Note
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2D map fitting#
Source modelling and fitting in stacked observations using the high level interface.
Prerequisites#
To understand how a general modelling and fitting works in gammapy, please refer to the 3D detailed analysis tutorial.
Context#
We often want the determine the position and morphology of an object. To do so, we don’t necessarily have to resort to a full 3D fitting but can perform a simple image fitting, in particular, in an energy range where the PSF does not vary strongly, or if we want to explore a possible energy dependence of the morphology.
Objective#
To localize a source and/or constrain its morphology.
Proposed approach#
The first step here, as in most analysis with DL3 data, is to create
reduced datasets. For this, we will use the Analysis class to create
a single set of stacked maps with a single bin in energy (thus, an
image which behaves as a cube). This, we will then model with a
spatial model of our choice, while keeping the spectral model fixed to
an integrated power law.
# %matplotlib inline
import astropy.units as u
import matplotlib.pyplot as plt
Setup#
As usual, we’ll start with some general imports…
from IPython.display import display
from gammapy.analysis import Analysis, AnalysisConfig
Check setup#
from gammapy.utils.check import check_tutorials_setup
check_tutorials_setup()
System:
python_executable : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/bin/python
python_version : 3.9.16
machine : x86_64
system : Linux
Gammapy package:
version : 1.1
path : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/gammapy
Other packages:
numpy : 1.24.3
scipy : 1.10.1
astropy : 5.2.2
regions : 0.7
click : 8.1.3
yaml : 6.0
IPython : 8.14.0
jupyterlab : not installed
matplotlib : 3.7.1
pandas : not installed
healpy : 1.16.2
iminuit : 2.21.3
sherpa : 4.15.1
naima : 0.10.0
emcee : 3.1.4
corner : 2.2.2
ray : 2.5.0
Gammapy environment variables:
GAMMAPY_DATA : /home/runner/work/gammapy-docs/gammapy-docs/gammapy-datasets/1.1
Creating the config file#
Now, we create a config file for out analysis. You may load this from disc if you have a pre-defined config file.
Here, we use 3 simulated CTA runs of the galactic center.
config = AnalysisConfig()
# Selecting the observations
config.observations.datastore = "$GAMMAPY_DATA/cta-1dc/index/gps/"
config.observations.obs_ids = [110380, 111140, 111159]
Technically, gammapy implements 2D analysis as a special case of 3D analysis (one bin in energy). So, we must specify the type of analysis as 3D, and define the geometry of the analysis.
config.datasets.type = "3d"
config.datasets.geom.wcs.skydir = {
"lon": "0 deg",
"lat": "0 deg",
"frame": "galactic",
} # The WCS geometry - centered on the galactic center
config.datasets.geom.wcs.width = {"width": "8 deg", "height": "6 deg"}
config.datasets.geom.wcs.binsize = "0.02 deg"
# The FoV radius to use for cutouts
config.datasets.geom.selection.offset_max = 2.5 * u.deg
config.datasets.safe_mask.methods = ["offset-max"]
config.datasets.safe_mask.parameters = {"offset_max": 2.5 * u.deg}
config.datasets.background.method = "fov_background"
config.fit.fit_range = {"min": "0.1 TeV", "max": "30.0 TeV"}
# We now fix the energy axis for the counts map - (the reconstructed energy binning)
config.datasets.geom.axes.energy.min = "0.1 TeV"
config.datasets.geom.axes.energy.max = "10 TeV"
config.datasets.geom.axes.energy.nbins = 1
config.datasets.geom.wcs.binsize_irf = 0.2 * u.deg
print(config)
AnalysisConfig
general:
log: {level: info, filename: null, filemode: null, format: null, datefmt: null}
outdir: .
n_jobs: 1
datasets_file: null
models_file: null
observations:
datastore: $GAMMAPY_DATA/cta-1dc/index/gps
obs_ids: [110380, 111140, 111159]
obs_file: null
obs_cone: {frame: null, lon: null, lat: null, radius: null}
obs_time: {start: null, stop: null}
required_irf: [aeff, edisp, psf, bkg]
datasets:
type: 3d
stack: true
geom:
wcs:
skydir: {frame: galactic, lon: 0.0 deg, lat: 0.0 deg}
binsize: 0.02 deg
width: {width: 8.0 deg, height: 6.0 deg}
binsize_irf: 0.2 deg
selection: {offset_max: 2.5 deg}
axes:
energy: {min: 0.1 TeV, max: 10.0 TeV, nbins: 1}
energy_true: {min: 0.5 TeV, max: 20.0 TeV, nbins: 16}
map_selection: [counts, exposure, background, psf, edisp]
background:
method: fov_background
exclusion: null
parameters: {}
safe_mask:
methods: [offset-max]
parameters: {offset_max: 2.5 deg}
on_region: {frame: null, lon: null, lat: null, radius: null}
containment_correction: true
fit:
fit_range: {min: 0.1 TeV, max: 30.0 TeV}
flux_points:
energy: {min: null, max: null, nbins: null}
source: source
parameters: {selection_optional: all}
excess_map:
correlation_radius: 0.1 deg
parameters: {}
energy_edges: {min: null, max: null, nbins: null}
light_curve:
time_intervals: {start: null, stop: null}
energy_edges: {min: null, max: null, nbins: null}
source: source
parameters: {selection_optional: all}
Getting the reduced dataset#
We now use the config file and create a single MapDataset containing
counts, background, exposure, psf and edisp maps.
