Sets \(f(t)\) and derivatives using cubic rational functions, such that the first derivative approaches a constant and the second derivative approaches zero. More...

#include <FixedSpeedCubic.hpp>

Public Member Functions
	FixedSpeedCubic (double initial_function_value, double initial_time, double velocity, double decay_timescale)

	FixedSpeedCubic (FixedSpeedCubic &&)=default

FixedSpeedCubic &	operator= (FixedSpeedCubic &&)=default

	FixedSpeedCubic (const FixedSpeedCubic &)=default

FixedSpeedCubic &	operator= (const FixedSpeedCubic &)=default

	WRAPPED_PUPable_decl_template (FixedSpeedCubic)

	FixedSpeedCubic (CkMigrateMessage *)

auto	get_clone () const -> std::unique_ptr< FunctionOfTime > override

std::array< DataVector, 1 >	func (const double t) const override
	Returns the function at an arbitrary time `t`. More...

std::array< DataVector, 2 >	func_and_deriv (const double t) const override
	Returns the function and its first derivative at an arbitrary time `t`. More...

std::array< DataVector, 3 >	func_and_2_derivs (const double t) const override
	Returns the function and the first two derivatives at an arbitrary time `t`. More...

std::array< double, 2 >	time_bounds () const override
	Returns the domain of validity of the function. More...

double	expiration_after (const double) const override
	The first expiration time after `time`. More...

void	pup (PUP::er &p) override

Public Member Functions inherited from domain::FunctionsOfTime::FunctionOfTime
	FunctionOfTime (FunctionOfTime &&)=default

FunctionOfTime &	operator= (FunctionOfTime &&)=default

	FunctionOfTime (const FunctionOfTime &)=default

FunctionOfTime &	operator= (const FunctionOfTime &)=default

virtual auto	get_clone () const -> std::unique_ptr< FunctionOfTime >=0

virtual std::array< double, 2 >	time_bounds () const =0
	Returns the domain of validity of the function. For FunctionsOfTime that allow a small amount of time extrapolation, `time_bounds` tells you the bounds including the allowed extrapolation interval. More...

virtual double	expiration_after (double time) const =0
	The first expiration time after `time`. More...

virtual void	update (double, DataVector, double)
	Updates the maximum derivative of the FunctionOfTime at a given time while also resetting the expiration. By default, a FunctionOfTime cannot be updated. More...

virtual std::array< DataVector, 1 >	func (double t) const =0
	The DataVector can be of any size. More...

virtual std::array< DataVector, 2 >	func_and_deriv (double t) const =0
	The DataVector can be of any size. More...

virtual std::array< DataVector, 3 >	func_and_2_derivs (double t) const =0
	The DataVector can be of any size. More...

	WRAPPED_PUPable_abstract (FunctionOfTime)

Friends
bool	operator== (const FixedSpeedCubic &lhs, const FixedSpeedCubic &rhs)

std::ostream &	operator<< (std::ostream &os, const FixedSpeedCubic &fixed_speed_cubic)

Detailed Description

Sets \(f(t)\) and derivatives using cubic rational functions, such that the first derivative approaches a constant and the second derivative approaches zero.

The resultant function of time is

\begin{align*} f(t) &= f_0 + \frac{v(t-t_0)^3}{\tau^2+(t-t_0)^2}, \end{align*}

where \(f_0\) is the value of the function \(f\) at the initial time \(t_0\), and \(v\) is the velocity that \(f^\prime(t)\) approaches on a timescale of \(\tau\).

Member Function Documentation

◆ expiration_after()

double domain::FunctionsOfTime::FixedSpeedCubic::expiration_after ( const double time ) const

inlineoverridevirtual

The first expiration time after time.

Details

For non-updatable functions, this returns infinity. For updatable functions, the first expiration time after time is found by determining the update immediately before time. The expiration time of this update is what is returned. If time happens to be an update itself, then the expiration of that update is returned.

Implements domain::FunctionsOfTime::FunctionOfTime.