def perform_casc_fit(config,
geom,
ps_model,
llh,
dataset,
on_radius=Angle("0.07 deg"),
B=1e-16,
plot=False):
"""
Perform the combined cascade fit
Parameters
----------
config: dict
Configuration dictionary
B: float
B-field strength
geom:`~gammapy.maps.WcsGeom` object
geometry of the dataset
on_radius: `~astropy.coordinates.Angle` object
Radius of ON region of IACT analysis
ps_model: `gammapy.model.modeling.models` object
Assumed point source model
llh: `simCRpropa.fermiinterp.LogLikeCubeFermi`
Interpolated Fermi likelihood cube
dataset: `~gammapy.datasets.SpectrumOnOffDataset`
The IACT data set
plot: bool
If true, generate diagnostic plots
Returns
-------
Tuple containing -2 * ln (likelihood values) for fit
on Fermi-LAT data only and combined fit
"""
logging.info(f" ------ B = {B:.2e} ------- ")
# Load the cascade
# generate a casc map with low
# spatial resolution to speed up calculations
ebl = EBLAbsorptionNormSpectralModel.read(
filename=config['global']['gammapy_ebl_file'],
redshift=config[src]['z_src'])
casc_file = config['global']['casc_file'].replace(
"*", "{0:.3f}".format(config[src]['z_casc']), 1)
casc_file = casc_file.replace("*", "{0:.2e}".format(B))
casc_1d = CascMap.gen_from_hd5f(
casc_file,
skycoord=geom.center_skydir,
width=2 * np.round(on_radius.value / geom.pixel_scales[0].value, 0) *
geom.pixel_scales[0].value,
binsz=geom.pixel_scales[0].value,
ebins=21,
id_detection=22,
smooth_kwargs={
'kernel': Gaussian2DKernel,
'threshold': 2.,
'steps': 50
})
# Initialize the cascade model
# use the best fit model for the intrinsic spectrum
logging.info("Initializing cascade model ...")
casc_spec = CascadeSpectralModel(casc_1d,
ps_model.spectral_model.model1.copy(),
ebl,
on_region,
rotation=config['global']['rotation'] *
u.deg,
tmax=config['global']['tmax'] * u.yr,
bias=0. * u.dimensionless_unscaled,
energy_unit_spectral_model="TeV",
use_gammapy_interp=False)
# Plot the total model
if plot:
energy_power = 2
fig = plt.figure(dpi=150)
ax = fig.add_subplot(111)
e_range = [1e-3, 10.] * u.TeV
casc_spec.add_primary = True
casc_spec.plot(ax=ax, energy_range=e_range, energy_power=energy_power)
ps_model.spectral_model.plot(ax=ax,
energy_range=e_range,
energy_power=energy_power)
casc_spec.add_primary = False
casc_spec.plot(ax=ax, energy_range=e_range, energy_power=energy_power)
casc_spec.add_primary = True
plt.ylim(1e-15, 3e-12)
ax.grid()
fig.savefig(f"plots/{src:s}_B{B}_casc+ps_models.png")
plt.close("all")
# Perform the fit with the cascade
casc_model = SkyModel(spectral_model=casc_spec, name='casc')
# limit the parameter ranges and change the tolerance
# index
casc_model.parameters['index'].min = llh.params['Index'].min()
casc_model.parameters['index'].max = llh.params['Index'].max()
# amplitude
casc_model.parameters[
'amplitude'].min = casc_model.parameters['amplitude'].value / 10.
casc_model.parameters[
'amplitude'].max = casc_model.parameters['amplitude'].value * 10.
# cutoff
casc_model.parameters['lambda_'].min = 1. / llh.params['Cutoff'].max()
casc_model.parameters['lambda_'].max = 1. / llh.params['Cutoff'].min()
casc_model.parameters['lambda_'].frozen = config['global']['fix_cutoff']
# bias between Fermi and HESS
casc_model.parameters['bias'].value = 0.
casc_model.parameters['bias'].frozen = config['global']['fix_bias']
logging.info(f"Initial parameters:\n{casc_model.parameters.to_table()}")
# interpolate the fermi likelihood for the right B field
# TODO: changes necessary if more than one coherence length or theta jet used
idb = np.where(llh.params["B"] == B)[0][0]
llh.interp_llh(
llh.params["B"][idb], # choose a B field - should match casc file
llh.params["maxTurbScale"]
[0], # choose a turb scale - should match casc file
llh.params["th_jet"]
[0], # choose a jet opening angle - should match casc file
method='linear',
)
# plot the interpolation
if plot:
fig = plt.figure(dpi=150)
ax = fig.add_subplot(111)
# plot a likelihood surface
# choose a slice in cut off energy
cut_id = 0
# build a grid of indices and norms
ii, nn = np.meshgrid(llh._params["Index"],
llh.log_norm_array,
indexing='ij')
# plot the log likehood grid
dlogl = 2. * (llh._llh_grid[cut_id] - llh._llh_grid[cut_id].max())
vmin = -100.
