{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0213f008",
   "metadata": {},
   "source": [
    "# Histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eadf8523",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy\n",
    "\n",
    "from smpl import animation, plot, stat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d706684b",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib notebook \n",
    "# plt.ioff()\n",
    "# Parameter\n",
    "n = 13\n",
    "bahnhs = 13\n",
    "p = 1.0 / bahnhs\n",
    "\n",
    "bahnh = np.array(range(bahnhs)) * 0\n",
    "datax = np.array(range(1, 14))\n",
    "datay = datax * 0\n",
    "c = 0\n",
    "\n",
    "\n",
    "# Approximate factorial by gamma\n",
    "def fac(n):\n",
    "    return scipy.special.gamma(n + 1)\n",
    "\n",
    "\n",
    "def update(a):\n",
    "    global bahnh, datax, datay, c, bahnhs\n",
    "    c += 1\n",
    "    bahnh = bahnh * 0\n",
    "    for i in range(n):\n",
    "        bahnh[np.random.randint(0, bahnhs)] += 1\n",
    "        if np.any(np.greater(bahnh, 1)):\n",
    "            datay[i] += 1\n",
    "    plot.data(\n",
    "        datax,\n",
    "        stat.poisson_dist(datay) / c,\n",
    "        init=True,\n",
    "        tight=False,\n",
    "        fmt=\"hist\",\n",
    "        ylabel=\"P(>1 Gäste bei beliebigem Bahnhof)\",\n",
    "        xlabel=\"$n$ Gäste\",\n",
    "        capsize=0,\n",
    "    )\n",
    "    plot.function(\n",
    "        lambda ni: 1.0 - fac(bahnhs) / (fac(bahnhs - ni) * bahnhs**ni),\n",
    "        xmin=0,\n",
    "        xmax=13,\n",
    "        label=\"$\\\\frac{b!}{(b-n)!b^n}$\",\n",
    "        function_color=\"orange\",\n",
    "    )\n",
    "\n",
    "\n",
    "def init():\n",
    "    global datay, bahnh, c\n",
    "    datay = datay * 0\n",
    "    bahnh = bahnh * 0\n",
    "    c = 0\n",
    "\n",
    "\n",
    "ani = animation.animate(\n",
    "    update=update, frames=np.linspace(0, 20, 2000), interval=10, blit=False\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "094ffe22",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6168f906",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.9.16 64-bit",
   "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": "3.9.16"
  },
  "vscode": {
   "interpreter": {
    "hash": "31f2aee4e71d21fbe5cf8b01ff0e069b9275f58929596ceb00d14d90e3e16cd6"
   }
  },
  "widgets": {
   "application/vnd.jupyter.widget-state+json": {
    "state": {},
    "version_major": 2,
    "version_minor": 0
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}