{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "64bb30da",
   "metadata": {},
   "source": [
    "# Interactive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85fc6b44",
   "metadata": {},
   "outputs": [],
   "source": [
    "from smpl_animation import animation\n",
    "from smpl import plot\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import numpy as np\n",
    "import tqdm\n",
    "import uncertainties as unc\n",
    "from uncertainties import unumpy\n",
    "from ipywidgets import widgets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76558a78",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fta(a,u=4.0):\n",
    "    plot.function(lambda x : u*x+a,xmin=-5,xmax=5,init=True,tight=False)\n",
    "print(\"Double click play for speedup.\")\n",
    "animation.interactive(fta,\n",
    "    widgets.Play(    value=0,    min=0,    max=100,    step=1,    interval=500,    description=\"Press play\", disabled=False),\n",
    "    widgets.FloatSlider(value=1,min=0,max=1,step=0.1,description=\"u\"),\n",
    "    prerender=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fdfa2b69",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fta(n = 1.0,u=4.0):\n",
    "    plot.function(lambda x : np.exp(n*np.log(x)-x)/u,xmin = 0.1,xmax=100,tight=False,init=False)\n",
    "    \n",
    "animation.interactive(fta,widgets.IntSlider(value=1,min=1,max=10,description=\"n\"),widgets.IntSlider(value=1,min=1,max=10,description=\"u\"),prerender=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7669ce4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fta(u=4.0):\n",
    "    animation.clear()\n",
    "    for a in np.linspace(0,10,100):\n",
    "        plot.function(lambda x : u*x+a,xmin=-5,xmax=5,init=True,tight=False)\n",
    "        animation.frame()\n",
    "\n",
    "    ani = animation.animate(interval=10,blit=True)\n",
    "    display(ani.widget_gif())\n",
    "animation.interactive(fta,widgets.FloatSlider(value=1,min=0,max=1,step=0.1,description=\"u\"),prerender=True,auto_png=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59c122db",
   "metadata": {},
   "outputs": [],
   "source": [
    "#%matplotlib notebook\n",
    "#plt.ioff()\n",
    "#import ipywidgets\n",
    "def fta(n = 1.0):\n",
    "    plot.function(lambda x : np.exp(n*np.log(x)-x),xmin = 0.1,xmax=100,tight=False,init=False)\n",
    "    plot.function(lambda x : np.exp(n*np.log(n)-n-(x-n)**2/2/n),xmin = 0.1,xmax=100,tight=False,init=False)\n",
    "    fac = np.math.factorial(n)\n",
    "    sti = np.sqrt(2* np.pi* n) *  n**n *np.exp(-n) \n",
    "    #print(\"FAKULTÄT(\"+str(n)+\") = \" + str(fac))\n",
    "    #print(\"STIRLING(\"+str(n)+\") = \" +  str(sti))\n",
    "    #print(\"REL-DIFF(\" + str(n)+\") = \"+ str((sti-fac)/fac*100) + \"%\")\n",
    "    \n",
    "animation.interactive(fta,  widgets.IntSlider(min=1, max=130, step=1, value=1,description=\"n\")) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f10bbf12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Approximate factorial by gamma\n",
    "def fac(n):\n",
    "    return scipy.special.gamma(n+1)\n",
    "\n",
    "plot.function(lambda n : (fac(n)-np.sqrt(2* np.pi* n) *  n**n *np.exp(-n))/fac(n) *100 ,xmin = 1,xmax=140,xlabel=\"N\", ylabel=\"Rel. diff. between factorial und stirling [%]\",label=\"\",logy=True,tight=False,init=True)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db9d23ad",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
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  "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"
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