Low level API

Introduction to Gammapy analysis using the low level API.

Prerequisites

• Understanding the gammapy data workflow, in particular what are DL3 events and instrument response functions (IRF).

• Understanding of the data reduction and modeling fitting process as shown in the analysis with the high level interface tutorial High level interface

Context

This notebook is an introduction to gammapy analysis this time using the lower level classes and functions the library. This allows to understand what happens during two main gammapy analysis steps, data reduction and modeling/fitting.

Objective: Create a 3D dataset of the Crab using the H.E.S.S. DL3 data release 1 and perform a simple model fitting of the Crab nebula using the lower level gammapy API.

Proposed approach

Here, we have to interact with the data archive (with the DataStore) to retrieve a list of selected observations (Observations). Then, we define the geometry of the MapDataset object we want to produce and the maker object that reduce an observation to a dataset.

We can then proceed with data reduction with a loop over all selected observations to produce datasets in the relevant geometry and stack them together (i.e.sum them all).

In practice, we have to:

• Create a DataStore poiting to the relevant data

• Apply an observation selection to produce a list of observations, a Observations object.

• Define a geometry of the Map we want to produce, with a sky projection and an energy range.

• Create a MapAxis for the energy

• Create a WcsGeom for the geometry

• Create the necessary makers:

  • the map dataset maker MapDatasetMaker

  • the background normalization maker, here a FoVBackgroundMaker

  • and usually the safe range maker : SafeMaskMaker

• Perform the data reduction loop. And for every observation:

  • Apply the makers sequentially to produce the current MapDataset

  • Stack it on the target one.

• Define the`~gammapy.modeling.models.SkyModel` to apply to the dataset.

• Create a Fit object and run it to fit the model parameters

• Apply a FluxPointsEstimator to compute flux points for the spectral part of the fit.

Setup

First, we setup the analysis by performing required imports.

from pathlib import Path
from astropy import units as u
from astropy.coordinates import SkyCoord
from regions import CircleSkyRegion

# %matplotlib inline
import matplotlib.pyplot as plt
from gammapy.data import DataStore
from gammapy.datasets import MapDataset
from gammapy.estimators import FluxPointsEstimator
from gammapy.makers import FoVBackgroundMaker, MapDatasetMaker, SafeMaskMaker
from gammapy.maps import MapAxis, WcsGeom
from gammapy.modeling import Fit
from gammapy.modeling.models import (
    FoVBackgroundModel,
    PointSpatialModel,
    PowerLawSpectralModel,
    SkyModel,
)
from gammapy.utils.check import check_tutorials_setup

Check setup

check_tutorials_setup()

System:

        python_executable      : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/bin/python
        python_version         : 3.9.15
        machine                : x86_64
        system                 : Linux


Gammapy package:

        version                : 1.0
        path                   : /home/runner/work/gammapy-docs/gammapy-docs/gammapy/.tox/build_docs/lib/python3.9/site-packages/gammapy


Other packages:

        numpy                  : 1.23.4
        scipy                  : 1.9.3
        astropy                : 5.1.1
        regions                : 0.7
        click                  : 8.1.3
        yaml                   : 6.0
        IPython                : 8.6.0
        jupyterlab             : not installed
        matplotlib             : 3.6.2
        pandas                 : not installed
        healpy                 : 1.16.1
        iminuit                : 2.17.0
        sherpa                 : 4.15.0
        naima                  : 0.10.0
        emcee                  : 3.1.3
        corner                 : 2.2.1


Gammapy environment variables:

        GAMMAPY_DATA           : /home/runner/work/gammapy-docs/gammapy-docs/gammapy-datasets/1.0

Defining the datastore and selecting observations

We first use the DataStore object to access the observations we want to analyse. Here the H.E.S.S. DL3 DR1.

data_store = DataStore.from_dir("$GAMMAPY_DATA/hess-dl3-dr1")

We can now define an observation filter to select only the relevant observations. Here we use a cone search which we define with a python dict.

