PIG 22 - Unified flux estimators API¶

• Author: Régis Terrier and Axel Donath

• Created: Nov 11, 2020

• Withdrawn: Nov 14th, 2021

• Status: withdrawn

• Discussion: GH 3075

Abstract¶

This pig proposes a uniform API for flux Estimator results. We discuss the introduction of a general FluxEstimate object that would allow flux type conversions and that would serve as a base class for FluxPoints and FluxMap class. The latter would allow easier handling of TSMapEstimator results, in particular regarding serialization and flux conversion.

Introduction¶

Flux estimation is performed by Estimators in gammapy. Some perform forward- folding methods to compute flux, ts, significance and errors at various positions or energy. This is the case of the FluxPointsEstimator, the LightCurveEstimator and the TSMapEstimator. Other perform backward folding methods to compute similar quantities (they compute excesses and associated ts and errors and divide by the exposure in reco energy to deduce flux quantities). This is the case of ExcessMapEstimator and ExcessProfileEstimator.

So far, the output of all these estimators is diverse and rely on different conventions for the definition of flux. There are four types of SED flux estimates described in the gamma astro data format. They are;

• dnde differential flux which is defined at a given e_ref

• e2dnde differential energy flux which is defined at a given e_ref

• flux integral flux defined between e_min and e_max

• eflux integral energy flux defined between e_min and e_max

To convert between these flux types, an assumption must be made on the spectral model.

Besides these, a useful SED type is the so-called likelihood type introduced by fermipy to represent SEDs and described in the gamma astro data format (ref). It uses reference fluxes expressed in the above flux types and a norm value that is used to derive the actual fluxes. Associated quantities are denoted norm_err, norm_ul etc.

What we have¶

So far, the only API in gammapy handling these different flux types is the FluxPoints object. It contains a Table representing one given format above and utility functions allow to convert the table into another format with e.g.:

fp_dnde = fp.to_sed_type("dnde")
fp_energy_flux = fp.to_sed_type("eflux", model=PowerLawSpectralModel(index=3))


The conversion is not possible in all directions.

The various estimators implemented so far return different objects.

• Map estimators return a dictionary of Map objects which are defined as flux types. Beyond the fixed flux type, there is no easy API to allow the user to serialize all the Maps at once.

• FluxPointsEstimator returns a FluxPoints object using the likelihood normalization scheme.

• LightCurveEstimator relies on the FluxPointsEstimator in each time interval but converts the output into a Table with one row per time interval and flux points stored as an array in each row.

• ExcessProfileEstimator computes an integral flux (flux type) in a list of regions and a list of energies. It returns a Table with one region per row, and energy dependent fluxes stored as an array in each row.

This diversity of output formats and flux types could be simplified with better design for flux quantities in gammapy. We propose below a generalized flux points API.

Proposal of API for flux estimate results¶

Introduce a FluxEstimate base class¶

First we propose that all Estimators compute quantities following a SED type inspired by the likelihood SED type. It would basically rely on the norm value and reference model to obtain fluxes in various formats. This is the basic ingredient of the current likelihood format described in the gadf but without the likelihood scan.

Using such a format, beyond the uniform behavior, has the advantage of making flux type conversion easier.

To limit code duplication (e.g. for flux conversions), we propose a common base class to describe the format and contain the required quantities.

class FluxEstimate:
"""General likelihood sed conversion class

Converts norm values into dnde, flux, etc.

