def test_excess_matching_significance_on_off_roundtrip(p):
if p["method"] == "direct":
pytest.skip()
s = significance_on_off(p["n_on"], p["n_off"], p["alpha"], p["method"])
excess = excess_matching_significance_on_off(p["n_off"], p["alpha"], s,
p["method"])
n_on = excess + background(p["n_off"], p["alpha"])
s2 = significance_on_off(n_on, p["n_off"], p["alpha"], p["method"])
assert_allclose(s, s2, atol=0.0001)
def test_excess_matching_significance_on_off():
# Negative significance should work
excess = excess_matching_significance_on_off(n_off=10,
alpha=0.1,
significance=-1)
assert_allclose(excess, -0.83198, atol=1e-3)
# Cases that can't be achieved with n_on >= 0 should return NaN
excess = excess_matching_significance_on_off(n_off=10,
alpha=0.1,
significance=-2)
assert np.isnan(excess)
# Arrays should work
excess = excess_matching_significance_on_off(n_off=[10, 20],
alpha=0.1,
significance=5)
assert_allclose(excess, [9.82966, 12.038423], atol=1e-3)
excess = excess_matching_significance_on_off(n_off=[10, 20],
alpha=0.1,
significance=5,
method="simple")
assert_allclose(excess, [26.05544, 27.03444], atol=1e-3)
excess = excess_matching_significance_on_off(n_off=10,
alpha=[0.1, 0.3],
significance=5)
assert_allclose(excess, [9.82966, 16.664516], atol=1e-3)
excess = excess_matching_significance_on_off(n_off=10,
alpha=0.1,
significance=[3, 5])
assert_allclose(excess, [4.818497, 9.82966], atol=1e-3)
excess = excess_matching_significance_on_off(n_off=[10, 20],
alpha=[0.1, 0.3],
significance=[3, 5])
assert_allclose(excess, [4.818497, 20.68810], atol=1e-3)
excess = excess_matching_significance_on_off(n_off=[[10, 20], [10, 20]],
alpha=0.1,
significance=5)
assert_allclose(excess, [[9.82966, 12.038423], [9.82966, 12.038423]],
atol=1e-3)
def estimate_min_excess(self, dataset):
"""Estimate minimum excess to reach the given significance.
Parameters
----------
dataset : `SpectrumDataset`
Spectrum dataset
Returns
-------
excess : `RegionNDMap`
Minimal excess
"""
n_off = dataset.counts_off.data
excess_counts = excess_matching_significance_on_off(
n_off=n_off, alpha=dataset.alpha.data, significance=self.sigma
)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
excess = dataset.background.copy()
excess.data = excess_counts
return excess
def run(self):
"""Run the computation."""
# TODO: let the user decide on energy binning
# then integrate bkg model and gamma over those energy bins.
energy = self.rmf.e_reco.center
bkg_counts = (self.bkg.quantity.to("1/s") * self.livetime).value
excess_counts = excess_matching_significance_on_off(
n_off=bkg_counts / self.alpha, alpha=self.alpha, significance=self.sigma
)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
model = PowerLawSpectralModel(
index=self.index, amplitude="1 cm-2 s-1 TeV-1", reference="1 TeV"
)
# TODO: simplify the following computation
predictor = SpectrumEvaluator(
model, aeff=self.arf, edisp=self.rmf, livetime=self.livetime
)
counts = predictor.compute_npred().data
phi_0 = excess_counts / counts
dnde_model = model(energy=energy)
diff_flux = (phi_0 * dnde_model * energy ** 2).to("erg / (cm2 s)")
# TODO: take self.bkg_sys into account
# and add a criterion 'bkg sys'
criterion = []
for idx in range(len(energy)):
if is_gamma_limited[idx]:
c = "gamma"
else:
c = "significance"
criterion.append(c)
table = Table(
[
Column(
data=energy,
name="energy",
format="5g",
description="Reconstructed Energy",
),
Column(
data=diff_flux,
name="e2dnde",
format="5g",
description="Energy squared times differential flux",
),
Column(
data=excess_counts,
name="excess",
format="5g",
description="Number of excess counts in the bin",
),
Column(
data=bkg_counts,
name="background",
format="5g",
description="Number of background counts in the bin",
),
Column(
data=criterion,
name="criterion",
description="Sensitivity-limiting criterion",
),
]
)
self._results_table = table
return table
def run(self):
"""Run the computation."""
# TODO: let the user decide on energy binning
# then integrate bkg model and gamma over those energy bins.
energy = self.irf.bkg.energy.log_center()
bkg_counts = (self.irf.bkg.data.data * self.livetime).value
excess_counts = excess_matching_significance_on_off(
n_off=bkg_counts / self.alpha,
alpha=self.alpha,
significance=self.sigma)
is_gamma_limited = excess_counts < self.gamma_min
excess_counts[is_gamma_limited] = self.gamma_min
model = PowerLaw(
index=self.slope,
amplitude=1 * u.Unit("cm-2 s-1 TeV-1"),
reference=1 * u.TeV,
)
# TODO: simplify the following computation
predictor = CountsPredictor(model,
aeff=self.irf.aeff,
edisp=self.irf.rmf,
livetime=self.livetime)
predictor.run()
counts = predictor.npred.data.data.value
phi_0 = excess_counts / counts * u.Unit("cm-2 s-1 TeV-1")
# TODO: should use model.__call__ here
dnde_model = model.evaluate(energy=energy,
index=self.slope,
amplitude=1,
reference=1 * u.TeV)
diff_flux = (phi_0 * dnde_model * energy**2).to("erg / (cm2 s)")
# TODO: take self.bkg_sys into account
# and add a criterion 'bkg sys'
criterion = []
for idx in range(len(energy)):
if is_gamma_limited[idx]:
c = "gamma"
else:
c = "significance"
criterion.append(c)
table = Table([
Column(
data=energy,
name="energy",
format="5g",
description="Reconstructed Energy",
),
Column(
data=diff_flux,
name="e2dnde",
format="5g",
description="Energy squared times differential flux",
),
Column(
data=excess_counts,
name="excess",
format="5g",
description="Number of excess counts in the bin",
),
Column(
data=bkg_counts,
name="background",
format="5g",
description="Number of background counts in the bin",
),
Column(
data=criterion,
name="criterion",
description="Sensitivity-limiting criterion",
),
])
self._results_table = table