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

The Bulirsch-Stoer algorithm. More...

#include <bulirsch_stoer_dense_out.hpp>

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

Public Types
typedef State	state_type
typedef Value	value_type
typedef Deriv	deriv_type
typedef Time	time_type
typedef Algebra	algebra_type
typedef Operations	operations_type
typedef Resizer	resizer_type
typedef dense_output_stepper_tag	stepper_category
typedef state_wrapper< state_type >	wrapped_state_type
typedef state_wrapper< deriv_type >	wrapped_deriv_type
typedef bulirsch_stoer_dense_out < State, Value, Deriv, Time, Algebra, Operations, Resizer >	controlled_error_bs_type
typedef inverse_time < time_type >::type	inv_time_type
typedef std::vector< value_type >	value_vector
typedef std::vector< time_type >	time_vector
typedef std::vector < inv_time_type >	inv_time_vector
typedef std::vector< value_vector >	value_matrix
typedef std::vector< size_t >	int_vector
typedef std::vector < wrapped_state_type >	state_vector_type
typedef std::vector < wrapped_deriv_type >	deriv_vector_type
typedef std::vector < deriv_vector_type >	deriv_table_type

Public Member Functions
	bulirsch_stoer_dense_out (value_type eps_abs=1E-6, value_type eps_rel=1E-6, value_type factor_x=1.0, value_type factor_dxdt=1.0, bool control_interpolation=false)
	Constructs the bulirsch_stoer class, including initialization of the error bounds. More...
template<class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
controlled_step_result	try_step (System system, const StateIn &in, const DerivIn &dxdt, time_type &t, StateOut &out, DerivOut &dxdt_new, time_type &dt)
	Tries to perform one step. More...
template<class StateType >
void	initialize (const StateType &x0, const time_type &t0, const time_type &dt0)
	Initializes the dense output stepper. More...
template<class System >
std::pair< time_type, time_type >	do_step (System system)
	Does one time step. More...
template<class StateOut >
void	calc_state (time_type t, StateOut &x) const
	Calculates the solution at an intermediate point within the last step. More...
const state_type &	current_state (void) const
	Returns the current state of the solution. More...
time_type	current_time (void) const
	Returns the current time of the solution. More...
const state_type &	previous_state (void) const
	Returns the last state of the solution. More...
time_type	previous_time (void) const
	Returns the last time of the solution. More...
time_type	current_time_step (void) const
	Returns the current step size. More...
void	reset ()
	Resets the internal state of the stepper. More...
template<class StateIn >
void	adjust_size (const StateIn &x)
	Adjust the size of all temporaries in the stepper manually. More...

Static Public Attributes
static const size_t	m_k_max = 8

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >

The Bulirsch-Stoer algorithm.

The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution. This class also provides dense output facility.

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

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 Algebra boost::numeric::odeint::bulirsch_stoer_dense_out< 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 bulirsch_stoer_dense_out< State , Value , Deriv , Time , Algebra , Operations , Resizer > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::controlled_error_bs_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 std::vector< deriv_vector_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::deriv_table_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 Deriv boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::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 std::vector< wrapped_deriv_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::deriv_vector_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 std::vector< size_t > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::int_vector

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 inverse_time< time_type >::type boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::inv_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 std::vector< inv_time_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::inv_time_vector

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 Operations boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::operations_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 Resizer boost::numeric::odeint::bulirsch_stoer_dense_out< 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 State boost::numeric::odeint::bulirsch_stoer_dense_out< 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 std::vector< wrapped_state_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::state_vector_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 dense_output_stepper_tag boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::stepper_category

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 Time boost::numeric::odeint::bulirsch_stoer_dense_out< 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 std::vector< time_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::time_vector

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 std::vector< value_vector > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::value_matrix

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 Value boost::numeric::odeint::bulirsch_stoer_dense_out< 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 std::vector< value_type > boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::value_vector

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 state_wrapper< deriv_type > boost::numeric::odeint::bulirsch_stoer_dense_out< 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 state_wrapper< state_type > boost::numeric::odeint::bulirsch_stoer_dense_out< 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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::bulirsch_stoer_dense_out ( value_type  eps_abs = 1E-6, value_type  eps_rel = 1E-6, value_type  factor_x = 1.0, value_type  factor_dxdt = 1.0, bool  control_interpolation = false  )

inline

Constructs the bulirsch_stoer class, including initialization of the error bounds.

Parameters

eps_abs	Absolute tolerance level.
eps_rel	Relative tolerance level.
factor_x	Factor for the weight of the state.
factor_dxdt	Factor for the weight of the derivative.
control_interpolation	Set true to additionally control the error of the interpolation.

References BOOST_USING_STD_MAX, BOOST_USING_STD_MIN, and boost::multiprecision::backends::i.

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 StateIn >

boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_size ( const StateIn &  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::modified_midpoint_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::adjust_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 StateOut >

boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::calc_state ( time_type  t, StateOut &  x  ) const

inline

Calculates the solution at an intermediate point within the last step.

Parameters

t	The time at which the solution should be calculated, has to be in the current time interval.
x	The output variable where the result is written into.

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::current_state ( void  ) const

inline

Returns the current state of the solution.

Returns

The current state of the solution x(t).

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::current_time ( void  ) const

inline

Returns the current time of the solution.

Returns

The current time of the solution t.

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::current_time_step ( void  ) const

inline

Returns the current step size.

Returns

The current 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 >

boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step ( System  system )

inline

Does one time step.

This is the main method that should be used to integrate an ODE with this stepper.

Note

initialize has to be called before using this method to set the initial conditions x,t and the stepsize.

Parameters

system

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

Returns

Pair with start and end time of the integration step.

References count, boost::numeric::odeint::fail, boost::xpressive::make_pair, boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::try_step(), and boost::detail::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>

template<class StateType >

boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::initialize ( const StateType &  x0, const time_type &  t0, const time_type &  dt0  )

inline

Initializes the dense output stepper.

Parameters

x0	The initial state.
t0	The initial time.
dt0	The initial time step.

References boost::numeric::odeint::detail::_1, boost::bind(), boost::numeric::odeint::copy(), boost::ref(), boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::reset(), and template.

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::previous_state ( void  ) const

inline

Returns the last state of the solution.

Returns

The last state of the solution x(t-dt).

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::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::previous_time ( void  ) const

inline

Returns the last time of the solution.

Returns

The last time of the solution t-dt.

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>

void boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::reset ( void  )

inline

Resets the internal state of the stepper.

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

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 , class DerivOut >

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

inline

Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

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.
dxdt	The derivative of state.
t	The value of the time. Updated if the step is successful.
out	Used to store the result of the step.
dt	The step size. Updated.

Returns

success if the step was accepted, fail otherwise.

References boost::numeric::BOOST_PREVENT_MACRO_SUBSTITUTION(), BOOST_USING_STD_MAX, BOOST_USING_STD_MIN, boost::numeric::odeint::modified_midpoint_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::do_step(), boost::sinks::event_log::error, boost::numeric::odeint::default_error_checker< Value, Algebra, Operations >::error(), boost::numeric::odeint::fail, boost::numeric::odeint::state_wrapper< V, Enabler >::m_v, boost::accumulators::extract::max, boost::accumulators::extract::min, boost::numeric::pow(), pow(), boost::numeric::odeint::modified_midpoint_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::set_steps(), boost::numeric::odeint::success, template, and boost::detail::type.

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

Member Data 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>

const size_t boost::numeric::odeint::bulirsch_stoer_dense_out< State, Value, Deriv, Time, Algebra, Operations, Resizer >::m_k_max = 8

static

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

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