Adding New Latin Hypercube Design Criteria

The LatinHypercubeSampling class offers a variety of methods for pairing the samples in a Latin hypercube design. These are specified by the criterion parameter (i.e. Random, Centered, MaxiMin, MinCorrelation). Each one of the Criteria classes can be found in latin_hypercube_criteria folder, with the Criterion baseclass defining their common interface. As a result, adding a new method is straightforward. This is done by creating a new class that implements the Criterion abstract baseclass. The base class requires the creation of a generate_samples() method that contains the algorithm for pairing the samples. This method retrieves the randomly generated samples generated in the baseclass in equal probability bins in each dimension and returns a set of samples that is paired according to the user’s desired criterion. The user may also pass criterion-specific parameters into the __init__() method of the generated class. The output of this function should be a numpy array of at least two-dimensions with the first dimension being the number of samples and the second dimension being the number of variables.

The Criterion class is imported using the following command:

>>> from UQpy.sampling.stratified_sampling.latin_hypercube_criteria.baseclass.Criterion import Criterion

class Criterion

abstract generate_samples(random_state)

Abstract method that must be overriden when generating creating new Latin Hypercube sampling criteria.

An example of a user-defined criterion is given below:

>>> class UserCriterion(Criterion):
>>>
>>>     def __init__(self):
>>>         super().__init__()
>>>
>>>     def generate_samples(self, random_state):
>>>         lhs_samples = np.zeros_like(self.samples)
>>>         samples_number = len(self._samples)
>>>         for j in range(self.samples.shape[1]):
>>>             if random_state is not None:
>>>                 order = random_state.permutation(samples_number)
>>>             else:
>>>                 order = np.random.permutation(samples_number)
>>>             lhs_samples[:, j] = self.samples[order, j]
>>>
>>>         return lhs_samplesAn example of a user-defined criterion is given below: