This is a fixed-text formatted version of a Jupyter notebook.
- Try online
- You can contribute with your own notebooks in this GitHub repository.
- Source files: image_fitting_with_sherpa.ipynb | image_fitting_with_sherpa.py
Fitting 2D images with Sherpa¶
Introduction¶
Sherpa is the X-ray satellite Chandra modeling and fitting application. It enables the user to construct complex models from simple definitions and fit those models to data, using a variety of statistics and optimization methods. The issues of constraining the source position and morphology are common in X- and Gamma-ray astronomy. This notebook will show you how to apply Sherpa to CTA data.
Here we will set up Sherpa to fit the counts map and loading the ancillary images for subsequent use. A relevant test statistic for data with Poisson fluctuations is the one proposed by Cash (1979). The simplex (or Nelder-Mead) fitting algorithm is a good compromise between efficiency and robustness. The source fit is best performed in pixel coordinates.
This tutorial has 2 important parts 1. Generating the Maps 2. The actual fitting with sherpa.
Since sherpa deals only with 2-dim images, the first part of this tutorial shows how to prepare gammapy maps to make classical images.
Necessary imports¶
In [1]:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
from astropy.io import fits
import astropy.units as u
from astropy.wcs import WCS
from astropy.coordinates import SkyCoord
from gammapy.extern.pathlib import Path
from gammapy.data import DataStore
from gammapy.irf import EnergyDispersion, make_mean_psf
from gammapy.maps import WcsGeom, MapAxis, Map
from gammapy.cube import MapMaker, PSFKernel
Generate the required Maps¶
We first generate the required maps using 3 simulated runs on the Galactic center, exactly as in the analysis_3d tutorial.
It is always advisable to make the maps on fine energy bins, and then sum them over to get an image.
In [2]:
# Define which data to use
data_store = DataStore.from_dir("$GAMMAPY_DATA/cta-1dc/index/gps/")
obs_ids = [110380, 111140, 111159]
observations = data_store.get_observations(obs_ids)
In [3]:
energy_axis = MapAxis.from_edges(
np.logspace(-1, 1.0, 10), unit="TeV", name="energy", interp="log"
)
geom = WcsGeom.create(
skydir=(0, 0),
binsz=0.02,
width=(10, 8),
coordsys="GAL",
proj="CAR",
axes=[energy_axis],
)
In [4]:
%%time
maker = MapMaker(geom, offset_max=4.0 * u.deg)
maps = maker.run(observations)
CPU times: user 38.7 s, sys: 2.27 s, total: 41 s
Wall time: 10.3 s
Making a PSF Map¶
Make a PSF map and weigh it with the exposure at the source position to get a 2D PSF
In [5]:
# mean PSF
src_pos = SkyCoord(0, 0, unit="deg", frame="galactic")
table_psf = make_mean_psf(observations, src_pos)
# PSF kernel used for the model convolution
psf_kernel = PSFKernel.from_table_psf(table_psf, geom, max_radius="0.3 deg")
# get the exposure at the source position
exposure_at_pos = maps["exposure"].get_by_coord(
{
"lon": src_pos.l.value,
"lat": src_pos.b.value,
"energy": energy_axis.center,
}
)
# now compute the 2D PSF
psf2D = psf_kernel.make_image(exposures=exposure_at_pos)
Make 2D images from 3D ones¶
Since sherpa image fitting works only with 2-dim images, we convert the
generated maps to 2D images using make_images() and save them as
fits files. The exposure is weighed with the spectrum before averaging
(assumed to be a power law by default).
