def spectral_model(self):
"""Best fit spectral model (`~gammapy.modeling.models.SpectralModel`)."""
d = self.data
spec_type = self.data["SpectrumType"].strip()
pars, errs = {}, {}
pars["amplitude"] = d["Flux_Density"]
errs["amplitude"] = d["Unc_Flux_Density"]
pars["reference"] = d["Pivot_Energy"]
if spec_type == "PowerLaw":
pars["index"] = d["PowerLaw_Index"]
errs["index"] = d["Unc_PowerLaw_Index"]
model = PowerLawSpectralModel(**pars)
elif spec_type == "LogParabola":
pars["alpha"] = d["Spectral_Index"]
pars["beta"] = d["beta"]
errs["alpha"] = d["Unc_Spectral_Index"]
errs["beta"] = d["Unc_beta"]
model = LogParabolaSpectralModel(**pars)
else:
raise ValueError(f"Invalid spec_type: {spec_type!r}")
model.parameters.set_parameter_errors(errs)
return model
def define_model():
crab_spectrum = LogParabolaSpectralModel(amplitude=1e-11 / u.cm**2 / u.s /
u.TeV,
reference=1 * u.TeV,
alpha=2.3,
beta=0.2)
crab_model = SkyModel(spatial_model=None,
spectral_model=crab_spectrum,
name="crab")
return crab_model
def setup(self):
self.model = LogParabolaSpectralModel(
amplitude=3.76e-11 * u.Unit("cm-2 s-1 TeV-1"),
reference=1 * u.TeV,
alpha=2.44,
beta=0.25,
)
self.model.covariance = [
[1.31e-23, 0, -6.80e-14, 3.04e-13],
[0, 0, 0, 0],
[-6.80e-14, 0, 0.00899, 0.00904],
[3.04e-13, 0, 0.00904, 0.0284],
]
def spectral_model(self):
"""Best fit spectral model (`~gammapy.modeling.models.SpectralModel`)."""
spec_type = self.data["SpectrumType"].strip()
pars, errs = {}, {}
pars["amplitude"] = self.data["Flux_Density"]
errs["amplitude"] = self.data["Unc_Flux_Density"]
pars["reference"] = self.data["Pivot_Energy"]
if spec_type == "PowerLaw":
pars["index"] = self.data["Spectral_Index"]
errs["index"] = self.data["Unc_Spectral_Index"]
model = PowerLawSpectralModel(**pars)
elif spec_type == "PLExpCutoff":
pars["index"] = self.data["Spectral_Index"]
pars["ecut"] = self.data["Cutoff"]
errs["index"] = self.data["Unc_Spectral_Index"]
errs["ecut"] = self.data["Unc_Cutoff"]
model = ExpCutoffPowerLaw3FGLSpectralModel(**pars)
elif spec_type == "LogParabola":
pars["alpha"] = self.data["Spectral_Index"]
pars["beta"] = self.data["beta"]
errs["alpha"] = self.data["Unc_Spectral_Index"]
errs["beta"] = self.data["Unc_beta"]
model = LogParabolaSpectralModel(**pars)
elif spec_type == "PLSuperExpCutoff":
# TODO: why convert to GeV here? Remove?
pars["reference"] = pars["reference"].to("GeV")
pars["index_1"] = self.data["Spectral_Index"]
pars["index_2"] = self.data["Exp_Index"]
pars["ecut"] = self.data["Cutoff"].to("GeV")
errs["index_1"] = self.data["Unc_Spectral_Index"]
errs["index_2"] = self.data["Unc_Exp_Index"]
errs["ecut"] = self.data["Unc_Cutoff"].to("GeV")
model = SuperExpCutoffPowerLaw3FGLSpectralModel(**pars)
else:
raise ValueError(f"Invalid spec_type: {spec_type!r}")
model.parameters.set_parameter_errors(errs)
return model
def spectral_model(self):
"""Best fit spectral model (`~gammapy.modeling.models.SpectralModel`)."""
