# 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Withdrawn: Nov 14th, 2021

Status: withdrawn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)
# Read from disk
new_flux_maps = FluxMap.read("my_flux_maps.fits")
```

### 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)
```

## Alternative¶

## 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.