Droplets_results.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import math\n",
    "import glob\n",
    "from utils import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "needle_d = np.zeros((2))\n",
    "needle_std = np.zeros((2))\n",
    "folder2 = 'drops/img/'\n",
    "features = ['noz_0_','white_0_']\n",
    "all_names = [folder2+feat for feat in features]\n",
    "M = []\n",
    "\n",
    "# Load calculated parameters for transformation\n",
    "poly_file = 'data/polynomials_2022.txt'\n",
    "p = magnification(poly_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Droplet with d $\\approx$ 5 mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250\n"
     ]
    }
   ],
   "source": [
    "#Correct names and folders\n",
    "folder1 = 'drops/res_noz_0/'\n",
    "# Correct name for target files\n",
    "name_feat = folder2 + 'noz_0_'\n",
    "\n",
    "#Obtain maximum intensity for one series\n",
    "M.append(obtain_intensity_maxima(all_names[0],(100,150)))\n",
    "max_gray=M[-1]\n",
    "\n",
    "# Load PTV data\n",
    "name = folder1+'rt_is.10???'\n",
    "filenames=sorted(glob.glob(name))\n",
    "N = len(filenames)\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_E = []\n",
    "gray_sum = []\n",
    "\n",
    "for j in range(100,151):\n",
    "    name = filenames[j]\n",
    "    a = np.loadtxt(name, skiprows=1)\n",
    "    \n",
    "    #Separate data into coordinates, add offset  between ptv and real positions(systematic error) \n",
    "    x = a[:,1]/10.\n",
    "    y = a[:,2]/10.\n",
    "    z = a[:,3]/10.\n",
    "    \n",
    "    for i in range(len(a)):\n",
    "        if -3<z[i] and z[i]<-2 and -3<y[i] and y[i]<15:\n",
    "            #Scale pixel to world with z position\n",
    "            scale = [p[j](a[i][3])*0.1 for j in range(4)]\n",
    "            #Find ID in each camera\n",
    "            ID = np.array([int(a[i][4]),int(a[i][5]),int(a[i][6]),int(a[i][7])],dtype=int)\n",
    "            #Use ID values to obtain axis lengths and intensity\n",
    "            al, b, gray = obtain_values_from_ID(ID,scale,name_feat,count=j)\n",
    "            gray_sum.append(gray)\n",
    "            d_E.append(np.sqrt(al*b)/resize(gray_sum[i]/max_gray,np.sqrt(al*b)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.262486993160219 0.21518197641205358\n"
     ]
    }
   ],
   "source": [
    "needle_d[0] = np.asarray(d_E).mean()\n",
    "needle_std[0] = np.asarray(d_E).std()\n",
