This function generates a Uniform sampling between $a$ (minimum) and $b$ (maximum).

u = uniform_sampling(parameters, method, n_samples, seed)

Input variables

Name	Description	Type
parameters	Dictionary of parameters for uniform distribution. Keys: 'min': Minimum value of the uniform distribution [Float] 'max': Maximum value of the uniform distribution [Float]	Dictionary
method	Sampling method. Supports the following values: 'mcs': Crude Monte Carlo Sampling 'lhs': Latin Hypercube Sampling	String
n_samples	Number of samples	Integer
seed	Seed for random number generation. Use None for a random seed	Integer or None

Output variables

Name	Description	Type
u	Random samples	List

Example 1

In this example, we will use the uniform_sampling function from the parepy_toolbox to generate two random samples ($n=400$) following a uniform distribution. The first set is sampled using the Monte Carlo Sampling (MCS) method, and the second using the Latin Hypercube Sampling (LHS) method. The range for both distributions is defined as $[10,20]$. The results are visualized using histograms with Kernel Density Estimates (KDE) plotted (using matplotlib lib) side-by-side for comparison.

# Libraries
import matplotlib.pyplot as plt

from parepy_toolbox import uniform_sampling

# Sampling
n = 400
x = uniform_sampling({'min': 10, 'max': 20}, 'mcs', n)
y = uniform_sampling({'min': 10, 'max': 20}, 'lhs', n)

# Plot
fig, axes = plt.subplots(1, 2, figsize=(7, 3))
sns.histplot(x, kde=True, bins=30, color='blue', ax=axes[0], alpha=0.6, edgecolor='black')
axes[0].set_title('MCS Sampling')
axes[0].set_xlabel('Values')
axes[0].set_ylabel('Density')
sns.histplot(y, kde=True, bins=30, color='green', ax=axes[1], alpha=0.6, edgecolor='black')
axes[1].set_title('LHS Sampling')
axes[1].set_xlabel('Values')
axes[1].set_ylabel('Density')
plt.tight_layout()
plt.show()

Figure 1. Uniform variable example.

Example 2

In this example, we will use the uniform_sampling function from the parepy_toolbox to generate two random samples ($n=3$) following a uniform distribution. Using the Monte Carlo algorithm and the specific seed (seed=25), we generated 3 times and compared the results.

# Library
from parepy_toolbox import uniform_sampling

# Sampling
n = 3
x0 = uniform_sampling({'min': 10, 'max': 20}, 'mcs', n, 25)
x1 = uniform_sampling({'min': 10, 'max': 20}, 'mcs', n, 25)
x2 = uniform_sampling({'min': 10, 'max': 20}, 'mcs', n, 25)
print(x0, '\n', x1, '\n', x2)

Output details.

[11.607212332320078, 15.003120351710036, 12.16598464462817] 
[11.607212332320078, 15.003120351710036, 12.16598464462817] 
[11.607212332320078, 15.003120351710036, 12.16598464462817]

Note that using the seed 25 by 3 times, we can generate the same values in a random variable.