adams_bashforth_coefficients.hpp>
Chris@16: #include <boost/numeric/odeint/stepper/detail/adams_bashforth_call_algebra.hpp>
Chris@16: #include <boost/numeric/odeint/stepper/detail/rotating_buffer.hpp>
Chris@16: 
Chris@101: #include <boost/mpl/arithmetic.hpp>
Chris@101: #include <boost/mpl/min_max.hpp>
Chris@101: #include <boost/mpl/equal_to.hpp>
Chris@101: 
Chris@101: namespace mpl = boost::mpl;
Chris@16: 
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace numeric {
Chris@16: namespace odeint {
Chris@16: 
Chris@101:     using mpl::int_;
Chris@101: 
Chris@101:     /* if N >= 4, returns the smallest even number > N, otherwise returns 4 */
Chris@101:     template < int N >
Chris@101:     struct order_helper
Chris@101:         : mpl::max< typename mpl::eval_if<
Chris@101:                         mpl::equal_to< mpl::modulus< int_< N >, int_< 2 > >,
Chris@101:                                        int_< 0 > >,
Chris@101:                         int_< N >, int_< N + 1 > >::type,
Chris@101:                     int_< 4 > >::type
Chris@101:     { };
Chris@16: 
Chris@16: template<
Chris@16: size_t Steps ,
Chris@16: class State ,
Chris@16: class Value = double ,
Chris@16: class Deriv = State ,
Chris@16: class Time = Value ,
Chris@101: class Algebra = typename algebra_dispatcher< State >::algebra_type ,
Chris@101: class Operations = typename operations_dispatcher< State >::operations_type ,
Chris@16: class Resizer = initially_resizer ,
Chris@101: class InitializingStepper = extrapolation_stepper< order_helper<Steps>::value, 
Chris@101:                                                    State, Value, Deriv, Time,
Chris@101:                                                    Algebra, Operations, Resizer >
Chris@16: >
Chris@16: class adams_bashforth : public algebra_stepper_base< Algebra , Operations >
Chris@16: {
Chris@16: 
Chris@16: #ifndef DOXYGEN_SKIP
Chris@16:     BOOST_STATIC_ASSERT(( Steps > 0 ));
Chris@16:     BOOST_STATIC_ASSERT(( Steps < 9 ));
Chris@16: #endif
Chris@16: 
Chris@16: public :
Chris@16: 
Chris@16:     typedef State state_type;
Chris@16:     typedef state_wrapper< state_type > wrapped_state_type;
Chris@16:     typedef Value value_type;
Chris@16:     typedef Deriv deriv_type;
Chris@16:     typedef state_wrapper< deriv_type > wrapped_deriv_type;
Chris@16:     typedef Time time_type;
Chris@16:     typedef Resizer resizer_type;
Chris@16:     typedef stepper_tag stepper_category;
Chris@16: 
Chris@16:     typedef InitializingStepper initializing_stepper_type;
Chris@16: 
Chris@101:     typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type;
Chris@101:     typedef typename algebra_stepper_base_type::algebra_type algebra_type;
Chris@101:     typedef typename algebra_stepper_base_type::operations_type operations_type;
Chris@16: #ifndef DOXYGEN_SKIP
Chris@16:     typedef adams_bashforth< Steps , State , Value , Deriv , Time , Algebra , Operations , Resizer , InitializingStepper > stepper_type;
Chris@16: #endif
Chris@16:     static const size_t steps = Steps;
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:     typedef unsigned short order_type;
Chris@16:     static const order_type order_value = steps;
Chris@16: 
Chris@16:     typedef detail::rotating_buffer< wrapped_deriv_type , steps > step_storage_type;
Chris@16: 
Chris@16: 
Chris@16:     
Chris@16:     order_type order( void ) const { return order_value; }
Chris@16: 
Chris@16:     adams_bashforth( const algebra_type &algebra = algebra_type() )
Chris@101:     : algebra_stepper_base_type( algebra ) ,
Chris@101:       m_step_storage() , m_resizer() , m_coefficients() ,
Chris@101:       m_steps_initialized( 0 ) , m_initializing_stepper()
Chris@16:     { }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:     /*
Chris@16:      * Version 1 : do_step( system , x , t , dt );
