def test_sky_gaussian():
# Test symmetric model
sigma = 1 * u.deg
model = GaussianSpatialModel(lon_0="5 deg", lat_0="15 deg", sigma=sigma)
assert model.parameters["sigma"].min == 0
val_0 = model(5 * u.deg, 15 * u.deg)
val_sigma = model(5 * u.deg, 16 * u.deg)
assert val_0.unit == "sr-1"
ratio = val_0 / val_sigma
assert_allclose(ratio, np.exp(0.5))
radius = model.evaluation_radius
assert radius.unit == "deg"
assert_allclose(radius.value, 5 * sigma.value)
# test the normalization for an elongated Gaussian near the Galactic Plane
m_geom_1 = WcsGeom.create(
binsz=0.05, width=(20, 20), skydir=(2, 2), frame="galactic", proj="AIT"
)
coords = m_geom_1.get_coord()
solid_angle = m_geom_1.solid_angle()
lon = coords.lon
lat = coords.lat
sigma = 3 * u.deg
model_1 = GaussianSpatialModel(
lon_0=2 * u.deg, lat_0=2 * u.deg, sigma=sigma, e=0.8, phi=30 * u.deg
)
vals_1 = model_1(lon, lat)
assert vals_1.unit == "sr-1"
assert_allclose(np.sum(vals_1 * solid_angle), 1, rtol=1.0e-3)
radius = model_1.evaluation_radius
assert radius.unit == "deg"
assert_allclose(radius.value, 5 * sigma.value)
# check the ratio between the value at the peak and on the 1-sigma isocontour
sigma = 4 * u.deg
semi_minor = 2 * u.deg
e = np.sqrt(1 - (semi_minor / sigma) ** 2)
model_2 = GaussianSpatialModel(
lon_0=0 * u.deg, lat_0=0 * u.deg, sigma=sigma, e=e, phi=0 * u.deg
)
val_0 = model_2(0 * u.deg, 0 * u.deg)
val_major = model_2(0 * u.deg, 4 * u.deg)
val_minor = model_2(2 * u.deg, 0 * u.deg)
assert val_0.unit == "sr-1"
ratio_major = val_0 / val_major
ratio_minor = val_0 / val_minor
assert_allclose(ratio_major, np.exp(0.5))
assert_allclose(ratio_minor, np.exp(0.5))
# check the rotation
model_3 = GaussianSpatialModel(
lon_0=0 * u.deg, lat_0=0 * u.deg, sigma=sigma, e=e, phi=90 * u.deg
)
val_minor_rotated = model_3(0 * u.deg, 2 * u.deg)
ratio_minor_rotated = val_0 / val_minor_rotated
assert_allclose(ratio_minor_rotated, np.exp(0.5))
assert isinstance(model.to_region(), EllipseSkyRegion)
lon_0="2 deg",
lat_0="2 deg",
sigma="1 deg",
e=0.7,
phi=phi,
frame="galactic",
)
geom = WcsGeom.create(skydir=model.position,
frame=model.frame,
width=(4, 4),
binsz=0.02)
ax = model.plot(geom=geom, add_cbar=True)
# illustrate size parameter
region = model.to_region().to_pixel(ax.wcs)
artist = region.as_artist(facecolor="none", edgecolor="red")
ax.add_artist(artist)
transform = ax.get_transform("galactic")
ax.scatter(2, 2, transform=transform, s=20, edgecolor="red", facecolor="red")
ax.text(1.5, 1.85, r"$(l_0, b_0)$", transform=transform, ha="center")
ax.plot([2, 2 + np.sin(phi)], [2, 2 + np.cos(phi)],
color="r",
transform=transform)
ax.vlines(x=2, color="r", linestyle="--", transform=transform, ymin=-5, ymax=5)
ax.text(2.25, 2.45, r"$\phi$", transform=transform)
# %%
# YAML representation
# -------------------