spec_type = self.data["SpectrumType"].strip()
pars, errs = {}, {}
pars["reference"] = self.data["Pivot_Energy"]
if spec_type == "PowerLaw":
pars["amplitude"] = self.data["PL_Flux_Density"]
pars["index"] = self.data["PL_Index"]
errs["amplitude"] = self.data["Unc_PL_Flux_Density"]
errs["index"] = self.data["Unc_PL_Index"]
model = PowerLawSpectralModel(**pars)
elif spec_type == "LogParabola":
pars["amplitude"] = self.data["LP_Flux_Density"]
pars["alpha"] = self.data["LP_Index"]
pars["beta"] = self.data["LP_beta"]
errs["amplitude"] = self.data["Unc_LP_Flux_Density"]
errs["alpha"] = self.data["Unc_LP_Index"]
errs["beta"] = self.data["Unc_LP_beta"]
model = LogParabolaSpectralModel(**pars)
elif spec_type == "PLSuperExpCutoff":
pars["amplitude"] = self.data["PLEC_Flux_Density"]
pars["index_1"] = self.data["PLEC_Index"]
pars["index_2"] = self.data["PLEC_Exp_Index"]
pars["expfactor"] = self.data["PLEC_Expfactor"]
errs["amplitude"] = self.data["Unc_PLEC_Flux_Density"]
errs["index_1"] = self.data["Unc_PLEC_Index"]
errs["index_2"] = np.nan_to_num(self.data["Unc_PLEC_Exp_Index"])
errs["expfactor"] = self.data["Unc_PLEC_Expfactor"]
model = SuperExpCutoffPowerLaw4FGLSpectralModel(**pars)
else:
raise ValueError(f"Invalid spec_type: {spec_type!r}")
model.parameters.set_parameter_errors(errs)
return model
model=SuperExpCutoffPowerLaw4FGLSpectralModel(
index_1=1.5,
index_2=2,
amplitude=1 / u.cm ** 2 / u.s / u.TeV,
reference=1 * u.TeV,
expfactor=1e-2,
),
val_at_2TeV=u.Quantity(0.3431043087721737, "cm-2 s-1 TeV-1"),
integral_1_10TeV=u.Quantity(1.2125247, "cm-2 s-1"),
eflux_1_10TeV=u.Quantity(3.38072082, "TeV cm-2 s-1"),
),
dict(
name="logpar",
model=LogParabolaSpectralModel(
alpha=2.3 * u.Unit(""),
amplitude=4 / u.cm ** 2 / u.s / u.TeV,
reference=1 * u.TeV,
beta=0.5 * u.Unit(""),
),
val_at_2TeV=u.Quantity(0.6387956571420305, "cm-2 s-1 TeV-1"),
integral_1_10TeV=u.Quantity(2.255689748270628, "cm-2 s-1"),
eflux_1_10TeV=u.Quantity(3.9586515834989267, "TeV cm-2 s-1"),
e_peak=0.74082 * u.TeV,
),
dict(
name="norm-logpar",
model=LogParabolaNormSpectralModel(
alpha=2.3 * u.Unit(""),
norm=4 * u.Unit(""),
reference=1 * u.TeV,
beta=0.5 * u.Unit(""),
),
def logpar_reference_model():
logpar = LogParabolaSpectralModel(amplitude="2e-12 cm-2s-1TeV-1",
alpha=1.5,
beta=0.5)
return SkyModel(spatial_model=PointSpatialModel(), spectral_model=logpar)
from astropy import units as u
import matplotlib.pyplot as plt
from gammapy.modeling.models import (
CompoundSpectralModel,
LogParabolaSpectralModel,
Models,
PowerLawSpectralModel,
SkyModel,
)
energy_range = [0.1, 100] * u.TeV
pwl = PowerLawSpectralModel(
index=2.0, amplitude="1e-12 cm-2 s-1 TeV-1", reference="1 TeV"
)
lp = LogParabolaSpectralModel(
amplitude="1e-12 cm-2 s-1 TeV-1", reference="10 TeV", alpha=2.0, beta=1.0
)
model = CompoundSpectralModel(pwl, lp, operator.add)
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="compound-model")
models = Models([model])
print(models.to_yaml())
"""
# %%
# 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 LogParabolaSpectralModel, Models, SkyModel
energy_range = [0.1, 100] * u.TeV
model = LogParabolaSpectralModel(
alpha=2.3,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference=1 * u.TeV,
beta=0.5,
)
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="log-parabola-model")
models = Models([model])
print(models.to_yaml())
ecpl.plot(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)
# assign covariance for plotting
ecpl.parameters.covariance = result_ecpl.parameters.covariance
ecpl.plot_error(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)
ax.set_ylim(1e-13, 1e-11)
# ## Log-Parabola Fit
#
# Finally we try to fit a `~gammapy.modeling.models.LogParabolaSpectralModel` model:
# In[ ]:
log_parabola = LogParabolaSpectralModel(alpha=2,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference="1 TeV",
beta=0.1)
model = SkyModel(spectral_model=log_parabola)
# In[ ]:
dataset_log_parabola = FluxPointsDataset(model, flux_points)
fitter = Fit([dataset_log_parabola])
result_log_parabola = fitter.run()
print(log_parabola)
# In[ ]:
ax = flux_points.plot(energy_power=2)
log_parabola.plot(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)
import logging
import numpy as np
from astropy.table import Table
from gammapy.estimators import FluxPoints
from astropy import units as u
from gammapy.modeling.models import LogParabolaSpectralModel
# ### HAWC flux points for Crab Nebula
# The HAWC flux point are taken from https://arxiv.org/pdf/1905.12518.pdf
# assigned to a `FluxPoints` object, then written to FITS.
crab_model = LogParabolaSpectralModel(amplitude="2.31e-13 TeV-1 cm-2 s-1",
alpha=2.73,
beta=0.06,
reference="7 TeV")
e_min = np.array([1, 1.78, 3.16, 5.62, 10.0, 17.8, 31.6, 56.2, 100, 177
]) * u.TeV
e_max = np.array([1.78, 3.16, 5.62, 10.0, 17.8, 31.6, 56.2, 100, 177, 316
]) * u.TeV
e_ref = np.array([1.04, 1.83, 3.24, 5.84, 10.66, 19.6, 31.6, 66.8, 118, 204
]) * u.TeV
ts = np.array([2734, 4112, 4678, 3683, 2259, 1237, 572, 105, 28.8, 0.14])
is_ul = np.array(
[False, False, False, False, False, False, False, False, False, True])
e2dnde = np.array([
3.63e-11, 2.67e-11, 1.92e-11, 1.24e-11, 8.15e-12, 5.23e-12, 3.26e-12,
1.23e-12, 8.37e-13, np.nan
]) * u.Unit("cm-2 s-1 TeV")
