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