analysis = Analysis(config)
analysis.get_observations()
analysis.get_datasets()
print(analysis.datasets["stacked"])
/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
warnings.warn(msg, UnitsWarning)
/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
warnings.warn(msg, UnitsWarning)
/home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/astropy/units/core.py:2097: UnitsWarning: '1/s/MeV/sr' did not parse as fits unit: Numeric factor not supported by FITS If this is meant to be a custom unit, define it with 'u.def_unit'. To have it recognized inside a file reader or other code, enable it with 'u.add_enabled_units'. For details, see https://docs.astropy.org/en/latest/units/combining_and_defining.html
warnings.warn(msg, UnitsWarning)
MapDataset
----------
Name : stacked
Total counts : 85625
Total background counts : 85624.99
Total excess counts : 0.01
Predicted counts : 85625.00
Predicted background counts : 85624.99
Predicted excess counts : nan
Exposure min : 8.46e+08 m2 s
Exposure max : 2.14e+10 m2 s
Number of total bins : 120000
Number of fit bins : 96602
Fit statistic type : cash
Fit statistic value (-2 log(L)) : nan
Number of models : 0
Number of parameters : 0
Number of free parameters : 0
The counts and background maps have only one bin in reconstructed energy. The exposure and IRF maps are in true energy, and hence, have a different binning based upon the binning of the IRFs. We need not bother about them presently.
print(analysis.datasets["stacked"].counts)
print(analysis.datasets["stacked"].background)
print(analysis.datasets["stacked"].exposure)
WcsNDMap
geom : WcsGeom
axes : ['lon', 'lat', 'energy']
shape : (400, 300, 1)
ndim : 3
unit :
dtype : float32
WcsNDMap
geom : WcsGeom
axes : ['lon', 'lat', 'energy']
shape : (400, 300, 1)
ndim : 3
unit :
dtype : float32
WcsNDMap
geom : WcsGeom
axes : ['lon', 'lat', 'energy_true']
shape : (400, 300, 16)
ndim : 3
unit : m2 s
dtype : float32
We can have a quick look of these maps in the following way:
analysis.datasets["stacked"].counts.reduce_over_axes().plot(vmax=10, add_cbar=True)
plt.show()
Modelling#
Now, we define a model to be fitted to the dataset. The important thing to note here is the dummy spectral model - an integrated powerlaw with only free normalisation. Here, we use its YAML definition to load it:
model_config = """
components:
- name: GC-1
type: SkyModel
spatial:
type: PointSpatialModel
frame: galactic
parameters:
- name: lon_0
value: 0.02
unit: deg
- name: lat_0
value: 0.01
unit: deg
spectral:
type: PowerLaw2SpectralModel
parameters:
- name: amplitude
value: 1.0e-12
unit: cm-2 s-1
- name: index
value: 2.0
unit: ''
frozen: true
- name: emin
value: 0.1
unit: TeV
frozen: true
- name: emax
value: 10.0
unit: TeV
frozen: true
"""
analysis.set_models(model_config)
We will freeze the parameters of the background
analysis.datasets["stacked"].background_model.parameters["tilt"].frozen = True
# To run the fit
analysis.run_fit()
# To see the best fit values along with the errors
display(analysis.models.to_parameters_table())
model type name value ... max frozen is_norm link
----------- -------- --------- ----------- ... --------- ------ ------- ----
GC-1 spectral amplitude 4.1790e-11 ... nan False True
GC-1 spectral index 2.0000e+00 ... nan True False
GC-1 spectral emin 1.0000e-01 ... nan True False
GC-1 spectral emax 1.0000e+01 ... nan True False
GC-1 spatial lon_0 -5.4771e-02 ... nan False False
GC-1 spatial lat_0 -5.3617e-02 ... 9.000e+01 False False
stacked-bkg spectral norm 9.9439e-01 ... nan False True
stacked-bkg spectral tilt 0.0000e+00 ... nan True False
stacked-bkg spectral reference 1.0000e+00 ... nan True False
