class TestSpectrumDataset:
"""Test fit on counts spectra without any IRFs"""
def setup(self):
self.nbins = 30
binning = np.logspace(-1, 1, self.nbins + 1) * u.TeV
self.source_model = SkyModel(spectral_model=PowerLawSpectralModel(
index=2.1,
amplitude=1e5 * u.Unit("cm-2 s-1 TeV-1"),
reference=0.1 * u.TeV,
))
self.livetime = 100 * u.s
aeff = EffectiveAreaTable.from_constant(binning, "1 cm2")
bkg_rate = np.ones(self.nbins) / u.s
bkg_expected = (bkg_rate * self.livetime).to_value("")
self.bkg = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=bkg_expected)
random_state = get_random_state(23)
flux = self.source_model.spectral_model.integral(
binning[:-1], binning[1:])
self.npred = (flux * aeff.data.data[0] * self.livetime).to_value("")
self.npred += bkg_expected
source_counts = random_state.poisson(self.npred)
self.src = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=source_counts)
self.dataset = SpectrumDataset(
models=self.source_model,
counts=self.src,
aeff=aeff,
livetime=self.livetime,
background=self.bkg,
name="test",
)
def test_data_shape(self):
assert self.dataset.data_shape[0] == self.nbins
def test_energy_range(self):
energy_range = self.dataset.energy_range
assert energy_range.unit == u.TeV
assert_allclose(energy_range.to_value("TeV"), [0.1, 10.0])
def test_cash(self):
"""Simple CASH fit to the on vector"""
fit = Fit([self.dataset])
result = fit.run()
# assert result.success
assert "minuit" in repr(result)
npred = self.dataset.npred().data.sum()
assert_allclose(npred, self.npred.sum(), rtol=1e-3)
assert_allclose(result.total_stat, -18087404.624, rtol=1e-3)
pars = result.parameters
assert_allclose(pars["index"].value, 2.1, rtol=1e-2)
assert_allclose(pars.error("index"), 0.00127, rtol=1e-2)
assert_allclose(pars["amplitude"].value, 1e5, rtol=1e-3)
assert_allclose(pars.error("amplitude"), 153.450, rtol=1e-2)
def test_fake(self):
"""Test the fake dataset"""
real_dataset = self.dataset.copy()
self.dataset.fake(314)
assert real_dataset.counts.data.shape == self.dataset.counts.data.shape
assert real_dataset.background.data.sum(
) == self.dataset.background.data.sum()
assert int(real_dataset.counts.data.sum()) == 907010
assert self.dataset.counts.data.sum() == 907331
def test_incorrect_mask(self):
mask_fit = np.ones(self.nbins, dtype=np.dtype("float"))
with pytest.raises(ValueError):
SpectrumDataset(
models=self.source_model,
counts=self.src,
livetime=self.livetime,
mask_fit=mask_fit,
background=self.bkg,
)
def test_set_model(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EDispKernel.from_diagonal_response(self.src.energy.edges,
self.src.energy.edges)
dataset = SpectrumDataset(None, self.src, self.livetime, None, aeff,
edisp, self.bkg)
spectral_model = PowerLawSpectralModel()
model = SkyModel(spectral_model=spectral_model, name="test")
dataset.models = model
assert dataset.models["test"] is model
models = Models([model])
dataset.models = models
assert dataset.models["test"] is model
def test_npred_models(self):
e_reco = MapAxis.from_energy_bounds("1 TeV", "10 TeV", nbin=3).edges
dataset = SpectrumDataset.create(e_reco=e_reco)
dataset.livetime = 1 * u.h
dataset.aeff.data.data += 1e10 * u.Unit("cm2")
pwl_1 = PowerLawSpectralModel(index=2)
pwl_2 = PowerLawSpectralModel(index=2)
model_1 = SkyModel(spectral_model=pwl_1)
model_2 = SkyModel(spectral_model=pwl_2)
dataset.models = Models([model_1, model_2])
npred = dataset.npred()
assert_allclose(npred.data.sum(), 64.8)
def test_str(self):
assert "SpectrumDataset" in str(self.dataset)
def test_spectrumdataset_create(self):
e_reco = u.Quantity([0.1, 1, 10.0], "TeV")
e_true = u.Quantity([0.05, 0.5, 5, 20.0], "TeV")
empty_dataset = SpectrumDataset.create(e_reco, e_true, name="test")
assert empty_dataset.name == "test"
assert empty_dataset.counts.total_counts == 0
assert empty_dataset.data_shape[0] == 2
assert empty_dataset.background.total_counts == 0
assert empty_dataset.background.energy.nbin == 2
assert empty_dataset.aeff.data.axis("energy").nbin == 3
assert empty_dataset.edisp.data.axis("e_reco").nbin == 2
assert empty_dataset.livetime.value == 0
assert len(empty_dataset.gti.table) == 0
assert empty_dataset.energy_range[0] is None
assert_allclose(empty_dataset.mask_safe, 0)
def test_spectrum_dataset_stack_diagonal_safe_mask(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EDispKernel.from_diagonal_response(self.src.energy.edges,
self.src.energy.edges)
