def test_containment():
g, g2 = Gauss2DPDF(sigma=1), Gauss2DPDF(sigma=2)
m = MultiGauss2D(sigmas=[1])
m2 = MultiGauss2D(sigmas=[1, 2], norms=[3, 4])
for theta in [0, 0.1, 1, 5]:
assert_allclose(m.containment_fraction(theta),
g.containment_fraction(theta))
actual = m2.containment_fraction(theta)
desired = 3 * g.containment_fraction(
theta) + 4 * g2.containment_fraction(theta)
assert_allclose(actual, desired)
def test_theta():
# Closure test
m = MultiGauss2D(sigmas=[1, 2] * u.deg, norms=[3, 4])
for theta in [0, 0.1, 1, 5] * u.deg:
c = m.containment_fraction(theta)
t = m.containment_radius(c)
assert_allclose(t, theta)
def test_theta():
# Closure test
m = MultiGauss2D(sigmas=[1, 2], norms=[3, 4])
for theta in [0, 0.1, 1, 5]:
c = m.containment_fraction(theta)
t = m.containment_radius(c)
assert_almost_equal(t, theta, decimal=5)
def test_call():
m = MultiGauss2D(sigmas=[1, 2], norms=[3, 4])
xy_max = 5 * m.max_sigma # integration range
integral = scipy.integrate.dblquad(m, -xy_max, xy_max,
lambda _: -xy_max,
lambda _: xy_max)[0]
assert_almost_equal(integral, 7, decimal=5)
def test_gauss_convolve():
# Convolution must add sigmas in square
m = MultiGauss2D(sigmas=[3], norms=[5])
m2 = m.gauss_convolve(4, 6)
assert_allclose(m2.sigmas, [5])
assert_allclose(m2.integral, 5 * 6)
# Check that convolve did not change the original
assert_allclose(m.sigmas, [3])
assert_allclose(m.norms, [5])
def to_MultiGauss2D(self, normalize=True):
"""Use this to compute containment angles and fractions.
Note: We have to set norm = 2 * A * sigma ^ 2, because in
MultiGauss2D norm represents the integral, and in HESS A
represents the amplitude at 0.
"""
sigmas, norms = [], []
for ii in range(1, self.n_gauss() + 1):
A = self.pars[f"A_{ii}"]
sigma = self.pars[f"sigma_{ii}"]
norm = self.pars["scale"] * 2 * A * sigma**2
sigmas.append(sigma)
norms.append(norm)
m = MultiGauss2D(sigmas, norms)
if normalize:
m.normalize()
return m
def evaluate_direct(rad, **kwargs):
"""Evaluate psf model
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value
**kwargs : dict
Parameters, see `required_parameters`
Returns
-------
value : `~numpy.ndarray`
PSF value
"""
sigmas, norms = get_sigmas_and_norms(**kwargs)
m = MultiGauss2D(sigmas=sigmas, norms=norms)
m.normalize()
return m(rad)
def evaluate_containment(rad, **kwargs):
"""Containment of the PSF at given axes coordinates
Parameters
----------
rad : `~astropy.units.Quantity`
Rad value
**kwargs : dict
Parameters, see `required_parameters`
Returns
-------
containment : `~numpy.ndarray`
Containment
"""
sigmas, norms = get_sigmas_and_norms(**kwargs)
m = MultiGauss2D(sigmas=sigmas, norms=norms)
m.normalize()
containment = m.containment_fraction(rad)
return containment
def psf_at_energy_and_theta(self, energy, theta):
"""
Get `~gammapy.modeling.models.MultiGauss2D` model for given energy and theta.
No interpolation is used.
Parameters
----------
energy : `~astropy.units.u.Quantity`
Energy at which a PSF is requested.
theta : `~astropy.coordinates.Angle`
Offset angle at which a PSF is requested.
Returns
-------
psf : `~gammapy.utils.gauss.MultiGauss2D`
Multigauss PSF object.
"""
energy = u.Quantity(energy)
theta = u.Quantity(theta)
sigmas, norms = [], []
pars = {"A_1": 1}
for interp_sigma in self._interp_sigmas:
sigma = interp_sigma((theta, energy))
sigmas.append(sigma)
for name, interp_norm in zip(["scale", "A_2", "A_3"],
self._interp_norms):
pars[name] = interp_norm((theta, energy))
for idx, sigma in enumerate(sigmas):
a = pars[f"A_{idx + 1}"]
norm = pars["scale"] * 2 * a * sigma**2
norms.append(norm)
m = MultiGauss2D(sigmas, norms)
m.normalize()
return m
def test_integral_normalize():
m = MultiGauss2D(sigmas=[1, 2], norms=[3, 4])
assert_allclose(m.integral, 7)
m.normalize()
assert_allclose(m.integral, 1)
def test_dpdtheta2():
m = MultiGauss2D(sigmas=[1, 2], norms=[3, 4])
theta2_max = (7 * m.max_sigma)**2
integral = scipy.integrate.quad(m.dpdtheta2, 0, theta2_max)[0]
assert_almost_equal(integral, 7, decimal=5)