import numpy as np
import matplotlib.pyplot as plt

X = np.linspace(-3, 3, num=1000)
domain = X
Y = np.log(np.abs(X**2) + 0.5)

def local_regression(X0, X, Y, tau) :
    X0 = [1, X0]
    X = [[1, i] for i in X]
    X = np.asarray(X)
    XW = (X.T) * np.exp(np.sum((X - X0) ** 2, axis=1) / (-2 * (tau ** 2)))
    beta = np.linalg.pinv(XW @ X) @ XW @ Y @ X0 # np.linearalgebra.pseudoinverse
    return beta
    
    
def draw(tau):
    prediction = [local_regression(x0, X, Y, tau) for x0 in domain]
    plt.plot(X, Y, 'o', color='black')
    plt.plot(domain, prediction, color='red')
    plt.show()
    
draw(0.1)

# OUTPUT :-  Graph