Chris@16:      *
Chris@16:      * solves the forwarding problem
Chris@16:      */
Chris@16:     template< class System , class StateInOut >
Chris@16:     void do_step( System system , StateInOut &x , time_type t , time_type dt )
Chris@16:     {
Chris@16:         do_step( system , x , t , x , dt );
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
Chris@16:      */
Chris@16:     template< class System , class StateInOut >
Chris@16:     void do_step( System system , const StateInOut &x , time_type t , time_type dt )
Chris@16:     {
Chris@16:         do_step( system , x , t , x , dt );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16:     /*
Chris@16:      * Version 2 : do_step( system , in , t , out , dt );
Chris@16:      *
Chris@16:      * solves the forwarding problem
Chris@16:      */
Chris@16: 
Chris@16:     template< class System , class StateIn , class StateOut >
Chris@16:     void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
Chris@16:     {
Chris@16:         do_step_impl( system , in , t , out , dt );
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateOut.
Chris@16:      */
Chris@16:     template< class System , class StateIn , class StateOut >
Chris@16:     void do_step( System system , const StateIn &in , time_type t , const StateOut &out , time_type dt )
Chris@16:     {
Chris@16:         do_step_impl( system , in , t , out , dt );
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     template< class StateType >
Chris@16:     void adjust_size( const StateType &x )
Chris@16:     {
Chris@16:         resize_impl( x );
Chris@16:     }
Chris@16: 
Chris@16:     const step_storage_type& step_storage( void ) const
Chris@16:     {
Chris@16:         return m_step_storage;
Chris@16:     }
Chris@16: 
Chris@16:     step_storage_type& step_storage( void )
Chris@16:     {
Chris@16:         return m_step_storage;
Chris@16:     }
Chris@16: 
Chris@16:     template< class ExplicitStepper , class System , class StateIn >
Chris@16:     void initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
Chris@16:     {
Chris@16:         typename odeint::unwrap_reference< ExplicitStepper >::type &stepper = explicit_stepper;
Chris@16:         typename odeint::unwrap_reference< System >::type &sys = system;
Chris@16: 
Chris@16:         m_resizer.adjust_size( x , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) );
Chris@16: 
Chris@101:         for( size_t i=0 ; i+1<steps ; ++i )
Chris@16:         {
Chris@16:             if( i != 0 ) m_step_storage.rotate();
Chris@16:             sys( x , m_step_storage[0].m_v , t );
Chris@101:             stepper.do_step_dxdt_impl( system, x, m_step_storage[0].m_v, t,
Chris@101:                                        dt );
Chris@16:             t += dt;
Chris@16:         }
Chris@16:         m_steps_initialized = steps;
Chris@16:     }
Chris@16: 
Chris@16:     template< class System , class StateIn >
Chris@16:     void initialize( System system , StateIn &x , time_type &t , time_type dt )
Chris@16:     {
Chris@16:         initialize( detail::ref( m_initializing_stepper ) , system , x , t , dt );
Chris@16:     }
Chris@16: 
Chris@16:     void reset( void )
Chris@16:     {
Chris@16:         m_steps_initialized = 0;
Chris@16:     }
Chris@16: 
Chris@16:     bool is_initialized( void ) const
Chris@16:     {
Chris@101:         return m_steps_initialized >= ( steps - 1 );
Chris@16:     }
Chris@16: 
Chris@16:     const initializing_stepper_type& initializing_stepper( void ) const { return m_initializing_stepper; }
Chris@16: 
Chris@16:     initializing_stepper_type& initializing_stepper( void ) { return m_initializing_stepper; }
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     template< class System , class StateIn , class StateOut >
