codac::SepProj Class Reference

Projection of a separator. More...

#include <codac_SepProj.h>

Inherits Sep.

Public Member Functions
	SepProj (Sep &sep, const IntervalVector &y_init, double prec)
	Construct a new Sep Proj object.
	SepProj (Sep &sep, const Interval &y_init, double prec)
	Construct a new Sep Proj object.
	~SepProj ()
	Destroy the Sep Proj object.
void	separate (IntervalVector &x_in, IntervalVector &x_out)
	Separate method.

Protected Member Functions
bool	process (IntervalVector &x_in, IntervalVector &x_out, IntervalVector &y, ImpactStatus &impact, bool use_point)
	SepProj::process Separate cartesian product [x_in].[y] and [x_out].[y] if an inner (or outer) contraction happends, the flags impact_cin is set to true and the removed part of the box is stored in first_cin_boxes.

Protected Attributes
Sep &	sep
	The Separator.
IntervalVector	y_init
	Initial box of the parameters (can be set dynamically)
double	prec
	precision
LargestFirst *	bsc
	internal variable used to count the number of call of the SepProj::process method

Detailed Description

Projection of a separator.

Given \(\mathbb{X}\subset\mathbb{R}^{n}\) and \(\mathbb{Y}\subset\mathbb{R}^{p}\). If \(\mathbb{Z}=\mathbb{X}\times\mathbb{Y}\), then the projection of a subset \(\mathbb{Z}_{1}\) of \(\mathbb{Z}\) onto \(\mathbb{X}\) (with respect to \(\mathbb{Y}\)) is defined as:

\( {proj}_{\mathbb{X}}(\mathbb{Z}_{1})=\left\{ \mathbf{x}\in\mathbb{X}\mid\exists\mathbf{y}\in\mathbb{Y},(\mathbf{x},\mathbf{y})\in\mathbb{Z}_{1}\right\}\)

Given a separator \(\mathcal{S}([\mathbf{x}],\left[\mathbf{y}\right])=\left\{ \mathcal{S}^{\text{in}}([\mathbf{x}],\left[\mathbf{y}\right]),\mathcal{S}^{\text{out}}([\mathbf{x}],\left[\mathbf{y}\right])\right\}\), the projection of \(\mathcal{S}\) is defined by :

\({proj}_{\mathbf{x}}(\mathcal{S})([\textbf{x}])=\left\{ \bigcap_{\textbf{y}\in[\textbf{y}]}\partial_{\textbf{x}}\mathcal{S}^{in}([\textbf{x}],\mathbf{y}),\bigcup_{\textbf{y}\in[\textbf{y}]}\partial_{\textbf{x}}\mathcal{S}^{out}([\textbf{x}],\mathbf{y})\right\}\)

The separator algorythm is inspired from the ibexlib ones but performs the inner and outer contraction concurently.

See Ibexlib (CtcForAll and CtcExist)[https://ibex-team.github.io/ibex-lib/contractor.html#exists-and-forall] documentation for more details.

Constructor & Destructor Documentation

SepProj() [1/2]

codac::SepProj::SepProj	(	Sep &	sep,
		const IntervalVector &	y_init,
		double	prec )

Construct a new Sep Proj object.

Parameters

sep	Separator to use for the projection. The input box dimension must be equal to dim([x]) + dim([y_init]). given a two IntervalVector \([\mathbf{x}]\) and \([\mathbf{y}]\), the separator is called with a new box \([\mathbf{z}] = [\mathbf{y}] X [\mathbf{y}]\).
y_init	Initial box for the parameters
prec	Bisection precision on the parameters (the contraction involves a bisection process on y)

SepProj() [2/2]

codac::SepProj::SepProj	(	Sep &	sep,
		const Interval &	y_init,
		double	prec )

Construct a new Sep Proj object.

Parameters

sep	Separator used for the projection. The input dimension must be equal to size(x) + size(y_init). given a two IntervalVector \([\mathbf{x}]\) and \([\mathbf{y}]\), the separator is called with a new box \([\mathbf{z}] = [\mathbf{y}] X [\mathbf{y}]\).
y_init	Initial Interval for the parameters
prec	Bisection precision on the parameters (the contraction involves a bisection process on y)

Member Function Documentation

separate()

void codac::SepProj::separate	(	IntervalVector &	x_in,
		IntervalVector &	x_out )

Separate method.

Parameters

x_in	the n-dimensional box \([\mathbf{x}_{\textrm{in}}]\) to be inner-contracted
x_out	the n-dimensional box \([\mathbf{x}_{\textrm{out}}]\) to be outer-contracted

process()

bool codac::SepProj::process ( IntervalVector & x_in, IntervalVector & x_out, IntervalVector & y, ImpactStatus & impact, bool use_point )

protected

SepProj::process Separate cartesian product [x_in].[y] and [x_out].[y] if an inner (or outer) contraction happends, the flags impact_cin is set to true and the removed part of the box is stored in first_cin_boxes.

Parameters

x_in	: projected inner box
x_out	: projected outer box
y	: parameter box
impact	: used to trace contraction of the input box
use_point

Returns

true if x_in or x_out is empty.

Member Data Documentation

bsc

LargestFirst* codac::SepProj::bsc

protected

internal variable used to count the number of call of the SepProj::process method

the outer contractor / inner contractor has an impact

store the firsr box contractor by the inner/ outer contractor

a bisector

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

• /home/simon/codac/src/core/separators/codac_SepProj.h