lec_7.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "42f8e5bd",
   "metadata": {},
   "source": [
    "#### convolution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "be203f99",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from pathlib import Path\n",
    "import matplotlib.pyplot as plt\n",
    "import gzip, pickle\n",
    "import matplotlib as mpl\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "161a807b",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "mpl.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b2a57631",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path  = Path('./data/mnist.pkl.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c7b6ae09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_path.exists()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9ba4cd4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = None\n",
    "with gzip.open(data_path, 'rb') as f:\n",
    "    data = pickle.load(f, encoding='latin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9cc66408",
   "metadata": {},
   "outputs": [],
   "source": [
    "((x_train, y_train), (x_val, y_val), _) = data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "70dd8b87",
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train, x_val, y_val) = map(torch.tensor, (x_train, y_train, x_val, y_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9da5c356",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([50000, 784]),\n",
       " torch.Size([50000]),\n",
       " torch.Size([10000, 784]),\n",
       " torch.Size([10000]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5fe6dbba",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_imgs = x_train.view(-1, 28, 28)\n",
    "xval_imgs = x_val.view(-1, 28, 28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6799090",
   "metadata": {},
   "outputs": [],
   "source": [
    "im3 = x_imgs[7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7d4c48a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a71f33d0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAsTAAALEwEAmpwYAAAN6klEQVR4nO3dX4xc9XnG8ecBNkiQgLxF0IVATQJIDZbqIAtVYIGrAIYVyOTCkS1ANkVsLoJlS5VaCy6CVCKhtqHiBqSNQDFVShTJxDYB5KxMKJSLCIM2sIQm/BGNHfyn4As7wvwxfnuxx9Fi7/xmPTNnzpj3+5FWM3vemTmvxn72nDO/OefniBCAL76Tmm4AQH8QdiAJwg4kQdiBJAg7kMQp/VyZbT76B2oWEZ5teVdbdtvX2/6d7bdsr+/mtQDUy52Os9s+WdLvJV0raaeklyStjIjfFp7Dlh2oWR1b9sslvRUR70TEJ5J+KmlZF68HoEbdhP08STtm/L6zWvY5tsdsb7e9vYt1AehSNx/QzbarcMxuekSMSxqX2I0HmtTNln2npPNn/P5VSe911w6AunQT9pckXWz7QttfkrRC0pbetAWg1zrejY+IQ7bvkrRV0smSHo2I13vWGYCe6njoraOVccwO1K6WL9UAOHEQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kETHUzZjcFxyySUta0NDQ8XnXnXVVcX6Qw89VKwfPny4WG/S5s2bW9ZWrFhRfO4nn3zS63Ya11XYbb8r6YCkzyQdiohFvWgKQO/1Ysv+dxHxfg9eB0CNOGYHkug27CHpl7Zftj022wNsj9nebnt7l+sC0IVud+OvjIj3bJ8tacL2/0TE8zMfEBHjksYlyXZ0uT4AHepqyx4R71W3eyX9XNLlvWgKQO91HHbbp9v+ypH7kq6TNNWrxgD0liM627O2/TVNb82l6cOB/4yIH7R5Drvxs7j00kuL9dWrVxfry5cvb1k76aTy3/Nzzz23WLddrHf6/6dpjz32WLG+bt26Yn3//v097Ka3ImLWf7SOj9kj4h1Jf9NxRwD6iqE3IAnCDiRB2IEkCDuQBGEHkuh46K2jlTH0NqstW7YU66Ojo33q5Fhf1KG3dq6++upi/cUXX+xTJ8ev1dAbW3YgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSIJLSQ+AiYmJYr2bcfa9e/cW64888kix3u4U2W4uJX3FFVcU6+3GunF82LIDSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKczz4ATjml/HWHkZGRjl/7008/LdZ3797d8Wt364wzzijWp6bK0xC0uwx2yaZNm4r1W265pVj/+OOPO1533TifHUiOsANJEHYgCcIOJEHYgSQIO5AEYQeS4Hz2AXDo0KFifceOHX3qpL+WLl1arM+bN6+2de/cubNYH+Rx9E613bLbftT2XttTM5YN256w/WZ1W9+/CoCemMtu/I8lXX/UsvWStkXExZK2Vb8DGGBtwx4Rz0vad9TiZZI2VPc3SLq5t20B6LVOj9nPiYhdkhQRu2yf3eqBtsckjXW4HgA9UvsHdBExLmlc4kQYoEmdDr3tsT0iSdVt+RKmABrXadi3SFpV3V8laXNv2gFQl7bns9t+XNISSWdJ2iPp+5I2SfqZpAsk/UHS8og4+kO82V6L3fhkVqxY0bJ25513Fp9b53Xjh4eHi/X9+/fXtu66tTqfve0xe0SsbFH6VlcdAegrvi4LJEHYgSQIO5AEYQeSIOxAEpziiqJ2l1Rev758DtRFF13UsjY0NNRRT3M1OTnZstbuEttfRGzZgSQIO5AEYQeSIOxAEoQdSIKwA0kQdiAJxtkHwPz584v12267rVi/5ppretjN5y1evLhYr3PK73anmbYb43/66adb1g4ePNhRTycytuxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kETbS0n3dGVJLyW9YMGCYn3Lli3F+gUXXNDLdo6LPetVif+szv8/Tz31VLG+bNmy2tZ9Imt1KWm27EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBOezD4B2Y9nt6nU66aTy9uDw4cO1rfvGG28s1m+44YZi/ZlnnullOye8tlt224/a3mt7asaye23/0fZk9TNab5sAujWX3fgfS7p+luX/HhELq5/WlwQBMBDahj0inpe0rw+9AKhRNx/Q3WX71Wo3f16rB9kes73d9vYu1gWgS52G/WFJX5e0UNIuST9s9cCIGI+IRRGxqMN1AeiBjsIeEXsi4rOIOCzpR5Iu721bAHqto7DbHpnx67clTbV6LIDB0Hac3fbjkpZIOsv2Tknfl7TE9kJJIeldSd+tr8UT39RU+W/hkiVLivVbb721WN+6dWvL2kcffVR8bt3uuOOOlrU1a9b0sRO0DXtErJxl8SM19AKgRnxdFkiCsANJEHYgCcIOJEHYgSS4lDRqdeaZZ7asffDBB1299k033VSsZz3FlUtJA8kRdiAJwg4kQdiBJAg7kARhB5Ig7EASXEoatVq6dGnTLaDClh1IgrADSRB2IAnCDiRB2IEkCDuQBGEHkmCcfY6GhoZa1q677rric5999tli/eDBgx31NAhuv/32Yv3BBx/sUydohy07kARhB5Ig7EAShB1IgrADSRB2IAnCDiTBOHtl8eLFxfo999zTsnbttdcWn3vhhRcW6zt27CjW6zQ8PFysj46OFusPPPBAsX7aaacdd09HtPv+QdPTUZ9o2m7ZbZ9v+1e237D9uu211fJh2xO236xu59XfLoBOzWU3/pCkf4iIv5b0t5K+Z/sbktZL2hYRF0vaVv0OYEC1DXtE7IqIV6r7ByS9Iek8ScskbagetkHSzTX1CKAHjuuY3fZ8Sd+U9GtJ50TELmn6D4Lts1s8Z0zSWJd9AujSnMNu+8uSNkpaFxH77VnnjjtGRIxLGq9eg4kdgYbMaejN9pCmg/6TiHiiWrzH9khVH5G0t54WAfRC2ymbPb0J3yBpX0Ssm7H8XyV9EBH3214vaTgi/rHNaw3sln1ycrJYX7BgQcev/fDDDxfrBw4c6Pi1u9Vu2PCyyy4r1ruZ8vu5554r1tu9bxs3bux43V9kraZsnstu/JWSbpP0mu3Jatndku6X9DPbd0j6g6TlPegTQE3ahj0i/ltSqwP0b/W2HQB14euyQBKEHUiCsANJEHYgCcIOJNF2nL2nK0s6zn4ia/dNyT179hTrTz75ZMva2rVri8/lFNbOtBpnZ8sOJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0kwzl5ZuHBhsb5mzZqWtVWrVvW4m955++23i/UPP/ywWH/hhReK9fHx8WJ9amqqWEfvMc4OJEfYgSQIO5AEYQeSIOxAEoQdSIKwA0kwzj5Hp556asva6tWri8+97777ivV588oT4G7atKlYn5iYaFnbvHlz8bm7d+8u1nHiYZwdSI6wA0kQdiAJwg4kQdiBJAg7kARhB5KYy/zs50t6TNJfSjosaTwiHrR9r6Q7Jf1f9dC7I+LpNq91wo6zAyeKVuPscwn7iKSRiHjF9lckvSzpZknfkfSniPi3uTZB2IH6tQr7XOZn3yVpV3X/gO03JJ3X2/YA1O24jtltz5f0TUm/rhbdZftV24/anvU7n7bHbG+3vb27VgF0Y87fjbf9ZUn/JekHEfGE7XMkvS8pJP2zpnf1/77Na7AbD9Ss42N2SbI9JOkXkrZGxAOz1OdL+kVEFGc/JOxA/To+EcbT03g+IumNmUGvPrg74tuSuIwoMMDm8mn8YkkvSHpN00NvknS3pJWSFmp6N/5dSd+tPswrvRZbdqBmXe3G9wphB+rH+exAcoQdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEk2l5wssfel/S/M34/q1o2iAa1t0HtS6K3TvWyt79qVejr+ezHrNzeHhGLGmugYFB7G9S+JHrrVL96YzceSIKwA0k0HfbxhtdfMqi9DWpfEr11qi+9NXrMDqB/mt6yA+gTwg4k0UjYbV9v+3e237K9vokeWrH9ru3XbE82PT9dNYfeXttTM5YN256w/WZ1O+scew31dq/tP1bv3aTt0YZ6O9/2r2y/Yft122ur5Y2+d4W++vK+9f2Y3fbJkn4v6VpJOyW9JGllRPy2r420YPtdSYsiovEvYNi+StKfJD12ZGot2/8iaV9E3F/9oZwXEf80IL3dq+Ocxrum3lpNM75aDb53vZz+vBNNbNkvl/RWRLwTEZ9I+qmkZQ30MfAi4nlJ+45avEzShur+Bk3/Z+m7Fr0NhIjYFRGvVPcPSDoyzXij712hr75oIuznSdox4/edGqz53kPSL22/bHus6WZmcc6Rabaq27Mb7udobafx7qejphkfmPeuk+nPu9VE2GebmmaQxv+ujIjLJN0g6XvV7irm5mFJX9f0HIC7JP2wyWaqacY3SloXEfub7GWmWfrqy/vWRNh3Sjp/xu9flfReA33MKiLeq273Svq5pg87BsmeIzPoVrd7G+7nzyJiT0R8FhGHJf1IDb531TTjGyX9JCKeqBY3/t7N1le/3rcmwv6SpIttX2j7S5JWSNrSQB/HsH169cGJbJ8u6ToN3lTUWyStqu6vkrS5wV4+Z1Cm8W41zbgafu8an/48Ivr+I2lU05/Ivy3pniZ6aNHX1yT9pvp5veneJD2u6d26TzW9R3SHpL+QtE3Sm9Xt8AD19h+antr7VU0Ha6Sh3hZr+tDwVUmT1c9o0+9doa++vG98XRZIgm/QAUkQdiAJwg4kQdiBJAg7kARhB5Ig7EAS/w+R5WmeDDnQtgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(im3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "773c98ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "top_edges = torch.tensor([\n",
    "    [-1, -1, -1],\n",
    "    [0, 0, 0],\n",
    "    [1, 1, 1]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "2bcd6c86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a725ebd0>"
      ]
     },
     "execution_count": 14,
     "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": [
    "plt.imshow(top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "da63c677",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type=\"text/css\">\n",
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       "  font-size: 8pt;\n",
       "  background-color: #f7fcf5;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row5_col11 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #dff3da;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row5_col12 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #dbf1d5;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row5_col13 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #92d28f;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row5_col14, #T_d4778_row5_col15, #T_d4778_row5_col16, #T_d4778_row5_col17, #T_d4778_row5_col18, #T_d4778_row5_col19, #T_d4778_row6_col13, #T_d4778_row6_col20, #T_d4778_row7_col9, #T_d4778_row7_col10, #T_d4778_row7_col11, #T_d4778_row7_col12, #T_d4778_row7_col13, #T_d4778_row7_col20, #T_d4778_row7_col21, #T_d4778_row7_col22, #T_d4778_row8_col10, #T_d4778_row8_col11, #T_d4778_row8_col20, #T_d4778_row8_col21, #T_d4778_row8_col22, #T_d4778_row9_col20, #T_d4778_row10_col20, #T_d4778_row11_col20 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #00441b;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row5_col20 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #319a50;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row5_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #f4fbf1;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row6_col9 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #caeac3;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row6_col10 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #5eb96b;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col11 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #00682a;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col12 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #006529;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col14, #T_d4778_row7_col14 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #00471c;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col15, #T_d4778_row6_col16, #T_d4778_row6_col17, #T_d4778_row6_col18, #T_d4778_row6_col19, #T_d4778_row7_col15, #T_d4778_row7_col16, #T_d4778_row7_col17, #T_d4778_row7_col18, #T_d4778_row7_col19, #T_d4778_row8_col18, #T_d4778_row8_col19, #T_d4778_row9_col19, #T_d4778_row10_col19, #T_d4778_row11_col18, #T_d4778_row11_col19, #T_d4778_row12_col17, #T_d4778_row12_col18, #T_d4778_row12_col19 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #00451c;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #40aa5d;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row6_col22 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #cbeac4;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row8_col9 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #46ae60;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row8_col12 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #006027;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row8_col13 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #6abf71;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row8_col14, #T_d4778_row8_col15, #T_d4778_row8_col16 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #6bc072;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row8_col17, #T_d4778_row11_col17 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #238b45;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row9_col9 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #f4fbf2;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row9_col10, #T_d4778_row9_col11 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #e7f6e2;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row9_col12 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #e9f7e5;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row9_col17, #T_d4778_row11_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #eff9ec;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row9_col18 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #006729;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row9_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #339c52;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row9_col22 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #e6f5e1;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row10_col17 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #acdea6;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row10_col18 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #005120;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row10_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #56b567;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row11_col16 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #a9dca3;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row12_col14 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #a7dba0;\n",
       "  color: #000000;\n",
       "}\n",
       "#T_d4778_row12_col15 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #0a7633;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row12_col16 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #004c1e;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row12_col20 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #127c39;\n",
       "  color: #f1f1f1;\n",
       "}\n",
       "#T_d4778_row12_col21 {\n",
       "  font-size: 8pt;\n",
       "  background-color: #f2faef;\n",
       "  color: #000000;\n",
       "}\n",
       "</style>\n",
       "<table id=\"T_d4778\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th class=\"blank level0\" >&nbsp;</th>\n",
       "      <th id=\"T_d4778_level0_col0\" class=\"col_heading level0 col0\" >0</th>\n",
       "      <th id=\"T_d4778_level0_col1\" class=\"col_heading level0 col1\" >1</th>\n",
       "      <th id=\"T_d4778_level0_col2\" class=\"col_heading level0 col2\" >2</th>\n",
       "      <th id=\"T_d4778_level0_col3\" class=\"col_heading level0 col3\" >3</th>\n",
       "      <th id=\"T_d4778_level0_col4\" class=\"col_heading level0 col4\" >4</th>\n",
       "      <th id=\"T_d4778_level0_col5\" class=\"col_heading level0 col5\" >5</th>\n",
       "      <th id=\"T_d4778_level0_col6\" class=\"col_heading level0 col6\" >6</th>\n",
       "      <th id=\"T_d4778_level0_col7\" class=\"col_heading level0 col7\" >7</th>\n",
       "      <th id=\"T_d4778_level0_col8\" class=\"col_heading level0 col8\" >8</th>\n",
       "      <th id=\"T_d4778_level0_col9\" class=\"col_heading level0 col9\" >9</th>\n",
       "      <th id=\"T_d4778_level0_col10\" class=\"col_heading level0 col10\" >10</th>\n",
       "      <th id=\"T_d4778_level0_col11\" class=\"col_heading level0 col11\" >11</th>\n",
       "      <th id=\"T_d4778_level0_col12\" class=\"col_heading level0 col12\" >12</th>\n",
       "      <th id=\"T_d4778_level0_col13\" class=\"col_heading level0 col13\" >13</th>\n",
       "      <th id=\"T_d4778_level0_col14\" class=\"col_heading level0 col14\" >14</th>\n",
       "      <th id=\"T_d4778_level0_col15\" class=\"col_heading level0 col15\" >15</th>\n",
       "      <th id=\"T_d4778_level0_col16\" class=\"col_heading level0 col16\" >16</th>\n",
       "      <th id=\"T_d4778_level0_col17\" class=\"col_heading level0 col17\" >17</th>\n",
       "      <th id=\"T_d4778_level0_col18\" class=\"col_heading level0 col18\" >18</th>\n",
       "      <th id=\"T_d4778_level0_col19\" class=\"col_heading level0 col19\" >19</th>\n",
       "      <th id=\"T_d4778_level0_col20\" class=\"col_heading level0 col20\" >20</th>\n",
       "      <th id=\"T_d4778_level0_col21\" class=\"col_heading level0 col21\" >21</th>\n",
       "      <th id=\"T_d4778_level0_col22\" class=\"col_heading level0 col22\" >22</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "      <td id=\"T_d4778_row0_col0\" class=\"data row0 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col1\" class=\"data row0 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col2\" class=\"data row0 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col3\" class=\"data row0 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col4\" class=\"data row0 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col5\" class=\"data row0 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col6\" class=\"data row0 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col7\" class=\"data row0 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col8\" class=\"data row0 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col9\" class=\"data row0 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col10\" class=\"data row0 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col11\" class=\"data row0 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col12\" class=\"data row0 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col13\" class=\"data row0 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col14\" class=\"data row0 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col15\" class=\"data row0 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col16\" class=\"data row0 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col17\" class=\"data row0 col17\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col18\" class=\"data row0 col18\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col19\" class=\"data row0 col19\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col20\" class=\"data row0 col20\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col21\" class=\"data row0 col21\" >0.00</td>\n",
       "      <td id=\"T_d4778_row0_col22\" class=\"data row0 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_d4778_row1_col0\" class=\"data row1 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col1\" class=\"data row1 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col2\" class=\"data row1 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col3\" class=\"data row1 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col4\" class=\"data row1 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col5\" class=\"data row1 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col6\" class=\"data row1 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col7\" class=\"data row1 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col8\" class=\"data row1 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col9\" class=\"data row1 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col10\" class=\"data row1 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col11\" class=\"data row1 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col12\" class=\"data row1 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col13\" class=\"data row1 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col14\" class=\"data row1 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col15\" class=\"data row1 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col16\" class=\"data row1 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col17\" class=\"data row1 col17\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col18\" class=\"data row1 col18\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col19\" class=\"data row1 col19\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col20\" class=\"data row1 col20\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col21\" class=\"data row1 col21\" >0.00</td>\n",
       "      <td id=\"T_d4778_row1_col22\" class=\"data row1 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_d4778_row2_col0\" class=\"data row2 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col1\" class=\"data row2 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col2\" class=\"data row2 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col3\" class=\"data row2 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col4\" class=\"data row2 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col5\" class=\"data row2 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col6\" class=\"data row2 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col7\" class=\"data row2 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col8\" class=\"data row2 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col9\" class=\"data row2 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col10\" class=\"data row2 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col11\" class=\"data row2 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col12\" class=\"data row2 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col13\" class=\"data row2 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col14\" class=\"data row2 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col15\" class=\"data row2 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col16\" class=\"data row2 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col17\" class=\"data row2 col17\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col18\" class=\"data row2 col18\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col19\" class=\"data row2 col19\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col20\" class=\"data row2 col20\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col21\" class=\"data row2 col21\" >0.00</td>\n",
       "      <td id=\"T_d4778_row2_col22\" class=\"data row2 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_d4778_row3_col0\" class=\"data row3 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col1\" class=\"data row3 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col2\" class=\"data row3 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col3\" class=\"data row3 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col4\" class=\"data row3 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col5\" class=\"data row3 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col6\" class=\"data row3 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col7\" class=\"data row3 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col8\" class=\"data row3 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col9\" class=\"data row3 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col10\" class=\"data row3 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col11\" class=\"data row3 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col12\" class=\"data row3 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col13\" class=\"data row3 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col14\" class=\"data row3 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col15\" class=\"data row3 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col16\" class=\"data row3 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col17\" class=\"data row3 col17\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col18\" class=\"data row3 col18\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col19\" class=\"data row3 col19\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col20\" class=\"data row3 col20\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col21\" class=\"data row3 col21\" >0.00</td>\n",
       "      <td id=\"T_d4778_row3_col22\" class=\"data row3 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_d4778_row4_col0\" class=\"data row4 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col1\" class=\"data row4 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col2\" class=\"data row4 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col3\" class=\"data row4 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col4\" class=\"data row4 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col5\" class=\"data row4 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col6\" class=\"data row4 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col7\" class=\"data row4 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col8\" class=\"data row4 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col9\" class=\"data row4 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col10\" class=\"data row4 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col11\" class=\"data row4 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col12\" class=\"data row4 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col13\" class=\"data row4 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col14\" class=\"data row4 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col15\" class=\"data row4 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col16\" class=\"data row4 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col17\" class=\"data row4 col17\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col18\" class=\"data row4 col18\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col19\" class=\"data row4 col19\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col20\" class=\"data row4 col20\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col21\" class=\"data row4 col21\" >0.00</td>\n",
       "      <td id=\"T_d4778_row4_col22\" class=\"data row4 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_d4778_row5_col0\" class=\"data row5 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col1\" class=\"data row5 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col2\" class=\"data row5 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col3\" class=\"data row5 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col4\" class=\"data row5 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col5\" class=\"data row5 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col6\" class=\"data row5 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col7\" class=\"data row5 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col8\" class=\"data row5 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col9\" class=\"data row5 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col10\" class=\"data row5 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row5_col11\" class=\"data row5 col11\" >0.15</td>\n",
       "      <td id=\"T_d4778_row5_col12\" class=\"data row5 col12\" >0.17</td>\n",
       "      <td id=\"T_d4778_row5_col13\" class=\"data row5 col13\" >0.41</td>\n",
       "      <td id=\"T_d4778_row5_col14\" class=\"data row5 col14\" >1.00</td>\n",
       "      <td id=\"T_d4778_row5_col15\" class=\"data row5 col15\" >0.99</td>\n",
       "      <td id=\"T_d4778_row5_col16\" class=\"data row5 col16\" >0.99</td>\n",
       "      <td id=\"T_d4778_row5_col17\" class=\"data row5 col17\" >0.99</td>\n",
       "      <td id=\"T_d4778_row5_col18\" class=\"data row5 col18\" >0.99</td>\n",
       "      <td id=\"T_d4778_row5_col19\" class=\"data row5 col19\" >0.99</td>\n",
       "      <td id=\"T_d4778_row5_col20\" class=\"data row5 col20\" >0.68</td>\n",
       "      <td id=\"T_d4778_row5_col21\" class=\"data row5 col21\" >0.02</td>\n",
       "      <td id=\"T_d4778_row5_col22\" class=\"data row5 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_d4778_row6_col0\" class=\"data row6 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col1\" class=\"data row6 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col2\" class=\"data row6 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col3\" class=\"data row6 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col4\" class=\"data row6 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col5\" class=\"data row6 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col6\" class=\"data row6 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col7\" class=\"data row6 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col8\" class=\"data row6 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row6_col9\" class=\"data row6 col9\" >0.17</td>\n",
       "      <td id=\"T_d4778_row6_col10\" class=\"data row6 col10\" >0.54</td>\n",
       "      <td id=\"T_d4778_row6_col11\" class=\"data row6 col11\" >0.88</td>\n",
       "      <td id=\"T_d4778_row6_col12\" class=\"data row6 col12\" >0.88</td>\n",
       "      <td id=\"T_d4778_row6_col13\" class=\"data row6 col13\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col14\" class=\"data row6 col14\" >0.99</td>\n",
       "      <td id=\"T_d4778_row6_col15\" class=\"data row6 col15\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col16\" class=\"data row6 col16\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col17\" class=\"data row6 col17\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col18\" class=\"data row6 col18\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col19\" class=\"data row6 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col20\" class=\"data row6 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row6_col21\" class=\"data row6 col21\" >0.62</td>\n",
       "      <td id=\"T_d4778_row6_col22\" class=\"data row6 col22\" >0.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_d4778_row7_col0\" class=\"data row7 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col1\" class=\"data row7 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col2\" class=\"data row7 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col3\" class=\"data row7 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col4\" class=\"data row7 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col5\" class=\"data row7 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col6\" class=\"data row7 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col7\" class=\"data row7 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col8\" class=\"data row7 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row7_col9\" class=\"data row7 col9\" >0.70</td>\n",
       "      <td id=\"T_d4778_row7_col10\" class=\"data row7 col10\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col11\" class=\"data row7 col11\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col12\" class=\"data row7 col12\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col13\" class=\"data row7 col13\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col14\" class=\"data row7 col14\" >0.99</td>\n",
       "      <td id=\"T_d4778_row7_col15\" class=\"data row7 col15\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col16\" class=\"data row7 col16\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col17\" class=\"data row7 col17\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col18\" class=\"data row7 col18\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col19\" class=\"data row7 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col20\" class=\"data row7 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col21\" class=\"data row7 col21\" >0.98</td>\n",
       "      <td id=\"T_d4778_row7_col22\" class=\"data row7 col22\" >0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_d4778_row8_col0\" class=\"data row8 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col1\" class=\"data row8 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col2\" class=\"data row8 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col3\" class=\"data row8 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col4\" class=\"data row8 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col5\" class=\"data row8 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col6\" class=\"data row8 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col7\" class=\"data row8 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col8\" class=\"data row8 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row8_col9\" class=\"data row8 col9\" >0.43</td>\n",
       "      <td id=\"T_d4778_row8_col10\" class=\"data row8 col10\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col11\" class=\"data row8 col11\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col12\" class=\"data row8 col12\" >0.90</td>\n",
       "      <td id=\"T_d4778_row8_col13\" class=\"data row8 col13\" >0.52</td>\n",
       "      <td id=\"T_d4778_row8_col14\" class=\"data row8 col14\" >0.52</td>\n",
       "      <td id=\"T_d4778_row8_col15\" class=\"data row8 col15\" >0.52</td>\n",
       "      <td id=\"T_d4778_row8_col16\" class=\"data row8 col16\" >0.52</td>\n",
       "      <td id=\"T_d4778_row8_col17\" class=\"data row8 col17\" >0.74</td>\n",
       "      <td id=\"T_d4778_row8_col18\" class=\"data row8 col18\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col19\" class=\"data row8 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col20\" class=\"data row8 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col21\" class=\"data row8 col21\" >0.98</td>\n",
       "      <td id=\"T_d4778_row8_col22\" class=\"data row8 col22\" >0.23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_d4778_row9_col0\" class=\"data row9 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col1\" class=\"data row9 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col2\" class=\"data row9 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col3\" class=\"data row9 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col4\" class=\"data row9 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col5\" class=\"data row9 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col6\" class=\"data row9 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col7\" class=\"data row9 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col8\" class=\"data row9 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col9\" class=\"data row9 col9\" >0.02</td>\n",
       "      <td id=\"T_d4778_row9_col10\" class=\"data row9 col10\" >0.11</td>\n",
       "      <td id=\"T_d4778_row9_col11\" class=\"data row9 col11\" >0.11</td>\n",
       "      <td id=\"T_d4778_row9_col12\" class=\"data row9 col12\" >0.09</td>\n",
       "      <td id=\"T_d4778_row9_col13\" class=\"data row9 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col14\" class=\"data row9 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col15\" class=\"data row9 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col16\" class=\"data row9 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row9_col17\" class=\"data row9 col17\" >0.05</td>\n",
       "      <td id=\"T_d4778_row9_col18\" class=\"data row9 col18\" >0.88</td>\n",
       "      <td id=\"T_d4778_row9_col19\" class=\"data row9 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row9_col20\" class=\"data row9 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row9_col21\" class=\"data row9 col21\" >0.67</td>\n",
       "      <td id=\"T_d4778_row9_col22\" class=\"data row9 col22\" >0.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "      <td id=\"T_d4778_row10_col0\" class=\"data row10 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col1\" class=\"data row10 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col2\" class=\"data row10 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col3\" class=\"data row10 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col4\" class=\"data row10 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col5\" class=\"data row10 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col6\" class=\"data row10 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col7\" class=\"data row10 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col8\" class=\"data row10 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col9\" class=\"data row10 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col10\" class=\"data row10 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col11\" class=\"data row10 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col12\" class=\"data row10 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col13\" class=\"data row10 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col14\" class=\"data row10 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col15\" class=\"data row10 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col16\" class=\"data row10 col16\" >0.00</td>\n",
       "      <td id=\"T_d4778_row10_col17\" class=\"data row10 col17\" >0.33</td>\n",
       "      <td id=\"T_d4778_row10_col18\" class=\"data row10 col18\" >0.95</td>\n",
       "      <td id=\"T_d4778_row10_col19\" class=\"data row10 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row10_col20\" class=\"data row10 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row10_col21\" class=\"data row10 col21\" >0.56</td>\n",
       "      <td id=\"T_d4778_row10_col22\" class=\"data row10 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "      <td id=\"T_d4778_row11_col0\" class=\"data row11 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col1\" class=\"data row11 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col2\" class=\"data row11 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col3\" class=\"data row11 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col4\" class=\"data row11 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col5\" class=\"data row11 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col6\" class=\"data row11 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col7\" class=\"data row11 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col8\" class=\"data row11 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col9\" class=\"data row11 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col10\" class=\"data row11 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col11\" class=\"data row11 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col12\" class=\"data row11 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col13\" class=\"data row11 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col14\" class=\"data row11 col14\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col15\" class=\"data row11 col15\" >0.00</td>\n",
       "      <td id=\"T_d4778_row11_col16\" class=\"data row11 col16\" >0.34</td>\n",
       "      <td id=\"T_d4778_row11_col17\" class=\"data row11 col17\" >0.74</td>\n",
       "      <td id=\"T_d4778_row11_col18\" class=\"data row11 col18\" >0.98</td>\n",
       "      <td id=\"T_d4778_row11_col19\" class=\"data row11 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row11_col20\" class=\"data row11 col20\" >0.98</td>\n",
       "      <td id=\"T_d4778_row11_col21\" class=\"data row11 col21\" >0.05</td>\n",
       "      <td id=\"T_d4778_row11_col22\" class=\"data row11 col22\" >0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_d4778_level0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "      <td id=\"T_d4778_row12_col0\" class=\"data row12 col0\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col1\" class=\"data row12 col1\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col2\" class=\"data row12 col2\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col3\" class=\"data row12 col3\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col4\" class=\"data row12 col4\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col5\" class=\"data row12 col5\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col6\" class=\"data row12 col6\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col7\" class=\"data row12 col7\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col8\" class=\"data row12 col8\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col9\" class=\"data row12 col9\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col10\" class=\"data row12 col10\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col11\" class=\"data row12 col11\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col12\" class=\"data row12 col12\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col13\" class=\"data row12 col13\" >0.00</td>\n",
       "      <td id=\"T_d4778_row12_col14\" class=\"data row12 col14\" >0.36</td>\n",
       "      <td id=\"T_d4778_row12_col15\" class=\"data row12 col15\" >0.83</td>\n",
       "      <td id=\"T_d4778_row12_col16\" class=\"data row12 col16\" >0.96</td>\n",
       "      <td id=\"T_d4778_row12_col17\" class=\"data row12 col17\" >0.98</td>\n",
       "      <td id=\"T_d4778_row12_col18\" class=\"data row12 col18\" >0.98</td>\n",
       "      <td id=\"T_d4778_row12_col19\" class=\"data row12 col19\" >0.98</td>\n",
       "      <td id=\"T_d4778_row12_col20\" class=\"data row12 col20\" >0.80</td>\n",
       "      <td id=\"T_d4778_row12_col21\" class=\"data row12 col21\" >0.04</td>\n",
       "      <td id=\"T_d4778_row12_col22\" class=\"data row12 col22\" >0.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x1a7254850>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(im3[:13, :23])\n",
    "df.style.format(precision=2).set_properties(**{'font-size': '8pt'}).background_gradient('Greens')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5596d370",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(im3[3:6, 14:17] * top_edges).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "26d7d586",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-0.0000, -0.0000, -0.0000],\n",
       "        [0.0000, 0.0000, 0.0000],\n",
       "        [0.9961, 0.9883, 0.9883]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(im3[3:6, 14:17] * top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2b7ba6ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-0.0234)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(im3[3:6, 14:17].to(dtype=torch.float) @ top_edges.to(dtype=torch.float)).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "63480888",
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_kernel(row, col, kernel):\n",
    "    return (im3[row-1:row+2, col-1:col+2] * kernel).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9d59f1e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apply_kernel(4, 15, top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9af1520b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(1, 27)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = range(1, 27)\n",
    "rng"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b8177885",
   "metadata": {},
   "outputs": [],
   "source": [
    "top_edges3 = [[apply_kernel(i, j, top_edges) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a3e95012",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a7494650>"
      ]
     },
     "execution_count": 23,
     "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": [
    "plt.imshow(top_edges3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e0786366",
   "metadata": {},
   "outputs": [],
   "source": [
    "left_edge = torch.tensor([\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1]\n",
    "]).float()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "8d0baa73",
   "metadata": {},
   "outputs": [],
   "source": [
    "lef_edges3 = [[apply_kernel(i, j, left_edge) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "0833baf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a7559350>"
      ]
     },
     "execution_count": 26,
     "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": [
    "plt.imshow(lef_edges3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f635cdab",
   "metadata": {},
   "source": [
    "#### convolutions in pytorch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "eb6d4a47",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn.functional as F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f3430f21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([28, 28])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6482bb2c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1, 28, 28])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im3[None,None,:,:].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4fe0eb64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9, 676])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = im3[None,None,:,:].float()\n",
    "inp_unf = F.unfold(inp, (3, 3))[0]\n",
    "inp_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "21b351a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 3])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left_edge.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d5eaaad9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-1.,  0.,  1., -1.,  0.,  1., -1.,  0.,  1.])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left_edge.view(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3eca08a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = left_edge.view(-1)\n",
