{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "**This is a fixed-text formatted version of a Jupyter notebook**\n",
    "\n",
    "- Try online [![Binder](https://static.mybinder.org/badge.svg)](https://mybinder.org/v2/gh/gammapy/gammapy-webpage/v0.17?urlpath=lab/tree/analysis_2.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",
    "[analysis_2.ipynb](../_static/notebooks/analysis_2.ipynb) |\n",
    "[analysis_2.py](../_static/notebooks/analysis_2.py)\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First analysis with gammapy library API\n",
    "\n",
    "## Prerequisites:\n",
    "\n",
    "- Understanding the gammapy data workflow, in particular what are DL3 events and intrument response functions (IRF).\n",
    "- Understanding of the data reduction and modeling fitting process as shown in the [first gammapy analysis with the high level interface tutorial](analysis_1.ipynb)\n",
    "\n",
    "## Context\n",
    "\n",
    "This notebook is an introduction to gammapy analysis this time using the lower level classes and functions\n",
    "the library.\n",
    "This allows to understand what happens during two main gammapy analysis steps, data reduction and modeling/fitting. \n",
    "\n",
    "**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.**\n",
    "\n",
    "## Proposed approach:\n",
    "\n",
    "Here, we have to interact with the data archive (with the `~gammapy.data.DataStore`) to retrieve a list of selected observations (`~gammapy.data.Observations`). Then, we define the geometry of the `~gammapy.datasets.MapDataset` object we want to produce and the maker object that reduce an observation\n",
    "to a dataset. \n",
    "\n",
    "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).\n",
    "\n",
    "In practice, we have to:\n",
    "- Create a `~gammapy.data.DataStore` poiting to the relevant data \n",
    "- Apply an observation selection to produce a list of observations, a `~gammapy.data.Observations` object.\n",
    "- Define a geometry of the Map we want to produce, with a sky projection and an energy range.\n",
    "    - Create a `~gammapy.maps.MapAxis` for the energy\n",
    "    - Create a `~gammapy.maps.WcsGeom` for the geometry\n",
    "- Create the necessary makers : \n",
    "    - the map dataset maker : `~gammapy.makers.MapDatasetMaker`\n",
    "    - the background normalization maker, here a `~gammapy.makers.FoVBackgroundMaker`\n",
    "    - and usually the safe range maker : `~gammapy.makers.SafeRangeMaker`\n",
    "- Perform the data reduction loop. And for every observation:\n",
    "    - Apply the makers sequentially to produce the current `~gammapy.datasets.MapDataset`\n",
    "    - Stack it on the target one.\n",
    "- Define the `~gammapy.modeling.models.SkyModel` to apply to the dataset.\n",
    "- Create a `~gammapy.modeling.Fit` object and run it to fit the model parameters\n",
    "- Apply a `~gammapy.estimators.FluxPointsEstimator` to compute flux points for the spectral part of the fit.\n",
    "\n",
    "## Setup\n",
    "First, we setup the analysis by performing required imports.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "from astropy import units as u\n",
    "from astropy.coordinates import SkyCoord\n",
    "from regions import CircleSkyRegion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from gammapy.data import DataStore\n",
    "from gammapy.datasets import MapDataset\n",
    "from gammapy.maps import WcsGeom, MapAxis, Map\n",
    "from gammapy.makers import MapDatasetMaker, SafeMaskMaker, FoVBackgroundMaker\n",
    "from gammapy.modeling.models import (\n",
    "    SkyModel,\n",
    "    PowerLawSpectralModel,\n",
    "    PointSpatialModel,\n",
    ")\n",
    "from gammapy.modeling import Fit\n",
    "from gammapy.estimators import FluxPointsEstimator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the datastore and selecting observations\n",
    "\n",
    "We first use the `~gammapy.data.DataStore` object to access the observations we want to analyse. Here the H.E.S.S. DL3 DR1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_store = DataStore.from_dir(\"$GAMMAPY_DATA/hess-dl3-dr1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now define an observation filter to select only the relevant observations. \n",
    "Here we use a cone search which we define with a python dict.\n",
    "\n",
    "We then filter the `ObservationTable` with `~gammapy.data.ObservationTable.select_observations()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "selection = dict(\n",
    "    type=\"sky_circle\",\n",
    "    frame=\"icrs\",\n",
    "    lon=\"83.633 deg\",\n",
    "    lat=\"22.014 deg\",\n",
    "    radius=\"5 deg\",\n",
    ")\n",
    "selected_obs_table = data_store.obs_table.select_observations(selection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now retrieve the relevant observations by passing their `obs_id` to the`~gammapy.data.DataStore.get_observations()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "observations = data_store.get_observations(selected_obs_table[\"OBS_ID\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preparing reduced datasets geometry\n",
    "\n",
    "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: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "energy_axis = MapAxis.from_energy_bounds(1.0, 10.0, 4, unit=\"TeV\")\n",
    "\n",
    "geom = WcsGeom.create(\n",
    "    skydir=(83.633, 22.014),\n",
    "    binsz=0.02,\n",
    "    width=(2, 2),\n",
    "    frame=\"icrs\",\n",
    "    proj=\"CAR\",\n",
    "    axes=[energy_axis],\n",
    ")\n",
    "\n",
    "# Reduced IRFs are defined in true energy (i.e. not measured energy).\n",
    "energy_axis_true = MapAxis.from_energy_bounds(\n",
    "    0.5, 20, 10, unit=\"TeV\", name=\"energy_true\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can define the target dataset with this geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "stacked = MapDataset.create(\n",
    "    geom=geom, energy_axis_true=energy_axis_true, name=\"crab-stacked\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data reduction\n",
    "\n",
    "### Create the maker classes to be used\n",
    "\n",
    "The `~gammapy.datasets.MapDatasetMaker` object is initialized as well as the `~gammapy.makers.SafeMaskMaker` that carries here a maximum offset selection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "offset_max = 2.5 * u.deg\n",
    "maker = MapDatasetMaker()\n",
    "maker_safe_mask = SafeMaskMaker(methods=[\"offset-max\"], offset_max=offset_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "circle = CircleSkyRegion(\n",
    "    center=SkyCoord(\"83.63 deg\", \"22.14 deg\"), radius=0.2 * u.deg\n",
    ")\n",
    "data = geom.region_mask(regions=[circle], inside=False)\n",
    "exclusion_mask = Map.from_geom(geom=geom, data=data)\n",
    "maker_fov = FoVBackgroundMaker(method=\"fit\", exclusion_mask=exclusion_mask)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform the data reduction loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Background norm obs 23523: 0.99\n",
      "Background norm obs 23526: 1.08\n",
      "Background norm obs 23559: 0.98\n",
      "Background norm obs 23592: 1.09\n",
      "CPU times: user 1.92 s, sys: 103 ms, total: 2.02 s\n",
      "Wall time: 2.03 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "for obs in observations:\n",
    "    # First a cutout of the target map is produced\n",
    "    cutout = stacked.cutout(\n",
    "        obs.pointing_radec, width=2 * offset_max, name=f\"obs-{obs.obs_id}\"\n",
    "    )\n",
    "    # A MapDataset is filled in this cutout geometry\n",
    "    dataset = maker.run(cutout, obs)\n",
    "    # fit background model\n",
    "    dataset = maker_fov.run(dataset)\n",
    "    print(\n",
    "        f\"Background norm obs {obs.obs_id}: {dataset.background_model.norm.value:.2f}\"\n",
    "    )\n",
    "    # The data quality cut is applied\n",
    "    dataset = maker_safe_mask.run(dataset, obs)\n",
    "    # The resulting dataset cutout is stacked onto the final one\n",
    "    stacked.stack(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MapDataset\n",
      "----------\n",
      "\n",
      "  Name                            : crab-stacked \n",
      "\n",
      "  Total counts                    : 2479 \n",
      "  Total predicted counts          : 2106.52\n",
      "  Total background counts         : 2106.52\n",
      "\n",
      "  Exposure min                    : 3.75e+08 m2 s\n",
      "  Exposure max                    : 3.48e+09 m2 s\n",
      "\n",
      "  Number of total bins            : 40000 \n",
      "  Number of fit bins              : 40000 \n",
      "\n",
      "  Fit statistic type              : cash\n",
      "  Fit statistic value (-2 log(L)) : 17780.34\n",
      "\n",
      "  Number of models                : 1 \n",
      "  Number of parameters            : 3\n",
      "  Number of free parameters       : 1\n",
      "\n",
      "  Component 0: BackgroundModel\n",
      "  \n",
      "    Name                      : crab-stacked-bkg\n",
      "    Datasets names            : ['crab-stacked']\n",
      "    Parameters:\n",
      "      norm                    :   1.000              \n",
      "      tilt         (frozen)   :   0.000              \n",
      "      reference    (frozen)   :   1.000  TeV         \n",
      "  \n",
      "  \n"
     ]
    }
   ],
   "source": [
    "print(stacked)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspect the reduced dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x288 with 2 Axes>,\n",
       " <matplotlib.axes._subplots.WCSAxesSubplot at 0x115d70748>,\n",
       " <matplotlib.colorbar.Colorbar at 0x11631dcc0>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stacked.counts.sum_over_axes().smooth(0.05 * u.deg).plot(\n",
    "    stretch=\"sqrt\", add_cbar=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save dataset to disk\n",
    "\n",
