\n",
"\n",
"**This is a fixed-text formatted version of a Jupyter notebook**\n",
"\n",
"- Try online [![Binder](https://mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.13?urlpath=lab/tree/image_fitting_with_sherpa.ipynb)\n",
"- You can contribute with your own notebooks in this\n",
"[GitHub repository](https://github.com/gammapy/gammapy/tree/master/tutorials).\n",
"- **Source files:**\n",
"[image_fitting_with_sherpa.ipynb](../_static/notebooks/image_fitting_with_sherpa.ipynb) |\n",
"[image_fitting_with_sherpa.py](../_static/notebooks/image_fitting_with_sherpa.py)\n",
"
\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fitting 2D images with Sherpa\n",
"\n",
"### Introduction\n",
"\n",
"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. \n",
"The issues of constraining the source position and morphology are common in X- and Gamma-ray astronomy. \n",
"This notebook will show you how to apply Sherpa to CTA data.\n",
"\n",
"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.\n",
"\n",
"This tutorial has 2 important parts\n",
"1. Generating the Maps\n",
"2. The actual fitting with sherpa.\n",
"\n",
"Since sherpa deals only with 2-dim images, the first part of this tutorial shows how to prepare gammapy maps to make classical images."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Necessary imports"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"from pathlib import Path\n",
"import numpy as np\n",
"from astropy.io import fits\n",
"import astropy.units as u\n",
"from astropy.coordinates import SkyCoord\n",
"from gammapy.data import DataStore\n",
"from gammapy.irf import make_mean_psf\n",
"from gammapy.maps import WcsGeom, MapAxis, Map\n",
"from gammapy.cube import MapMaker, PSFKernel"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Generating the required Maps\n",
"\n",
"We first generate the required maps using 3 simulated runs on the Galactic center, exactly as in the [analysis_3d](analysis_3d.ipynb) tutorial.\n",
"\n",
"It is always advisable to make the maps on fine energy bins, and then sum them over to get an image."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Define which data to use\n",
"data_store = DataStore.from_dir(\"$GAMMAPY_DATA/cta-1dc/index/gps/\")\n",
"obs_ids = [110380, 111140, 111159]\n",
"observations = data_store.get_observations(obs_ids)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"energy_axis = MapAxis.from_edges(\n",
" np.logspace(-1, 1.0, 10), unit=\"TeV\", name=\"energy\", interp=\"log\"\n",
")\n",
"geom = WcsGeom.create(\n",
" skydir=(0, 0),\n",
" binsz=0.02,\n",
" width=(10, 8),\n",
" coordsys=\"GAL\",\n",
" proj=\"CAR\",\n",
" axes=[energy_axis],\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING: Tried to get polar motions for times after IERS data is valid. Defaulting to polar motion from the 50-yr mean for those. This may affect precision at the 10s of arcsec level [astropy.coordinates.builtin_frames.utils]\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 10.3 s, sys: 1.94 s, total: 12.3 s\n",
"Wall time: 12.3 s\n"
]
}
],
"source": [
"%%time\n",
"maker = MapMaker(geom, offset_max=4.0 * u.deg)\n",
"maps = maker.run(observations)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Making a PSF Map\n",
"\n",
"Make a PSF map and weigh it with the exposure at the source position to get a 2D PSF "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# mean PSF\n",
"src_pos = SkyCoord(0, 0, unit=\"deg\", frame=\"galactic\")\n",
"table_psf = make_mean_psf(observations, src_pos)\n",
"\n",
"# PSF kernel used for the model convolution\n",
"psf_kernel = PSFKernel.from_table_psf(table_psf, geom, max_radius=\"0.3 deg\")\n",
"\n",
"# get the exposure at the source position\n",
"exposure_at_pos = maps[\"exposure\"].get_by_coord(\n",
" {\n",
" \"lon\": src_pos.l.value,\n",
" \"lat\": src_pos.b.value,\n",
" \"energy\": energy_axis.center,\n",
" }\n",
")\n",
"\n",
"# now compute the 2D PSF\n",
"psf2D = psf_kernel.make_image(exposures=exposure_at_pos)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Make 2D images from 3D ones\n",
"\n",
"Since sherpa image fitting works only with 2-dim images,\n",
"we convert the generated maps to 2D images using `run_images()` and save them as fits files. The exposure is weighed with the spectrum before averaging (assumed to be a power law by default).\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"maps = maker.run_images()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"Path(\"analysis_3d\").mkdir(exist_ok=True)\n",
"\n",
"maps[\"counts\"].write(\"analysis_3d/counts_2D.fits\", overwrite=True)\n",
"maps[\"background\"].write(\"analysis_3d/background_2D.fits\", overwrite=True)\n",
"maps[\"exposure\"].write(\"analysis_3d/exposure_2D.fits\", overwrite=True)\n",
"fits.writeto(\"analysis_3d/psf_2D.fits\", psf2D.data, overwrite=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Analysis using sherpha\n",
"\n",
"### Read the maps and store them in a sherpa model\n",
"\n",
"We now have the prepared files which sherpa can read. \n",
"This part of the notebook shows how to do image analysis using sherpa"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"WARNING: imaging routines will not be available, \n",
"failed to import sherpa.image.ds9_backend due to \n",
"'RuntimeErr: DS9Win unusable: Could not find ds9 on your PATH'\n",
"WARNING: failed to import sherpa.astro.xspec; XSPEC models will not be available\n"
]
}
],
"source": [
"import sherpa.astro.ui as sh\n",
"\n",
"sh.set_stat(\"cash\")\n",
"sh.set_method(\"simplex\")\n",
"\n",
"sh.load_image(\"analysis_3d/counts_2D.fits\")\n",
"sh.set_coord(\"logical\")\n",
"\n",
"sh.load_table_model(\"expo\", \"analysis_3d/exposure_2D.fits\")\n",
"sh.load_table_model(\"bkg\", \"analysis_3d/background_2D.fits\")\n",
"sh.load_psf(\"psf\", \"analysis_3d/psf_2D.fits\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To speed up this tutorial, we change the fit optimazation method to Levenberg-Marquardt and fix a required tolerance. This can make the fitting less robust, and in practise, you can skip this step unless you understand what is going on."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"sh.set_method(\"levmar\")\n",
"sh.set_method_opt(\"xtol\", 1e-5)\n",
"sh.set_method_opt(\"ftol\", 1e-5)\n",
"sh.set_method_opt(\"gtol\", 1e-5)\n",
"sh.set_method_opt(\"epsfcn\", 1e-5)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"name = levmar\n",
"ftol = 1e-05\n",
"xtol = 1e-05\n",
"gtol = 1e-05\n",
"maxfev = None\n",
"epsfcn = 1e-05\n",
"factor = 100.0\n",
"verbose = 0\n"
]
}
],
"source": [
"print(sh.get_method())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"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."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"sh.set_full_model(bkg)\n",
"bkg.ampl = 1\n",
"sh.freeze(bkg)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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