Intersection#

Module for Intersection class.

class Intersection(geometries)[source]#

Bases: OperationInterface

PINA implementation of Intersection of Domains. Given two sets \(A\) and \(B\) then the domain difference is defined as:

\[A \cap B = \{x \mid x \in A \land x \in B\},\]

with \(x\) a point in \(\mathbb{R}^N\) and \(N\) the dimension of the geometry space.

Parameters:

geometries (list) – A list of geometries from pina.geometry such as EllipsoidDomain or CartesianDomain. The intersection will be taken between all the geometries in the list. The resulting geometry will be the intersection of all the geometries in the list.

Example:
>>> # Create two ellipsoid domains
>>> ellipsoid1 = EllipsoidDomain({'x': [-1, 1], 'y': [-1, 1]})
>>> ellipsoid2 = EllipsoidDomain({'x': [0, 2], 'y': [0, 2]})
>>> # Create a Intersection of the ellipsoid domains
>>> intersection = Intersection([ellipsoid1, ellipsoid2])
is_inside(point, check_border=False)[source]#

Check if a point is inside the Intersection domain.

Parameters:

  • point (torch.Tensor) – Point to be checked.

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

Returns:

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

Return type:

bool

sample(n, mode='random', variables='all')[source]#

Sample routine for Intersection domain.

Parameters:

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

  • mode (str) – Mode for sampling, defaults to random. Available modes include: random.

  • variables (str | list[str]) – Variables to be sampled, defaults to all.

Returns:

Returns LabelTensor of n 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]})
>>> # Create a Intersection of the ellipsoid domains
>>> intersection = Intersection([cartesian1, cartesian2])
>>> # Sample
>>> intersection.sample(n=5)
    LabelTensor([[1.7697, 1.8654],
                [1.2841, 1.1208],
                [1.7289, 1.9843],
                [1.3332, 1.2448],
                [1.9902, 1.4458]])
>>> len(intersection.sample(n=5)
    5