User Design Criterion

This example illustrates use of user-defined latin hypercube design criteria. In particular:

• How to define the Monte Carlo sampling method supported by UQpy

• How to append new samples to the existing ones

• How to transform existing samples to the unit hypercube

• How to plot histograms for each one of the sampled parameters and 2D scatter of the produced samples

Initially we have to import the necessary modules.

from UQpy.sampling import LatinHypercubeSampling
import matplotlib.pyplot as plt
from UQpy.distributions import Uniform
from UQpy.sampling.stratified_sampling.latin_hypercube_criteria import *
from UQpy.sampling.stratified_sampling.latin_hypercube_criteria import Criterion

Create user-defined criterion

In order to create a user defined criterion, a concrete implementation of the Criterion abstract class must be created. The generate_samples method must be implemented, which receives as input the random_state, the randomly generated latin hypercube samples.

class UserCriterion(Criterion):
    def generate_samples(self, random_state):
        lhs_samples = np.zeros_like(self.samples)
        for j in range(self.samples.shape[1]):
            order = np.random.permutation(self.samples.shape[0])
            lhs_samples[:, j] = self.samples[order, j]
        return lhs_samples

Define Latin Hypercube sampling

In order to initialize the LatinHypercube sampling class, the user needs to define a list of distributions for each one of the parameters that need to be sampled.

Apart from the distributions list, the number of samples nsamples to be drawn is required. The random_state parameter defines the seed of the random generator.

Finally, the design criterion can be defined by the user. The default case is the Random. For more details on the various criteria you can refer to the documentation of the criteria Random, Centered, Maximin, MinCorrelation

In the case of user-defined criteria an instantiation of the UserCriterion class is provided instead of the built-in criteria.

dist1 = Uniform(loc=0., scale=1.)
dist2 = Uniform(loc=0., scale=1.)

lhs_user_defined = LatinHypercubeSampling(distributions=[dist1, dist2], nsamples=5,
                                          criterion=UserCriterion())
print(lhs_user_defined._samples)

[[0.68090275 0.60549567]
 [0.14175822 0.5948103 ]
 [0.39720161 0.39503455]
 [0.88606061 0.18531564]
 [0.44924163 0.86012738]]

Plot the samples

The samples generated using the LatinHypercube sampling method can be retrieved using the samples attribute. This attribute is a numpy.ndarray.

# plot the samples
fig, ax = plt.subplots()
plt.title('LHS sampling - User Criterion')
plt.scatter(lhs_user_defined._samples[:, 0], lhs_user_defined._samples[:, 1], marker='o')
ax.yaxis.grid(True)
ax.xaxis.grid(True)
plt.ylim(0, 1)
plt.xlim(0, 1)
plt.show()