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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Advanced model manipulation and fitting in Python"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "<div align=\"right\"><a href=\"../../../_downloads/advanced-python-fitting.ipynb\" download=\"advanced-python-fitting.ipynb\"><img src=\"../../../_static/download-notebook.jpg\" alt=\"Download Notebook\" height=\"40\"></a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial you will learn to perform some more advanced model manipulation and fitting from Python. You can use these methods in an interactive Python session to explore your dataset and improve the known model of the sky. You can also use them in a Python pipeline to test multiple model hypotheses and select the one that is most appropriate.\n",
    "\n",
    "As usual we start by importing the gammalib, ctools, and cscripts Python modules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import gammalib\n",
    "import ctools\n",
    "import cscripts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this tutorial we will also use the matplotlib package for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulated dataset\n",
    "\n",
    "For the tutorial we will simulate a small dataset. We start by defining the Instrument Response Function and energy range that we will use all along."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "caldb = 'prod2'\n",
    "irf = 'South_0.5h'\n",
    "emin = 0.1 #TeV\n",
    "emax = 160. #TeV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we proceed to simulate the dataset. It consists of an hour of observations of the Crab nebula region, as usual pointed at a slightly offset position from the target. The input model is different from the one you have been using so far and contains some surprises. Don't look at it until you have completed the exercises at the end of the tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "evfile = 'events.fits'\n",
    "\n",
    "obssim = ctools.ctobssim()\n",
    "\n",
    "obssim['ra'] = 83.63\n",
    "obssim['dec'] = 22.51\n",
    "obssim['rad'] = 5.0\n",
    "obssim['tmin'] = 0\n",
    "obssim['tmax'] = 3600\n",
    "obssim['emin'] = emin\n",
    "obssim['emax'] = emax\n",
    "obssim['caldb'] = caldb\n",
    "obssim['irf'] = irf\n",
    "obssim['inmodel'] = '$CTOOLS/share/models/crab_beyond.xml'\n",
    "obssim['outevents'] = evfile\n",
    "\n",
    "obssim.execute()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have saved the events on disk in the file `events.fits`. In this way you can easily re-use the code below by substituting `events.fits` with your own event list of observation definition XML file.\n",
    "\n",
    "We will peek at the simulated dataset by displaying a skymap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "skymap = ctools.ctskymap()\n",
    "\n",
    "skymap['inobs'] = evfile\n",
    "skymap['emin'] = emin\n",
    "skymap['emax'] = emax\n",
    "skymap['nxpix'] = 40\n",
    "skymap['nypix'] = 40\n",
    "skymap['binsz'] = 0.02\n",
    "skymap['proj'] = 'TAN'\n",
    "skymap['coordsys'] = 'CEL'\n",
    "skymap['xref'] = 83.63\n",
    "skymap['yref'] = 22.01\n",
    "skymap['bkgsubtract'] = 'IRF'\n",
    "skymap['caldb'] = caldb\n",
    "skymap['irf'] = irf\n",
    "\n",
    "skymap.run()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BELSI/7X+/383Q6bAKVkOns/b4X3APxypTjxX6darG2+o12rzqABXqOq9ItIH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\nLAKhfIMgCBaB/x9Cm8epUtmYrAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e220b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We slightly smooth the map for display to suppress statistical fluctuations\n",
    "skymap.skymap().smooth('GAUSSIAN',0.02)\n",
    "\n",
    "from matplotlib.colors import SymLogNorm\n",
    "# The SymLogNorm scale is a Log scale for both positive and negative values\n",
    "# and is linear within a certain range around 0\n",
    "\n",
    "ax = plt.subplot()\n",
    "plt.imshow(skymap.skymap().array(),origin='lower',\n",
    "           extent=[83.63+0.02*20,83.63-0.02*20,22.01-0.02*20,22.01+0.02*20],\n",
    "           # boundaries of the coord grid\n",
    "           norm=SymLogNorm(1)) # the scale will be linear within +-1 count \n",
    "ax.set_xlabel('R.A. (deg)')\n",
    "ax.set_ylabel('Dec (deg)')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model fitting and residual inspection\n",
    "\n",
    "First, we will fit the usual Crab model to the data. We will be using a 3D unbinned analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "like = ctools.ctlike()\n",
    "\n",
    "like['inobs'] = evfile\n",
    "like['caldb'] = caldb\n",
    "like['irf'] = irf\n",
    "like['inmodel'] = '$CTOOLS/share/models/crab.xml'\n",
    "\n",
    "like.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual it is wise to look at the output from the optimizer. We will also store the best-fit minus log-likelihood value for later usage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== GOptimizerLM ===\n",
      " Optimized function value ..: 310147.111\n",
      " Absolute precision ........: 0.005\n",
      " Acceptable value decrease .: 2\n",
      " Optimization status .......: converged\n",