Parameters
----------
data : dict of Map or Table
Mappable containing the sed likelihood data
spectral_model : SpectralModel
Reference spectral model
energy_axis : MapAxis
Reference energy axis
"""
def __init__(self, data, spectral_model, energy_axis=None):
self._data = data
self.spectral_model = spectral_model
self.energy_axis = energy_axis

@property
def dnde_ref(self):
"""Reference differential flux""
energy = self.energy_axis.center
return = self.spectral_model(energy)

@property
def dnde(self):
"""Differential flux"""
return self._data["norm"] * self.dnde_ref

@property
def flux(self):
"""Integral flux"""
energy = self.energy_axis.edges
flux_ref = self.spectral_model.integral(energy[:-1], energy[1:])
return self._data["norm"] * flux_ref


Practically, this allows easy manipulation of flux quantities between formats:

fpe = FluxPointsEtimator()
fp = fpe.run(datasets)

print(fp.dnde)
print(fp.eflux_err)

# but also get excess number estimate
fp.excess


TODO: what to do with counts based quantities? Introduce an ExcessEstimate?

Introduce a FluxMap API¶

Handling a simple dictionary of Maps is not very convenient. It is complex to perform flux transform, it is more complex to provide standard plotting functions for instance. More importantly, there is no way to serialize the maps with their associated quantities and other information. It could be useful to export the GTI table of the Dataset that was used to extract the map or its meta table. Some information on the way the flux was obtained could be kept as well (e.g. spatial model assumed or correlation radius used).

The FluxMap would inherit from the general likelihood SED class discussed above and could include the possibility to export the resulting maps (in particular the norm_scan maps) after sparsification according to the format definition from fermipy and presented in gamma astro data format.

In addition, utilities to extract flux points at various positions could be provided.

Typical usage would be:

model = SkyModel(PointSpatialModel(), PowerLawSpectralModel(index=2.5))

estimator = TSMapEstimator(model, energy_edges=[0.2, 1.0, 10.0]*u.TeV)

flux_maps = estimator.run(dataset)

# plot differential flux map in each energy band
flux_maps.dnde.plot_grid()

# plot energy flux map in each energy band
flux_maps.eflux.plot_grid()

# one can access other quantities
flux_maps.sqrt_ts.plot_grid()
flux_maps.excess.plot_grid()

# Extract flux points at selected positions
positions = SkyCoord([225.31, 200.4], [35.65, 25.3], unit="deg", frame="icrs")
fp = flux_maps.get_flux_points(positions)
fp.plot()

# Save to disk as a fits file
flux_maps.write("my_flux_maps.fits", overwrite=True)



Introduce a FluxPointsCollection API¶

Several estimators return a set of FluxPoints . It is the case of the LightCurveEstimator, a light curve being a time ordered list of fluxes. It is also the case of the ExcessProfileEstimator which return a list of flux points ordered along a direction or radially. In the current implementation, they produce an ~astropy.Table where each row contain an array of fluxes representing flux points at a given time or position.

This solution is not ideal. It introduces a different container logic than the FluxPoints for which one row represents one energy.

A dedicated API could be introduced to support these objects. In order to keep the logic used in FluxPoints, a flat table Table could be used to store the various fluxes, where each row would represent the flux at a given energy, time, position etc.

Astropy provides a mechanism to group table rows according to column entries. It is then possible to extract the relevant FluxPoints object, representing the simple flux points or the lightcurve.

A possible implementation could follow the following lines:

energy_columns = ["e_min", "e_max", "e_ref"]
time_columns = ["t_min", "t_max"]

class FluxPointsCollection:
def __init__(self, table):
self.table = table

if all(_ in self.table.keys() for _ in energy_columns ):
self._energy_table = self.table.group_by(energy_columns)
else:
raise TypeError("Table does not describe a flux point. Missing energy columns.")

self._time_groups = None
if all(_ in self.table.keys() for _ in time_columns):
self._time_table = self.table.group_by(time_columns)

def flux_points_at_time(self, time):
if self._time_table is None:
raise KeyError("No time information")

index = np.where((time - self.t_min) <= 0)[0][0]
return self.__class__(self._time_table.groups[index])

def lightcurve_at_energy(self, energy):
if self._time_table is None:
raise KeyError("No time information")

index = np.where((energy - self.e_min) <= 0)[0][0]
return self.__class__(self._energy_table.groups[index])


Keeping dedicated classes for specific types is an open question. While it might not be needed, it also provides a more explicit API for the user as well as specific functionalities. In particular, plotting is specific to each type. So will be I/O once specific data formats have been introduced.

