spectral_fit.ipynb

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   "source": [
    "# Spectral fitting example"
   ]
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    "The goal of this notebook is to get familiar with 3ML and get a concrete idea on the spectral fitting will work. \n",
    "\n",
    "[3ML](https://threeml.readthedocs.io/) is a high-level interface that allows multiple dataset form different instruments to be used coherently to fit the parameters of source model. A source model typically consists on a list of sources with a parametrized spectral shapes, sky locations and, for extended sources, shape. Polarization is also possible. A \"coherent\" analysis, in this context, means that the source model parameters are fitted using all available datasets simultanously, rather than performing individual fits and finding a well-suited common model a posteriori. \n",
    "\n",
    "In order for a dataset to be included in 3ML, each instrument needs to provide a \"plugin\". Each plugin is responsible for reading the data, convolving the source model (provided by 3ML) with the instrument response, and returning a likelihood. In our case, we'll compute a binned Poisson likelihood:\n",
    "\n",
    "$$\n",
    "\\log \\mathcal{L}(\\mathbf{x}) = \\sum_i \\log \\frac{\\lambda_i(\\mathbf{x})^{d_i} \\exp (-\\lambda_i)}{d_i!}\n",
    "$$\n",
    "\n",
    "where $d_i$ are the counts on each bin and $\\lambda_i$ are the _expected_ counts, given a source model with parameters $\\mathbf{x}$. \n",
    "\n",
    "In this example, we will fit a single point source with a known location. We'll assume the background is known and fixed. Finally, we will fit a power law:\n",
    "\n",
    "$$\n",
    "F(E) = K \\left(\\frac{E}{E_{piv}}\\right)^{-index}\n",
    "$$\n",
    "\n",
    "\n",
    "where $K$ (normalization) and the spectral index are the only free parameters, while $E_{piv}$ is the pivot energy which is fixed (and arbitrary).\n",
    "\n",
    "Considering these assumptions:\n",
    "\n",
    "$$\n",
    "\\lambda_i(\\mathbf{x}) = b_i + s_i(\\mathbf{x}) = b_i + s_i(\\mathrm{norm}, \\mathrm{index})\n",
    "$$\n",
    "\n",
    "where $b_i$ are the estimated counts due to background on each bin, and $s_i$ are the corresponding expected counts from the source.\n",
    "\n",
    "The goal is then to find the values of $\\mathbf{x} = [\\mathrm{norm}, \\mathrm{index}]$ that maximize $\\mathcal{L}$. These are the best estimation of the parameters.\n",
    "\n",
    "The final module needs to also fit the background, handle multiple point-like and extended sources, as well as all the spectral models supported by 3ML. Eventually, it will also fit the polarization angle. However, this simple example already contains all the necessary pieces to do a fit."
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   "source": [
    "## Dependecies"
   ]
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       "\u001b[38;5;46m        \u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m We have set the min_value of K to \u001b[0m\u001b[1;37m1e-99\u001b[0m\u001b[1;38;5;251m because there was a postive transform  \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=490229;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py\u001b\\\u001b[2mparameter.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=734224;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py#704\u001b\\\u001b[2m704\u001b[0m\u001b]8;;\u001b\\\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> We have set the min_value of K to </span><span style=\"color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold\">1e-99</span><span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> because there was a postive transform   </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">parameter.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py#704\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">704</span></a>\n",
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       "\u001b[38;5;46m        \u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m We have set the min_value of K to \u001b[0m\u001b[1;37m1e-99\u001b[0m\u001b[1;38;5;251m because there was a postive transform  \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=419624;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py\u001b\\\u001b[2mparameter.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=647088;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py#704\u001b\\\u001b[2m704\u001b[0m\u001b]8;;\u001b\\\n"
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       "\u001b[38;5;46m        \u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m We have set the min_value of F to \u001b[0m\u001b[1;37m1e-99\u001b[0m\u001b[1;38;5;251m because there was a postive transform  \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=365766;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py\u001b\\\u001b[2mparameter.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=151977;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py#704\u001b\\\u001b[2m704\u001b[0m\u001b]8;;\u001b\\\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> We have set the min_value of K to </span><span style=\"color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold\">1e-99</span><span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> because there was a postive transform   </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">parameter.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/astromodels/core/parameter.py#704\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">704</span></a>\n",
       "</pre>\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> but are inform you about optional packages that can be installed                  </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">__init__.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#37\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">37</span></a>\n",
       "</pre>\n"
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       "\u001b[38;5;46m        \u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m but are inform you about optional packages that can be installed                 \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=474622;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=928111;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#37\u001b\\\u001b[2m37\u001b[0m\u001b]8;;\u001b\\\n"
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       "</pre>\n"
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       "\u001b[38;5;46m        \u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m \u001b[0m\u001b[1;31m to disable these messages, turn off start_warning in your config file\u001b[0m\u001b[1;38;5;251m           \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=742723;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=859154;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#40\u001b\\\u001b[2m40\u001b[0m\u001b]8;;\u001b\\\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> ROOT minimizer not available                                                </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">minimization.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py#1345\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">1345</span></a>\n",
       "</pre>\n"
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      ]
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> Multinest minimizer not available                                           </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">minimization.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py#1357\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">1357</span></a>\n",
       "</pre>\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">15:40:09 </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> PyGMO is not available                                                      </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">minimization.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py#1369\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">1369</span></a>\n",
       "</pre>\n"
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       "\u001b[38;5;46m15:40:09\u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m PyGMO is not available                                                     \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=390631;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py\u001b\\\u001b[2mminimization.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=214205;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/minimizer/minimization.py#1369\u001b\\\u001b[2m1369\u001b[0m\u001b]8;;\u001b\\\n"
      ]
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">15:40:09 </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> The cthreeML package is not installed. You will not be able to use plugins which  </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">__init__.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#94\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">94</span></a>\n",
       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">require the C/C++ interface (currently HAWC)                                       </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">              </span>\n",
       "</pre>\n"
      ],
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       "\u001b[38;5;46m15:40:09\u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m The cthreeML package is not installed. You will not be able to use plugins which \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=228131;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\u001b\\\u001b[2m__init__.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=873113;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#94\u001b\\\u001b[2m94\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[38;5;46m         \u001b[0m         \u001b[1;38;5;251mrequire the C/C++ interface \u001b[0m\u001b[1;38;5;251m(\u001b[0m\u001b[1;38;5;251mcurrently HAWC\u001b[0m\u001b[1;38;5;251m)\u001b[0m\u001b[1;38;5;251m                                      \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b[2m              \u001b[0m\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> Could not import plugin HAWCLike.py. Do you have the relative instrument         </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">__init__.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#144\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">144</span></a>\n",
       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">software installed and configured?                                                </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">               </span>\n",
       "</pre>\n"
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       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">performances in 3ML                                                               </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">               </span>\n",
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       "\u001b[38;5;46m         \u001b[0m         \u001b[1;38;5;251mperformances in 3ML                                                              \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b[2m               \u001b[0m\n"
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       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">performances in 3ML                                                               </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">               </span>\n",
       "</pre>\n"
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       "\u001b[38;5;46m         \u001b[0m         \u001b[1;38;5;251mperformances in 3ML                                                              \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b[2m               \u001b[0m\n"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> Env. variable NUMEXPR_NUM_THREADS is not set. Please set it to </span><span style=\"color: #c0c0c0; text-decoration-color: #c0c0c0; font-weight: bold\">1</span><span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> for optimal     </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">__init__.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/__init__.py#387\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">387</span></a>\n",
       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">performances in 3ML                                                               </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">               </span>\n",
