# régression linéaire chapitre 1 Incertitude-type

import numpy as np
import matplotlib.pyplot as plt

t = np.array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.])
U = np.array([2.016, 1.453, 1.025, 0.714, 0.516, 0.386, 0.263, 0.175, 0.149, 0.106, 0.057])
u_t = 0.2
u_U = 0.2
ln_U = np.log(U)
u_ln_U = u_U / U

a, b = np.polyfit(t, ln_U, 1)

plt.figure()
plt.errorbar(t, ln_U, xerr = u_t, yerr=u_ln_U, fmt='.')
plt.plot(t, a*t + b, label='régression linéaire')
plt.legend()
plt.grid()
plt.xlabel('t (s)')
plt.ylabel('ln(U/1V)')
plt.show()

print('tau =', -1/a, 's')