Draw an ellipse starting from different parameterizations

Draw ellipse

# Given ellipticity parameters (e1, e2) and size s = det(Q)**(1/4)
# https://github.com/dkirkby/desietcimg/blob/master/desietcimg/plot.py
def draw_ellipse_se1e2(ax, x0, y0, s, g1, g2, nsigmas=1, **ellipseopts):
    g = np.sqrt(g1 ** 2 + g2 ** 2)
    if g > 1:
        raise ValueError('g1 ** 2 + g2 ** 2 > 1')
    center = np.array([x0, y0])
    angle = np.rad2deg(0.5 * np.arctan2(g2, g1))
    ratio = np.sqrt((1 + g) / (1 - g))
    width = 2 * s * ratio * nsigmas
    height  = 2 * s / ratio * nsigmas
    kwargs = dict(color='r', ls='-', lw=2, alpha=0.7, fill=False)
    kwargs.update(ellipseopts)
    ellipse = matplotlib.patches.Ellipse(center, width, height, angle, **kwargs)
    ax.add_artist(ellipse)

# Given covariance parameters
# https://github.com/dkirkby/MachineLearningStatistics/blob/master/mls/plot.py
def draw_ellipse_cov(ax, center, cov, nsigmas=2, **ellipseopts):
    U, s, _ = np.linalg.svd(cov)
    angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
    width, height = 2 * nsigmas * np.sqrt(s.T)
    kwargs = dict(color='w', ls='-', lw=2, fill=False)
    kwargs.update(ellipseopts)
    ellipse = matplotlib.patches.Ellipse(center, width, height, angle, **kwargs)
    ax.add_artist(ellipse)