codac2::LohnerAlgorithm Class Reference

Simple first order Lohner algorithm to perform guaranteed integration of a system \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\). More...

#include <codac2_CtcLohner.h>

Public Member Functions
	LohnerAlgorithm (const AnalyticFunction< VectorType > *f, double h, bool forward, const IntervalVector &u0, int contractions=1, double eps=0.1)
	Creates a Lohner algorithm object.
const IntervalVector &	integrate (unsigned int steps, double H=-1)
	integrate the system over a given number of steps
void	contractStep (const IntervalVector &x)
	contract the global & local enclosure of the previous integration step
const IntervalVector &	getLocalEnclosure () const
	Returns the current global enclosure, i.e. the box enclosing the trajectories between times \(k-1\) and \(k\).
const IntervalVector &	getGlobalEnclosure () const
	Returns the current local enclosure, i.e. the box enclosing the trajectories at time \(k\).

Detailed Description

Simple first order Lohner algorithm to perform guaranteed integration of a system \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\).

Constructor & Destructor Documentation

LohnerAlgorithm()

codac2::LohnerAlgorithm::LohnerAlgorithm	(	const AnalyticFunction< VectorType > *	f,
		double	h,
		bool	forward,
		const IntervalVector &	u0,
		int	contractions = 1,
		double	eps = 0.1 )

Creates a Lohner algorithm object.

Parameters

f	function defining the system \(\dot{\mathbf{x}}=\mathbf{f}(\mathbf{x})\)
h	time step of the integration method
forward	forward integration if true, backaward otherwise
u0	initial condition of the system
contractions	number of contractions of the global enclosure by the estimated local enclosure
eps	inflation parameter for the global enclosure

Member Function Documentation

integrate()

const IntervalVector & codac2::LohnerAlgorithm::integrate	(	unsigned int	steps,
		double	H = -1 )

integrate the system over a given number of steps

Parameters

steps	number of steps to integrate
H	parameter to overwrite the integration time step

Returns

enclosure of the system's state

contractStep()

void codac2::LohnerAlgorithm::contractStep

(

const IntervalVector &

x

)

contract the global & local enclosure of the previous integration step

Parameters

x	estimation of the global enclosure

getLocalEnclosure()

const IntervalVector & codac2::LohnerAlgorithm::getLocalEnclosure

(

)

const

Returns the current global enclosure, i.e. the box enclosing the trajectories between times \(k-1\) and \(k\).

Returns

global enclosure

getGlobalEnclosure()

const IntervalVector & codac2::LohnerAlgorithm::getGlobalEnclosure

(

)

const

Returns the current local enclosure, i.e. the box enclosing the trajectories at time \(k\).

Returns

local enclosure \([\mathbf{x}_{k}]\)

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

• /home/simon/codac-simon/src/core/contractors/codac2_CtcLohner.h