livetime = self.livetime
dataset1 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp,
background=self.bkg.copy(),
)
livetime2 = 0.5 * livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:],
2 * aeff.data.data)
bkg2 = CountsSpectrum(
self.src.energy.edges[:-1],
self.src.energy.edges[1:],
data=2 * self.bkg.data,
)
safe_mask2 = np.ones_like(self.src.data, bool)
safe_mask2[0] = False
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp,
background=bkg2,
mask_safe=safe_mask2,
)
dataset1.stack(dataset2)
assert_allclose(dataset1.counts.data[1:], self.src.data[1:] * 2)
assert_allclose(dataset1.counts.data[0], self.src.data[0])
assert dataset1.livetime == 1.5 * self.livetime
assert_allclose(dataset1.background.data[1:], 3 * self.bkg.data[1:])
assert_allclose(dataset1.background.data[0], self.bkg.data[0])
assert_allclose(
dataset1.aeff.data.data.to_value("m2"),
4.0 / 3 * aeff.data.data.to_value("m2"),
)
assert_allclose(dataset1.edisp.pdf_matrix[1:], edisp.pdf_matrix[1:])
assert_allclose(dataset1.edisp.pdf_matrix[0],
0.5 * edisp.pdf_matrix[0])
def test_spectrum_dataset_stack_nondiagonal_no_bkg(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp1 = EDispKernel.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.1, 0.0)
livetime = self.livetime
dataset1 = SpectrumDataset(counts=None,
livetime=livetime,
aeff=aeff,
edisp=edisp1,
background=None)
livetime2 = livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:], aeff.data.data)
edisp2 = EDispKernel.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.2, 0.0)
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp2,
background=None,
)
dataset1.stack(dataset2)
assert dataset1.counts is None
assert dataset1.background is None
assert dataset1.livetime == 2 * self.livetime
assert_allclose(dataset1.aeff.data.data.to_value("m2"),
aeff.data.data.to_value("m2"))
assert_allclose(dataset1.edisp.get_bias(1 * u.TeV), 0.0, atol=1.2e-3)
assert_allclose(dataset1.edisp.get_resolution(1 * u.TeV),
0.1581,
atol=1e-2)
def test_info_dict(self):
info_dict = self.dataset.info_dict()
assert_allclose(info_dict["n_on"], 907010)
assert_allclose(info_dict["background"], 3000.0)
assert_allclose(info_dict["significance"], 2924.522174)
assert_allclose(info_dict["excess"], 904010)
assert_allclose(info_dict["livetime"].value, 1e2)
assert info_dict["name"] == "test"
@requires_dependency("matplotlib")
def test_peek(self):
with mpl_plot_check():
self.dataset.peek()
self.dataset.edisp = None
with mpl_plot_check():
self.dataset.peek()
@requires_dependency("matplotlib")
def test_plot_fit(self):
with mpl_plot_check():
self.dataset.plot_fit()
class TestSpectrumDataset:
"""Test fit on counts spectra without any IRFs"""
def setup(self):
self.nbins = 30
binning = np.logspace(-1, 1, self.nbins + 1) * u.TeV
self.source_model = PowerLawSpectralModel(index=2.1,
amplitude=1e5 / u.TeV / u.s,
reference=0.1 * u.TeV)
self.livetime = 100 * u.s
bkg_rate = np.ones(self.nbins) / u.s
bkg_expected = bkg_rate * self.livetime
self.bkg = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=bkg_expected)
random_state = get_random_state(23)
self.npred = (self.source_model.integral(binning[:-1], binning[1:]) *
self.livetime)
self.npred += bkg_expected
source_counts = random_state.poisson(self.npred)
self.src = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=source_counts)
self.dataset = SpectrumDataset(
model=self.source_model,
counts=self.src,
livetime=self.livetime,
background=self.bkg,
)
def test_data_shape(self):
assert self.dataset.data_shape[0] == self.nbins
def test_energy_range(self):
energy_range = self.dataset.energy_range
assert energy_range.unit == u.TeV
assert_allclose(energy_range.to_value("TeV"), [0.1, 10.0])
def test_cash(self):
"""Simple CASH fit to the on vector"""
fit = Fit(self.dataset)
result = fit.run()
assert result.success
assert "minuit" in repr(result)
npred = self.dataset.npred().data.sum()
assert_allclose(npred, self.npred.sum(), rtol=1e-3)
assert_allclose(result.total_stat, -18087404.624, rtol=1e-3)
pars = result.parameters
assert_allclose(pars["index"].value, 2.1, rtol=1e-2)
assert_allclose(pars.error("index"), 0.00127, rtol=1e-2)
assert_allclose(pars["amplitude"].value, 1e5, rtol=1e-3)
assert_allclose(pars.error("amplitude"), 153.450, rtol=1e-2)
def test_fake(self):
"""Test the fake dataset"""
real_dataset = self.dataset.copy()
self.dataset.fake(314)
assert real_dataset.counts.data.shape == self.dataset.counts.data.shape