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       "\u001b[38;5;46m         \u001b[0m         \u001b[1;38;5;251mperformances in 3ML                                                              \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b[2m               \u001b[0m\n"
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   ],
   "source": [
    "# 3ML stuff\n",
    "from threeML import PluginPrototype, Model, Powerlaw, Broken_powerlaw, SmoothlyBrokenPowerLaw, Cutoff_powerlaw, PointSource, JointLikelihood, DataList\n",
    "from astromodels import Parameter\n",
    "\n",
    "# We'll use histpy's Histogram and mhealpy's HealpixMap as the basis\n",
    "# develop cosipy. These object (or a derivative) will be passed around by \n",
    "# the different modules.\n",
    "from histpy import Histogram, Axis\n",
    "from mhealpy import HealpixMap\n",
    "\n",
    "# Needed for coordinate conversion.\n",
    "# cosipy uses astropy coordinates, with a custom\n",
    "# SpacecraftFrame (coordinate frame attached to COSI)\n",
    "from astropy.coordinates import SkyCoord\n",
    "from cosipy.coordinates import SpacecraftFrame, Attitude\n",
    "\n",
    "# cosipy uses astropy units\n",
    "import astropy.units as u\n",
    "from astropy.time import Time\n",
    "from astropy.units import Quantity\n",
    "\n",
    "# Other cosipy modules. Eventually the data classes and \n",
    "# SC pos/attitude modules will be needed too.\n",
    "from cosipy.response.FullDetectorResponse import FullDetectorResponse\n",
    "\n",
    "#Other standard libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import factorial\n",
    "from scipy import stats\n",
    "import collections"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "908a515d-0ba8-45aa-8567-9ff410ddaba5",
   "metadata": {},
   "source": [
    "## 3ML plugin"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf941fdd-2832-42b0-a754-71a4b8227819",
   "metadata": {},
   "source": [
    "A 3ML plugin is any class that inherits from 3ML's `PluginPrototype` class. The main two methods that need to be implemented are:\n",
    "* `set_model`, which translates a 3ML source model into instrument-specific data. In our case, we convolve the source position and spectrum with the COSI response in order to obtain the spected counts from the source.\n",
    "* `get_log_likelihood`, which return the logarithm of the likelihood (computed with the equation above) that 3ML will combine with the likelihood from other instruments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f0c1221e-e9d2-4417-baa9-ae7594a2b48f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class COSILike(PluginPrototype):\n",
    "    def __init__(self, name, dr, data, bkg, sc_orientation, **kwargs):\n",
    "        \"\"\"\n",
    "        COSI 3ML plugin\n",
    "        \n",
    "        Parameters\n",
    "        ----------\n",
    "        name : str\n",
    "            Plugin name e.g. \"cosi\". Needs to have a distinct name with respect to other plugins in the same analysis\n",
    "        dr : Path\n",
    "            Path to full detector response\n",
    "        data: histpy.Histogram\n",
    "            Binned data. Note: Eventually this should be a cosipy data class\n",
    "        bkg: histpy.Histogram\n",
    "            Binned background model. Note: Eventually this should be a cosipy data class\n",
    "        sc_orientation: array\n",
    "            Pair of timestamps (astropy.Time) and attitudes (scoord.Attitude) that describe\n",
    "            the orientation of the spacecraft for the duration of the data included in\n",
    "            the analysis. Note: this will eventually be handled by the SC location and\n",
    "            orientation module\n",
    "        \"\"\"\n",
    "        \n",
    "        # create the hash for the nuisance parameters. We have none for now.\n",
    "        nuisance_parameters = collections.OrderedDict()\n",
    "\n",
    "        # call the prototype constructor. Boilerplate.\n",
    "        super(COSILike, self).__init__(name, nuisance_parameters)\n",
    "\n",
    "        # User inputs needed to compute the likelihood\n",
    "        self._dr = FullDetectorResponse.open(dr)\n",
    "        self._data = data\n",
    "        self._bkg = bkg\n",
    "        self._sc_orientation = sc_orientation\n",
    "    \n",
    "        # Place-holder for cached data.\n",
    "        self._model = None\n",
    "        self._source = None\n",
    "        self._psr = None\n",
    "        self._signal = None\n",
    "        \n",
    "    def set_model(self, model):\n",
    "        \"\"\"\n",
    "        Set the model to be used in the joint minimization.\n",
    "        \n",
    "        Parameters:\n",
    "            model: LikelihoodModel\n",
    "                Any model supported by astromodel. However, this simple plugin only support single \n",
    "                point-sources with a power law spectrum\n",
    "        \"\"\"\n",
    "        \n",
    "        # Check for limitations\n",
    "        if len(model.extended_sources) != 0 or len(model.particle_sources):\n",
    "            raise RuntimeError(\"Only point source models are supported\")\n",
    "        \n",
    "        sources = model.point_sources\n",
    "        \n",
    "        if len(sources) != 1:\n",
    "            raise RuntimeError(\"Only one for now\")\n",
    "        \n",
    "        # Get expectation\n",
    "        for name,source in sources.items():\n",
    "\n",
    "            if self._source is None:\n",
    "                self._source = source\n",
    "                     \n",
    "            # Compute point source response for source position\n",
    "            # See also the Detector Response and Source Injector tutorials\n",
    "            if self._psr is None:\n",
    "            \n",
    "                coord = self._source.position.sky_coord\n",
    "            \n",
    "                dwell_time_map = self._get_dwell_time_map(coord)\n",
    "            \n",
    "                self._psr = self._dr.get_point_source_response(dwell_time_map)\n",
    "            \n",
    "            elif source.position != self._source.position:\n",
    "                \n",
    "                raise RuntimeError(\"No change in position for now\")\n",
    "\n",
    "            # Convolve with spectrum\n",
    "            # See also the Detector Response and Source Injector tutorials\n",
    "            spectrum = source.spectrum.main.shape\n",
    "                \n",
    "            self._signal = self._psr.get_expectation(spectrum).project(['Em', 'Phi', 'PsiChi'])\n",
    "            \n",
    "        # Cache\n",
    "        self._model = model\n",
    "\n",
    "    def get_log_like(self):\n",
    "\n",
    "        # Recompute the expectation if any parameter in the model changed\n",
    "        if self._model is None:\n",
    "            log.error(\"You need to set the model first\")\n",
    "        \n",
    "        self.set_model(self._model)\n",
    "        \n",
    "        # Compute \"lambda\" in the equations above\n",
    "        expectation = self._signal.contents + self._bkg.contents\n",
    "        \n",
    "        data = self._data.contents # Into an array\n",
    "        \n",
    "        # Compute the log-likelihood from the equations above\n",
    "        log_like = np.sum(np.log(np.power(expectation, data) * \n",
    "                             np.exp(-expectation) / \n",
    "                             factorial(data)))\n",
    "        \n",
    "        return log_like\n",
    "\n",
    "    def inner_fit(self):\n",
    "        \"\"\"\n",
    "        This fits nuisance parameters, but we have none for now.\n",
    "        \"\"\"\n",
    "        \n",
    "        return self.get_log_like()\n",
    "    \n",
    "    def _get_dwell_time_map(self, coord):\n",
    "        \"\"\"\n",
    "        This will be eventually be provided by another module\n",
    "        \"\"\"\n",
    "        \n",
    "        # The dwell time map has the same pixelation (base) as the detector response.\n",
    "        # We start with an empty map\n",
    "        dwell_time_map = HealpixMap(base = self._dr, \n",
    "                                    unit = u.s, \n",
    "                                    coordsys = SpacecraftFrame())\n",
    "\n",
    "        # Get timestamps and attitude values\n",
    "        timestamps, attitudes = zip(*self._sc_orientation)\n",
    "            \n",
    "        for attitude,duration in zip(attitudes[:-1], np.diff(timestamps)):\n",
    "\n",
    "            local_coord = coord.transform_to(SpacecraftFrame(attitude = attitude))\n",
    "\n",
    "            # Here we add duration in between timestamps using interpolations\n",
    "            pixels, weights = dwell_time_map.get_interp_weights(local_coord)\n",
    "\n",
    "            for p,w in zip(pixels, weights):\n",
    "                dwell_time_map[p] += w*duration.to(u.s)\n",
    "        \n",
    "        return dwell_time_map"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7e564f1-8cbf-44cd-a0ed-8b08ccb250dc",
   "metadata": {},
   "source": [
    "## 3ML fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f03c5ee-9f04-4977-85ec-8328b53e0de5",
   "metadata": {},
   "source": [
    "Fitting in 3ML begins by instantiating all plugins. Each one needs different inputs, specific to each instrument. Although 3ML was designed to fit data from multiple instruments, we can also fit data from a single detector without any changes to the workflow. For now, \"cosi\" is our only plugin:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4741594f-3281-46e9-a195-e0fc4733b96e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inputs needed by the COSI plugin\n",
    "# We'll use fake data from the \"Source injector\" tutorial\n",
    "dr = \"/Users/eneights/work/COSI/data_challenge_2/intro_cosipy/test_data/FlatContinuumIsotropic.LowRes.binnedimaging.imagingresponse.area.nside8.cosipy.h5\"\n",
    "\n",
    "data = Histogram.open(\"data.h5\")\n",
    "bkg = Histogram.open(\"bkg.h5\")\n",
    "signal = Histogram.open(\"signal.h5\")\n",
    "\n",
    "# 1s duration. Spacecraft aligned with the ICRS ([0,0,0,1] = Identity)\n",
    "sc_orientation = [(Time('2025-01-01T13:02:01.00'), Attitude.from_quat([0,0,0,1])), \n",
    "                  (Time('2025-01-01T13:02:02.00'), Attitude.from_quat([0,0,0,1]))]\n",
    "\n",
    "# Instantiate the plugin\n",
    "# Note that we'll use 3x the signal we injected before. \n",
    "cosi = COSILike(\"cosi\",\n",
    "                dr = dr,\n",
    "                data = bkg + 3*signal, \n",
    "                bkg = bkg, \n",
    "                sc_orientation = sc_orientation)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c10c8ac6-07e9-4c87-b8ab-acdb30410d73",
   "metadata": {},
   "source": [
    "The next step is to initialize the model that contains all free parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f459020d-169f-4a68-9062-610e6e6b06d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Our model will contain a single source with a power law spectrum\n",
    "spectrum = Powerlaw()\n",
    "\n",
    "# Setting the parameter to something reasonable helps the fitting to converge\n",
    "index = -2\n",
    "piv = 1 * u.keV\n",
    "K = 1 / u.cm / u.cm / u.s / u.keV\n",
    "spectrum.index.value = index\n",
    "spectrum.K.value = K.value\n",
    "spectrum.piv.value = piv.value\n",
    "spectrum.K.unit = K.unit\n",
    "spectrum.piv.unit = piv.unit\n",
    "\n",
    "# Optional: change pivot energy\n",
    "# The pivot value is arbitrary, ideally nothing should depend on it\n",
    "# However, it is recommended to choose a value near the energy\n",
    "# for which the detector is most sensitive ir onder to minimize\n",
    "# the correlation between the normalization and spectral index.\n",
    "# Try setting it to 500 keV and see how the results change\n",
    "# piv =  500 * u.keV\n",
    "# K = spectrum(500) / u.cm / u.cm / u.s / u.keV\n",
    "# spectrum.K.value = K.value\n",
    "# spectrum.piv.value = piv.value\n",
    "# spectrum.K.unit = K.unit\n",
    "# spectrum.piv.unit = piv.unit\n",
    "\n",
    "# Point source instance, at the know location (from the \"Source Injectior\" tutorial)\n",
    "source = PointSource(\"source\", # The name of the source is arbitrary, but needs to be unique\n",
    "                     ra = 20, #deg \n",
    "                     dec = 40, #deg\n",
    "                     spectral_shape = spectrum)\n",
    "\n",
    "# Adding the source to the model\n",
    "# If we had multiple sources, we would do Model(source1, source2, ...)\n",
    "model = Model(source)\n",
    "\n",
    "# Optional: if you want to call get_log_like manually, then you\n",
    "# also need to set the model manually. 3ML does this internanlly during the fit though\n",
    "cosi.set_model(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c39f58a3-80d6-42a0-afe6-077590a25397",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ul>\n",
       "\n",
       "<li>description: A simple power-law</li>\n",
       "\n",
       "<li>formula: $ K~\\frac{x}{piv}^{index} $</li>\n",
       "\n",
       "<li>parameters: \n",
       "<ul>\n",
       "\n",
       "<li>K: \n",
       "<ul>\n",
       "\n",
       "<li>value: 1.0</li>\n",
       "\n",
       "<li>desc: Normalization (differential flux at the pivot value)</li>\n",
       "\n",
       "<li>min_value: 1e-30</li>\n",
       "\n",
       "<li>max_value: 1000.0</li>\n",
       "\n",
       "<li>unit: keV-1 s-1 cm-2</li>\n",
       "\n",
       "<li>is_normalization: True</li>\n",
       "\n",
       "<li>delta: 0.1</li>\n",
       "\n",
       "<li>free: True</li>\n",
       "\n",
       "</ul>\n",
       "\n",
       "</li>\n",
       "\n",
       "<li>piv: \n",
       "<ul>\n",
       "\n",
       "<li>value: 1.0</li>\n",
       "\n",
       "<li>desc: Pivot value</li>\n",
       "\n",
       "<li>min_value: None</li>\n",
       "\n",
       "<li>max_value: None</li>\n",
       "\n",
       "<li>unit: keV</li>\n",
       "\n",
       "<li>is_normalization: False</li>\n",
       "\n",
       "<li>delta: 0.1</li>\n",
       "\n",
       "<li>free: False</li>\n",
       "\n",
       "</ul>\n",
       "\n",
       "</li>\n",
       "\n",
       "<li>index: \n",
       "<ul>\n",
       "\n",
       "<li>value: -2.0</li>\n",
       "\n",
       "<li>desc: Photon index</li>\n",
       "\n",
       "<li>min_value: -10.0</li>\n",
       "\n",
       "<li>max_value: 10.0</li>\n",
       "\n",
       "<li>unit: </li>\n",
       "\n",
       "<li>is_normalization: False</li>\n",
       "\n",
       "<li>delta: 0.20099999999999998</li>\n",
       "\n",
       "<li>free: True</li>\n",
       "\n",
       "</ul>\n",
       "\n",
       "</li>\n",
       "\n",
       "</ul>\n",
       "\n",
       "</li>\n",
       "\n",
       "</ul>\n"
      ],
      "text/plain": [
       "  * description: A simple power-law\n",
       "  * formula: $ K~\\frac{x}{piv}^{index} $\n",
       "  * parameters:\n",
       "    * K:\n",
       "      * value: 1.0\n",
       "      * desc: Normalization (differential flux at the pivot value)\n",
       "      * min_value: 1.0e-30\n",
       "      * max_value: 1000.0\n",
       "      * unit: keV-1 s-1 cm-2\n",
       "      * is_normalization: true\n",
       "      * delta: 0.1\n",
       "      * free: true\n",
       "    * piv:\n",
       "      * value: 1.0\n",
       "      * desc: Pivot value\n",
       "      * min_value: null\n",
       "      * max_value: null\n",
       "      * unit: keV\n",
       "      * is_normalization: false\n",
       "      * delta: 0.1\n",
       "      * free: false\n",
       "    * index:\n",
       "      * value: -2.0\n",
       "      * desc: Photon index\n",
       "      * min_value: -10.0\n",
       "      * max_value: 10.0\n",
       "      * unit: ''\n",
       "      * is_normalization: false\n",
       "      * delta: 0.20099999999999998\n",
       "      * free: true"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spectrum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e946154f-4364-4125-b2e9-0b8ed2372671",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Corresponding parameters, for reference\n",
    "norm_inj = 3e-1 # 1/keV/cm2/s (3x the injected signal)\n",
    "piv_inj = 1 # keV\n",
    "index_inj = -1.7 "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31232d2f-0f8b-44c1-8c37-cf1cb72afdb1",
   "metadata": {},
   "source": [
    "And finally, let 3ML maximize the likelihood:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0f25a244-dd9d-4bf0-aa9b-8de8981cdbe0",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">15:40:52 </span><span style=\"color: #00ffaf; text-decoration-color: #00ffaf\">INFO    </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> set the minimizer to minuit                                             </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/classicMLE/joint_likelihood.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">joint_likelihood.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/classicMLE/joint_likelihood.py#1042\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">1042</span></a>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[38;5;46m15:40:52\u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;49mINFO    \u001b[0m \u001b[1;38;5;251m set the minimizer to minuit                                            \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=848958;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/classicMLE/joint_likelihood.py\u001b\\\u001b[2mjoint_likelihood.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=670893;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/classicMLE/joint_likelihood.py#1042\u001b\\\u001b[2m1042\u001b[0m\u001b]8;;\u001b\\\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ff00; text-decoration-color: #00ff00\">15:40:59 </span><span style=\"color: #af5fd7; text-decoration-color: #af5fd7\">WARNING </span> <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\"> get_number_of_data_points not implemented, values for statistical        </span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/plugin_prototype.py\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">plugin_prototype.py</span></a><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">:</span><a href=\"file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/plugin_prototype.py#128\" target=\"_blank\"><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">128</span></a>\n",
       "<span style=\"color: #00ff00; text-decoration-color: #00ff00\">         </span>         <span style=\"color: #c6c6c6; text-decoration-color: #c6c6c6; font-weight: bold\">measurements such as AIC or BIC are unreliable                            </span><span style=\"color: #7f7f7f; text-decoration-color: #7f7f7f\">                       </span>\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[38;5;46m15:40:59\u001b[0m\u001b[38;5;46m \u001b[0m\u001b[38;5;134mWARNING \u001b[0m \u001b[1;38;5;251m get_number_of_data_points not implemented, values for statistical       \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b]8;id=107899;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/plugin_prototype.py\u001b\\\u001b[2mplugin_prototype.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=339422;file:///Users/eneights/opt/anaconda3/envs/cosipy/lib/python3.9/site-packages/threeML/plugin_prototype.py#128\u001b\\\u001b[2m128\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[38;5;46m         \u001b[0m         \u001b[1;38;5;251mmeasurements such as AIC or BIC are unreliable                           \u001b[0m\u001b[1;38;5;251m \u001b[0m\u001b[2m                       \u001b[0m\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
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     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Best fit values:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;4;38;5;49mBest fit values:\u001b[0m\n",
       "\n"
      ]
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     "output_type": "display_data"
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>result</th>\n",
       "      <th>unit</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>parameter</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>source.spectrum.main.Powerlaw.K</th>\n",
       "      <td>(3.0 -1.8 +5) x 10^-1</td>\n",
       "      <td>1 / (cm2 keV s)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>source.spectrum.main.Powerlaw.index</th>\n",
       "      <td>-1.70 +/- 0.15</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    result             unit\n",
       "parameter                                                                  \n",
       "source.spectrum.main.Powerlaw.K      (3.0 -1.8 +5) x 10^-1  1 / (cm2 keV s)\n",
       "source.spectrum.main.Powerlaw.index         -1.70 +/- 0.15                 "
      ]
     },
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Correlation matrix:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[1;4;38;5;49mCorrelation matrix:\u001b[0m\n",
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div><table id=\"table10940611936\">\n",
       "<tr><td>1.00</td><td>-0.99</td></tr>\n",
       "<tr><td>-0.99</td><td>1.00</td></tr>\n",
       "</table></div>"
      ],
      "text/plain": [
       " 1.00 -0.99\n",
       "-0.99  1.00"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Values of -log(likelihood) at the minimum:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[1;4;38;5;49mValues of -\u001b[0m\u001b[1;4;38;5;49mlog\u001b[0m\u001b[1;4;38;5;49m(\u001b[0m\u001b[1;4;38;5;49mlikelihood\u001b[0m\u001b[1;4;38;5;49m)\u001b[0m\u001b[1;4;38;5;49m at the minimum:\u001b[0m\n",
       "\n"
      ]
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    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>-log(likelihood)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cosi</th>\n",
       "      <td>4540.459283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total</th>\n",
       "      <td>4540.459283</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       -log(likelihood)\n",
       "cosi        4540.459283\n",
       "total       4540.459283"
      ]
     },
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     "output_type": "display_data"
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    {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Values of statistical measures:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[1;4;38;5;49mValues of statistical measures:\u001b[0m\n",
       "\n"
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>statistical measures</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>AIC</th>\n",
       "      <td>9078.918566</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIC</th>\n",
       "      <td>9080.918566</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     statistical measures\n",
       "AIC           9078.918566\n",
       "BIC           9080.918566"
      ]
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    {
     "data": {
      "text/plain": [
       "(                                        value  negative_error  positive_error  \\\n",
       " source.spectrum.main.Powerlaw.K      0.300053       -0.184138        0.491229   \n",
       " source.spectrum.main.Powerlaw.index -1.700008       -0.157835        0.152505   \n",
       " \n",
       "                                         error             unit  \n",
       " source.spectrum.main.Powerlaw.K      0.337684  1 / (cm2 keV s)  \n",
       " source.spectrum.main.Powerlaw.index  0.155170                   ,\n",
       "        -log(likelihood)\n",
       " cosi        4540.459283\n",
       " total       4540.459283)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Gather all plugins. \n",
    "# If we had multiple instruments, we would do e.g. DataList(cosi, lat, hawc, ...)\n",
    "plugins = DataList(cosi)\n",
    "\n",
    "# Put model and pluging together\n",
    "like = JointLikelihood(model, plugins, verbose = False)\n",
    "\n",
    "# Maximum likelihood\n",
    "like.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d423b50-005e-4974-a18b-526680f9277c",
   "metadata": {},
   "source": [
    "Compare this with the values used for the injection."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90664217-0b7d-4168-91f3-4312613d994b",
   "metadata": {},
   "source": [
    "## 3ML error propagation and plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9e73b29-93ec-40bc-84f4-5897c8f0ce11",
   "metadata": {},
   "source": [
    "The summary of the results above tell you the optimal values of `K` and `index`, as well as the errors. You typically want to propagate these into the error in the flux at different energies, and plot the spectrum. Let's do that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "70303f86-eec7-483f-845e-0f0724ea52fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Best fit values:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\u001b[1;4;38;5;49mBest fit values:\u001b[0m\n",
       "\n"
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       "      <th></th>\n",