      " Number of parameters ......: 10\n",
      " Number of free parameters .: 4\n",
      " Number of iterations ......: 10\n",
      " Lambda ....................: 1e-09\n"
     ]
    }
   ],
   "source": [
    "print(like.opt())\n",
    "\n",
    "like1 = like.opt().value()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fit has properly converged after 10 iterations. Let's take a look at the best-fit model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== GModels ===\n",
      " Number of models ..........: 2\n",
      " Number of parameters ......: 10\n",
      "=== GModelSky ===\n",
      " Name ......................: Crab\n",
      " Instruments ...............: all\n",
      " Instrument scale factors ..: unity\n",
      " Observation identifiers ...: all\n",
      " Model type ................: PointSource\n",
      " Model components ..........: \"PointSource\" * \"PowerLaw\" * \"Constant\"\n",
      " Number of parameters ......: 6\n",
      " Number of spatial par's ...: 2\n",
      "  RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)\n",
      "  DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)\n",
      " Number of spectral par's ..: 3\n",
      "  Prefactor ................: 3.53407186484023e-16 +/- 6.13239441118338e-18 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)\n",
      "  Index ....................: -2.28003948199797 +/- 0.0145823226642845 [-0,-5]  (free,scale=-1,gradient)\n",
      "  PivotEnergy ..............: 300000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)\n",
      " Number of temporal par's ..: 1\n",
      "  Normalization ............: 1 (relative value) (fixed,scale=1,gradient)\n",
      "=== GCTAModelIrfBackground ===\n",
      " Name ......................: CTABackgroundModel\n",
      " Instruments ...............: CTA\n",
      " Instrument scale factors ..: unity\n",
      " Observation identifiers ...: all\n",
      " Model type ................: \"PowerLaw\" * \"Constant\"\n",
      " Number of parameters ......: 4\n",
      " Number of spectral par's ..: 3\n",
      "  Prefactor ................: 1.00695509680653 +/- 0.00831375832092445 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)\n",
      "  Index ....................: 0.00506439697818556 +/- 0.00509750451889964 [-5,5]  (free,scale=1,gradient)\n",
      "  PivotEnergy ..............: 1000000 [10000,1000000000] MeV (fixed,scale=1000000,gradient)\n",
      " Number of temporal par's ..: 1\n",
      "  Normalization ............: 1 (relative value) (fixed,scale=1,gradient)\n"
     ]
    }
   ],
   "source": [
    "print(like.obs().models())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The background model reproduces well the data, since its best-fit normalization is 1 and the index/tilt is 0. The Crab nebula has a best-fit spectral index of 2.28.\n",
    "\n",
    "To assess whether the model reproduces well the data spatially we will calculate a residual map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "resmap = cscripts.csresmap(like.obs())\n",
    "\n",
    "resmap['algorithm'] = 'SIGNIFICANCE'\n",
    "resmap['emin'] = emin\n",
    "resmap['emax'] = emax\n",
    "resmap['nxpix'] = 40\n",
    "resmap['nypix'] = 40\n",
    "resmap['binsz'] = 0.02\n",
    "resmap['proj'] = 'TAN'\n",
    "resmap['coordsys'] = 'CEL'\n",
    "resmap['xref'] = 83.63\n",
    "resmap['yref'] = 22.01\n",
    "\n",
    "resmap.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be inspecting several of these residual maps along the tutorial, so we define a function to plot them, and apply it to our latest run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_residuals(resid):\n",
    "    # We slightly smooth the map for display to suppress statistical fluctuations\n",
    "    resid.smooth('GAUSSIAN',0.04)\n",
    "    #plotting\n",
    "    fig = plt.figure()\n",
    "    ax = plt.subplot()\n",
    "    plt.imshow(resid.array(),origin='lower',\n",
    "               cmap='bwr',vmin=-3,vmax=3,\n",
    "               extent=[83.63+0.02*20,83.63-0.02*20,22.01-0.02*20,22.01+0.02*20])\n",
    "            # boundaries of the coord grid\n",
    "    ax.set_xlabel('R.A. (deg)')\n",
    "    ax.set_ylabel('Dec (deg)')\n",
    "    cbar = plt.colorbar()\n",
    "    cbar.set_label('Significance ($\\sigma$)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Uh+jFaH7969W26Cn04hCjYz3VIYoR9ZSXKN53sROOGakxa9fW69cJcwU46uRp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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10befc748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_residuals(resmap._resmap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding model components\n",
    "\n",
    "The residual map shows a cluster of positive residuals on the South-West of the Crab nebula. Is this another source? To test this hypothesis we will add a point source at the position that we can guess from the residual map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "newpntsrc = gammalib.GModelSky(gammalib.GModelSpatialPointSource(83.7,21.9),\n",
    "                               gammalib.GModelSpectralPlaw(1.e-17,-2.,gammalib.GEnergy(3.e5,'MeV')),\n",
