boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > Class Template Reference

An implementation of the Euler method. More...

#include <euler.hpp>

Inheritance diagram for boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >:

Collaboration diagram for boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >:

Public Types
typedef explicit_stepper_base < euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 1, State, Value, Deriv, Time, Algebra, Operations, Resizer >	stepper_base_type
typedef stepper_base_type::state_type	state_type
typedef stepper_base_type::value_type	value_type
typedef stepper_base_type::deriv_type	deriv_type
typedef stepper_base_type::time_type	time_type
typedef stepper_base_type::algebra_type	algebra_type
typedef stepper_base_type::operations_type	operations_type
typedef stepper_base_type::resizer_type	resizer_type
typedef stepper_base_type::stepper_type	stepper_type
typedef stepper_base_type::wrapped_state_type	wrapped_state_type
typedef stepper_base_type::wrapped_deriv_type	wrapped_deriv_type
typedef explicit_stepper_base < euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >	internal_stepper_base_type
typedef stepper_tag	stepper_category
typedef algebra_stepper_base < Algebra, Operations >	algebra_stepper_base_type
typedef unsigned short	order_type

Public Member Functions
	euler (const algebra_type &algebra=algebra_type())
	Constructs the euler class. More...
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)
	This method performs one step. More...
template<class StateOut , class StateIn1 , class StateIn2 >
void	calc_state (StateOut &x, time_type t, const StateIn1 &old_state, time_type t_old, const StateIn2 &current_state, time_type t_new) const
	This method is used for continuous output and it calculates the state x at a time t from the knowledge of two states old_state and current_state at time points t_old and t_new. More...
template<class StateType >
void	adjust_size (const StateType &x)
	Adjust the size of all temporaries in the stepper manually. More...
order_type	order (void) const
void	do_step (System system, StateInOut &x, time_type t, time_type dt)
	This method performs one step. More...
void	do_step (System system, const StateInOut &x, time_type t, time_type dt)
	Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. More...
boost::disable_if < boost::is_same< DerivIn, time_type >, void >::type	do_step (System system, StateInOut &x, const DerivIn &dxdt, time_type t, time_type dt)
	The method performs one step. More...
void	do_step (System system, const StateIn &in, time_type t, StateOut &out, time_type dt)
	The method performs one step. More...
void	do_step (System system, const StateIn &in, const DerivIn &dxdt, time_type t, StateOut &out, time_type dt)
	The method performs one step. More...
void	adjust_size (const StateIn &x)
	Adjust the size of all temporaries in the stepper manually. More...
algebra_type &	algebra ()
const algebra_type &	algebra () const

Static Public Attributes
static const order_type	order_value

Protected Attributes
wrapped_deriv_type	m_dxdt
algebra_type	m_algebra

Detailed Description

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 boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >

An implementation of the Euler method.

The Euler method is a very simply solver for ordinary differential equations. This method should not be used for real applications. It is only useful for demonstration purposes. Step size control is not provided but trivial continuous output is available.

This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern), see explicit_stepper_base

Template Parameters

State	The state type.
Value	The value type.
Deriv	The type representing the time derivative of the state.
Time	The time representing the independent variable - the time.
Algebra	The algebra type.
Operations	The operations type.
Resizer	The resizer policy type.

Member Typedef Documentation

typedef algebra_stepper_base< Algebra , Operations > boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::algebra_stepper_base_type

inherited

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>

typedef stepper_base_type::algebra_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::algebra_type

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>

typedef stepper_base_type::deriv_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::deriv_type

typedef explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order , State , Value , Deriv , Time , Algebra , Operations , Resizer > boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::internal_stepper_base_type

inherited

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>

typedef stepper_base_type::operations_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::operations_type

typedef unsigned short boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::order_type

inherited

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>

typedef stepper_base_type::resizer_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::resizer_type

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>

typedef stepper_base_type::state_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::state_type

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>

typedef explicit_stepper_base< euler< State , Value , Deriv , Time , Algebra , Operations , Resizer > , 1 , State , Value , Deriv , Time , Algebra , Operations , Resizer > boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::stepper_base_type

typedef stepper_tag boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::stepper_category

inherited

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>

typedef stepper_base_type::stepper_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::stepper_type

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>

typedef stepper_base_type::time_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::time_type

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>

typedef stepper_base_type::value_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::value_type

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>

typedef stepper_base_type::wrapped_deriv_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::wrapped_deriv_type

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>

typedef stepper_base_type::wrapped_state_type boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::wrapped_state_type

Constructor & Destructor Documentation

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>

boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::euler ( const algebra_type &  algebra = algebra_type() )

inline

Constructs the euler class.