       "      <th>result</th>\n",
       "      <th>unit</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>parameter</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>source.spectrum.main.Powerlaw.K</th>\n",
       "      <td>(3.0 -1.8 +5) x 10^-1</td>\n",
       "      <td>1 / (cm2 keV s)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>source.spectrum.main.Powerlaw.index</th>\n",
       "      <td>-1.70 +/- 0.15</td>\n",
       "      <td></td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
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      "text/plain": [
       "                                                    result             unit\n",
       "parameter                                                                  \n",
       "source.spectrum.main.Powerlaw.K      (3.0 -1.8 +5) x 10^-1  1 / (cm2 keV s)\n",
       "source.spectrum.main.Powerlaw.index         -1.70 +/- 0.15                 "
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Correlation matrix:</span>\n",
       "\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n",
       "\u001b[1;4;38;5;49mCorrelation matrix:\u001b[0m\n",
       "\n"
      ]
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      "text/html": [
       "<div><table id=\"table10942425120\">\n",
       "<tr><td>1.00</td><td>-0.99</td></tr>\n",
       "<tr><td>-0.99</td><td>1.00</td></tr>\n",
       "</table></div>"
      ],
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       " 1.00 -0.99\n",
       "-0.99  1.00"
      ]
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     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Values of -log(likelihood) at the minimum:</span>\n",
       "\n",
       "</pre>\n"
      ],
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       "\n",
       "\u001b[1;4;38;5;49mValues of -\u001b[0m\u001b[1;4;38;5;49mlog\u001b[0m\u001b[1;4;38;5;49m(\u001b[0m\u001b[1;4;38;5;49mlikelihood\u001b[0m\u001b[1;4;38;5;49m)\u001b[0m\u001b[1;4;38;5;49m at the minimum:\u001b[0m\n",
       "\n"
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       "      <th></th>\n",
       "      <th>-log(likelihood)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cosi</th>\n",
       "      <td>4540.459283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>total</th>\n",
       "      <td>4540.459283</td>\n",
       "    </tr>\n",
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       "       -log(likelihood)\n",
       "cosi        4540.459283\n",
       "total       4540.459283"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "<span style=\"color: #00ffaf; text-decoration-color: #00ffaf; font-weight: bold; text-decoration: underline\">Values of statistical measures:</span>\n",
       "\n",
       "</pre>\n"
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       "\n",
       "\u001b[1;4;38;5;49mValues of statistical measures:\u001b[0m\n",
       "\n"
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       "     statistical measures\n",
       "AIC           9078.918566\n",
       "BIC           9080.918566"
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     "text": [
      "None\n",
      "  * source (point source):\n",
      "    * position:\n",
      "      * ra:\n",
      "        * value: 20.0\n",
      "        * desc: Right Ascension\n",
      "        * min_value: 0.0\n",
      "        * max_value: 360.0\n",
      "        * unit: deg\n",
      "        * is_normalization: false\n",
      "      * dec:\n",
      "        * value: 40.0\n",
      "        * desc: Declination\n",
      "        * min_value: -90.0\n",
      "        * max_value: 90.0\n",
      "        * unit: deg\n",
      "        * is_normalization: false\n",
      "      * equinox: J2000\n",
      "    * spectrum:\n",
      "      * main:\n",
      "        * Powerlaw:\n",
      "          * K:\n",
      "            * value: 0.3000528939622899\n",
      "            * desc: Normalization (differential flux at the pivot value)\n",
      "            * min_value: 1.0e-30\n",
      "            * max_value: 1000.0\n",
      "            * unit: keV-1 s-1 cm-2\n",
      "            * is_normalization: true\n",
      "          * piv:\n",
      "            * value: 1.0\n",
      "            * desc: Pivot value\n",
      "            * min_value: null\n",
      "            * max_value: null\n",
      "            * unit: keV\n",
      "            * is_normalization: false\n",
      "          * index:\n",
      "            * value: -1.7000076851771695\n",
      "            * desc: Photon index\n",
      "            * min_value: -10.0\n",
      "            * max_value: 10.0\n",
      "            * unit: ''\n",
      "            * is_normalization: false\n",
      "        * polarization: {}\n",
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Propagate the errors to the \"evaluate_at\" method of the spectrum\n",
    "results = like.results\n",
    "\n",
    "print(results.display())\n",
    "\n",
    "parameters = {par.name:results.get_variates(par.path)\n",
    "              for par in results.optimized_model[\"source\"].parameters.values()\n",
    "              if par.free}\n",
    "\n",
    "results_err = results.propagate(results.optimized_model[\"source\"].spectrum.main.shape.evaluate_at, **parameters)\n",
    "\n",
    "print(results.optimized_model[\"source\"])\n",
    "\n",
    "# Evaluate at multiple energy values, for plotting\n",
    "energy = np.geomspace(200*u.keV,5*u.MeV).to_value(u.keV)\n",
    "\n",
    "flux_lo = np.zeros_like(energy)\n",
    "flux_median = np.zeros_like(energy)\n",
    "flux_hi = np.zeros_like(energy)\n",
    "\n",
    "for i, e in enumerate(energy):\n",
    "    \n",
    "    flux = results_err(e)\n",
    "\n",
    "    flux_median[i] = flux.median\n",
    "    flux_lo[i], flux_hi[i] = flux.equal_tail_interval(cl=0.68)\n",
    "\n",
    "    \n",
    "# Plot\n",
    "fig,ax = plt.subplots()\n",
    "\n",
    "ax.plot(energy, energy*energy*flux_median, label = \"Measured (best)\")\n",
    "\n",
    "ax.fill_between(energy, energy*energy*flux_lo, energy*energy*flux_hi, alpha = .5, label = \"Measured (errors)\")\n",
    "\n",
    "energy_inj = np.geomspace(1e2, 1e4)\n",
    "ax.plot(energy_inj, energy_inj*energy_inj*norm_inj*(energy_inj/piv_inj)**index_inj, color = 'black', ls = \":\", label = \"Injected\")\n",
