tik_reg.py

import numpy as np
from scipy.optimize import minimize

def least_squares(A, b, x0): # Least-squares solution for Ax=b, initial guess of x0
    return minimize(
        lambda x: np.linalg.norm(A.dot(x) - b),
        x0,
    )

def least_squares_tikhonov(A, b, alpha, x0): # Least squares for Ax=b with simple Tikhonov regularization
    return minimize(
        lambda x: np.linalg.norm(A.dot(x) - b) + alpha * np.linalg.norm(x),
        x0,
    )

def least_squares_generalized_tikhonov(A, b, Gamma, x0): # Least squares with generalized Tikhonov regularization
    return minimize(
        lambda x: np.linalg.norm(A.dot(x) - b) + np.linalg.norm(Gamma.dot(x)),
        x0,
    )