def spectral_model(self):
"""Best fit spectral model `~gammapy.modeling.models.SpectralModel`."""
pars, errs = {}, {}
pars["amplitude"] = self.data["Flux"]
pars["emin"], pars["emax"] = self.energy_range
pars["index"] = self.data["Spectral_Index"]
errs["amplitude"] = self.data["Unc_Flux"]
errs["index"] = self.data["Unc_Spectral_Index"]
model = PowerLaw2SpectralModel(**pars)
model.parameters.set_parameter_errors(errs)
return model
def get_test_cases():
e_true = Quantity(np.logspace(-1, 2, 120), "TeV")
e_reco = Quantity(np.logspace(-1, 2, 100), "TeV")
return [
dict(model=PowerLawSpectralModel(amplitude="1e2 TeV-1"),
e_true=e_true,
npred=999),
dict(
model=PowerLaw2SpectralModel(amplitude="1",
emin="0.1 TeV",
emax="100 TeV"),
e_true=e_true,
npred=1,
),
dict(
model=PowerLawSpectralModel(amplitude="1e-11 TeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
livetime="10 h",
npred=1448.05960,
),
dict(
model=PowerLawSpectralModel(reference="1 GeV",
amplitude="1e-11 GeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
livetime="30 h",
npred=4.34417881,
),
dict(
model=PowerLawSpectralModel(amplitude="1e-11 TeV-1 cm-2 s-1"),
aeff=EffectiveAreaTable.from_parametrization(e_true),
edisp=EnergyDispersion.from_gauss(e_reco=e_reco,
e_true=e_true,
bias=0,
sigma=0.2),
livetime="10 h",
npred=1437.450076,
),
dict(
model=TemplateSpectralModel(
energy=[0.1, 0.2, 0.3, 0.4] * u.TeV,
values=[4.0, 3.0, 1.0, 0.1] * u.Unit("TeV-1"),
),
e_true=[0.1, 0.2, 0.3, 0.4] * u.TeV,
npred=0.554513062,
),
]
def sky_model(self, sigma=0.3, A0=1e-12):
spatial_model = GaussianSpatialModel(frame="galactic")
spatial_model.lon_0.value = self.skydir.galactic.l.value
spatial_model.lat_0.value = self.skydir.galactic.b.value
spatial_model.sigma.value = sigma
spectral_model = PowerLaw2SpectralModel()
amplitude = A0 * sigma * sigma
spectral_model.amplitude.value = amplitude
spectral_model.index.value = 2.3
spectral_model.emin.quantity = 1.0 * u.TeV
spectral_model.emax.quantity = 10.0 * u.TeV
model_simu = SkyModel(
spatial_model=spatial_model,
spectral_model=spectral_model,
name="model-simu",
)
return model_simu
dict(
name="norm-powerlaw",
model=PowerLawNormSpectralModel(
tilt=2 * u.Unit(""),
norm=4.0 * u.Unit(""),
reference=1 * u.TeV,
),
val_at_2TeV=u.Quantity(1.0, ""),
integral_1_10TeV=u.Quantity(3.6, "TeV"),
eflux_1_10TeV=u.Quantity(9.210340371976184, "TeV2"),
),
dict(
name="powerlaw2",
model=PowerLaw2SpectralModel(
amplitude=u.Quantity(2.9227116204223784, "cm-2 s-1"),
index=2.3 * u.Unit(""),
emin=1 * u.TeV,
emax=10 * u.TeV,
),
val_at_2TeV=u.Quantity(4 * 2.0 ** (-2.3), "cm-2 s-1 TeV-1"),
integral_1_10TeV=u.Quantity(2.9227116204223784, "cm-2 s-1"),
eflux_1_10TeV=u.Quantity(6.650836884969039, "TeV cm-2 s-1"),
),
dict(
name="ecpl",
model=ExpCutoffPowerLawSpectralModel(
index=1.6 * u.Unit(""),
amplitude=4 / u.cm ** 2 / u.s / u.TeV,
reference=1 * u.TeV,
lambda_=0.1 / u.TeV,
),
val_at_2TeV=u.Quantity(1.080321705479446, "cm-2 s-1 TeV-1"),
See also: https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/source_models.html
"""
# %%
# Example plot
# ------------
# Here is an example plot of the model:
from astropy import units as u
import matplotlib.pyplot as plt
from gammapy.modeling.models import Models, PowerLaw2SpectralModel, SkyModel
energy_range = [0.1, 100] * u.TeV
model = PowerLaw2SpectralModel(
amplitude=u.Quantity(1e-12, "cm-2 s-1"),
index=2.3,
emin=1 * u.TeV,
emax=10 * u.TeV,
)
model.plot(energy_range)
plt.grid(which="both")
# %%
# YAML representation
# -------------------
# Here is an example YAML file using the model:
model = SkyModel(spectral_model=model, name="power-law2-model")
models = Models([model])
print(models.to_yaml())
# Note that even when doing a 2D analysis, it is better to use fine energy bins in the beginning and then sum them over. This is to ensure that the background shape can be approximated by a power law function in each energy bin. The `run_images()` can be used to compute maps in fine bins and then squash them to have one bin. This can be done by specifying `keep_dims = True`. This will compute a summed counts and background maps, and a spectral weighted exposure map.
# In[ ]:
stacked = MapDataset.create(geom)
# In[ ]:
get_ipython().run_cell_magic(
'time', '',
'maker = MapDatasetMaker(selection=["counts", "exposure", "background"])\nmaker_safe_mask = SafeMaskMaker(methods=["offset-max"], offset_max=4.0 * u.deg)\n\ndatasets = []\n\nfor obs in observations:\n cutout = stacked.cutout(obs.pointing_radec, width="8 deg")\n dataset = maker.run(cutout, obs)\n dataset = maker_safe_mask.run(dataset, obs)\n datasets.append(dataset)\n stacked.stack(dataset)'
)
# In[ ]:
spectrum = PowerLaw2SpectralModel(index=2)
dataset_2d = stacked.to_image(spectrum=spectrum)
maps2D = {
"counts": dataset_2d.counts,
"exposure": dataset_2d.exposure,
"background": dataset_2d.background_model.map,
}
# For a typical 2D analysis, using an energy dispersion usually does not make sense. A PSF map can be made as in the regular 3D case, taking care to weight it properly with the spectrum.
# In[ ]:
# mean PSF
geom2d = maps2D["exposure"].geom
src_pos = SkyCoord(0, 0, unit="deg", frame="galactic")