In [6]:
maps = maker.make_images()
In [7]:
Path("analysis_3d").mkdir(exist_ok=True)
maps["counts"].write("analysis_3d/counts_2D.fits", overwrite=True)
maps["background"].write("analysis_3d/background_2D.fits", overwrite=True)
maps["exposure"].write("analysis_3d/exposure_2D.fits", overwrite=True)
fits.writeto("analysis_3d/psf_2D.fits", psf2D.data, overwrite=True)
Read the maps and store them in a sherpa model¶
We now have the prepared files which sherpa can read. This part of the notebook shows how to do image analysis using sherpa
In [8]:
import sherpa.astro.ui as sh
sh.set_stat("cash")
sh.set_method("simplex")
sh.load_image("analysis_3d/counts_2D.fits")
sh.set_coord("logical")
sh.load_table_model("expo", "analysis_3d/exposure_2D.fits")
sh.load_table_model("bkg", "analysis_3d/background_2D.fits")
sh.load_psf("psf", "analysis_3d/psf_2D.fits")
WARNING: imaging routines will not be available,
failed to import sherpa.image.ds9_backend due to
'RuntimeErr: DS9Win unusable: Could not find ds9 on your PATH'
WARNING: failed to import sherpa.astro.xspec; XSPEC models will not be available
/Users/deil/software/anaconda3/envs/gammapy-dev/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: Unable to load the ciao_version module to determine version number- defaulting 'group' version to 0.0.0
return f(*args, **kwds)
In principle one might first want to fit the background amplitude. However the background estimation method already yields the correct normalization, so we freeze the background amplitude to unity instead of adjusting it. The (smoothed) residuals from this background model are then computed and shown.
In [9]:
sh.set_full_model(bkg)
bkg.ampl = 1
sh.freeze(bkg)
In [10]:
resid = Map.read("analysis_3d/counts_2D.fits")
resid.data = sh.get_data_image().y - sh.get_model_image().y
resid_smooth = resid.smooth(width=4)
resid_smooth.plot(add_cbar=True);
Find and fit the brightest source¶
We then find the position of the maximum in the (smoothed) residuals map, and fit a (symmetrical) Gaussian source with that initial position:
In [11]:
yp, xp = np.unravel_index(
np.nanargmax(resid_smooth.data), resid_smooth.data.shape
)
ampl = resid_smooth.get_by_pix((xp, yp))[0]
# creates g0 as a gauss2d instance
sh.set_full_model(bkg + psf(sh.gauss2d.g0) * expo)
g0.xpos, g0.ypos = xp, yp
sh.freeze(g0.xpos, g0.ypos) # fix the position in the initial fitting step
# fix exposure amplitude so that typical exposure is of order unity
expo.ampl = 1e-9
sh.freeze(expo)
sh.thaw(g0.fwhm, g0.ampl) # in case frozen in a previous iteration
g0.fwhm = 10 # give some reasonable initial values
g0.ampl = ampl
In [12]:
%%time
sh.fit()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<timed eval> in <module>
<string> in fit(id, *otherids, **kwargs)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in fit(self, id, *otherids, **kwargs)
9449 """
9450 kwargs['bkg_only'] = False
-> 9451 self._fit(id, *otherids, **kwargs)
9452
9453 def fit_bkg(self, id=None, *otherids, **kwargs):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _fit(self, id, *otherids, **kwargs)
9546 ids, f = self._get_bkg_fit(id, otherids)
9547 else:
-> 9548 ids, f = self._get_fit(id, otherids)
9549
9550 if 'filter_nan' in kwargs and kwargs.pop('filter_nan'):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_fit(self, id, otherids, estmethod)
7467 def _get_fit(self, id, otherids=(), estmethod=None):
7468
-> 7469 fit_to_ids, datasets, models = self._prepare_fit(id, otherids)
7470
7471 self._add_extra_data_and_models(fit_to_ids, datasets, models)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _prepare_fit(self, id, otherids)
7442 mod = None
7443 if i in self._models or i in self._sources:
-> 7444 mod = self._get_model(i)
7445
7446 # The issue with putting a try/catch here is that if an exception
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_model(self, id)
5507 data = self.get_data(id)
5508 model, is_source = self._get_model_status(id)
-> 5509 return self._add_convolution_models(id, data, model, is_source)
5510
5511 def _get_source(self, id=None):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
8394 model = \
8395 sherpa.ui.utils.Session._add_convolution_models(self, id, data,
-> 8396 model, is_source)
8397 id = self._fix_id(id)
8398 if (isinstance(data, sherpa.astro.data.DataPHA) and is_source):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in <listcomp>(.0)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/instrument.py in fold(self, data)
1097
1098 def fold(self, data):
-> 1099 _PSFModel.fold(self, data)
1100
1101 # Set WCS coordinates of kernel data set to match source data set.
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in fold(self, data)
555 # FIXME how will we know the native dimensionality of the
556 # raveled model without the values?
--> 557 self._check_pixel_size(data)
558
559 kargs = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in _check_pixel_size(self, data)
718 if hasattr(self.kernel, "sky"):
719 # This corresponds to the case when the kernel is actually a psf image, not just a model.
--> 720 psf_pixel_size = self.kernel.sky.cdelt
721 data_pixel_size = data.sky.cdelt
722
AttributeError: 'NoneType' object has no attribute 'cdelt'
Fit all parameters of this Gaussian component, fix them and re-compute the residuals map.
In [13]:
sh.thaw(g0.xpos, g0.ypos)
sh.fit()
sh.freeze(g0)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-13-d0c708c71933> in <module>
1 sh.thaw(g0.xpos, g0.ypos)
----> 2 sh.fit()
3 sh.freeze(g0)
<string> in fit(id, *otherids, **kwargs)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in fit(self, id, *otherids, **kwargs)
9449 """
9450 kwargs['bkg_only'] = False
-> 9451 self._fit(id, *otherids, **kwargs)
9452
9453 def fit_bkg(self, id=None, *otherids, **kwargs):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _fit(self, id, *otherids, **kwargs)
9546 ids, f = self._get_bkg_fit(id, otherids)
9547 else:
-> 9548 ids, f = self._get_fit(id, otherids)
9549
9550 if 'filter_nan' in kwargs and kwargs.pop('filter_nan'):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_fit(self, id, otherids, estmethod)
7467 def _get_fit(self, id, otherids=(), estmethod=None):
7468
-> 7469 fit_to_ids, datasets, models = self._prepare_fit(id, otherids)
7470
7471 self._add_extra_data_and_models(fit_to_ids, datasets, models)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _prepare_fit(self, id, otherids)
7442 mod = None
7443 if i in self._models or i in self._sources:
-> 7444 mod = self._get_model(i)
7445
7446 # The issue with putting a try/catch here is that if an exception
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_model(self, id)
5507 data = self.get_data(id)
5508 model, is_source = self._get_model_status(id)
-> 5509 return self._add_convolution_models(id, data, model, is_source)
5510
5511 def _get_source(self, id=None):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
8394 model = \
8395 sherpa.ui.utils.Session._add_convolution_models(self, id, data,
-> 8396 model, is_source)
8397 id = self._fix_id(id)
8398 if (isinstance(data, sherpa.astro.data.DataPHA) and is_source):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in <listcomp>(.0)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/instrument.py in fold(self, data)
1097
1098 def fold(self, data):
-> 1099 _PSFModel.fold(self, data)
1100
1101 # Set WCS coordinates of kernel data set to match source data set.
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in fold(self, data)
555 # FIXME how will we know the native dimensionality of the
556 # raveled model without the values?
--> 557 self._check_pixel_size(data)
558
559 kargs = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in _check_pixel_size(self, data)
718 if hasattr(self.kernel, "sky"):
719 # This corresponds to the case when the kernel is actually a psf image, not just a model.
--> 720 psf_pixel_size = self.kernel.sky.cdelt
721 data_pixel_size = data.sky.cdelt
722
AttributeError: 'NoneType' object has no attribute 'cdelt'
In [14]:
resid.data = sh.get_data_image().y - sh.get_model_image().y
resid_smooth = resid.smooth(width=3)
resid_smooth.plot();
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-14-8dacc4a753bc> in <module>
----> 1 resid.data = sh.get_data_image().y - sh.get_model_image().y
2 resid_smooth = resid.smooth(width=3)
3 resid_smooth.plot();
<string> in get_model_image(id)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in get_model_image(self, id)
14355
14356 """
> 14357 self._prepare_imageobj(id, self._modelimage)
14358 return self._modelimage
14359
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _prepare_imageobj(self, id, imageobj, model)
14264 imageobj.prepare_image(self.get_data(id), self.get_source(id))
14265 else:
> 14266 imageobj.prepare_image(self.get_data(id), self.get_model(id))
14267 return imageobj
14268
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in get_model(self, id)
5611
5612 """
-> 5613 return self._get_model(id)
5614
5615 def _runparamprompt(self, pars):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_model(self, id)
5507 data = self.get_data(id)
5508 model, is_source = self._get_model_status(id)
-> 5509 return self._add_convolution_models(id, data, model, is_source)
5510
5511 def _get_source(self, id=None):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
8394 model = \
8395 sherpa.ui.utils.Session._add_convolution_models(self, id, data,
-> 8396 model, is_source)
8397 id = self._fix_id(id)
8398 if (isinstance(data, sherpa.astro.data.DataPHA) and is_source):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in <listcomp>(.0)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/instrument.py in fold(self, data)
1097
1098 def fold(self, data):
-> 1099 _PSFModel.fold(self, data)
1100
1101 # Set WCS coordinates of kernel data set to match source data set.
