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Source files: event_sampling.ipynb | event_sampling.py

Event Sampling¶

Prerequisites¶

To understand how to generate a Model and a MapDataset, and how to fit the data, please refer to the gammapy.modeling.models.SkyModel and simulate_3d.

Context¶

This tutorial describes how to sample events from an observation of a one (or more) gamma-ray source(s). The main aim of the tutorial will be to set the minimal configuration needed to deal with the Gammapy event-sampler and how to obtain an output photon event list.

The core of the event sampling lies into the Gammapy gammapy.datasets.MapDatasetEventSampler class, which is based on the inverse cumulative distribution function (Inverse CDF).

The gammapy.datasets.MapDatasetEventSampler takes in input a gammapy.datasets.Dataset object containing the spectral, spatial and temporal properties of the source(s) of interest.

The gammapy.datasets.MapDatasetEventSampler class evaluates the map of predicted counts (npred) per bin of the given Sky model, and the npred map is then used to sample the events. In particular, the output of the event-sampler will be a set of events having information about their true coordinates, true energies and times of arrival.

To these events, IRF corrections (i.e. PSF and energy dispersion) can also further applied in order to obtain reconstructed coordinates and energies of the sampled events.

At the end of this process, you will obtain an event-list in FITS format.

Objective¶

Describe the process of sampling events from a given Sky model and obtaining an output event-list.

Proposed approach¶

In this section, we will show how to define a gammapy.data.Observations and to create a gammapy.datasets.Dataset object (for more info on gammapy.datasets.Dataset objects, please visit this link). These are both necessary for the event sampling. Then, we will define the Sky model from which we sample events.

In this tutorial, we propose two examples for sampling events: one chosing a point-like source and one using a template map.

Setup¶

As usual, let’s start with some general imports…

[1]:

%matplotlib inline

[2]:

import matplotlib.pyplot as plt
from pathlib import Path
import numpy as np
import copy
import astropy.units as u
from astropy.io import fits
from astropy.coordinates import SkyCoord
from gammapy.data import DataStore, GTI, Observation
from gammapy.datasets import MapDataset, MapDatasetEventSampler
from gammapy.maps import MapAxis, WcsGeom, Map
from gammapy.irf import load_cta_irfs
from gammapy.makers import MapDatasetMaker
from gammapy.modeling import Fit
from gammapy.modeling.models import (
    Model,
    Models,
    SkyModel,
    PowerLawSpectralModel,
    PointSpatialModel,
    GaussianSpatialModel,
    SkyDiffuseCube,
)
from regions import CircleSkyRegion

Define an Observation¶

You can firstly create a gammapy.data.Observations object that contains the pointing position, the GTIs and the IRF you want to consider.

Hereafter, we chose the IRF of the South configuration used for the CTA DC1 and we set the pointing position of the simulated field at the Galactic Center. We also fix the exposure time to 1 hr.

Let’s start with some initial settings:

[3]:

IRF_FILE = (
    "$GAMMAPY_DATA/cta-1dc/caldb/data/cta/1dc/bcf/South_z20_50h/irf_file.fits"
)

POINTING = SkyCoord(0.0, 0.0, frame="galactic", unit="deg")
LIVETIME = 1 * u.hr

Now you can create the observation:

[4]:

irfs = load_cta_irfs(IRF_FILE)
observation = Observation.create(
    obs_id=1001, pointing=POINTING, livetime=LIVETIME, irfs=irfs
)

Define the MapDataset¶

Let’s generate the gammapy.datasets.Dataset object: we define the energy axes (true and reconstruncted), the migration axis and the geometry of the observation.

This is a crucial point for the correct configuration of the event sampler. Indeed the spatial and energetic binning should be treaten carefully and… the finer the better. For this reason, we suggest to define the energy axes by setting a minimum binning of least 10-20 bins per decade for all the sources of interest. The spatial binning may instead be different from source to source and, at first order, it should be adopted a binning significantly smaller than the expected source size.

For the examples that will be shown hereafter, we set the geometry of the dataset to a field of view of 2degx2deg and we bin the spatial map with pixels of 0.02 deg.

