Libraries like NumPy

NumPy Random Number Generation

NumPy’s random module (now deprecated; use numpy.random directly) provides functions for generating various random numbers and distributions. It’s significantly faster than Python’s built-in random module, especially for large arrays.

Key Functions & Concepts:

• numpy.random.rand(d0, d1, ..., dn): Creates an array of the given shape and fills it with random floats sampled from a uniform distribution over [0, 1).

import numpy as np

# 3x3 array of random floats between 0 and 1
random_array = np.random.rand(3, 3)
print(random_array)

• numpy.random.randn(d0, d1, ..., dn): Creates an array of the given shape and fills it with random floats sampled from a standard normal (Gaussian) distribution (mean=0, standard deviation=1).

# 2x2 array of random floats from a standard normal distribution
normal_array = np.random.randn(2, 2)
print(normal_array)

• numpy.random.randint(low, high=None, size=None, dtype=int): Returns random integers from low (inclusive) to high (exclusive). If high is None, then results are from 0 to low.

# 5 random integers between 1 and 10 (inclusive)
random_integers = np.random.randint(1, 11, 5) # 11 is exclusive
print(random_integers)

• numpy.random.choice(a, size=None, replace=True, p=None): Generates a random sample from a given array a. replace=True allows sampling with replacement (same element can be selected multiple times). p specifies probabilities for each element in a.

# Sample 3 elements from an array with replacement
my_array = np.array(1, 2, 3, 4, 5)
sample = np.random.choice(my_array, size=3, replace=True)
print(sample)


# Sample with probabilities
probabilities = np.array([0.1, 0.2, 0.3, 0.2, 0.2) # must sum to 1
weighted_sample = np.random.choice(my_array, size=3, replace=True, p=probabilities)
print(weighted_sample)

• numpy.random.seed(seed): Sets the seed for the random number generator. Using the same seed will produce the same sequence of random numbers. This is crucial for reproducibility.

np.random.seed(42) # set seed to 42
print(np.random.rand(2))
np.random.seed(42) # setting it again produces the same results
print(np.random.rand(2))

• Other Distributions: NumPy provides functions for generating random numbers from many other probability distributions, including binomial, exponential, Poisson, etc. Refer to the NumPy documentation for a complete list. (NumPy Distributions)

• Generating Random Matrices: NumPy offers convenient ways to create random matrices with specific properties (e.g., symmetric, orthogonal, etc.).(Random Matrix Generation)

Deprecated random Module:

The top-level numpy.random module is now preferred over the older np.random module. While the older module might still work in some cases, it is recommended to transition to the newer approach for better compatibility and future-proofing.

Note: For more advanced random number generation and statistical simulations, consider using libraries like SciPy.(SciPy Statistical Functions)