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

Parameters

algebra

A copy of algebra is made and stored inside explicit_stepper_base.

Member Function Documentation

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>

template<class StateType >

boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_size ( const StateType &  x )

inline

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.

References boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 1, State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_size().

void boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_size ( const StateIn &  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.

Referenced by boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_size().

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.

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>

template<class StateOut , class StateIn1 , class StateIn2 >

boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state ( StateOut &  x, time_type  t, const StateIn1 &  old_state, time_type  t_old, const StateIn2 &  current_state, time_type  t_new  ) const

inline

This method is used for continuous output and it calculates the state x at a time t from the knowledge of two states old_state and current_state at time points t_old and t_new.

References boost::polygon::delta(), boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::m_algebra, boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 1, State, Value, Deriv, Time, Algebra, Operations, Resizer >::m_dxdt, and template.

void boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, StateInOut &  x, time_type  t, time_type  dt  )

inlineinherited

This method performs one step.

It transforms the result in-place.

Parameters

system	The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.
x	The state of the ODE which should be solved. After calling do_step the result is updated in x.
t	The value of the time, at which the step should be performed.
dt	The step size.

void boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const StateInOut &  x, time_type  t, time_type  dt  )

inlineinherited

Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.

boost::disable_if< boost::is_same< DerivIn , time_type > , void >::type boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, StateInOut &  x, const DerivIn &  dxdt, time_type  t, time_type  dt  )

inlineinherited

The method performs one step.

Additionally to the other method the derivative of x is also passed to this method. It is supposed to be used in the following way:

sys( x , dxdt , t );
stepper.do_step( sys , x , dxdt , t , dt );

The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this case the method could not be distinguished from other do_step versions.

Note

This method does not solve the forwarding problem.

Parameters

system	The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
x	The state of the ODE which should be solved. After calling do_step the result is updated in x.
dxdt	The derivative of x at t.
t	The value of the time, at which the step should be performed.
dt	The step size.

void boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const StateIn &  in, time_type  t, StateOut &  out, time_type  dt  )

inlineinherited

The method performs one step.

The state of the ODE is updated out-of-place.

Note

This method does not solve the forwarding problem.

Parameters

system	The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
in	The state of the ODE which should be solved. in is not modified in this method
t	The value of the time, at which the step should be performed.
out	The result of the step is written in out.
dt	The step size.

References boost::numeric::odeint::detail::_1, boost::bind(), boost::numeric::odeint::explicit_stepper_base< Stepper, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::m_dxdt, boost::numeric::odeint::state_wrapper< V, Enabler >::m_v, boost::ref(), template, and boost::detail::type.

void boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system, const StateIn &  in, const DerivIn &  dxdt, time_type  t, StateOut &  out, time_type  dt  )

inlineinherited

The method performs one step.

The state of the ODE is updated out-of-place. Furthermore, the derivative of x at t is passed to the stepper. It is supposed to be used in the following way:

sys( in , dxdt , t );
stepper.do_step( sys , in , dxdt , t , out , dt );

Note

This method does not solve the forwarding problem.

Parameters

system	The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
in	The state of the ODE which should be solved. in is not modified in this method
dxdt	The derivative of x at t.
t	The value of the time, at which the step should be performed.
out	The result of the step is written in out.
dt	The step size.

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>

template<class System , class StateIn , class DerivIn , class StateOut >

boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step_impl ( System  system, const StateIn &  in, const DerivIn &  dxdt, time_type  t, StateOut &  out, time_type  dt  )

inline

This method performs one step.

The derivative dxdt of in at the time t is passed to the method. The result is updated out of place, hence the input is in in and the output in out. Access to this step functionality is provided by explicit_stepper_base and do_step_impl should not be called directly.

Parameters

system	The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.
in	The state of the ODE which should be solved. in is not modified in this method
dxdt	The derivative of x at t.
t	The value of the time, at which the step should be performed.
out	The result of the step is written in out.
dt	The step size.

References boost::numeric::odeint::algebra_stepper_base< Algebra, Operations >::m_algebra, and template.

order_type boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::order ( void  ) const

inlineinherited

Returns

Returns the order of the stepper.

References boost::numeric::odeint::explicit_stepper_base< Stepper, Order, State, Value, Deriv, 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().

wrapped_deriv_type boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::m_dxdt

protectedinherited

Referenced by boost::numeric::odeint::euler< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state().

const order_type boost::numeric::odeint::explicit_stepper_base< euler< State, Value, Deriv, Time, Algebra, Operations, Resizer > , Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >::order_value

staticinherited

---

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

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