This is a fixed-text formatted version of a Jupyter notebook

# Modeling and fitting 2D images using Gammapy¶

## Prerequisites:¶

• To understand how a generel modelling and fiiting works in gammapy, please refer to the analysis_3d 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 dependance 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.

## Setup¶

[1]:

%matplotlib inline
import astropy.units as u
import numpy as np
from astropy.coordinates import SkyCoord
from astropy.time import Time
from regions import CircleSkyRegion
from astropy.coordinates import Angle

import logging

log = logging.getLogger(__name__)


Now let’s import gammapy specific classes and functions

[2]:

from gammapy.analysis import Analysis, AnalysisConfig


## 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.

[3]:

config = AnalysisConfig()
# Selecting the observations
config.observations.datastore = "$GAMMAPY_DATA/cta-1dc/index/gps/" config.observations.obs_ids = [110380, 111140, 111159]  Technically, gammapy implements 2D analysis as a special case of 3D analysis (one one bin in energy). So, we must specify the type of analysis as 3D, and define the geometry of the analysis. [4]:  config.datasets.type = "3d" config.datasets.geom.wcs.skydir = { "lon": "0 deg", "lat": "0 deg", "frame": "galactic", } # The WCS geometry - centered on the galactic center config.datasets.geom.wcs.fov = {"width": "10 deg", "height": "8 deg"} config.datasets.geom.wcs.binsize = "0.02 deg" # The FoV radius to use for cutouts config.datasets.geom.selection.offset_max = 3.5 * u.deg # We now fix the energy axis for the counts map - (the reconstructed energy binning) config.datasets.geom.axes.energy.min = "0.1 TeV" config.datasets.geom.axes.energy.max = "10 TeV" config.datasets.geom.axes.energy.nbins = 1 config.datasets.geom.wcs.binsize_irf = 0.2 * u.deg  [5]:  print(config)  AnalysisConfig general: log: {level: info, filename: null, filemode: null, format: null, datefmt: null} outdir: . observations: datastore:$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}
datasets:
type: 3d
stack: true
geom:
wcs:
skydir: {frame: galactic, lon: 0.0 deg, lat: 0.0 deg}
binsize: 0.02 deg
fov: {width: 10.0 deg, height: 8.0 deg}
binsize_irf: 0.2 deg
selection: {offset_max: 3.5 deg}
axes:
energy: {min: 0.1 TeV, max: 10.0 TeV, nbins: 1}
energy_true: {min: 0.1 TeV, max: 10.0 TeV, nbins: 30}
map_selection: [counts, exposure, background, psf, edisp]
background:
method: null
exclusion: null
parameters: {}
methods: [aeff-default]
parameters: {}
on_region: {frame: null, lon: null, lat: null, radius: null}
containment_correction: true
fit:
fit_range: {min: 0.1 TeV, max: 10.0 TeV}
flux_points:
energy: {min: 0.1 TeV, max: 10.0 TeV, nbins: 30}
source: source
parameters: {}



## Getting the reduced dataset¶

We now use the config file and create a single MapDataset containing counts, background, exposure, psf and edisp maps.

[6]:

%%time
analysis = Analysis(config)
analysis.get_observations()
analysis.get_datasets()

Setting logging config: {'level': 'INFO', 'filename': None, 'filemode': None, 'format': None, 'datefmt': None}
Fetching observations.
Number of selected observations: 3
Creating geometry.
Creating datasets.
No background maker set for 3d analysis. Check configuration.
Processing observation 110380
No thresholds defined for obs Observation

obs id            : 110380
tstart            : 59235.50
tstop             : 59235.52
duration          : 1800.00 s
pointing (icrs)   : 267.7 deg, -29.6 deg

Processing observation 111140
No thresholds defined for obs Observation

obs id            : 111140
tstart            : 59275.50
tstop             : 59275.52
duration          : 1800.00 s
pointing (icrs)   : 264.2 deg, -29.5 deg

Processing observation 111159
No thresholds defined for obs Observation

obs id            : 111159
tstart            : 59276.50
tstop             : 59276.52
duration          : 1800.00 s
pointing (icrs)   : 266.0 deg, -27.0 deg


CPU times: user 9.86 s, sys: 3.34 s, total: 13.2 s
Wall time: 13.9 s

[7]:

print(analysis.datasets["stacked"])

MapDataset
----------

Name                            : stacked

Total counts                    : 143121
Total predicted counts          : 125042.02
Total background counts         : 125042.02

Exposure min                    : 0.00e+00 m2 s
Exposure max                    : 1.87e+10 m2 s

Number of total bins            : 200000
Number of fit bins              : 186500

Fit statistic type              : cash
Fit statistic value (-2 log(L)) : 294443.11

Number of models                : 1
Number of parameters            : 3
Number of free parameters       : 1

Component 0: BackgroundModel

Name                      : stacked-bkg
Datasets names            : ['stacked']
Parameters:
norm                    :   1.000
tilt         (frozen)   :   0.000
reference    (frozen)   :   1.000  TeV



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.

[8]:

print(analysis.datasets["stacked"].counts)

WcsNDMap

geom  : WcsGeom
axes  : ['lon', 'lat', 'energy']
shape : (500, 400, 1)
ndim  : 3
unit  :
dtype : float32


[9]:

print(analysis.datasets["stacked"].background_model.map)

WcsNDMap

geom  : WcsGeom
axes  : ['lon', 'lat', 'energy']
shape : (500, 400, 1)
ndim  : 3
unit  :
dtype : float64


[10]:

print(analysis.datasets["stacked"].exposure)

WcsNDMap

geom  : WcsGeom
axes  : ['lon', 'lat', 'energy_true']
shape : (500, 400, 30)
ndim  : 3
unit  : m2 s
dtype : float32



## 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:

[11]:

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
"""

[12]:

analysis.set_models(model_config)

Reading model.
Models

Component 0: SkyModel

Name                      : GC-1
Datasets names            : None
Spectral model type       : PowerLaw2SpectralModel
Spatial  model type       : PointSpatialModel
Temporal model type       : None
Parameters:
amplitude               :   1.00e-12  1 / (cm2 s)
index        (frozen)   :   2.000
emin         (frozen)   :   0.100  TeV
emax         (frozen)   :  10.000  TeV
lon_0                   :   0.020  deg
lat_0                   :   0.010  deg



We will freeze the parameters of the background

[13]:

analysis.datasets["stacked"].background_model.parameters["norm"].frozen = True
analysis.datasets["stacked"].background_model.parameters["tilt"].frozen = True

[14]:

# To run the fit
analysis.run_fit()

Fitting datasets.
OptimizeResult

backend    : minuit
method     : minuit
success    : False
message    : Optimization failed.
nfev       : 24
total stat : 0.00


[15]:

# To see the best fit values along with the errors
analysis.fit_result.parameters.to_table()

[15]:

Table length=9
namevalueunitminmaxfrozenerror
str9float64str8float64float64boolfloat64
norm1.000e+000.000e+00nanTrue0.000e+00
tilt0.000e+00nannanTrue0.000e+00
reference1.000e+00TeVnannanTrue0.000e+00
amplitude1.000e-12cm-2 s-1nannanFalsenan
index2.000e+00nannanTrue0.000e+00
emin1.000e-01TeVnannanTrue0.000e+00
emax1.000e+01TeVnannanTrue0.000e+00
lon_02.000e-02degnannanFalsenan
lat_01.000e-02degnannanFalsenan
[ ]: