compute a SVD perturbation version A of X

import numpy as np
from scipy.linalg import svd

def svd_perturbation(X, epsilon):
    U, S, Vt = svd(X, full_matrices=False)
    S_perturbed = np.sqrt(S**2 + epsilon**2)
    A = U.dot(np.diag(S_perturbed)).dot(Vt)
    return A

# Example usage
X = np.array([[1, 2, 3],
              [4, 5, 6],
              [7, 8, 9]])

epsilon = 0.1
A = svd_perturbation(X, epsilon)

print("Original Matrix X:")
print(X)

print("\nPerturbed Matrix A:")
print(A)