Simplex Sampling

This example shows the use of the Simplex sampling class. In particular:

• How to define the Simplex sampling method supported by UQpy

• How to draw samples using Simplex sampling

• How to plot simplices as well as their corresponding samples.

Initially we have to import the necessary modules.

from UQpy.sampling import SimplexSampling
import numpy as np
import matplotlib.pyplot as plt

Define Simplices

Create an array of 3 points in 2-D, which will be the vertex coordinates of the simplex.

vertex = np.array([[0, 0], [0.5, 1], [1, 0]])

Add new samples to existing sampling object

Use Simplex class to generate uniformly distributed samples. This class needs two input parameters, i.e. nodes and nsamples. Nodes are the vertex coordinates of simplex and nsamples is the number of new samples to be generated. In this example, we are generating ten new samples inside our simplex.

x = SimplexSampling(nodes=vertex, nsamples=10, random_state=1)

Plot the samples of the simplex

A schematic illustration of the 2-D simplex and new samples generated using Simplex class are presented below.

plt.plot(np.array([0, 0.5, 1, 0]), np.array([0, 1, 0, 0]), color='blue')
plt.scatter(x.samples[:, 0], x.samples[:, 1], color='red')
plt.show()

User can also define a Simplex object using vertices and generate samples using run() method.

y = SimplexSampling(nodes=vertex)
y.run(nsamples=5)