We then filter the ObservationTable with select_observations.

selection = dict(
    type="sky_circle",
    frame="icrs",
    lon="83.633 deg",
    lat="22.014 deg",
    radius="5 deg",
)
selected_obs_table = data_store.obs_table.select_observations(selection)

We can now retrieve the relevant observations by passing their obs_id to the get_observations method.

observations = data_store.get_observations(selected_obs_table["OBS_ID"])

Preparing reduced datasets geometry

Now we define a reference geometry for our analysis, We choose a WCS based geometry with a binsize of 0.02 deg and also define an energy axis:

energy_axis = MapAxis.from_energy_bounds(1.0, 10.0, 4, unit="TeV")

geom = WcsGeom.create(
    skydir=(83.633, 22.014),
    binsz=0.02,
    width=(2, 2),
    frame="icrs",
    proj="CAR",
    axes=[energy_axis],
)

# Reduced IRFs are defined in true energy (i.e. not measured energy).
energy_axis_true = MapAxis.from_energy_bounds(
    0.5, 20, 10, unit="TeV", name="energy_true"
)

Now we can define the target dataset with this geometry.

stacked = MapDataset.create(
    geom=geom, energy_axis_true=energy_axis_true, name="crab-stacked"
)

Data reduction

Create the maker classes to be used

The MapDatasetMaker object is initialized as well as the SafeMaskMaker that carries here a maximum offset selection.

offset_max = 2.5 * u.deg
maker = MapDatasetMaker()
maker_safe_mask = SafeMaskMaker(
    methods=["offset-max", "aeff-max"], offset_max=offset_max
)

circle = CircleSkyRegion(center=SkyCoord("83.63 deg", "22.14 deg"), radius=0.2 * u.deg)
exclusion_mask = ~geom.region_mask(regions=[circle])
maker_fov = FoVBackgroundMaker(method="fit", exclusion_mask=exclusion_mask)

Perform the data reduction loop

for obs in observations:
    # First a cutout of the target map is produced
    cutout = stacked.cutout(
        obs.pointing_radec, width=2 * offset_max, name=f"obs-{obs.obs_id}"
    )
    # A MapDataset is filled in this cutout geometry
    dataset = maker.run(cutout, obs)
    # The data quality cut is applied
    dataset = maker_safe_mask.run(dataset, obs)
    # fit background model
    dataset = maker_fov.run(dataset)
    print(
        f"Background norm obs {obs.obs_id}: {dataset.background_model.spectral_model.norm.value:.2f}"
    )
    # The resulting dataset cutout is stacked onto the final one
    stacked.stack(dataset)

print(stacked)

Background norm obs 23523: 0.99
Background norm obs 23526: 1.08
Background norm obs 23559: 0.99
Background norm obs 23592: 1.10
MapDataset
----------

  Name                            : crab-stacked

  Total counts                    : 2479
  Total background counts         : 2112.97
  Total excess counts             : 366.03

  Predicted counts                : 2112.97
  Predicted background counts     : 2112.97
  Predicted excess counts         : nan

  Exposure min                    : 3.75e+08 m2 s
  Exposure max                    : 3.48e+09 m2 s

  Number of total bins            : 40000
  Number of fit bins              : 40000

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

  Number of models                : 0
  Number of parameters            : 0
  Number of free parameters       : 0

Inspect the reduced dataset

stacked.counts.sum_over_axes().smooth(0.05 * u.deg).plot(stretch="sqrt", add_cbar=True)

<WCSAxesSubplot: >

Save dataset to disk

It is common to run the preparation step independent of the likelihood fit, because often the preparation of maps, PSF and energy dispersion is slow if you have a lot of data. We first create a folder:

path = Path("analysis_2")
path.mkdir(exist_ok=True)

And then write the maps and IRFs to disk by calling the dedicated write method:

filename = path / "crab-stacked-dataset.fits.gz"
stacked.write(filename, overwrite=True)

Define the model

We first define the model, a SkyModel, as the combination of a point source SpatialModel with a powerlaw SpectralModel:

target_position = SkyCoord(ra=83.63308, dec=22.01450, unit="deg")
spatial_model = PointSpatialModel(
    lon_0=target_position.ra, lat_0=target_position.dec, frame="icrs"
)

spectral_model = PowerLawSpectralModel(
    index=2.702,
    amplitude=4.712e-11 * u.Unit("1 / (cm2 s TeV)"),
    reference=1 * u.TeV,
)

sky_model = SkyModel(
    spatial_model=spatial_model, spectral_model=spectral_model, name="crab"
)

bkg_model = FoVBackgroundModel(dataset_name="crab-stacked")

Now we assign this model to our reduced dataset:

stacked.models = [sky_model, bkg_model]

Fit the model

The Fit class is orchestrating the fit, connecting the stats method of the dataset to the minimizer. By default, it uses iminuit.