    "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:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = Path(\"analysis_2\")\n",
    "path.mkdir(exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then write the maps and IRFs to disk by calling the dedicated `~gammapy.datasets.MapDataset.write()` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = path / \"crab-stacked-dataset.fits.gz\"\n",
    "stacked.write(filename, overwrite=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the model\n",
    "We first define the model, a `SkyModel`, as the combination of a point source `SpatialModel` with a powerlaw `SpectralModel`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "target_position = SkyCoord(ra=83.63308, dec=22.01450, unit=\"deg\")\n",
    "spatial_model = PointSpatialModel(\n",
    "    lon_0=target_position.ra, lat_0=target_position.dec, frame=\"icrs\"\n",
    ")\n",
    "\n",
    "spectral_model = PowerLawSpectralModel(\n",
    "    index=2.702,\n",
    "    amplitude=4.712e-11 * u.Unit(\"1 / (cm2 s TeV)\"),\n",
    "    reference=1 * u.TeV,\n",
    ")\n",
    "\n",
    "sky_model = SkyModel(\n",
    "    spatial_model=spatial_model, spectral_model=spectral_model, name=\"crab\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we assign this model to our reduced dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "stacked.models.append(sky_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit the model\n",
    "\n",
    "The `~gammapy.modeling.Fit` class is orchestrating the fit, connecting the `stats` method of the dataset to the minimizer. By default, it uses `iminuit`.\n",
    "\n",
    "Its contructor takes a list of dataset as argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "------------------------------------------------------------------\n",
      "| FCN = 1.624E+04               |     Ncalls=123 (123 total)     |\n",
      "| EDM = 6.07E-05 (Goal: 1E-05)  |            up = 1.0            |\n",
      "------------------------------------------------------------------\n",
      "|  Valid Min.   | Valid Param.  | Above EDM | Reached call limit |\n",
      "------------------------------------------------------------------\n",
      "|     True      |     True      |   False   |       False        |\n",
      "------------------------------------------------------------------\n",
      "| Hesse failed  |   Has cov.    | Accurate  | Pos. def. | Forced |\n",
      "------------------------------------------------------------------\n",
      "|     False     |     True      |   True    |   True    | False  |\n",
      "------------------------------------------------------------------\n",
      "CPU times: user 3.58 s, sys: 78.4 ms, total: 3.65 s\n",
      "Wall time: 3.67 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "fit = Fit([stacked])\n",
    "result = fit.run(optimize_opts={\"print_level\": 1})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `FitResult` contains information on the fitted parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<i>Table length=8</i>\n",
       "<table id=\"table4671312896\" class=\"table-striped table-bordered table-condensed\">\n",
       "<thead><tr><th>name</th><th>value</th><th>unit</th><th>min</th><th>max</th><th>frozen</th><th>error</th></tr></thead>\n",
       "<thead><tr><th>str9</th><th>float64</th><th>str14</th><th>float64</th><th>float64</th><th>bool</th><th>float64</th></tr></thead>\n",
       "<tr><td>norm</td><td>9.370e-01</td><td></td><td>0.000e+00</td><td>nan</td><td>False</td><td>2.199e-02</td></tr>\n",
       "<tr><td>tilt</td><td>0.000e+00</td><td></td><td>nan</td><td>nan</td><td>True</td><td>0.000e+00</td></tr>\n",
       "<tr><td>reference</td><td>1.000e+00</td><td>TeV</td><td>nan</td><td>nan</td><td>True</td><td>0.000e+00</td></tr>\n",
       "<tr><td>index</td><td>2.596e+00</td><td></td><td>nan</td><td>nan</td><td>False</td><td>1.001e-01</td></tr>\n",
       "<tr><td>amplitude</td><td>4.555e-11</td><td>cm-2 s-1 TeV-1</td><td>nan</td><td>nan</td><td>False</td><td>3.669e-12</td></tr>\n",
       "<tr><td>reference</td><td>1.000e+00</td><td>TeV</td><td>nan</td><td>nan</td><td>True</td><td>0.000e+00</td></tr>\n",
       "<tr><td>lon_0</td><td>8.362e+01</td><td>deg</td><td>nan</td><td>nan</td><td>False</td><td>3.120e-03</td></tr>\n",
       "<tr><td>lat_0</td><td>2.202e+01</td><td>deg</td><td>-9.000e+01</td><td>9.000e+01</td><td>False</td><td>2.969e-03</td></tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<Table length=8>\n",
       "   name     value        unit         min        max    frozen   error  \n",
       "   str9    float64      str14       float64    float64   bool   float64 \n",
       "--------- --------- -------------- ---------- --------- ------ ---------\n",
       "     norm 9.370e-01                 0.000e+00       nan  False 2.199e-02\n",
       "     tilt 0.000e+00                       nan       nan   True 0.000e+00\n",
       "reference 1.000e+00            TeV        nan       nan   True 0.000e+00\n",
       "    index 2.596e+00                       nan       nan  False 1.001e-01\n",
       "amplitude 4.555e-11 cm-2 s-1 TeV-1        nan       nan  False 3.669e-12\n",
       "reference 1.000e+00            TeV        nan       nan   True 0.000e+00\n",
       "    lon_0 8.362e+01            deg        nan       nan  False 3.120e-03\n",
       "    lat_0 2.202e+01            deg -9.000e+01 9.000e+01  False 2.969e-03"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.parameters.to_table()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspecting residuals\n",
    "\n",
    "For any fit it is usefull to inspect the residual images. We have a few option on the dataset object to handle this. First we can use `.plot_residuals()` to plot a residual image, summed over all energies: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.axes._subplots.WCSAxesSubplot at 0x11475dba8>, None)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stacked.plot_residuals(method=\"diff/sqrt(model)\", vmin=-0.5, vmax=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In addition we can aslo specify a region in the map to show the spectral residuals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "region = CircleSkyRegion(\n",
    "    center=SkyCoord(\"83.63 deg\", \"22.14 deg\"), radius=0.5 * u.deg\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<matplotlib.axes._subplots.WCSAxesSubplot at 0x1156ad470>,\n",
       " <matplotlib.axes._subplots.AxesSubplot at 0x116735e80>)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "stacked.plot_residuals(\n",
    "    region=region, method=\"diff/sqrt(model)\", vmin=-0.5, vmax=0.5\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also directly access the `.residuals()` to get a map, that we can plot interactively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "residuals = stacked.residuals(method=\"diff\")\n",
    "residuals.smooth(\"0.08 deg\").plot_interactive(\n",
    "    cmap=\"coolwarm\", vmin=-0.1, vmax=0.1, stretch=\"linear\", add_cbar=True\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the fitted spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making a butterfly plot \n",
    "\n",
    "The `SpectralModel` component can be used to produce a, so-called, butterfly plot showing the enveloppe of the model taking into account parameter uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "spec = sky_model.spectral_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can actually do the plot using the `plot_error` method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "energy_range = [1, 10] * u.TeV\n",
    "spec.plot(energy_range=energy_range, energy_power=2)\n",
    "ax = spec.plot_error(energy_range=energy_range, energy_power=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing flux points\n",
    "\n",
    "We can now compute some flux points using the `~gammapy.estimators.FluxPointsEstimator`. \n",
    "\n",
    "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. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "e_edges = [1, 2, 4, 10] * u.TeV\n",
    "fpe = FluxPointsEstimator(e_edges=e_edges, source=\"crab\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3.2 s, sys: 39.4 ms, total: 3.24 s\n",
      "Wall time: 3.28 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "flux_points = fpe.run(datasets=[stacked])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1168648d0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = spec.plot_error(energy_range=energy_range, energy_power=2)\n",
    "flux_points.plot(ax=ax, energy_power=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.0"
  },
  "nbsphinx": {
   "orphan": true
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {
     "1783ddfbfe4a4ba197bf19b6f407f64d": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "DescriptionStyleModel",
      "state": {
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "DescriptionStyleModel",
       "_view_count": null,
       "_view_module": "@jupyter-widgets/base",
       "_view_module_version": "1.2.0",
       "_view_name": "StyleView",
       "description_width": "initial"
      }
     },
     "17d1a461802d477ea8f4e0bd88204c09": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.5.0",
      "model_name": "RadioButtonsModel",
      "state": {
       "_dom_classes": [],
       "_model_module": "@jupyter-widgets/controls",
       "_model_module_version": "1.5.0",
       "_model_name": "RadioButtonsModel",
       "_options_labels": [
        "linear",
        "sqrt",
        "log"
       ],
       "_view_count": null,
       "_view_module": "@jupyter-widgets/controls",
       "_view_module_version": "1.5.0",
       "_view_name": "RadioButtonsView",
       "description": "Select stretch:",
       "description_tooltip": null,
       "disabled": false,
       "index": 0,
       "layout": "IPY_MODEL_9a69d524726748da8fb7998ae9c71f33",
       "style": "IPY_MODEL_620c4308addd4bb48755d61fbe3433f8"
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