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in fold(self, data)
555 # FIXME how will we know the native dimensionality of the
556 # raveled model without the values?
--> 557 self._check_pixel_size(data)
558
559 kargs = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in _check_pixel_size(self, data)
718 if hasattr(self.kernel, "sky"):
719 # This corresponds to the case when the kernel is actually a psf image, not just a model.
--> 720 psf_pixel_size = self.kernel.sky.cdelt
721 data_pixel_size = data.sky.cdelt
722
AttributeError: 'NoneType' object has no attribute 'cdelt'
Iteratively find and fit additional sources¶
Instantiate additional Gaussian components, and use them to iteratively fit sources, repeating the steps performed above for component g0. (The residuals map is shown after each additional source included in the model.) This takes some time…
In [15]:
# initialize components with fixed, zero amplitude
for i in range(1, 10):
model = sh.create_model_component("gauss2d", "g" + str(i))
model.ampl = 0
sh.freeze(model)
gs = [g0, g1, g2]
sh.set_full_model(bkg + psf(g0 + g1 + g2) * expo)
In [16]:
%%time
for i in range(1, len(gs)):
yp, xp = np.unravel_index(
np.nanargmax(resid_smooth.data), resid_smooth.data.shape
)
ampl = resid_smooth.get_by_pix((xp, yp))[0]
gs[i].xpos, gs[i].ypos = xp, yp
gs[i].fwhm = 10
gs[i].ampl = ampl
sh.thaw(gs[i].fwhm)
sh.thaw(gs[i].ampl)
sh.fit()
sh.thaw(gs[i].xpos)
sh.thaw(gs[i].ypos)
sh.fit()
sh.freeze(gs[i])
resid.data = sh.get_data_image().y - sh.get_model_image().y
resid_smooth = resid.smooth(width=6)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<timed exec> in <module>
<string> in fit(id, *otherids, **kwargs)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in fit(self, id, *otherids, **kwargs)
9449 """
9450 kwargs['bkg_only'] = False
-> 9451 self._fit(id, *otherids, **kwargs)
9452
9453 def fit_bkg(self, id=None, *otherids, **kwargs):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _fit(self, id, *otherids, **kwargs)
9546 ids, f = self._get_bkg_fit(id, otherids)
9547 else:
-> 9548 ids, f = self._get_fit(id, otherids)
9549
9550 if 'filter_nan' in kwargs and kwargs.pop('filter_nan'):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_fit(self, id, otherids, estmethod)
7467 def _get_fit(self, id, otherids=(), estmethod=None):
7468
-> 7469 fit_to_ids, datasets, models = self._prepare_fit(id, otherids)
7470
7471 self._add_extra_data_and_models(fit_to_ids, datasets, models)
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _prepare_fit(self, id, otherids)
7442 mod = None
7443 if i in self._models or i in self._sources:
-> 7444 mod = self._get_model(i)
7445
7446 # The issue with putting a try/catch here is that if an exception
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_model(self, id)
5507 data = self.get_data(id)
5508 model, is_source = self._get_model_status(id)
-> 5509 return self._add_convolution_models(id, data, model, is_source)
5510
5511 def _get_source(self, id=None):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
8394 model = \
8395 sherpa.ui.utils.Session._add_convolution_models(self, id, data,
-> 8396 model, is_source)
8397 id = self._fix_id(id)
8398 if (isinstance(data, sherpa.astro.data.DataPHA) and is_source):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in <listcomp>(.0)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/instrument.py in fold(self, data)
1097
1098 def fold(self, data):
-> 1099 _PSFModel.fold(self, data)
1100
1101 # Set WCS coordinates of kernel data set to match source data set.
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in fold(self, data)
555 # FIXME how will we know the native dimensionality of the
556 # raveled model without the values?
--> 557 self._check_pixel_size(data)
558
559 kargs = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in _check_pixel_size(self, data)
718 if hasattr(self.kernel, "sky"):
719 # This corresponds to the case when the kernel is actually a psf image, not just a model.