    "print(np.asarray(d_E).mean(), np.asarray(d_E).std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Droplet with d $\\approx$ 2.4 mm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "250\n"
     ]
    }
   ],
   "source": [
    "folder1 = 'multi_drops/res_white_0/'\n",
    "folder2 = 'multi_drops/img/'\n",
    "# Correct name for target files\n",
    "name_feat = folder2 + 'white_0_'\n",
    "\n",
    "#Obtain maximum intensity for one series\n",
    "M.append(obtain_intensity_maxima(all_names[1],(100,150)))\n",
    "max_gray=M[-1]\n",
    "\n",
    "# Load PTV data\n",
    "name = folder1+'rt_is.10???'\n",
    "filenames=sorted(glob.glob(name))\n",
    "N = len(filenames)\n",
    "print(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_E = []\n",
    "gray_sum = []\n",
    "\n",
    "for j in range(100,150):\n",
    "    name = filenames[j]\n",
    "    a = np.loadtxt(name, skiprows=1)\n",
    "    \n",
    "    #Separate data into coordinates, add offset  between ptv and real positions(systematic error) \n",
    "    x = a[:,1]/10.\n",
    "    y = a[:,2]/10.\n",
    "    z = a[:,3]/10.\n",
    "    \n",
    "    for i in range(len(a)):\n",
    "        if -4<z[i] and z[i]<-1:\n",
    "            #Scale pixel to world with z position\n",
    "            scale = [p[j](a[i][3])*0.1 for j in range(4)]\n",
    "            #Find ID in each camera\n",
    "            ID = np.array([int(a[i][4]),int(a[i][5]),int(a[i][6]),int(a[i][7])],dtype=int)\n",
    "            #Use ID values to obtain axis lengths and intensity\n",
    "            al, b, gray = obtain_values_from_ID(ID,scale,name_feat,count=j)\n",
    "            gray_sum.append(gray)\n",
    "            d_E.append(np.sqrt(al*b)/resize(gray_sum[i]/max_gray,np.sqrt(al*b)))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.515277679075556 0.12234556415519979\n"
     ]
    }
   ],
   "source": [
    "needle_d[1] = np.asarray(d_E).mean()\n",
    "needle_std[1] = np.asarray(d_E).std()\n",
    "print(np.asarray(d_E).mean(), np.asarray(d_E).std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measured data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "D_needle = np.array([5.073,2.429])\n",
