Strata Class

The Strata class is imported using the following command:

>>> from UQpy.sampling.stratified_sampling.strata.baseclass.Strata import Strata

The Strata class is the parent class that defines the geometric decomposition of the parameter space. All geometric decompositions in the Strata class are performed on the n-dimensional unit \([0, 1]^n\) hypercube. Specific stratifications are performed by subclassing the Strata class. There are currently three stratifications available in the Strata class, defined through the subclasses Rectangular, Voronoi, and Delaunay.

Methods

class Strata(seeds=None, random_state=None)

Define a geometric decomposition of the n-dimensional unit hypercube into disjoint and space-filling strata.

This is the parent class for all spatial stratified_sampling. This parent class only provides the framework for stratification and cannot be used directly for the stratification. Stratification is done by calling the child class for the desired stratification.

Parameters:

seeds (Optional[ndarray]) – Define the seed points for the strata. See specific subclass for definition of the seed points.

abstract stratify()

Perform the stratification of the unit hypercube. It is overwritten by the subclass. This method must exist in any subclass of the Strata class.

abstract sample_strata(nsamples_per_stratum, random_state)

Abstract class that need to be implemented in each new Stratum. It defines a way to draw samples from each stratum.

Parameters:

• nsamples_per_stratum – Number of samples to draw in each stratum

• random_state – Random seed used to initialize the pseudo-random number generator. Default is None. If an int is provided, this sets the seed for an object of numpy.random.RandomState. Otherwise, the object itself can be passed directly.

Returns:

A tuple containing the new samples contained in the strata as well as their corresponding weights.

abstract calculate_strata_metrics(index)

Abstract method that calculates stratum metrics needed in order for the sampling algorithm to decide which stratum to refine

Parameters:

index – Stratum index

Returns:

A list containing the metric of each stratum.

Attributes

Strata.seeds: ndarray

Seed points for the strata. See specific subclass for definition of the seed points.

Strata.volume: ndarray

An array of dimension (strata_number, ) containing the volume of each stratum.