[5]:

ENERGY_AXIS = MapAxis.from_energy_bounds(
    "0.1 TeV", "100 TeV", nbin=10, per_decade=True
)
ENERGY_AXIS_TRUE = MapAxis.from_energy_bounds(
    "0.03 TeV", "300 TeV", nbin=20, per_decade=True, name="energy_true"
)
MIGRA_AXIS = MapAxis.from_bounds(
    0.5, 2, nbin=150, node_type="edges", name="migra"
)

WCS_GEOM = WcsGeom.create(
    skydir=POINTING,
    width=(2, 2),
    binsz=0.02,
    frame="galactic",
    axes=[ENERGY_AXIS],
)

In the following, the dataset is created by selecting the effective area, background model, the PSF and the Edisp from the IRF. The dataset thus produced can be saved into a FITS file just using the write() function. We put it into the evt_sampling sub-folder:

[6]:

%%time
empty = MapDataset.create(
    WCS_GEOM, energy_axis_true=ENERGY_AXIS_TRUE, migra_axis=MIGRA_AXIS
)
maker = MapDatasetMaker(selection=["exposure", "background", "psf", "edisp"])
dataset = maker.run(empty, observation)

Path("event_sampling").mkdir(exist_ok=True)
dataset.write("./event_sampling/dataset.fits", overwrite=True)

CPU times: user 1.49 s, sys: 510 ms, total: 2 s
Wall time: 2.03 s

Define the Sky model: a point-like source¶

Now let’s define a Sky model (see how to create it here) for a point-like source centered 0.5 deg far from the Galactic Center and with a power-law spectrum. We then save the model into a yaml file.

[7]:

spectral_model_pwl = PowerLawSpectralModel(
    index=2, amplitude="1e-12 TeV-1 cm-2 s-1", reference="1 TeV"
)
spatial_model_point = PointSpatialModel(
    lon_0="0 deg", lat_0="0.5 deg", frame="galactic"
)
sky_model_pntpwl = SkyModel(
    spectral_model=spectral_model_pwl,
    spatial_model=spatial_model_point,
    name="point-pwl",
)

models_pntpwl = Models([sky_model_pntpwl])

file_model = "./event_sampling/point-pwl.yaml"
models_pntpwl.write(file_model, overwrite=True)

Sampling the source and background events¶

Now, we can finally add the gammapy.modeling.models.SkyModel we want to event-sample to the gammapy.datasets.Dataset container:

[8]:

dataset.models.extend(models_pntpwl)
print(dataset.models)

Models

Component 0: BackgroundModel

  Name                      : 5x1qxXyj-bkg
  Datasets names            : ['5x1qxXyj']
  Parameters:
    norm                    :   1.000
    tilt         (frozen)   :   0.000
    reference    (frozen)   :   1.000  TeV

Component 1: SkyModel

  Name                      : point-pwl
  Datasets names            : None
  Spectral model type       : PowerLawSpectralModel
  Spatial  model type       : PointSpatialModel
  Temporal model type       : None
  Parameters:
    index                   :   2.000
    amplitude               :   1.00e-12  1 / (cm2 s TeV)
    reference    (frozen)   :   1.000  TeV
    lon_0                   :   0.000  deg
    lat_0                   :   0.500  deg

The next step shows how to sample the events with the gammapy.datasets.MapDatasetEventSampler class. The class requests a random number seed generator (that we set with random_state=0), the gammapy.datasets.Dataset and the gammapy.data.Observations object. From the latter, the gammapy.datasets.MapDatasetEventSampler class takes all the meta data information.

[9]:

%%time
sampler = MapDatasetEventSampler(random_state=0)
events = sampler.run(dataset, observation)

CPU times: user 1.08 s, sys: 96.6 ms, total: 1.17 s
Wall time: 1.18 s

The output of the event-sampler is an event list with coordinates, energies and time of arrivals of the source and background events. Source and background events are flagged by the MC_ID identifier (where 0 is the default identifier for the background).