    "                               gammalib.GModelTemporalConst(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have defined a sky model object that has three components:\n",
    "\n",
    "- a spatial model, which is a point source at the position guessed from the residual map;\n",
    "- a spectral model which is a power law with spectral index 2, and a flux which approximately 1/10 of the Crab nebula;\n",
    "- a temporal model which is a constant.\n",
    "\n",
    "We will name this source Src1, and free its position (fixed by default when a new source is created), so that we can fit it to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "newpntsrc.name('Src1')\n",
    "newpntsrc['RA'].free()\n",
    "newpntsrc['DEC'].free()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally we append the new source to the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<gammalib.model.GModelSky; proxy of <Swig Object of type 'GModelSky *' at 0x10e91f9c0> >"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like.obs().models().append(newpntsrc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and we fit the model including the new source to the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "like.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Does the addition of the new source provide a better fit to the data? We can quantify this using the test statistic (TS) given by twice the log-likelihood difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "189.7624766129302\n"
     ]
    }
   ],
   "source": [
    "like2 = like.opt().value()\n",
    "\n",
    "ts = -2 * (like2 - like1)\n",
    "print(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TS is expected to be distributed as a $\\chi^2$ with n degrees of freedom, where n is the additional number of degrees of freedom in the model including the new source, in our case 4 (RA, Dec, Prefactor, and Index). The integral of the $\\chi^2$ from TS to $\\infty$ is the chance probability that the likelihood improved by that much due to statistical fluctuations. A large value, like the one we got, means that the chance probability is very low, thus we are likely to have found a new source.\n",
    "\n",
    "To make sure the new source improves the data/model agreement we will look again at the residual map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3rGyvTR3DesLMTqosDCRpAX1a8ypJkrlBvxlWM/sw8GFJ/83M/tVM+6tjWP9C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e5bac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resmap.models(like.obs().models())\n",
    "resmap.run()\n",
    "\n",
    "plot_residuals(resmap._resmap)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The addition of the new point source has flattened the spatial residuals, even though the fit is not perfect yet obvisouly. From now on we will fix the position of Scr1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "like.obs().models()['Src1']['RA'].fix()\n",
    "like.obs().models()['Src1']['DEC'].fix()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Modifying the spectral models\n",
    "\n",
    "Next we will check if the model agrees well with the data at all energies. We will start by defining a function to make and plot residual maps in separate energy ranges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def resmap_erange(ebounds):\n",
    "    for elow, eup in ebounds:\n",
    "        resmap['emin'] = elow\n",
    "        resmap['emax'] = eup\n",
    "        resmap.models(like.obs().models()) # we make sure we are using the latest best-fit model\n",
    "        resmap.run()\n",
    "        plot_residuals(resmap._resmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HsH5D0tuBRZLOAd4A/MN0L9wJRkaqhfuaiAjRw/b6WBpscftaji+geccun+fk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\nG8zs6il08QJgs5n9rN2RJUk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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e8f4518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6iR1rEAT9ZbCTCe6Q9KzOGzP7JpCdpTR2rEEQ9J/BU151+H3g05I2A3cAxwPfy+2ktdlJ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\nCcEaBEHQMCFYgyAIGiYEaxAEQcP8fylbjMqvtib2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10af94278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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73UPVsRkVMCSGe0rrVyX9ku07BslkrPVY7wOQdLztznFcvydpA0Xba0RE/4a3xvoq4DRJ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\nRETNElgjImr2/wHfKy0tKmP2AQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b67b940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resmap_erange([[emin,1.],\n",
    "              [1.,10.],\n",
    "              [10.,emax]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most obvious problem is a negative residual cluster at the position of the Crab nebula at the highest energies. We will change the spectral model of the crab nebula and test if this improves the fit. We will use an exponentially cutoff power-law rather than a simple power law. We will use as starting values for the Prefactor and Index the current best-fit values and tentatively set the cutoff energy at 1 TeV."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "crab = like.obs().models()['Crab']\n",
    "\n",
    "expplaw = gammalib.GModelSpectralExpPlaw()\n",
    "\n",
