boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer > Class Template Reference

Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order. More...

#include <symplectic_rkn_sb3a_m4_mclachlan.hpp>

Inheritance diagram for boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >:

Collaboration diagram for boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >:

Public Types
typedef symplectic_nystroem_stepper_base < 5, 4, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >	stepper_base_type
typedef stepper_base_type::algebra_type	algebra_type
typedef stepper_base_type::value_type	value_type
typedef algebra_stepper_base < Algebra, Operations >	algebra_stepper_base_type
typedef algebra_stepper_base_type::operations_type	operations_type
typedef Coor	coor_type
typedef Momentum	momentum_type
typedef std::pair< coor_type, momentum_type >	state_type
typedef CoorDeriv	coor_deriv_type
typedef state_wrapper < coor_deriv_type >	wrapped_coor_deriv_type
typedef MomentumDeriv	momentum_deriv_type
typedef state_wrapper < momentum_deriv_type >	wrapped_momentum_deriv_type
typedef std::pair < coor_deriv_type, momentum_deriv_type >	deriv_type
typedef Time	time_type
typedef Resizer	resizer_type
typedef stepper_tag	stepper_category
typedef symplectic_nystroem_stepper_base < NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >	internal_stepper_base_type
typedef unsigned short	order_type
typedef boost::array < value_type, num_of_stages >	coef_type

Public Member Functions
	symplectic_rkn_sb3a_m4_mclachlan (const algebra_type &algebra=algebra_type())
	Constructs the symplectic_rkn_sb3a_m4_mclachlan. More...
order_type	order (void) const
void	do_step (System system, const StateInOut &state, time_type t, time_type dt)
	This method performs one step. More...
void	do_step (System system, StateInOut &state, time_type t, time_type dt)
	Same function as above. More...
void	do_step (System system, CoorInOut &q, MomentumInOut &p, time_type t, time_type dt)
	This method performs one step. More...
void	do_step (System system, const CoorInOut &q, const MomentumInOut &p, time_type t, time_type dt)
	Same function as do_step( system , q , p , t , dt ). More...
void	do_step (System system, const StateIn &in, time_type t, StateOut &out, time_type dt)
	This method performs one step. More...
void	adjust_size (const StateType &x)
	Adjust the size of all temporaries in the stepper manually. More...
const coef_type &	coef_a (void) const
	Returns the coefficients a. More...
const coef_type &	coef_b (void) const
	Returns the coefficients b. More...
algebra_type &	algebra ()
const algebra_type &	algebra () const

Static Public Attributes
static const size_t	num_of_stages
static const order_type	order_value

Protected Attributes
algebra_type	m_algebra

Detailed Description

template<class Coor, class Momentum = Coor, class Value = double, class CoorDeriv = Coor, class MomentumDeriv = Coor, class Time = Value, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>
class boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >

Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order.

The method is of fourth order and has five stages. It is described HERE. This method can be used with multiprecision types since the coefficients are defined analytically.

ToDo: add reference to paper.

Template Parameters

Order	The order of the stepper.
Coor	The type representing the coordinates q.
Momentum	The type representing the coordinates p.
Value	The basic value type. Should be something like float, double or a high-precision type.
CoorDeriv	The type representing the time derivative of the coordinate dq/dt.
MomemtnumDeriv	The type representing the time derivative of the momentum dp/dt.
Time	The type representing the time t.
Algebra	The algebra.
Operations	The operations.
Resizer	The resizer policy.

Member Typedef Documentation

typedef algebra_stepper_base< Algebra , Operations > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::algebra_stepper_base_type

inherited

template<class Coor , class Momentum = Coor, class Value = double, class CoorDeriv = Coor, class MomentumDeriv = Coor, class Time = Value, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef stepper_base_type::algebra_type boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::algebra_type

typedef boost::array< value_type , num_of_stages > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::coef_type

inherited

typedef CoorDeriv boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::coor_deriv_type

inherited

typedef Coor boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::coor_type

inherited

typedef std::pair< coor_deriv_type , momentum_deriv_type > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::deriv_type

inherited

typedef symplectic_nystroem_stepper_base< NumOfStages , Order , Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::internal_stepper_base_type

inherited

typedef MomentumDeriv boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::momentum_deriv_type

inherited

typedef Momentum boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::momentum_type

inherited

typedef algebra_stepper_base_type::operations_type boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::operations_type

inherited

typedef unsigned short boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::order_type

inherited

typedef Resizer boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::resizer_type

inherited

typedef std::pair< coor_type , momentum_type > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::state_type

inherited

template<class Coor , class Momentum = Coor, class Value = double, class CoorDeriv = Coor, class MomentumDeriv = Coor, class Time = Value, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef symplectic_nystroem_stepper_base< 5 , 4 , Coor , Momentum , Value , CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer > boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::stepper_base_type

typedef stepper_tag boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::stepper_category

inherited

typedef Time boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::time_type

inherited

template<class Coor , class Momentum = Coor, class Value = double, class CoorDeriv = Coor, class MomentumDeriv = Coor, class Time = Value, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

typedef stepper_base_type::value_type boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::value_type

typedef state_wrapper< coor_deriv_type> boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::wrapped_coor_deriv_type

inherited

typedef state_wrapper< momentum_deriv_type > boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::wrapped_momentum_deriv_type

inherited

Constructor & Destructor Documentation

template<class Coor , class Momentum = Coor, class Value = double, class CoorDeriv = Coor, class MomentumDeriv = Coor, class Time = Value, class Algebra = typename algebra_dispatcher< Coor >::algebra_type, class Operations = typename operations_dispatcher< Coor >::operations_type, class Resizer = initially_resizer>

boost::numeric::odeint::symplectic_rkn_sb3a_m4_mclachlan< Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::symplectic_rkn_sb3a_m4_mclachlan ( const algebra_type &  algebra = algebra_type() )

inline

Constructs the symplectic_rkn_sb3a_m4_mclachlan.

