plot_equiprobability.py

from matplotlib.patches import Ellipse
import matplotlib as mpl

ax = plt.gca(); ax.set_xlabel('X'); ax.set_ylabel('Y')
plt.scatter(X_raw[:, 0], X_raw[:, 1], c='#B8860B', alpha=0.5)
plt.scatter(X_mean[0], X_mean[1], c='red', s=50)

U_, s_, _ = LA.svd(np.cov(X, rowvar=False), full_matrices=False)
angle = np.degrees(np.arctan2(U_[1,0], U_[0,0]))
width, height = 2 * np.sqrt(s_)

for nsig in range(1, 4):
    args = [X_mean, nsig*width, nsig*height, angle]
    kwargs = dict(color='#008000', alpha=1./(nsig+.5), linewidth=2, fill=False)
    ell = mpl.patches.Ellipse(*args, **kwargs)
    ell.set_clip_box(ax.bbox)
    ax.add_artist(ell)
    # Or also below works as well
    # ax.add_patch(Ellipse(*args,**kwargs))