Chris@16:     void do_step_impl( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
Chris@16:     {
Chris@16:         typename odeint::unwrap_reference< System >::type &sys = system;
Chris@16:         if( m_resizer.adjust_size( in , detail::bind( &stepper_type::template resize_impl<StateIn> , detail::ref( *this ) , detail::_1 ) ) )
Chris@16:         {
Chris@16:             m_steps_initialized = 0;
Chris@16:         }
Chris@16: 
Chris@101:         if( m_steps_initialized + 1 < steps )
Chris@16:         {
Chris@16:             if( m_steps_initialized != 0 ) m_step_storage.rotate();
Chris@16:             sys( in , m_step_storage[0].m_v , t );
Chris@101:             m_initializing_stepper.do_step_dxdt_impl(
Chris@101:                 system, in, m_step_storage[0].m_v, t, out, dt );
Chris@101:             ++m_steps_initialized;
Chris@16:         }
Chris@16:         else
Chris@16:         {
Chris@16:             m_step_storage.rotate();
Chris@16:             sys( in , m_step_storage[0].m_v , t );
Chris@101:             detail::adams_bashforth_call_algebra< steps , algebra_type , operations_type >()( this->m_algebra , in , out , m_step_storage , m_coefficients , dt );
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16: 
Chris@16:     template< class StateIn >
Chris@16:     bool resize_impl( const StateIn &x )
Chris@16:     {
Chris@16:         bool resized( false );
Chris@16:         for( size_t i=0 ; i<steps ; ++i )
Chris@16:         {
Chris@16:             resized |= adjust_size_by_resizeability( m_step_storage[i] , x , typename is_resizeable<deriv_type>::type() );
Chris@16:         }
Chris@16:         return resized;
Chris@16:     }
Chris@16: 
Chris@16:     step_storage_type m_step_storage;
Chris@16:     resizer_type m_resizer;
Chris@101:     detail::adams_bashforth_coefficients< value_type , steps > m_coefficients;
Chris@16:     size_t m_steps_initialized;
Chris@16:     initializing_stepper_type m_initializing_stepper;
Chris@16: 
Chris@16: };
Chris@16: 
Chris@16: 
Chris@16: /***** DOXYGEN *****/
Chris@16: 
Chris@16: /**
Chris@16:  * \class adams_bashforth
Chris@16:  * \brief The Adams-Bashforth multistep algorithm.
Chris@16:  *
Chris@16:  * The Adams-Bashforth method is a multi-step algorithm with configurable step
Chris@16:  * number. The step number is specified as template parameter Steps and it 
Chris@16:  * then uses the result from the previous Steps steps. See also
Chris@16:  * <a href="http://en.wikipedia.org/wiki/Linear_multistep_method">en.wikipedia.org/wiki/Linear_multistep_method</a>.
Chris@16:  * Currently, a maximum of Steps=8 is supported.
Chris@16:  * The method is explicit and fulfills the Stepper concept. Step size control
Chris@16:  * or continuous output are not provided.
Chris@16:  * 
Chris@16:  * This class derives from algebra_base and inherits its interface via
Chris@16:  * CRTP (current recurring template pattern). For more details see
Chris@16:  * algebra_stepper_base.
Chris@16:  *
Chris@16:  * \tparam Steps The number of steps (maximal 8).
Chris@16:  * \tparam State The state type.
Chris@16:  * \tparam Value The value type.
Chris@16:  * \tparam Deriv The type representing the time derivative of the state.
Chris@16:  * \tparam Time The time representing the independent variable - the time.
Chris@16:  * \tparam Algebra The algebra type.
Chris@16:  * \tparam Operations The operations type.
Chris@16:  * \tparam Resizer The resizer policy type.
Chris@16:  * \tparam InitializingStepper The stepper for the first two steps.
Chris@16:  */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn adams_bashforth::adams_bashforth( const algebra_type &algebra )
Chris@16:      * \brief Constructs the adams_bashforth class. This constructor can be used as a default
Chris@16:      * constructor if the algebra has a default constructor. 