This constructor can be used as a default constructor if the algebra has a default constructor.

Parameters

algebra

A copy of algebra is made and stored inside explicit_stepper_base.

Member Function Documentation

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::adjust_size ( const StateType &  x )

inlineinherited

Adjust the size of all temporaries in the stepper manually.

Parameters

x	A state from which the size of the temporaries to be resized is deduced.

template<class Algebra, class Operations>

algebra_type & boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::algebra ( )

inlineinherited

Returns

A reference to the algebra which is held by this class.

template<class Algebra, class Operations>

const algebra_type & boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::algebra ( ) const

inlineinherited

Returns

A const reference to the algebra which is held by this class.

const coef_type& boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::coef_a ( void  ) const

inlineinherited

Returns the coefficients a.

const coef_type& boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::coef_b ( void  ) const

inlineinherited

Returns the coefficients b.

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const StateInOut &  state, time_type  t, time_type  dt  )

inlineinherited

This method performs one step.

The system can be either a pair of two function object describing the momentum part and the coordinate part or one function object describing only the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state is updated in-place.

Note

boost::ref or std::ref can be used for the system as well as for the state. So, it is correct to write stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , make_pair( std::ref( q ) , std::ref( p ) ) , t , dt ).

This method solves the forwarding problem.

Parameters

system	The system, can be represented as a pair of two function object or one function object. See above.
state	The state of the ODE. It is a pair of Coor and Momentum. The state is updated in-place, therefore, the new value of the state will be written into this variable.
t	The time of the ODE. It is not advanced by this method.
dt	The time step.

References boost::detail::type.

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, StateInOut &  state, time_type  t, time_type  dt  )

inlineinherited

Same function as above.

It differs only in a different const specifier in order to solve the forwarding problem, can be used with Boost.Range.

References boost::detail::type.

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, CoorInOut &  q, MomentumInOut &  p, time_type  t, time_type  dt  )

inlineinherited

This method performs one step.

The system can be either a pair of two function object describing the momentum part and the coordinate part or one function object describing only the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state is updated in-place.

Note

boost::ref or std::ref can be used for the system. So, it is correct to write stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , q , p , t , dt ).

This method solves the forwarding problem.

Parameters

system	The system, can be represented as a pair of two function object or one function object. See above.
q	The coordinate of the ODE. It is updated in-place. Therefore, the new value of the coordinate will be written into this variable.
p	The momentum of the ODE. It is updated in-place. Therefore, the new value of the momentum will be written info this variable.
t	The time of the ODE. It is not advanced by this method.
dt	The time step.

References boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step(), boost::xpressive::make_pair, and boost::ref().

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const CoorInOut &  q, const MomentumInOut &  p, time_type  t, time_type  dt  )

inlineinherited

Same function as do_step( system , q , p , t , dt ).

It differs only in a different const specifier in order to solve the forwarding problem, can be called with Boost.Range.

References boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step(), boost::xpressive::make_pair, and boost::ref().

void boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const StateIn &  in, time_type  t, StateOut &  out, time_type  dt  )

inlineinherited

This method performs one step.

The system can be either a pair of two function object describing the momentum part and the coordinate part or one function object describing only the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state is updated out-of-place.

Note

boost::ref or std::ref can be used for the system. So, it is correct to write stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , x_in , t , x_out , dt ).

This method NOT solve the forwarding problem.

Parameters

system	The system, can be represented as a pair of two function object or one function object. See above.
in	The state of the ODE, which is a pair of coordinate and momentum. The state is updated out-of-place, therefore the new value is written into out
t	The time of the ODE. It is not advanced by this method.
out	The new state of the ODE.
dt	The time step.

References boost::detail::type.

order_type boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::order ( void  ) const

inlineinherited

Returns

Returns the order of the stepper.

References boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::order_value.

Member Data Documentation

template<class Algebra, class Operations>

algebra_type boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::m_algebra

protectedinherited

Referenced by boost::numeric::odeint::algebra_stepper_base< algebra_type, operations_type >::algebra(), boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state(), boost::numeric::odeint::runge_kutta_dopri5< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state(), boost::numeric::odeint::velocity_verlet< Coor, Velocity, Value, Acceleration, Time, TimeSq, Algebra, Operations, Resizer >::do_step(), boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::modified_midpoint< state_type, value_type, deriv_type, time_type, algebra_type, operations_type, resizer_type >::do_step_impl(), boost::numeric::odeint::runge_kutta4_classic< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::runge_kutta_dopri5< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::runge_kutta_cash_karp54_classic< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), boost::numeric::odeint::explicit_error_generic_rk< 6, 5, 5, 4, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl(), and boost::numeric::odeint::explicit_generic_rk< 4, 4, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl().

const size_t boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::num_of_stages

staticinherited

const order_type boost::numeric::odeint::symplectic_nystroem_stepper_base< NumOfStages, Order, Coor, Momentum, Value, CoorDeriv, MomentumDeriv, Time, Algebra, Operations, Resizer >::order_value

staticinherited

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The documentation for this class was generated from the following file:

• boost_1_57_0/boost/numeric/odeint/stepper/symplectic_rkn_sb3a_m4_mclachlan.hpp