[10]:

print(f"Source events: {(events.table['MC_ID'] == 2).sum()}")
print(f"Background events: {(events.table['MC_ID'] == 0).sum()}")

Source events: 178
Background events: 11804

We can inspect the properties of the simulated events as follows:

[11]:

events.peek()

../_images/notebooks_event_sampling_28_0.png

By default, the gammapy.datasets.MapDatasetEventSampler fills the metadata keyword OBJECT in the event list using the first model of the SkyModel object. You can change it with the following commands:

[12]:

events.table.meta["OBJECT"] = dataset.models[1].name

Let’s write the event list and its GTI extension to a FITS file. We make use of fits library in astropy:

[13]:

primary_hdu = fits.PrimaryHDU()
hdu_evt = fits.BinTableHDU(events.table)
hdu_gti = fits.BinTableHDU(dataset.gti.table, name="GTI")
hdu_all = fits.HDUList([primary_hdu, hdu_evt, hdu_gti])
hdu_all.writeto("./event_sampling/events_0001.fits", overwrite=True)

Generate a skymap¶

A skymap of the simulated events can be obtained with:

[14]:

counts = Map.create(
    frame="galactic", skydir=(0, 0.0), binsz=0.02, npix=(100, 100)
)
counts.fill_events(events)
counts.plot(add_cbar=True);

../_images/notebooks_event_sampling_34_0.png

Fit the simulated data¶

We can now check the sake of the event sampling by fitting the data (a tutorial of source fitting is here and here). We make use of the same gammapy.modeling.models.Models adopted for the simulation. Hence, we firstly read the gammapy.datasets.Dataset and the model file, and we fill the gammapy.datasets.Dataset with the sampled events.

[15]:

dataset = MapDataset.read("./event_sampling/dataset.fits")
models_sim_point = Models.read("./event_sampling/point-pwl.yaml")

counts = Map.from_geom(WCS_GEOM)
counts.fill_events(events)

dataset.counts = counts
dataset.models.extend(models_sim_point)

Let’s fit the data and look at the results:

[16]:

%%time
fit = Fit([dataset])
result = fit.run(optimize_opts={"print_level": 1})
print(result)

------------------------------------------------------------------
| FCN = 7.137E+04               |     Ncalls=100 (100 total)     |
| EDM = 2.26E-05 (Goal: 1E-05)  |            up = 1.0            |
------------------------------------------------------------------
|  Valid Min.   | Valid Param.  | Above EDM | Reached call limit |
------------------------------------------------------------------
|     True      |     True      |   False   |       False        |
------------------------------------------------------------------
| Hesse failed  |   Has cov.    | Accurate  | Pos. def. | Forced |
------------------------------------------------------------------
|     False     |     True      |   True    |   True    | False  |
------------------------------------------------------------------
OptimizeResult

        backend    : minuit
        method     : minuit
        success    : True
        message    : Optimization terminated successfully.
        nfev       : 100
        total stat : 71371.11

CPU times: user 13.2 s, sys: 601 ms, total: 13.8 s
Wall time: 13.9 s

[17]:

result.parameters.to_table()

[17]:

Table length=8

name	value	unit	min	max	frozen	error
str9	float64	str14	float64	float64	bool	float64
norm	9.894e-01		0.000e+00	nan	False	9.154e-03
tilt	0.000e+00		nan	nan	True	0.000e+00
reference	1.000e+00	TeV	nan	nan	True	0.000e+00
index	1.998e+00		nan	nan	False	6.349e-02
amplitude	1.042e-12	cm-2 s-1 TeV-1	nan	nan	False	9.926e-14
reference	1.000e+00	TeV	nan	nan	True	0.000e+00
lon_0	1.272e-03	deg	nan	nan	False	3.447e-03
lat_0	5.022e-01	deg	-9.000e+01	9.000e+01	False	3.424e-03

The results looks great!

Extended source using a template¶

The event sampler can also work with a template model. Here we use the interstellar emission model map of the Fermi 3FHL, which can be found in the GAMMAPY data repository.