    "std_needle = np.array([0.067,0.081])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Estimated diameter [mm]')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TgaTvRsQfSFpD+Us2g74YKumKdN35wGKSW0efJrl99PLBbs+sXrZt28bChQt5/vnnXRC2tqLkhp0BFqZ38Eg6rtzyzJlC3XR1dUVvb2+9d2sdbu3atSxatIiIYMaMGS4IW8uRtCIiusotq3hG0H+ZphFf+GbNYM+ePSxZsoQnnnjCBWFrW9UuDe2kzCWhfjk7lJm1JBeErVNUOyM4HEDSdcCLwDdJbvm8hIH7Bpi1NBeErdPkvX309yIiO/TDDZIeA/62gJjMGiZbED7llFOYMWOGC8LW9vImgn2SLgG+Q3KpaA6wr7CozBogWxB2D2HrJHkTwR+SjBI6jyQRPJLOM2t5Lghbp8vboew5kgHizNqKC8Jmgxh0zqyd9PX1sXz5cpYuXeqCsHU8JwLrOO4hbLY/JwLrKC4Imx2oWoeycg+TeV1EfLG24ZgVwwVhs4FVOyPo7zT2NuC3SUYLBXgf8HBRQZnVkgvCZpVV61n8eQBJ3wdOj4id6efPkTy20qxpuSBslk/eGsFE4LXM59eA42sejVmNuCBsll/eRPBN4N8kLSTpUDYbuLWwqMwOggvCZoOTt0PZ30haApyTzro8Iv69uLDMBs8FYbOhGczto78G7IiIb0g6UtIJEfFsUYGZDYYLwmZDlysRSLoW6CK5e+gbwAjgWyQPqDdrGBeEzQ5e3jOC2cA7gJUAEbFJUsXnEUgaSXKL6RvT/dwREdeWtJkG3A30n1n0RMR1eYO3zrZ9+3Z6eno8ZLTZQcqbCF6LiJAUAJJG5VhnD3B+ROySNAJYLmlJRDxa0m5ZRMwcRMxmBxSETz31VCQ1OiyzlpQ3EXxX0o3AWEkfBT4MfLXSChERwK7044j0NeBjL83ycEHYrPby3jX0d5J+F9hBUif4bEQ8UG09ScOBFcCvA/8QEY+VaXaWpCeATcDVEbGuzHbmAnMBX//tYC4ImxVDyQ/3Ko2k6yPiv1WbV2H9scBC4MqIWJuZPxroSy8fTQfmRcSJlbbV1dUVvb29eXZrbaK0INzd3e0fBGaDJGlFRHSVW5b359Tvlpl3Qd4AImIbsBR4b8n8HRGxK51eDIyQ9Ja827X2t337dm655RYefPBBTj75ZK644gonAbMaqzb66MeBPwYmSVqdWXQ4yeMqK617JPDLiNgm6VDg3cD1JW2OAX6aFqLPIElMPx/8n2HtKFsQ/sAHPsBpp53mgrBZAarVCL4NLAH+J/CZzPydEfGLKuuOA25J6wTDgO9GxCJJVwBExHzgIuDjkvYCrwIXR55rVdbWXBA2q69cNYLXG0tHAa/fqB0RzxcRVCWuEbS3bEH4nHPOcUHYrEYq1Qjy9ix+H/BF4K3AFuA44Eng5FoFaZ3NPYTNGidvP4K/Bs4EfhAR75B0HjCnuLCsk7iHsFlj5U0Ev4yIn0saJmlYRDwo6frqq5lV5oKwWePlTQTbJB1GMnbQbZK2AHuLC8vanQvCZs0jbyKYBewG/gy4BBgDeHA4G5LSHsJTp05l+PDhjQ7LrGPlHWLiZXi9J/C9hUZkbcsFYbPmlPeuoY+RnAG8CvQBIhlAblJxoVk7cUHYrHnlvTR0NXByRLxUZDDWnlwQNmtueRPBfwCvFBmItR8XhM1aQ95EcA3wL5IeI3ngDAAR8SeFRGUtzwVhs9aRNxHcCPwIWENSIzArq7QgfOmll3Lcccc1OiwzqyBvItgbEVcVGom1PBeEzVpT3kTwYPqUsHvZ/9JQtRFIrUO4IGzWuvImgj9M36/JzPPto+aCsFkbyNuh7ISiA7HW44KwWXuo9oSy8yPiR5K6yy2PiJ5iwrJm5h7CZu2l2hnBuSR3C72vzLIAnAg6zPbt21m4cCE/+clPXBA2axMVE0FEXJtOXhcRz2aXSfLlog6zbt06Fi1aRF9fnwvCZm0kb7H4TuD0knl3AL810AqSRpIMW/3GdD93ZBJLfxsB84DpJD2XL4uIlTljsjpxQdisvVWrEZxE8jjKMSV1gtFknl08gD3A+RGxS9IIYLmkJRHxaKbNBcCJ6eudwA3puzWJF154gTvvvNMFYbM2Vu2M4G3ATGAs+9cJdgIfrbRiRASwK/04In1FSbNZwK1p20cljZU0LiI25wvfiuKCsFnnqFYjuBu4W9JZEfGvg924pOHACuDXgX+IiMdKmhwLbMh83pjO2y8RpJ3Z5gL+MqoDF4TNOsuwnO1mSxotaYSkH0p6SdIHq60UEfsi4jeB8cAZkk4paVKu0lh61kBELIiIrojoOvLII3OGbEOxbt065s+fz+bNm/nABz5Ad3e3k4BZm8tbLH5PRHxa0mySX+2/DzwIfCvPyhGxTdJS4L3A2syijcCEzOfxwKacMVkN7dmzh/vvv59Vq1a5IGzWYfImghHp+3Tg9oj4RbXbBiUdCfwyTQKHAu8Gri9pdg/wSUnfISkSb3d9oP5cEDbrbHkTwb2SniJ5VOUfp1/yu6usMw64Ja0TDAO+GxGLJF0BEBHzgcUkyeVpkttHLx/C32BD5CGjzQxAyQ07ORpKbwJ2RMQ+SaOAwyPixUKjK6Orqyt6e3vrvdu244KwWWeRtCIiusotq1gslvTpzMd3R8Q+gIh4GfDTyVqUC8JmllXtrqGLM9PXlCx7b41jsYLt2bOHu+++mzvuuIMjjjiCj33sY0yePNnDRJh1uGo1Ag0wXe6zNbEXXniBnp4etm7d6oKwme2nWiKIAabLfbYm5IKwmVVTLRFMlrSD5Nf/oek06WdfVG5yLgibWR7VhpjwtYMW5SGjzSyvvP0IrEVkewgfe+yxdHd38+Y3v7nRYZlZE3MiaCPZHsLnnHMO5557rgvCZlaVE0EbcEHYzA6GE0GLc0HYzA6WE0ELc0HYzGrBiaAFuSBsZrXkRNBiXBA2s1pzImgRfX19PPLIIzz44IMuCJtZTTkR1NG0acn70qWDWy9bED755JOZOXOmC8JmVjNOBE0uWxCeNWuWRws1s5pzImhSLgibWb04ETSh/oLw1q1bXRA2s8IVlggkTQBuBY4B+oAFETGvpM004G7g2XRWT0RcV1RMjdTXBzfdBJMmwc6dMGoUDBtW2mb/HsKXXXaZC8JmVrgizwj2An8eESslHQ6skPRARKwvabcsImYWGEfD9fXBli0wdy4sXw5TpsDtt8NRR/0qGbggbGaNUlgiiIjNwOZ0eqekJ4FjgdJE0Jb67xCC5Exg7txf3S20dCnMmQMLFsBHPwpHHrmOri4XhM2sMepSI5B0PPAO4LEyi8+S9ASwCbg6ItbVI6Z6mjQpORPIWr4cJk0KTjrpHsaNW8URR7ggbGaNUXgikHQYcCfwpxGxo2TxSuC4iNglaTpwF3BimW3MBeYCTJw4sdiAayTbV2DnzuRyUHbelCnw4os7GTdulQvCZtZQiiju0cOSRgCLgH+OiC/maP8c0BURLw3UpqurK3p7e2sXZB301wjmzPlVjeDWW19j9eofcMopJ7sgbGaFk7QiIrrKLSvyriEBXwOeHCgJSDoG+GlEhKQzgGHAz4uKqVGGDUsKwzfd1McJJ4hNm7azceOPOf/88zj00EMbHZ6ZdbgiLw2dDXwIWCNpVTrvL4CJABExH7gI+LikvcCrwMVR5ClKAz355Dpuv30RUh8XXngBZ555hgvCZtYUirxraDlQ8ZsuIr4CfKWoGJrBa6+9xpIlS1i1ahWvvnos69d384UvuCBsZs3DPYsL9MILL9DT08MvfvELF4TNrGk5ERSgf8jopUuXcthhh7mHsJk1NSeCGivtITxjxgwXhM2sqTkR1JCHjDazVuREUAPZgrCHjDazVuNEcJBcEDazVudEMEQuCJtZu3AiGAIXhM2snTgRDFJ/QXjfvn0uCJtZW3AiyMkFYTNrV04EObggbGbtzImgAheEzawTOBEMwAVhM+sUTgRluCBsZp3EiSAjWxB+61vfyoUXXuiCsJm1PSeClAvCZtapOj4RuCBsZp2uoxOBC8JmZh2cCNavX8+9997rgrCZdbzCEoGkCcCtwDFAH7AgIuaVtBEwD5gOvAJcFhEri4oJXBA2MytV5BnBXuDPI2KlpMOBFZIeiIj1mTYXACemr3cCN6TvhcgWhKdMmcK0adNcEDazjldYIoiIzcDmdHqnpCeBY4FsIpgF3BoRATwqaaykcem6NbV+/XruvPNODjvsMC699FKOP/74Wu/CzKwl1aVGIOl44B3AYyWLjgU2ZD5vTOftlwgkzQXmph93SfrxEEN5C/DSVVddNcTVC/MW4KVGBzGAZo3NcQ2O4xqcdoxrwNshC08Ekg4D7gT+NCJ2lC4us0ocMCNiAbCgBrH0RkTXwW6n1po1Lmje2BzX4Diuwem0uIbVeoNZkkaQJIHbIqKnTJONwITM5/HApiJjMjOz/RWWCNI7gr4GPBkRXxyg2T3AHylxJrC9iPqAmZkNrMhLQ2cDHwLWSFqVzvsLYCJARMwHFpPcOvo0ye2jlxcYD9Tg8lJBmjUuaN7YHNfgOK7B6ai4lNywY2ZmnarQGoGZmTU/JwIzsw7XdolA0gRJD0p6UtI6SZ8q00aSvizpaUmrJZ3eJHFNk7Rd0qr09dk6xDVS0r9JeiKN6/Nl2jTieOWJq+7HK7Pv4ZL+XdKiMsvqfrxyxtXI4/WcpDXpfnvLLG/IMcsRV0OOWdq59g5JT6XfGWeVLK/t8YqItnoB44DT0+nDgf8L/EZJm+nAEpJ+DGcCjzVJXNOARXU+XgIOS6dHkHT6O7MJjleeuOp+vDL7vgr4drn9N+J45YyrkcfrOeAtFZY35JjliKshxwy4BfhIOv0GYGyRx6vtzggiYnOkA9dFxE6gf2iLrNeHtoiIR4GxksY1QVx1lx6DXenHEemr9A6CRhyvPHE1hKTxwAzgqwM0qfvxyhlXM2vIMWtGkkYDU0luvyciXouIbSXNanq82i4RZGnwQ1vURYW4AM5KL4cskXRyneIZnt7iuwV4ICKa4njliAsacLyALwGfJhlVt5xG/fv6EpXjgsYcL0iS+PclrVAyZEypRh2zanFB/Y/ZJOBnwDfSy3xflTSqpE1Nj1fbJgLVYGiLIlSJayVwXERMBv4euKseMUXEvoj4TZKe3WdIOqWkSUOOV4646n68JM0EtkTEikrNyswr9HjljKsh/75SZ0fE6SQjDn9C0tSS5Y36f7JaXI04ZocApwM3RMQ7gJeBz5