Exclusion

Module for the Exclusion Operation.

class Exclusion(geometries)

Bases: OperationInterface

Implementation of the exclusion operation between of a list of domains.

Given two sets \(A\) and \(B\), define the exclusion of the two sets as:

\[A \setminus B = \{x \mid x \in A \land x \in B \land x \not\in(A \lor B)\},\]

where \(x\) is a point in \(\mathbb{R}^N\).

Initialization of the Exclusion class.

Parameters:

geometries (list[DomainInterface]) – A list of instances of the DomainInterface class on which the exclusion operation is performed.

Example:

>>> # Create two ellipsoid domains
>>> ellipsoid1 = EllipsoidDomain({'x': [-1, 1], 'y': [-1, 1]})
>>> ellipsoid2 = EllipsoidDomain({'x': [0, 2], 'y': [0, 2]})
>>> # Define the exclusion between the domains
>>> exclusion = Exclusion([ellipsoid1, ellipsoid2])

is_inside(point, check_border=False)

Check if a point is inside the resulting domain.

Parameters:

• point (LabelTensor) – Point to be checked.

• check_border (bool) – If True, the border is considered inside the domain. Default is False.

Returns:

True if the point is inside the domain, False otherwise.

Return type:

bool

sample(n, mode='random', variables='all')

Sampling routine.

Parameters:

• n (int) – Number of points to sample.

• mode (str) – Sampling method. Default is random. Available modes: random sampling, random;

• variables (list[str]) – variables to be sampled. Default is all.

Raises:

NotImplementedError – If the sampling method is not implemented.

Returns:

Sampled points.

Return type:

LabelTensor

Example:

>>> # Create two Cartesian domains
>>> cartesian1 = CartesianDomain({'x': [0, 2], 'y': [0, 2]})
>>> cartesian2 = CartesianDomain({'x': [1, 3], 'y': [1, 3]})
>>> # Define the exclusion between the domains
>>> Exclusion = Exclusion([cartesian1, cartesian2])
>>> # Sample
>>> Exclusion.sample(n=5)
    LabelTensor([[2.4187, 1.5792],
                [2.7456, 2.3868],
                [2.3830, 1.7037],
                [0.8636, 1.8453],
                [0.1978, 0.3526]])
>>> len(Exclusion.sample(n=5)
    5