import numpy as np
import matplotlib.pyplot as plt

n = 50
N = 1000
m = 15

x = np.linspace(-3, 3, n)
X = np.linspace(-3, 3, N)

pix = np.pi * x
y = np.sin(pix) / (pix) + 0.1 * x + 0.05 * np.random.randn(n)

p = np.zeros([m * 2 + 1, n])
P = np.zeros([m * 2 + 1, N])
p[0] = np.ones(n)
P[0] = np.ones(N)
for j in range(1, m + 1):
    p[2 * j - 1] = np.sin(j / 2 * x)
    p[2 * j + 0] = np.cos(j / 2 * x)
    P[2 * j - 1] = np.sin(j / 2 * X)
    P[2 * j + 0] = np.cos(j / 2 * X)
p = p.T
P = P.T

t1 = np.dot(np.linalg.pinv(p), y)
F1 = np.dot(P, t1)

rmtx = np.diag(np.hstack((np.ones(11), np.zeros(20))))
t2 = np.dot(np.linalg.pinv(p.dot(rmtx)), y)
F2 = np.dot(P, t2)

plt.plot(x, y, 'bo')
plt.plot(X, F1, 'g-')
plt.plot(X, F2, 'r-.')

plt.show()