Delaunay

The DelaunayStrata class is imported using the following command:

>>> from UQpy.sampling.stratified_sampling.strata.DelaunayStrata import DelaunayStrata

Methods

class DelaunayStrata(seeds=None, seeds_number=None, dimension=None, random_state=None)[source]

Define a geometric decomposition of the n-dimensional unit hypercube into disjoint and space-filling Delaunay strata of n-dimensional simplexes. Delaunay is a child class of the Strata class.

Parameters:

seeds (Optional[ndarray]) – An array of dimension \(N * n\) specifying the seeds of all strata. The seeds of the strata are the coordinates of the vertices of the Delaunay cells. The user must provide seeds or seeds_number and dimension. Note that, if seeds does not include all corners of the unit hypercube, they are added.
seeds_number (Optional[int]) – The number of seeds to randomly generate. Seeds are generated by random sampling on the unit hypercube. In addition, the class also adds seed points at all corners of the unit hypercube. The user must provide seeds or seeds_number and dimension
dimension (Optional[ndarray]) – The dimension of the unit hypercube in which to generate random seeds. Used only if seeds_number is provided. The user must provide seeds or seeds_number and dimension

stratify()[source]: Perform the stratification of the unit hypercube. It is overwritten by the subclass. This method must exist in any subclass of the Strata class.

static compute_delaunay_centroid_volume(vertices)[source]

This function computes the centroid and volume of a Delaunay simplex from its vertices.

Parameters:: vertices – Coordinates of the vertices of the simplex.
Returns:: Centroid and Volume of the Delaunay simplex.

Attributes

DelaunayStrata.delaunay: Delaunay: Defines a Delaunay decomposition of the set of seed points and all corner points.

DelaunayStrata.centroids: list: A list of the vertices for each Delaunay stratum on the unit hypercube.