Its constructor takes a list of dataset as argument.

fit = Fit(optimize_opts={"print_level": 1})
result = fit.run([stacked])

The FitResult contains information about the optimization and parameter error calculation.

print(result)

OptimizeResult

        backend    : minuit
        method     : migrad
        success    : True
        message    : Optimization terminated successfully.
        nfev       : 140
        total stat : 16240.97

CovarianceResult

        backend    : minuit
        method     : hesse
        success    : True
        message    : Hesse terminated successfully.

The fitted parameters are visible from the Models object.

print(stacked.models.to_parameters_table())

     model         type      name     value    ...    max    frozen is_norm link
---------------- -------- --------- ---------- ... --------- ------ ------- ----
            crab spectral     index 2.6000e+00 ...       nan  False   False
            crab spectral amplitude 4.5905e-11 ...       nan  False    True
            crab spectral reference 1.0000e+00 ...       nan   True   False
            crab  spatial     lon_0 8.3619e+01 ...       nan  False   False
            crab  spatial     lat_0 2.2024e+01 ... 9.000e+01  False   False
crab-stacked-bkg spectral      norm 9.3479e-01 ...       nan  False    True
crab-stacked-bkg spectral      tilt 0.0000e+00 ...       nan   True   False
crab-stacked-bkg spectral reference 1.0000e+00 ...       nan   True   False

Inspecting residuals

For any fit it is useful to inspect the residual images. We have a few options on the dataset object to handle this. First we can use plot_residuals_spatial to plot a residual image, summed over all energies:

stacked.plot_residuals_spatial(method="diff/sqrt(model)", vmin=-0.5, vmax=0.5)

<WCSAxesSubplot: >

In addition, we can also specify a region in the map to show the spectral residuals:

region = CircleSkyRegion(center=SkyCoord("83.63 deg", "22.14 deg"), radius=0.5 * u.deg)

stacked.plot_residuals(
    kwargs_spatial=dict(method="diff/sqrt(model)", vmin=-0.5, vmax=0.5),
    kwargs_spectral=dict(region=region),
)

(<WCSAxesSubplot: >, <AxesSubplot: xlabel='Energy [TeV]', ylabel='Residuals (data - model)'>)

We can also directly access the .residuals() to get a map, that we can plot interactively:

residuals = stacked.residuals(method="diff")
residuals.smooth("0.08 deg").plot_interactive(
    cmap="coolwarm", vmin=-0.2, vmax=0.2, stretch="linear", add_cbar=True
)

interactive(children=(SelectionSlider(continuous_update=False, description='Select energy:', layout=Layout(width='50%'), options=('1.00 TeV - 1.78 TeV', '1.78 TeV - 3.16 TeV', '3.16 TeV - 5.62 TeV', '5.62 TeV - 10.00 TeV'), style=SliderStyle(description_width='initial'), value='1.00 TeV - 1.78 TeV'), RadioButtons(description='Select stretch:', options=('linear', 'sqrt', 'log'), style=DescriptionStyle(description_width='initial'), value='linear'), Output()), _dom_classes=('widget-interact',))

Plot the fitted spectrum

Making a butterfly plot

The SpectralModel component can be used to produce a, so-called, butterfly plot showing the envelope of the model taking into account parameter uncertainties:

spec = sky_model.spectral_model

Now we can actually do the plot using the plot_error method:

energy_bounds = [1, 10] * u.TeV
spec.plot(energy_bounds=energy_bounds, energy_power=2)
ax = spec.plot_error(energy_bounds=energy_bounds, energy_power=2)

Computing flux points

We can now compute some flux points using the FluxPointsEstimator.

Besides the list of datasets to use, we must provide it the energy intervals on which to compute flux points as well as the model component name.

energy_edges = [1, 2, 4, 10] * u.TeV
fpe = FluxPointsEstimator(energy_edges=energy_edges, source="crab")

flux_points = fpe.run(datasets=[stacked])

ax = spec.plot_error(energy_bounds=energy_bounds, energy_power=2)
flux_points.plot(ax=ax, energy_power=2)

<AxesSubplot: xlabel='Energy [TeV]', ylabel='dnde [TeV / (cm2 s)]'>