    "expplaw['Prefactor'].value(crab['Prefactor'].value())\n",
    "expplaw['Index'].value(crab['Index'].value())\n",
    "expplaw['PivotEnergy'].value(crab['PivotEnergy'].value())\n",
    "expplaw['CutoffEnergy'].value(1.e6)\n",
    "\n",
    "crab.spectral(expplaw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now fit the modified model to the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "like.run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and use TS to quantify the model improvement (in this case we have only one additional degree of freedom, the ctuoff energy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "310.5695030956995\n"
     ]
    }
   ],
   "source": [
    "like3 = like.opt().value()\n",
    "\n",
    "ts = -2 * (like3 - like2)\n",
    "print(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model improvement was again significant. Let's look at the fit results for the Crab nebula."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== GModelSky ===\n",
      " Name ......................: Crab\n",
      " Instruments ...............: all\n",
      " Instrument scale factors ..: unity\n",
      " Observation identifiers ...: all\n",
      " Model type ................: PointSource\n",
      " Model components ..........: \"PointSource\" * \"ExponentialCutoffPowerLaw\" * \"Constant\"\n",
      " Number of parameters ......: 7\n",
      " Number of spatial par's ...: 2\n",
      "  RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)\n",
      "  DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)\n",
      " Number of spectral par's ..: 4\n",
      "  Prefactor ................: 3.58899978654062e-16 +/- 7.19484631702262e-18 [0,infty[ ph/cm2/s/MeV (free,scale=1,gradient)\n",
      "  Index ....................: -1.83073898300316 +/- 0.0225679479297 [-10,10]  (free,scale=1,gradient)\n",
      "  CutoffEnergy .............: 3269842.84729316 +/- 121006.120369777 [0.1,infty[ MeV (free,scale=1,gradient)\n",
      "  PivotEnergy ..............: 300000 MeV (fixed,scale=1,gradient)\n",
      " Number of temporal par's ..: 1\n",
      "  Normalization ............: 1 (relative value) (fixed,scale=1,gradient)\n"
     ]
    }
   ],
   "source": [
    "print(crab)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The best-fit cutoff energy is 3.3 TeV, which seems consistent with the behavior in the energy-bands residual maps above. Note that this has changed significantly the Index value, that now is 1.83. We will check the residual maps again to make sure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Y2d9LOrPphZIkSaA/91iBDwN/CfwYRdKpqftZVrbXpo5hPWZmx1Xum0kaok9r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\naViTJElaJg1rkiRJy/xfKkbb+gLNvU8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ea2fe80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VFMFZJlawUtiBnW9mGyTNB9ZLWgvcDbyRX4QhrCDpeRRC9XgKRdlXJF1vZt9r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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec15518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oHGtKjTUiOtdF55XtR3oO9wLc/l0Lsju7V+skPQjcM8Eli4AtHRWnS3mumWem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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e47c7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "resmap_erange([[emin,1.],\n",
    "              [1.,10.],\n",
    "              [10.,emax]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we actually have an excess at the highest energies. In spite of the significant likelihood improvement the model is not quite perfect yet. Is there perhaps a new spectral component appearing at high energies? We will test if the addition of a power-law spectral component with a hard index (2). It will be added to the exponentially-cutoff power law in a composite spectral model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "expplaw2 = like.obs().models()['Crab'].spectral().clone() \n",
    "\n",
    "newcomp = gammalib.GModelSpectralPlaw(1.e-18,-2.,gammalib.GEnergy(1,'TeV'))\n",
    "\n",
    "comp_spec = gammalib.GModelSpectralComposite()\n",
    "comp_spec.append(expplaw2)\n",
    "comp_spec.append(newcomp)\n",
    "\n",
    "like.obs().models()['Crab'].spectral(comp_spec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's fit this new model to the data and check the likelihood improvement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "305.8644116757205\n"
     ]
    }
   ],
   "source": [
    "like.run()\n",
    "\n",
    "like4 = like.opt().value()\n",
    "ts = -2 * (like4 - like3)\n",
    "print(ts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood improvement is again significant, but did we already find the best possible model of the sky?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises \n",
    "\n",
    "- Test other spectral models for the Crab nebula, such as log-parabola and broken power law. Can you say what the best spectral model is?\n",
    "- What can you say from the residual maps about the spectrum of Src1? Try looking at the residuals below and above 300 GeV.\n",
    "- Replace the 2 sources with a single extended source (disk). Can you say which of the two hypotheses is describing the data better?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}