    "\n",
    "ax.set_xscale(\"log\")\n",
    "\n",
    "ax.set_yscale(\"log\")\n",
    "\n",
    "ax.set_xlim(1e2, 1e4)\n",
    "ax.set_ylim(1e-1, 1000)\n",
    "\n",
    "ax.set_xlabel(\"Energy [keV]\")\n",
    "ax.set_ylabel(r\"$E^2 \\frac{dN}{dE}$ [keV cm$^{-2}$ s$^{-1}$]\")\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a318389-657a-4209-bb5e-5519be2c36ba",
   "metadata": {},
   "source": [
    "## TS grid (brute force fitting)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a41ef423-2214-4ab9-87d4-b575c7bf4c0d",
   "metadata": {},
   "source": [
    "The function `fit()` above is simply finding the maximum value of `cosi.get_log_like()`, and then using the difference in likelihood as a function of each parameter to find the errors and correlations. It can be enlightening to see this visually, so let's see how the likelihood profile looks by evaluating it at multiple location in grid. This might take a few minutes, it's a _brute_ force method after all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7abcf2e6-48cb-4a47-9127-e0297a76037e",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i = 28/29  j = 29/30"
     ]
    }
   ],
   "source": [
    "# Find a reasonable range to evaluate, based on the 99% confidence intervals\n",
    "index_range = results.get_equal_tailed_interval('source.spectrum.main.Powerlaw.index', cl = .99)\n",
    "norm_range = results.get_equal_tailed_interval('source.spectrum.main.Powerlaw.K', cl = .99)\n",
    "log_like = Histogram([Axis(np.linspace(*index_range, 30), label = \"index\"), \n",
    "                      Axis(np.linspace(*norm_range, 31), label = \"norm\")])\n",
    "for i in range(log_like.axes['index'].nbins):\n",
    "    for j in range(log_like.axes['norm'].nbins):\n",
    "        # Progress\n",
    "        print(f\"\\ri = {i:2d}/{log_like.axes['index'].nbins}  j = {j:2d}/{log_like.axes['norm'].nbins}\", end = \"\")\n",
    "        # Change the spectrum parameters\n",
    "        spectrum.K.value = log_like.axes['norm'].centers[j]\n",
    "        spectrum.index.value = log_like.axes['index'].centers[i]\n",
    "        # Recompute the likelihood\n",
    "        log_like[i,j] = cosi.get_log_like()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7485e63-4c82-4eea-bc5a-b020af4fe555",
   "metadata": {},
   "source": [
    "The log likelihood can also be used in hypothesis testing. Given the likelihood for a null-hypothesis model $\\mathcal{L}_0$, Wilks' theorem says that, when the sample size approaches infinity, the test statistic\n",
    "\n",
    "$$\n",
    "TS = 2 \\frac{\\mathrm{max} \\mathcal{L}}{\\mathrm{max} \\mathcal{L}_0}\n",
    "$$\n",
    "\n",
    "approaches a $\\chi^2$ distribution under the null-hypothesis. The number of degrees of freedom equals to the difference in the number of parameters between the alternative and the null hypothesis (all parameter of the null hypothesis must be present in the alternative hypothesis, aka _nested models_). Although this only applies for large sample size, it is usually a good first approximation. \n",
    "\n",
    "To make this more concrete, a common null hypothesis is that there is no source, only background, and the alternative hypothesis is that there is a source. In our example, the alternative model has 2 degrees of freedom (normalization and index), and the null-hypothesis had none (because we assummed the background is known and fixed).\n",
    "\n",
    "Since the $\\mathcal{L}_0$ is just a constant, we can compute it directly once and for all:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2848e269-b171-45a9-b123-9d71b425fd2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the normalization to 0, that is, background-only null-hypothesis\n",
    "spectrum.K.value = spectrum.K.min_value # min_value is a very small value, approx 0. However, it can't be exactly 0 for some internal numerical reason\n",
    "\n",
    "# Compute the likelihood\n",
    "log_like0 = cosi.get_log_like()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "839229bb-3435-43f8-a2e1-0b2bb9a94169",
   "metadata": {},
   "source": [
    "The TS is then"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5d8eb72d-0af5-457c-a68b-687e88c0ef03",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected significance: 10.4 sigma\n"
     ]
    }
   ],
   "source": [
    "ts = 2*(log_like - log_like0)\n",
    "\n",
    "# Getting the maximum\n",
    "# Note that, in our case, since log_like0 is a constant,\n",
    "# max(TS) = 2\n",
    "argmax = np.unravel_index(np.argmax(ts), ts.nbins)\n",
    "\n",
    "ts_max = ts[argmax]\n",
    "\n",
    "# And converting to significance based on Wilk's theorem\n",
    "print(f\"Expected significance: {stats.norm.isf(stats.chi2.sf(ts_max, df = 2)):.1f} sigma\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8533a5c-648d-4849-8586-853cd8fd6e7e",
   "metadata": {},
   "source": [
    "Finally, let's plot the TS profile vs the free parameters, find the maximumum and use Wilk's theorem to estimate a confidence interval. \n",
    "\n",
    "Note that since `log_like0` does not depend on the source parameters, TS looks the same as `log_like`, up to a constant and a factor of 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ebfbe5e7-b535-428f-aad9-4cf4344ace98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots()\n",
    "\n",
    "_,plot = ts.plot(ax, vmin = 0, colorbar = False)\n",
    "\n",
    "ax.scatter([ts.axes['index'].centers[argmax[0]]],[ts.axes['norm'].centers[argmax[1]]], label = \"Max TS\")\n",
    "ax.scatter([index_inj],[norm_inj*(spectrum.piv.value/piv_inj)**index_inj], marker = \"x\", label = \"Injected\")\n",
    "# Here we also use Wilk's theorem to find the DeltaTS that corresponse to a 90% containment confidence\n",
    "ts_thresh = ts_max - stats.chi2.isf(1-.9, df = 2)\n",
    "contours = ax.contour(ts.axes['index'].centers, \n",
    "                      ts.axes['norm'].centers, \n",
    "                      ts.contents.transpose(), \n",
    "                      [ts_thresh], colors = 'red')\n",
    "contours.collections[0].set_label(\"90% cont.\")\n",
    "\n",
    "cbar = fig.colorbar(plot)\n",
    "cbar.ax.set_ylabel(\"TS\")\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "01cce033-21aa-4790-8dad-e465a0b27f77",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}