# check if most points have higher dlogl,
# and if so, adjust color scaling
if dlogl[dlogl > vmin].size < 10:
vmin = 3. * dlogl[dlogl < 0].max()
im = ax.pcolormesh(ii, nn, dlogl, cmap=cmap_name, vmin=vmin, vmax=0)
ax.annotate("$E_\mathrm{{cut}} = {0:.0f}$TeV".format(
llh.params["Cutoff"][cut_id]),
xy=(0.05, 0.95),
xycoords='axes fraction',
color='w',
va='top',
fontsize='x-large')
plt.colorbar(im, label='$\ln\mathcal{L}$')
ax.tick_params(direction='out')
plt.xlabel("$\Gamma$")
plt.ylabel("$\log_{10}(N)$")
plt.grid(color='0.7', ls=':')
plt.subplots_adjust(bottom=0.2, left=0.2)
fig.savefig(
"plots/{1:s}_lnl_fermi_grid_Ecut{0:.0f}TeV_B{2}.png".format(
llh.params["Cutoff"][cut_id], src, B))
plt.close("all")
# initialize prior data set
logging.info("Initializing data set with priors")
prior_stack = PriorSpectrumDatasetOnOff.from_spectrum_dataset_fermi_interp(
dataset, llh_fermi_interp=None)
# add the interpolator to the data set
prior_stack.llh_fermi_interp = llh.interp
# add the reference energy at which interpolation was performed (in MeV)
prior_stack.ref_energy = src_dict['spectral_pars']['Scale']['value']
prior_stack.models = casc_model
logging.info("Performing combined fit")
fit_casc = Fit([prior_stack])
fit_result_casc = fit_casc.run(optimize_opts=dict(
print_level=2, tol=10., migrad_opts=dict(ncall=1000)))
logging.info(f"Parameters after fit:\n{casc_model.parameters.to_table()}")
logging.info(f"Total stat after fit {fit_result_casc.total_stat}")
logging.info(f"Fermi logl after fit {prior_stack.llh_fermi}")
# plot the flux points
if plot:
fig = plt.figure(dpi=150)
ax = flux_points.plot(energy_power=2., label='data', marker='o')
if not casc_model.parameters['bias'].value == 0.:
fp = flux_points.table.copy()
fp['e_ref'] *= 1. + casc_model.parameters['bias'].value
fp['e_min'] *= 1. + casc_model.parameters['bias'].value
fp['e_max'] *= 1. + casc_model.parameters['bias'].value
fp_rescale = FluxPoints(fp)
fp_rescale.plot(ax=ax,
energy_power=2.,
label='data rescaled',
marker='o',
color='green')
# plot the final model
e_range = [1e-3, 10.] * u.TeV
# total model
casc_model.spectral_model.add_primary = True
casc_model.spectral_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Total',
color='k')
casc_model.spectral_model.plot_error(ax=ax,
energy_range=e_range,
energy_power=2)
# point source
obs_model = casc_model.spectral_model.intrinsic_spectral_model * casc_model.spectral_model.ebl
# cascade
casc_model.spectral_model.add_primary = False
casc_model.spectral_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Cascade',
color='k',
ls='-.')
casc_model.spectral_model.add_primary = True
if casc_model.parameters['bias'].value == 0.:
obs_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Point source',
color='k',
ls='--')
else:
casc_model.parameters['bias'].value = 0.
obs_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Point source',
color='green',
ls='--')
casc_model.spectral_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Total, bias = 0',
color='green',
ls=':')
# cascade
casc_model.spectral_model.add_primary = False
casc_model.spectral_model.plot(ax=ax,
energy_range=e_range,
energy_power=2,
label='Cascade',
color='green',
ls='-.')
