permutation_matrix.py

# Function to create a random permutation matrix of some size
import numpy as np


def r_pmatrix(dim):
    """
    Random Permutation Matrix (r_pmatrix)
    Create a random permutation matrix P such that PM shuffles the rows of M, for some matrix M
    :param dim: dimension of (square) permutation matrix
    :return: P, permutation matrix
    """
    idx = [xx for xx in range(dim)]
    np.random.shuffle(idx)
    return np.eye(dim)[idx, :]


if __name__ == "__main__":
    # Create a permutation matrix
    n = 4
    p = r_pmatrix(n)
    # Create some n by 2 matrix
    a = np.arange(2*n).reshape(n, 2)
    # Print a, p, and p @ a
    print(f"A =\n{a},\nP=\n{p},\nPA=\n{p @ a}")
    # Determinant is always between -1 and 1
    print(f"Determinant of P: {np.linalg.det(p)}")