--> 720 psf_pixel_size = self.kernel.sky.cdelt
721 data_pixel_size = data.sky.cdelt
722
AttributeError: 'NoneType' object has no attribute 'cdelt'
In [17]:
resid_smooth.plot(add_cbar=True);
Generating output table and Test Statistics estimation¶
When adding a new source, one needs to check the significance of this new source. A frequently used method is the Test Statistics (TS). This is done by comparing the change of statistics when the source is included compared to the null hypothesis (no source ; in practice here we fix the amplitude to zero).
\(TS = Cstat(source) - Cstat(no source)\)
The criterion for a significant source detection is typically that it should improve the test statistic by at least 25 or 30. We have added only 3 sources to save time, but you should keep doing this till del(stat) is less than the required number.
In [18]:
from astropy.stats import gaussian_fwhm_to_sigma
from astropy.table import Table
rows = []
for g in gs:
ampl = g.ampl.val
g.ampl = 0
stati = sh.get_stat_info()[0].statval
g.ampl = ampl
statf = sh.get_stat_info()[0].statval
delstat = stati - statf
geom = resid.geom
coord = geom.pix_to_coord((g.xpos.val, g.ypos.val))
pix_scale = geom.pixel_scales.mean().deg
sigma = g.fwhm.val * pix_scale * gaussian_fwhm_to_sigma
rows.append(
dict(delstat=delstat, glon=coord[0], glat=coord[1], sigma=sigma)
)
table = Table(rows=rows, names=rows[0])
for name in table.colnames:
table[name].format = ".5g"
table
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-18-bdd7ade33e59> in <module>
6 ampl = g.ampl.val
7 g.ampl = 0
----> 8 stati = sh.get_stat_info()[0].statval
9 g.ampl = ampl
10 statf = sh.get_stat_info()[0].statval
<string> in get_stat_info()
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in get_stat_info(self)
7614
7615 """
-> 7616 return self._get_stat_info()
7617
7618 def get_fit_results(self):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _get_stat_info(self)
9560 def _get_stat_info(self):
9561
-> 9562 ids, datasets, models = self._prepare_fit(None)
9563
9564 extra_ids = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _prepare_fit(self, id, otherids)
7442 mod = None
7443 if i in self._models or i in self._sources:
-> 7444 mod = self._get_model(i)
7445
7446 # The issue with putting a try/catch here is that if an exception
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _get_model(self, id)
5507 data = self.get_data(id)
5508 model, is_source = self._get_model_status(id)
-> 5509 return self._add_convolution_models(id, data, model, is_source)
5510
5511 def _get_source(self, id=None):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
8394 model = \
8395 sherpa.ui.utils.Session._add_convolution_models(self, id, data,
-> 8396 model, is_source)
8397 id = self._fix_id(id)
8398 if (isinstance(data, sherpa.astro.data.DataPHA) and is_source):
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in _add_convolution_models(self, id, data, model, is_source)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/ui/utils.py in <listcomp>(.0)
5500 model = self._add_psf(id, data, model)
5501 else:
-> 5502 [psf.fold(data) for psf in self._psf_models if psf in model]
5503
5504 return model
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/astro/instrument.py in fold(self, data)
1097
1098 def fold(self, data):
-> 1099 _PSFModel.fold(self, data)
1100
1101 # Set WCS coordinates of kernel data set to match source data set.
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in fold(self, data)
555 # FIXME how will we know the native dimensionality of the
556 # raveled model without the values?
--> 557 self._check_pixel_size(data)
558
559 kargs = {}
~/software/anaconda3/envs/gammapy-dev/lib/python3.7/site-packages/sherpa/instrument.py in _check_pixel_size(self, data)
718 if hasattr(self.kernel, "sky"):
719 # This corresponds to the case when the kernel is actually a psf image, not just a model.
--> 720 psf_pixel_size = self.kernel.sky.cdelt
721 data_pixel_size = data.sky.cdelt
722
AttributeError: 'NoneType' object has no attribute 'cdelt'
Exercises¶
- Keep adding sources till there are no more significat ones in the field. How many Gaussians do you need?
- Use other morphologies for the sources (eg: disk, shell) rather than only Gaussian.
- Compare the TS between different models
More about sherpa¶
These are good resources to learn more about Sherpa:
- https://python4astronomers.github.io/fitting/fitting.html
- https://github.com/DougBurke/sherpa-standalone-notebooks
You could read over the examples there, and try to apply a similar analysis to this dataset here to practice.
If you want a deeper understanding of how Sherpa works, then these proceedings are good introductions: