convolutional neural networks.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "def reset_graph(seed=42):\n",
    "    tf.reset_default_graph()\n",
    "    tf.set_random_seed(seed)\n",
    "    np.random.seed(seed)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"cnn\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_image(image):\n",
    "    plt.imshow(image, cmap=\"gray\", interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")\n",
    "\n",
    "def plot_color_image(image):\n",
    "    plt.imshow(image.astype(np.uint8),interpolation=\"nearest\")\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolutional layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "The Python Imaging Library (PIL) is required to load data from jpeg files",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    748\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 749\u001b[1;33m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    750\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: cannot import name 'imread'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\misc\\pilutil.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     18\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m     \u001b[1;32mfrom\u001b[0m \u001b[0mPIL\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mImage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mImageFilter\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     20\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'PIL'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    750\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 751\u001b[1;33m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpilutil\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    752\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\misc\\pilutil.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m     \u001b[1;32mimport\u001b[0m \u001b[0mImage\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m     \u001b[1;32mimport\u001b[0m \u001b[0mImageFilter\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'Image'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-7-ee76aeb5563a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdatasets\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mload_sample_image\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mchina\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mload_sample_image\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"china.jpg\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mflower\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mload_sample_image\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"flower.jpg\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mimage\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mchina\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m150\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;36m220\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m130\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;36m250\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mheight\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwidth\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mchannels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_image\u001b[1;34m(image_name)\u001b[0m\n\u001b[0;32m    795\u001b[0m     \u001b[1;33m(\u001b[0m\u001b[1;36m427\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m640\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    796\u001b[0m     \"\"\"\n\u001b[1;32m--> 797\u001b[1;33m     \u001b[0mimages\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mload_sample_images\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    798\u001b[0m     \u001b[0mindex\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    799\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfilename\u001b[0m \u001b[1;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mimages\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfilenames\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    751\u001b[0m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpilutil\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    752\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 753\u001b[1;33m         raise ImportError(\"The Python Imaging Library (PIL) \"\n\u001b[0m\u001b[0;32m    754\u001b[0m                           \"is required to load data from jpeg files\")\n\u001b[0;32m    755\u001b[0m     \u001b[0mmodule_path\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdirname\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__file__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"images\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: The Python Imaging Library (PIL) is required to load data from jpeg files"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_sample_image\n",
    "china = load_sample_image(\"china.jpg\")\n",
    "flower = load_sample_image(\"flower.jpg\")\n",
    "image = china[150:220, 130:250]\n",
    "height, width, channels = image.shape\n",
    "image_grayscale = image.mean(axis=2).astype(np.float32)\n",
    "images = image_grayscale.reshape(1, height, width, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "The Python Imaging Library (PIL) is required to load data from jpeg files",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    748\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 749\u001b[1;33m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    750\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: cannot import name 'imread'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\misc\\pilutil.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     18\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 19\u001b[1;33m     \u001b[1;32mfrom\u001b[0m \u001b[0mPIL\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mImage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mImageFilter\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     20\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'PIL'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    750\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 751\u001b[1;33m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpilutil\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    752\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\scipy\\misc\\pilutil.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m     \u001b[1;32mimport\u001b[0m \u001b[0mImage\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     22\u001b[0m     \u001b[1;32mimport\u001b[0m \u001b[0mImageFilter\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'Image'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-3397ea3700fa>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdatasets\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mload_sample_images\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 4\u001b[1;33m \u001b[0mdataset\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mload_sample_images\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimages\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat32\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      5\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mheight\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mwidth\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mchannels\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdataset\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\users\\zhuowu\\appdata\\local\\programs\\python\\python36\\lib\\site-packages\\sklearn\\datasets\\base.py\u001b[0m in \u001b[0;36mload_sample_images\u001b[1;34m()\u001b[0m\n\u001b[0;32m    751\u001b[0m             \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmisc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpilutil\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mimread\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    752\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 753\u001b[1;33m         raise ImportError(\"The Python Imaging Library (PIL) \"\n\u001b[0m\u001b[0;32m    754\u001b[0m                           \"is required to load data from jpeg files\")\n\u001b[0;32m    755\u001b[0m     \u001b[0mmodule_path\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mjoin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdirname\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__file__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m\"images\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: The Python Imaging Library (PIL) is required to load data from jpeg files"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_sample_images\n",
    "\n",
    "dataset = np.array(load_sample_images().images, dtype=np.float32)\n",
    "batch_size, height, width, channels = dataset.shape\n",
    "\n",
    "filters_test = np.zeros(shape=(7, 7, channels, 2), dtype=np.float32)\n",
    "filters_test[:, 3, :, 0] = 1     #vertical lines\n",
    "filters_test[3, :, :, 1] = 1\n",
    "\n",
    "X = tf.placeholder(tf.float32, shape=(None, height, width, channels))\n",
    "convolution = tf.nn.conv2d(X, filters, strides=[1, 2, 2, 1], padding=\"SAME\")\n",
    "\n",
    "with tf.session() as sess:\n",
    "    output = sess.run(convolution, feed_dict={X:dataset})\n",
    "    \n",
    "plt.imshow(output[0, :, :, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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