S0qenxastEoCYd2qJaXBGxo/9ySEQsBkZIekvRcWX2vw1YCry3ZFFDhwIZKK4GHa+zgfdLeg74DnC+pG+VtGnE8aoaVyP/fUXEpvR9C7AQOKOkSUP+jVWLq0HHbCOwMXMGfAdJYihtU7Pj1XaJQGrOoS3yxCXpmLQdks4g+e/z84LjOlLS2HT6UODdwFMlzRpxvKrG1YjjFRHXRMT4iDgeuBj4UUR8sKRZ3Y9XnrgacbzSfY1S8kwS0ksc7wHWljRrxL+xqnE16N/Yi8AGSW9LZ/0O+w/fDzU+Xu34qMpmHNoib1wXAR+XtBd4Fbg40lsECjQOuEXScJJ/5N+NiEWSrsjE1YjjlSeuRhyvsprgeOWJq1HH62hgYfp9egjw7Yi4vwmOWZ64GnXMrgRuk/QG4Bng8iKPl4eYMDPrcG13acjMzAbHicDMrMM5EZiZdTgnAjOzDudEYGbW4ZwIzMw6nBOB1ZykkPTNzOdDJP1MZYZGbiaSduVo8zlJV6fT10l6d8Ex/UUNtrFU0o8lvb8WMZVs+78oGQq5qf/bWmVOBFaEl4FT0h7BAL8LvNCIQCQV1mkyIj4bET8oavupQSeCtBNeqUsi4p4axLOfiPgn4CO13q7VlxOBFWUJyZDIAHOA2/sXpF37vy7p8XR0xVnp/OMlLZO0Mn29K50/TtLDSh4MslbSOen8XZltXiTp5nT6ZklflPQgcL2k/yTpfiUjTC6TdFLa7gRJ/5rG8YWB/hBJf5n+ov4B8LbM/JslXZROfzbdzlpJCzLDEiyV9H/S+J+U9NuSeiT9P0l/ndnWB5U8iGeVpBuVjLz6v4BD03m3DdSu/1ikZyiPAfs9xKTM31M1pvS/xVNKRr5cK+k2Se+W9EjarnSsIGtl0YCHVPjV3i9gF3AayWBZI4FVZB7wAfwP4IPp9FiSh/SMAn4NGJnOPxHoTaf/HPjLdHo4cHj/fjL7vAi4OZ2+GVgEDE8//xA4MZ1+J8k4PJCO15JOfyK7vcx2fwtYk8Y2mqRL/9WZ/VyUTr85s843gfel00uB69PpT5EMDDYOeCPJwGFHAG8H7gVGpO3+MRNX9m+s1C6APxjgv8dSoKvkc7WYjgf2AqeS/GBcAXydZNTLWcBdme29/t/Wr9Z8teNYQ9YEImK1kucuzCEZFyXrPSQjZV6dfh5JMubSJuArkn4T2Af853T548DXlYzeeldErMoRwvciYp+SYb/fBXwv/ZEOyRceJOM/XZhOfxO4vsx2zgEWRsQrAJIGurxynqRPkySMNwPrSL60IUk4kCSUdZEODibpGZIRJKeQJJzH0xgPJXkGQ6nfqdBuH8nItnlVi2kb8GxErEnnrwN+GBEhaQ1JorA24URgRboH+DuSX4xHZOYLuDAifpxtLOlzwE+BySS/QncDRMTDSsaJnwF8U9L/johb2X/89ZEl+345fR8GbIvkuQbl5Blsq2IbSSNJfp13RcSG9O/IxrMnfe/LTPd/PoTkeNwSEddUiaNSu90Rsa/K+lnVYqLM/D1l2lgbcI3AivR14Lr+X5UZ/wxcmbmO/o50/hhgc0T0kYzU2n/9+ziSh67cRDKUd//Y7D+V9HZJw4DZ5QKI5OE/z0r6/XRbkjQ5XfwIyZDNAJcM8Dc8DMyWdKiSIYvfV6ZN/5f+S+kZyEUDbGsgPwQuknRUGuOb078Z4JfpmVC1dmZD5kRghYmIjRExr8yiL5A8g3i1pLXpZ0h+VV8q6VGSy0L9v+qnAask/TvJpZz+bX6GpBbwI6DSWOyXAP9V0hMkl2xmpfM/RfJUqsdJklC5v2El8E8kdY47gWVl2mwDbiK5zHIXyaWs3CJiPfDfSR6ZuBp4gOSaPcACkuN0W5V2ZkPmYajN2pykpSQF7t6Ctj8t3f7MIrZvxfMZgVn7+wVwswrqUEZyJre11tu2+vEZgZlZh/MZgZlZh3MiMDPrcE4EZmYdzonAzKzD/X86xNF3Zbv/KgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(D_needle,needle_d,yerr=needle_std,xerr=std_needle,ecolor='b',c='w',marker='o',markerfacecolor='b')\n",
    "\n",
    "### Identity line ###\n",
    "x = np.linspace(2,6,20)\n",
    "plt.plot(x,x,c='gray')\n",
    "#####################\n",
    "\n",
    "plt.ylim(2,6)\n",
    "plt.xlabel('Measured diameter [mm]')\n",
    "plt.ylabel('Estimated diameter [mm]')\n",
    "#plt.savefig('drop-estimation-size.png',dpi=300,bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}