Chris@16:      * \param algebra A copy of algebra is made and stored.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn order_type adams_bashforth::order( void ) const
Chris@16:      * \brief Returns the order of the algorithm, which is equal to the number of steps.
Chris@16:      * \return order of the method.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::do_step( System system , StateInOut &x , time_type t , time_type dt )
Chris@16:      * \brief This method performs one step. It transforms the result in-place.
Chris@16:      *
Chris@16:      * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
Chris@16:      *               Simple System concept.
Chris@16:      * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
Chris@16:      * \param t The value of the time, at which the step should be performed.
Chris@16:      * \param dt The step size.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt )
Chris@16:      * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.
Chris@16:      *
Chris@16:      * \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
Chris@16:      *               Simple System concept.
Chris@16:      * \param in The state of the ODE which should be solved. in is not modified in this method
Chris@16:      * \param t The value of the time, at which the step should be performed.
Chris@16:      * \param out The result of the step is written in out.
Chris@16:      * \param dt The step size.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::adjust_size( const StateType &x )
Chris@16:      * \brief Adjust the size of all temporaries in the stepper manually.
Chris@16:      * \param x A state from which the size of the temporaries to be resized is deduced.
Chris@16:      */
Chris@16: 
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn const step_storage_type& adams_bashforth::step_storage( void ) const
Chris@16:      * \brief Returns the storage of intermediate results.
Chris@16:      * \return The storage of intermediate results.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn step_storage_type& adams_bashforth::step_storage( void )
Chris@16:      * \brief Returns the storage of intermediate results.
Chris@16:      * \return The storage of intermediate results.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::initialize( ExplicitStepper explicit_stepper , System system , StateIn &x , time_type &t , time_type dt )
Chris@16:      * \brief Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer.
Chris@16:      * \param explicit_stepper the stepper used to fill the buffer of previous step results
Chris@16:      * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
Chris@16:      *               Simple System concept.
Chris@16:      * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x.
Chris@16:      * \param t The value of the time, at which the step should be performed.
Chris@16:      * \param dt The step size.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::initialize( System system , StateIn &x , time_type &t , time_type dt )
Chris@16:      * \brief Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer.
Chris@16:      * \note The state x and time t are updated to the values after Steps-1 initial steps.
Chris@16:      * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the
Chris@16:      *               Simple System concept.
Chris@16:      * \param x The initial state of the ODE which should be solved, updated in this method.
Chris@16:      * \param t The initial value of the time, updated in this method.
Chris@16:      * \param dt The step size.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn void adams_bashforth::reset( void )
Chris@16:      * \brief Resets the internal buffer of the stepper.
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn bool adams_bashforth::is_initialized( void ) const
Chris@16:      * \brief Returns true if the stepper has been initialized.
Chris@16:      * \return bool true if stepper is initialized, false otherwise
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn const initializing_stepper_type& adams_bashforth::initializing_stepper( void ) const
Chris@16:      * \brief Returns the internal initializing stepper instance.
Chris@16:      * \return initializing_stepper
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn const initializing_stepper_type& adams_bashforth::initializing_stepper( void ) const
Chris@16:      * \brief Returns the internal initializing stepper instance.
Chris@16:      * \return initializing_stepper
Chris@16:      */
Chris@16: 
Chris@16:     /**
Chris@16:      * \fn initializing_stepper_type& adams_bashforth::initializing_stepper( void )
Chris@16:      * \brief Returns the internal initializing stepper instance.
Chris@16:      * \return initializing_stepper
Chris@16:      */
Chris@16: 
Chris@16: } // odeint
Chris@16: } // numeric
Chris@16: } // boost
Chris@16: 
Chris@16: 
Chris@16: 
Chris@16: #endif // BOOST_NUMERIC_ODEINT_STEPPER_ADAMS_BASHFORTH_HPP_INCLUDED