t=np.arange(dt,10,dt)
theta = np.array(j_i)
traj = pd.DataFrame({'t': t, 'x': theta[:]})
print((time))
print((theta))
def compute_msd(trajectory, t_step, coords=['x']):

    tau = trajectory['t'].copy()
    shifts = np.floor(tau / t_step).astype(np.int)
    msds = np.zeros(shifts.size)
    msds_std = np.zeros(shifts.size)

    for i, shift in enumerate(shifts):
        diffs = trajectory[coords] - trajectory[coords].shift(-shift)
        sqdist = np.square(diffs).sum(axis=1)
        msds[i] = sqdist.mean()
        msds_std[i] = sqdist.std()

    msds = pd.DataFrame({'msds': msds, 'tau': tau, 'msds_std': msds_std})
    return msds

# Compute MSD
msd = compute_msd(traj, t_step=dt, coords=['x'])

print(msd.head(10))

# Plot MSD
ax = msd.plot(x="tau", y="msds", logx=True, logy=True, legend=False)
ax.fill_between(msd['tau'], msd['msds'] - msd['msds_std'], msd['msds'] + msd['msds_std'], alpha=0.2)


    # np.savetxt("MSD%d"%k, MSD)
    # np.savetxt("Tau%d"%k,tau_i)



plt.show()