We proceed following the same steps showed above and we finally have a look at the event’s properties:

[18]:

diffuse = SkyDiffuseCube.read(
    "$GAMMAPY_DATA/fermi-3fhl-gc/gll_iem_v06_gc.fits.gz"
)
models_diffuse = Models([diffuse])

file_model = "./event_sampling/diffuse.yaml"
models_diffuse.write(file_model, overwrite=True)

[19]:

dataset = MapDataset.read("./event_sampling/dataset.fits")
dataset.models.extend(models_diffuse)
print(dataset.models)

Models

Component 0: BackgroundModel

  Name                      : avWdQV1s-bkg
  Datasets names            : ['avWdQV1s']
  Parameters:
    norm                    :   1.000
    tilt         (frozen)   :   0.000
    reference    (frozen)   :   1.000  TeV

Component 1: SkyDiffuseCube

  Name                      : gll_iem_v06_gc.fits
  Datasets names            : None
  Parameters:
    norm                    :   1.000
    tilt         (frozen)   :   0.000
    reference    (frozen)   :   1.000  TeV

[20]:

%%time
sampler = MapDatasetEventSampler(random_state=0)
events = sampler.run(dataset, observation)

CPU times: user 2.66 s, sys: 494 ms, total: 3.15 s
Wall time: 3.16 s

[21]:

events.peek()

../_images/notebooks_event_sampling_45_0.png

Simulate mutiple event list¶

In some user case, you may want to sample events from a number of observations. In this section, we show how to simulate a set of event lists. For simplicity we consider only one point-like source, observed three times for 1 hr and assuming the same pointing position.

Let’s firstly define the time start and the livetime of each observation:

[22]:

tstarts = [1, 5, 7] * u.hr
livetimes = [1, 1, 1] * u.hr

[23]:

for idx, tstart in enumerate(tstarts):

    observation = Observation.create(
        obs_id=idx,
        pointing=POINTING,
        tstart=tstart,
        livetime=livetimes[idx],
        irfs=irfs,
    )

    dataset = maker.run(empty, observation)
    dataset.models.extend(models_pntpwl)

    sampler = MapDatasetEventSampler(random_state=idx)
    events = sampler.run(dataset, observation)
    events.table.write(
        f"./event_sampling/events_{idx:04d}.fits", overwrite=True
    )

You can now load the event list with Datastore.from_events_files() and make your own analysis following the instructions in the `analysis_2 <analysis_2.ipynb>`__ tutorial.

[24]:

path = Path("./event_sampling/")
paths = list(path.rglob("events*.fits"))
data_store = DataStore.from_events_files(paths)
data_store.obs_table

[24]:

ObservationTable length=3

OBS_ID	RA_PNT	DEC_PNT	GLON_PNT	GLAT_PNT	ZEN_PNT	ALT_PNT	AZ_PNT	ONTIME	LIVETIME	DEADC	TSTART	TSTOP	DATE-OBS	TIME-OBS	DATE-END	TIME-END	N_TELS	OBJECT	TELESCOP	CALDB	IRF	EVENTS_FILENAME	EVENT_COUNT
	deg	deg	deg	deg	deg	deg	deg	s	s		s	s
int64	float64	float64	float64	float64	float64	str6	str5	float64	float64	float64	float64	float64	str13	str13	str13	str13	str1	str9	str3	str3	str12	str31	int64
2	266.4049882865447	-28.93617776179147	0.0	4.4527765540489235e-14	70.0	20.000	0.000	3600.0	3600.0	0.0	25199.99999979045	28800.00000020955	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE		point-pwl	CTA	1dc	South_z20_50	event_sampling/events_0002.fits	12232
0	266.4049882865447	-28.93617776179147	0.0	4.4527765540489235e-14	70.0	20.000	0.000	3600.0	3600.0	0.0	3599.999999790452	7200.000000209548	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE		point-pwl	CTA	1dc	South_z20_50	event_sampling/events_0000.fits	11982
1	266.4049882865447	-28.93617776179147	0.0	4.4527765540489235e-14	70.0	20.000	0.000	3600.0	3600.0	0.0	18000.00000020955	21600.0	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE	NOT AVAILABLE		point-pwl	CTA	1dc	South_z20_50	event_sampling/events_0001.fits	12171

Exercises¶

Try to sample events for an extended source (e.g. a radial gaussian morphology);
Change the spatial model and the spectrum of the simulated Sky model;
Include a temporal model in the simulation