assert real_dataset.background.data.sum(
) == self.dataset.background.data.sum()
assert int(real_dataset.counts.data.sum()) == 907010
assert self.dataset.counts.data.sum() == 907331
def test_incorrect_mask(self):
mask_fit = np.ones(self.nbins, dtype=np.dtype("float"))
with pytest.raises(ValueError):
SpectrumDataset(
model=self.source_model,
counts=self.src,
livetime=self.livetime,
mask_fit=mask_fit,
background=self.bkg,
)
def test_set_model(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EnergyDispersion.from_diagonal_response(
self.src.energy.edges, self.src.energy.edges)
dataset = SpectrumDataset(None, self.src, self.livetime, None, aeff,
edisp, self.bkg)
with pytest.raises(AttributeError):
dataset.parameters
dataset.model = self.source_model
assert dataset.parameters[0] == self.source_model.parameters[0]
def test_str(self):
assert "SpectrumDataset" in str(self.dataset)
def test_spectrumdataset_create(self):
e_reco = u.Quantity([0.1, 1, 10.0], "TeV")
e_true = u.Quantity([0.05, 0.5, 5, 20.0], "TeV")
empty_dataset = SpectrumDataset.create(e_reco, e_true)
assert empty_dataset.counts.total_counts == 0
assert empty_dataset.data_shape[0] == 2
assert empty_dataset.background.total_counts == 0
assert empty_dataset.background.energy.nbin == 2
assert empty_dataset.aeff.data.axis("energy").nbin == 3
assert empty_dataset.edisp.data.axis("e_reco").nbin == 2
assert empty_dataset.livetime.value == 0
assert len(empty_dataset.gti.table) == 0
assert empty_dataset.energy_range[0] is None
assert_allclose(empty_dataset.mask_safe, 0)
def test_spectrum_dataset_stack_diagonal_safe_mask(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EnergyDispersion.from_diagonal_response(
self.src.energy.edges, self.src.energy.edges)
livetime = self.livetime
dataset1 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime,
aeff=aeff,
edisp=edisp,
background=self.bkg.copy(),
)
livetime2 = 0.5 * livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:],
2 * aeff.data.data)
bkg2 = CountsSpectrum(
self.src.energy.edges[:-1],
self.src.energy.edges[1:],
data=2 * self.bkg.data,
)
safe_mask2 = np.ones_like(self.src.data, bool)
safe_mask2[0] = False
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp,
background=bkg2,
mask_safe=safe_mask2,
)
dataset1.stack(dataset2)
assert_allclose(dataset1.counts.data[1:], self.src.data[1:] * 2)
assert_allclose(dataset1.counts.data[0], self.src.data[0])
assert dataset1.livetime == 1.5 * self.livetime
assert_allclose(dataset1.background.data[1:], 3 * self.bkg.data[1:])
assert_allclose(dataset1.background.data[0], self.bkg.data[0])
assert_allclose(
dataset1.aeff.data.data.to_value("m2"),
4.0 / 3 * aeff.data.data.to_value("m2"),
)
assert_allclose(dataset1.edisp.pdf_matrix[1:], edisp.pdf_matrix[1:])
assert_allclose(dataset1.edisp.pdf_matrix[0],
0.5 * edisp.pdf_matrix[0])
def test_spectrum_dataset_stack_nondiagonal_no_bkg(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp1 = EnergyDispersion.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.1, 0.0)
livetime = self.livetime
dataset1 = SpectrumDataset(counts=None,
livetime=livetime,
aeff=aeff,
edisp=edisp1,
background=None)
livetime2 = livetime
aeff2 = EffectiveAreaTable(self.src.energy.edges[:-1],
self.src.energy.edges[1:], aeff.data.data)
edisp2 = EnergyDispersion.from_gauss(self.src.energy.edges,
self.src.energy.edges, 0.2, 0.0)
dataset2 = SpectrumDataset(
counts=self.src.copy(),
livetime=livetime2,
aeff=aeff2,
edisp=edisp2,
background=None,
)
dataset1.stack(dataset2)
assert dataset1.counts is None
assert dataset1.background is None
assert dataset1.livetime == 2 * self.livetime
assert_allclose(dataset1.aeff.data.data.to_value("m2"),
aeff.data.data.to_value("m2"))
assert_allclose(dataset1.edisp.get_bias(1 * u.TeV), 0.0, atol=1e-3)
assert_allclose(dataset1.edisp.get_resolution(1 * u.TeV),
0.1581,
atol=1e-2)
edisp = cta_irf["edisp"].to_energy_dispersion(offset=offset,
e_true=energy,
e_reco=energy)
edisp.plot_matrix()
print(edisp.data)
# In[ ]:
dataset = SpectrumDataset(aeff=aeff,
edisp=edisp,
model=model_ref,
livetime=livetime,
obs_id=0)
dataset.fake(random_state=42)
# In[ ]:
# Take a quick look at the simulated counts
dataset.counts.plot()
# ## Include Background
#
# In this section we will include a background component. Furthermore, we will also simulate more than one observation and fit each one individually in order to get average fit results.