We also note that FluxPointsDataset rely on FluxPoints object for now. An important missing feature is the ability of using these for temporal model evaluation. TemporalModel might requires a GTI.

Unification of flux estimators?¶

Most estimators actually do the same thing: LightCurveEstimator is simply grouping datasets in time intervals and applies FluxPointsEstimator in each interval. Similarly, the ExcessProfileEstimator is performing a similar thing in different regions. The necessity of a specific estimator for all these tasks is then questionable. Currently, the responsibility of an estimator is to group and reproject datasets in the relevant intervals or group of data and then to apply a general flux or excess estimate.

In practice there are two different types of estimators. We can distinguish these:

• Flux estimators perform a fit of all individual counts inside the requested range (energy-bin and/or spatial box) to obtain a flux given a certain physical model. Because it relies on a fit of the complete model,this approach allows to take into account fluctuations of other parameters by performing re-optimization.

• Excess estimators sum all counts inside the requested range and estimate the corresponding excess counts taking into account background and other signal contributions from other sources. No explicit fit is actually performed, since we rely on CountsStatistics classes. The flux is then deduced computing the ratio of measured excess to total npred in a given model assumption.

Currently, the FluxPointsEstimator and the LightCurveEstimator belong to the first category. The TSMapEstimator a priori belongs there as well although our current implementation does not allow for other parameters re-optimization. A more general implementation could also rely on FluxPointsEstimator.

The ExcessMapEstimator and ExcessProfileEstimator are following the second approach (as their name suggest), but they still provide flux estimates through the excess/npred ratio. We note that flux points and light curve can also be estimated through this approach to provide rapid estimates.

So we propose to introduce the following simplified estimator API:

• FluxPointsEstimator, which handles multiple sources, time intervals and energy bins, using “forward folding”

• FluxMapEstimator, which handles multiple energy bins, using “forward folding”

• ExcessPointsEstimator, which handles multiple regions, time intervals and energy bins, using “backward folding”

• ExcessMapEstimator, which handles multiple energy bins, using “backward folding”

Excess estimators¶

We can unify and clarify the general approach by introducing estimators following each of the methods.

A general flux estimator already exists, it is the FluxEstimator. It is the base of the FluxPointsEstimator.

An equivalent ExcessEstimator could be added. Technically, it would mostly encapsulate functionalities provided by the CountsStatistics.

Generalist estimators¶

It is possible to create a generalist FluxPointsEstimator that could return a general FluxPointsCollection without knowing a priori what type of grouping is applied to the datasets. This would allow to perform lightcurve or region-based flux estimates with the same API. This would allow a direct generalization of the FluxPointsEstimator to cover other problematic e.g. flux estimation in phase to build phase curves, flux estimation in different observation condition or instrument states to study systematic effects.

The main change required for this is to move dataset grouping to the Datasets level.

Outlook¶

Selection by time is already possible on Datasets thanks to the select_time(t_min, t_max) method. This functionality could be extended to other quantities characterizing the datasets.

So in future we could add more general grouping functionality on the Datasets. It could internally rely on the grouping of the meta table: Datasets.meta_table.group_by. It would require the table to be present in memory and be recomputed each time the Datasets object is updated. Then retrieving a set of datasets could be done by Datasets.get_group_by_idx().

# group datasets according to phase
phase_axis = MapAxis.from_bounds(0., 1., 10, name="phase", unit="")
datasets.group_by_axis(phase_axis)
datasets_in_phase_bin_3 = datasets.get_group_by_idx(3)
`

Decision¶

The authors have decided to withdraw the PIG. Most of the proposed changes have been implemented independently with review and discussions on individuals PRs.