{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example how-to create a signal time PDF"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "In this example we demonstrate how to create a signal time PDF with a gaussian shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from matplotlib import (\n",
    "    pyplot as plt,\n",
    ")\n",
    "\n",
    "from skyllh.core.config import (\n",
    "    Config,\n",
    ")\n",
    "from skyllh.core.detsigyield import (\n",
    "    NullDetSigYieldBuilder,\n",
    ")\n",
    "from skyllh.core.flux_model import (\n",
    "    GaussianTimeFluxProfile,\n",
    "    NullFluxModel,\n",
    ")\n",
    "from skyllh.core.livetime import (\n",
    "    Livetime,\n",
    ")\n",
    "from skyllh.core.parameters import (\n",
    "    ParameterModelMapper,\n",
    ")\n",
    "from skyllh.core.signalpdf import (\n",
    "    SignalTimePDF,\n",
    ")\n",
    "from skyllh.core.source_hypo_grouping import (\n",
    "    SourceHypoGroup,\n",
    "    SourceHypoGroupManager,\n",
    ")\n",
    "from skyllh.core.source_model import (\n",
    "    SourceModel,\n",
    ")\n",
    "from skyllh.core.storage import (\n",
    "    DataFieldRecordArray,\n",
    ")\n",
    "from skyllh.core.trialdata import (\n",
    "    TrialDataManager,\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The :py:class:`~skyllh.core.signalpdf.SignalTimePDF` class provides a \n",
    "generalized time PDF class, which requires a \n",
    ":py:class:`~skyllh.core.livetime.Livetime` instance and a \n",
    ":py:class:`~skyllh.core.flux_model.TimeFluxProfile` instance."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "First we need to create a (default) configuration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "cfg = Config()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Now let's construct the ``Livetime`` instance with three detector on-time\n",
    "intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "livetime_data = np.array([\n",
    "        [1, 3], \n",
    "        [4, 7],\n",
    "        [8, 9],\n",
    "    ],\n",
    "    dtype=np.float64)\n",
    "livetime = Livetime(livetime_data)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Now we can construct the time flux profile. We choose a gaussian profile. \n",
    "Other profiles exist as well, e.g. the \n",
    ":py:class:`~skyllh.core.flux_model.BoxTimeFluxProfile`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "time_flux_profile = GaussianTimeFluxProfile(t0=4, sigma_t=0.2, cfg=cfg)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "The ``t_start`` and ``t_stop`` properties of the profile tell us how far the \n",
    "time profile extends: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t_start = 2.5132311244600647\n",
      "t_stop = 5.486768875539935\n"
     ]
    }
   ],
   "source": [
    "print(f't_start = {time_flux_profile.t_start}')\n",
    "print(f't_stop = {time_flux_profile.t_stop}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Finally, we can construct the :py:class:`~skyllh.core.signalpdf.SignalTimePDF`\n",
    "instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigpdf = SignalTimePDF( \n",
    "    livetime=livetime, \n",
    "    time_flux_profile=time_flux_profile,\n",
    "    cfg=cfg)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "In order to evaluate our time PDF, we need to create some SkyLLH framework\n",
    "infrastructure first. The :py:meth:`~skyllh.core.pdf.PDF.get_pd` method requires\n",
    "a :py:class:`~skyllh.core.trialdata.TrialDataManager` instance, which we create\n",
    "now. We initialize the trial data manager with trial data containing the \n",
    "``time`` values we want to evaluate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "outputs": [],
   "source": [
    "shg_mgr = SourceHypoGroupManager(\n",
    "    SourceHypoGroup(\n",
    "        sources=SourceModel(),\n",
    "        fluxmodel=NullFluxModel(),\n",
    "        detsigyield_builders=NullDetSigYieldBuilder())\n",
    ")\n",
    "\n",
    "pmm = ParameterModelMapper(\n",
    "    models=shg_mgr.source_list)\n",
    "\n",
    "t = np.linspace(0, 10, int(10/0.05))\n",
    "events = DataFieldRecordArray(np.array(t, dtype=[('time', np.float64)]))\n",
    "\n",
    "tdm = TrialDataManager()\n",
    "tdm.initialize_trial(\n",
    "    shg_mgr=shg_mgr, \n",
    "    pmm=pmm,\n",
    "    events=events)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "The PDF instance needs to get initialized with the trial data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigpdf.initialize_for_new_trial(tdm=tdm)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Now we can evaluate PDF. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "(pd, grads) = sigpdf.get_pd(\n",
    "    tdm=tdm, \n",
    "    params_recarray=pmm.create_src_params_recarray())"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "We can verify the normalization of the PDF to unity by integrating the \n",
    "probability density values over time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total integral = 1.0200980782124147\n"
     ]
    }
   ],
   "source": [
    "total_integral = np.sum(pd[1:]*np.diff(t))\n",
    "print(f'total integral = {total_integral}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "We can also plot the PDF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'probability density / time$^{-1}$')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 4))\n",
    "ax = fig.add_subplot()\n",
    "ax.plot(t, pd, drawstyle='steps')\n",
    "ax.set_xlabel('time')\n",
    "ax.set_ylabel(r'probability density / time$^{-1}$')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": "3.10.6"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}