import numpy as np
import matplotlib.pylab as plt
%matplotlib inline
# generáljunk zajos jeleket
x = np.arange(1000)
y = 0.000321 * x**2 + 20*np.random.randn(len(x))
plt.plot(x, y, 'k.', linewidth = 5)
plt.show()

# illesszünk görbét
M = np.column_stack((x**2,)) # construct design matrix
k, _, _, _ = np.linalg.lstsq(M, y, rcond=None) # least-square fit of M * k = y

# jelenítsük meg
plt.plot(x, y, 'k.', x, k*x**2, 'r', linewidth = 5)
plt.legend(('measurement', 'fit'), loc=2)
plt.title('best fit: y = {:.8f} * x**2'.format(k[0]))
plt.show()