# In[ ]:
# We assume a PowerLaw shape of the background as well
bkg_model = PowerLaw(index=2.5,
amplitude=1e-11 * u.Unit("cm-2 s-1 TeV-1"),
class TestSpectrumDataset:
"""Test fit on counts spectra without any IRFs"""
def setup(self):
self.nbins = 30
binning = np.logspace(-1, 1, self.nbins + 1) * u.TeV
self.source_model = PowerLaw(index=2.1,
amplitude=1e5 / u.TeV / u.s,
reference=0.1 * u.TeV)
self.livetime = 100 * u.s
bkg_rate = np.ones(self.nbins) / u.s
bkg_expected = bkg_rate * self.livetime
self.bkg = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=bkg_expected)
random_state = get_random_state(23)
self.npred = (self.source_model.integral(binning[:-1], binning[1:]) *
self.livetime)
self.npred += bkg_expected
source_counts = random_state.poisson(self.npred)
self.src = CountsSpectrum(energy_lo=binning[:-1],
energy_hi=binning[1:],
data=source_counts)
self.dataset = SpectrumDataset(
model=self.source_model,
counts=self.src,
livetime=self.livetime,
background=self.bkg,
)
def test_data_shape(self):
assert self.dataset.data_shape[0] == self.nbins
def test_energy_range(self):
energy_range = self.dataset.energy_range
assert energy_range.unit == u.TeV
assert_allclose(energy_range.to_value("TeV"), [0.1, 10.0])
def test_cash(self):
"""Simple CASH fit to the on vector"""
fit = Fit(self.dataset)
result = fit.run()
assert result.success
assert "minuit" in repr(result)
npred = self.dataset.npred().data.sum()
assert_allclose(npred, self.npred.sum(), rtol=1e-3)
assert_allclose(result.total_stat, -18087404.624, rtol=1e-3)
pars = result.parameters
assert_allclose(pars["index"].value, 2.1, rtol=1e-2)
assert_allclose(pars.error("index"), 0.00127, rtol=1e-2)
assert_allclose(pars["amplitude"].value, 1e5, rtol=1e-3)
assert_allclose(pars.error("amplitude"), 153.450, rtol=1e-2)
def test_fake(self):
"""Test the fake dataset"""
real_dataset = self.dataset.copy()
self.dataset.fake(314)
assert real_dataset.counts.data.shape == self.dataset.counts.data.shape
assert real_dataset.background.data.sum(
) == self.dataset.background.data.sum()
assert int(real_dataset.counts.data.sum()) == 907010
assert self.dataset.counts.data.sum() == 907331
def test_incorrect_mask(self):
mask_fit = np.ones(self.nbins, dtype=np.dtype("float"))
with pytest.raises(ValueError):
SpectrumDataset(
model=self.source_model,
counts=self.src,
livetime=self.livetime,
mask_fit=mask_fit,
background=self.bkg,
)
def test_set_model(self):
aeff = EffectiveAreaTable.from_parametrization(self.src.energy.edges,
"HESS")
edisp = EnergyDispersion.from_diagonal_response(
self.src.energy.edges, self.src.energy.edges)
dataset = SpectrumDataset(None, self.src, self.livetime, None, aeff,
edisp, self.bkg)
with pytest.raises(AttributeError):
dataset.parameters
dataset.model = self.source_model
assert dataset.parameters[0] == self.source_model.parameters[0]
def test_str(self):
assert "SpectrumDataset" in str(self.dataset)