casc_model.spectral_model.add_primary = True
pass
# fermi SED
SEDPlotter.plot_sed(
sed,
ax=ax,
ms=6.,
marker='.',
color='C1',
mec='C1',
alpha=1.,
noline=False,
band_alpha=0.2,
line_alpha=0.5,
band_linestyle='-',
label="Fermi",
flux_unit='TeV cm-2 s-1',
energy_unit='TeV',
print_name=False,
# apply bias to fermi data, in fit it's the other way around
#bias=casc_model.parameters['bias'].value
)
ax.legend(loc='lower center')
plt.ylim(3e-15, 2e-10)
plt.xlim(1e-3, 2e1)
fig.savefig(f"plots/final_fits_{src:s}_b{B}.png")
plt.close("all")
# plot a likelihood surface for best cut value
if plot:
par_amp = prior_stack.models['casc'].parameters['amplitude']
amp = np.logspace(
np.log10(par_amp.value) - 1.,
np.log10(par_amp.value) + .5, 100)
amp *= par_amp.unit
par_idx = prior_stack.models['casc'].parameters['index']
idx = np.linspace(par_idx.value - .5, par_idx.value + 1., 120)
idx *= par_idx.unit
ii, aa = np.meshgrid(idx, amp, indexing='ij')
c_stat = prior_stack.get_llh_fermi(amplitude=aa.reshape(-1),
index=ii.reshape(-1),
set_attribute=False).reshape(
aa.shape)
#ii, nn = np.meshgrid(idx, llh.log_norm_array, indexing='ij')
#c_stat = np.zeros((idx.shape[0], amp.shape[0]))
#for i, iidx in enumerate(idx):
#for j, a in enumerate(amp):
#c_stat[i,j] = prior_stack.get_llh_fermi(amplitude=a, index=iidx, set_attribute=False)
#c_stat = np.zeros((idx.shape[0], llh.log_norm_array.shape[0]))
#for i, iidx in enumerate(idx.value):
# for j, log_norm in enumerate(llh.log_norm_array):
# c_stat[i,j] = prior_stack.get_llh_fermi(amplitude=10.**log_norm * u.Unit('MeV-1 s-1 cm-2'),
# index=iidx * u.dimensionless_unscaled,
# set_attribute=False,
# reference=prior_stack._ref_energy * u.MeV)
d_cstat = 2. * (c_stat - c_stat.min())
fig = plt.figure(dpi=150)
ax = fig.add_subplot(111)
vmin = 0.
vmax = 300.
im = ax.pcolormesh(ii.value,
np.log10(aa.value),
d_cstat,
cmap=cmap_name,
vmin=vmin,
vmax=vmax)
#im = ax.pcolormesh(ii, nn, d_cstat, cmap=cmap_name, vmin=vmin, vmax=vmax)
ax.annotate("$E_\mathrm{{cut}} = {0:.2f}$TeV, $B={1:.2e}$G".format(
1. / prior_stack.models['casc'].parameters['lambda_'].value, B),
xy=(0.05, 0.95),
xycoords='axes fraction',
color='k',
va='top',
fontsize='x-large')
plt.colorbar(im, label='$-2\Delta\ln\mathcal{L}$')
ax.plot(par_idx.value,
np.log10(par_amp.value),
ms=10.,
marker='*',
mec='k')
ax.tick_params(direction='out')
plt.xlabel("$\Gamma$")
plt.ylabel(
"$\log_{10}(N_\mathrm{H.E.S.S.}) = \log_{10}((E_{0,{Fermi}} / E_{0,\mathrm{H.E.S.S.}})^{-\Gamma}N_{Fermi})$",
fontsize='medium')
plt.grid(color='0.7', ls=':')
plt.subplots_adjust(bottom=0.2, left=0.2)
fig.savefig("plots/{0:s}_lnl_fermi_interp_B{1}.png".format(src, B))
plt.close("all")
return prior_stack, prior_stack.llh_fermi, fit_result_casc.total_stat
llh.get_llh_one_source(src, norm_key='dnde_src')
# Define the model for the intrinsic / observed blazar spectrum
epl = ExpCutoffPowerLawSpectralModel(
amplitude=1e-12 * u.Unit("cm-2 s-1 TeV-1"),
index=1.6 * u.dimensionless_unscaled,
lambda_=0.1 * u.Unit("TeV-1"),
reference=1 * u.TeV,
)
#epl.parameters['lambda_'].min = 0.
#epl.parameters['lambda_'].max = 1.
epl.parameters['lambda_'].min = 1. / llh.params['Cutoff'].max()
epl.parameters['lambda_'].max = 1. / llh.params['Cutoff'].min()
ebl = EBLAbsorptionNormSpectralModel.read(
filename=config['global']['gammapy_ebl_file'],
redshift=config[src]['z_src'])
obs = epl * ebl
# fit the point source model
# without the cascade
logging.info("Fitting IACT data with point source")
ps_model = SkyModel(spectral_model=obs.copy(), name='ps')
dataset_stack[0].models = ps_model
fit_1d = Fit(dataset_stack)
fit_result_ps = fit_1d.run(optimize_opts=dict(
print_level=1, tol=0.1, migrad_opts=dict(ncall=1000)))
ps_model.parameters.to_table()
ps_model_table = ps_model.spectral_model.model1.parameters.to_table()