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4a718f3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([676])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_unf = w @ inp_unf\n",
    "out_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "3659de12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([26, 26])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out = out_unf.view(26, 26)\n",
    "out.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0556e2e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a760d850>"
      ]
     },
     "execution_count": 36,
     "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": [
    "plt.imshow(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "256c9f9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.42 ms ± 685 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 1 [[apply_kernel(i, j, left_edge) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "123b5d05",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "86 µs ± 24.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 100 (w@F.unfold(inp, (3, 3))[0]).view(26, 26)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "aebd8702",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 4.27 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "97.8 µs ± 43.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[W NNPACK.cpp:64] Could not initialize NNPACK! Reason: Unsupported hardware.\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 100 F.conv2d(inp, left_edge[None, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "b6442077",
   "metadata": {},
   "outputs": [],
   "source": [
    "dig1_edge = torch.tensor([\n",
    "    [0, -1, 1],\n",
    "    [-1, 1, 0],\n",
    "    [1, 0, 0]\n",
    "]).float()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "9fde493f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a75fc510>"
      ]
     },
     "execution_count": 41,
     "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": [
    "plt.imshow(dig1_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "53de350b",
   "metadata": {},
   "outputs": [],
   "source": [
    "dig2_edge = torch.tensor([\n",
    "    [1, -1, 0],\n",
    "    [0, 1, -1],\n",
    "    [0, 0, 1]\n",
    "]).float()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "62dcb6f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a76cb3d0>"
      ]
     },
     "execution_count": 43,
     "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": [
    "plt.imshow(dig2_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8a2bd8b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16, 1, 28, 28])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xb = x_imgs[:16][:,None]\n",
    "xb.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "2cd438fb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 1, 3, 3])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edge_kernels = torch.stack([left_edge, top_edges, dig1_edge, dig2_edge])[:,None]\n",
    "edge_kernels.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "70c65951",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16, 4, 26, 26])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch_features = F.conv2d(xb, edge_kernels)\n",
    "batch_features.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d0952010",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a7789950>"
      ]
     },
     "execution_count": 47,
     "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": [
    "im0 = xb[1, 0]\n",
    "plt.imshow(im0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "1bb23ee5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a7479990>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAATsAAAD6CAYAAADeH+BiAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAsTAAALEwEAmpwYAAAer0lEQVR4nO3dW2yU17UH8P8KARNzN/c7gXAJNElJnEtze0lpkkot9KFqUXXEkajSSudUVO1D0DkvlfqCVKkvTVQ1UlE4bZRrU0GjtAgQoU0bCA4hCcaAwdwx92uAkADrPHj6Za9le2bsmfnmG+//T0Leaz7j2SnLu9+3Zl9EVUFE1NfdUu0OEBGlgYMdEUWBgx0RRYGDHRFFgYMdEUWBgx0RRaGkwU5EnhKR3SKyV0SWl6tTRNXG3O57pLfz7ESkH4A9ABYAOAJgK4DFqrqzu79TX1+vw4cP79X7UXm1t7efVtXR1e5HFjG3a9f58+dx5coV6erarSX83AcA7FXVNgAQkVcALATQbUIMHz4cP/rRj0p4SyqXX/ziFwer3YcMY27XqN/97nfdXivlMXYigMNBfCT3miEiz4hIk4g0XblypYS3I0oNc7sPKmWw6+pWsdMzsaq+oKqNqtpYX19fwtsRpYa53QeVMtgdATA5iCcBOFZad4gygbndB5Uy2G0FMFNEbheRAQC+D2BNebpFVFXM7T6o1x9QqOp1EflvAGsB9AOwUlWby9YzoiphbvdNpXwaC1V9G8DbZeoLUWYwt/uekga7GA0cONDEDQ0NJq6rqzPx/v37Tbxv375uf57/Wbfddluv+0nUUz63J060H0DPmzfPxD5fz549a+Lm5i9vho8ePWquffbZZ73uZ29xuRgRRYGDHRFFgY+xRQhv7+fMmWOuDRkyxMTHjuWfoXDz5k0Th7f6o0fb1Vvz58/vUT+JeipfbvvH1unTp5v4llvsvdLkyZNNfOutXw4v/fv3N9d27drV886WiHd2RBQFDnZEFAUOdkQUBdbsuuCnfMycOTNp+7rFuXPnTOxrctevXzexr3McPvzlevPTp0+ba7NnzzaxnxrgfxZRIT63Z82albRvv/12c+3GjRsmXrPGLiI5efKkiUeOHGniwYMHJ+2wfgcAfi3x1atXTVyJI17520JEUeBgR0RR4GBHRFGIsmYnYrcr83WMGTNmmHjatGlJ29fg/DKYnTvtZrYnTpwwsZ+7FNYq3n33XXMtnIMHAFOmTDHx2LFjQRTyue1rY2GNDrB1umvXrplrO3bsyBsfOnTIxL6G3NjYmLT9nFFf3/M/+8yZMyg33tkRURQ42BFRFDjYEVEUoqzZTZo0ycRjxowxsa/hhdvRHDhwwFzzWzb5uUl+rWxY/wOABQsWJO3jx4+ba75m169fPxOzZkfehAkTTOxrxH4uXVhT3rNnj7nW1tZmYv974Y+OvHz5sonDLZ/8fNRBgwaZ2M8hrQTe2RFRFDjYEVEUONgRURSiqNn5eoDft2vEiBEm9lup7969O2n7fbj8Hl6+/udrfH6u3OLFi5P23r17zbVf/epXJvZzk+69915Q3Hxujxo1ysS+zubnhX744YdJ+1//+pe55uvPw4YNM7HPR1+zC+vZfh3t1KlTTVyJtbAe7+yIKAoc7IgoCn32MTbfdtN++odf0rV9+3YTb968OWn75Tf33HOPif0yF/+Y8emnn5p46NChSfvxxx83137zm9+Y+NSpUyb22+LwNLI45Mtt/6jppzNt3brVxFu2bEnaBw8eNNd8fvmlaGHuAsCVK1dMHG5R5qep+OMMvEuXLpm4HKeR8c6OiKLAwY6IosDBjoii0GdqdgMGDDBxeJq537Lp/PnzJt62bZuJ/fSS8CN0P3XE83UNv3zHL5MJp734+p9f1ua3bT9y5IiJw+3jqe/wuR3mlJ/+8fnnn5vYb8MUTqMC7O+C3zrdTz354osvTOy3dPK/G2E//ZQYH/vfm7q6OhP7XO8N3tkRURQ42BFRFAoOdiKyUkROisiO4LUGEVknIq25ryPy/QyiLGJux6WYmt2LAJ4D8H/Ba8sBbFDVFSKyPBc/W/7udc8/4/tlW3Pnzk3afmuktWvXmtgvk/HHIYY1E18j8XOLfF3N1wv90rSwNhHWGYHO2/H4LXf8UjTW7HrsRdRAbo8fP97E4VIrn6s+l//617+a2G85FtaF/dGd/fv3N7Ff0uXnyvk6XFgD9P9NFy5cQD7+v6scCt7ZqerfAZx1Ly8EsCrXXgVgUXm7RVR5zO249LZmN1ZV2wEg93VMd98oIs+ISJOINPm7IKIMYm73URX/gEJVX1DVRlVt9EutiGoZc7u29Hae3QkRGa+q7SIyHsDJgn+jzPw6UL/9dLhl+auvvmqu/eUvfzGxn9Pjtzu/8847k3ZDQ4O5Fm49DXReO9uTXwI/b2ncuHEm9nWM9vb2on82Fa3que3XU/s1qOF8N390pz+Os7W11cQ+f8PYzwn162xL4et9fp13Gnp7Z7cGwJJcewmA1eXpDlHVMbf7qGKmnrwM4D0As0XkiIgsBbACwAIRaQWwIBcT1RTmdlwKPsaq6uJuLj1R5r4QpYq5HZeaXRs7ffp0E99xxx0mDmsZa9asMddaWlpM/LWvfc3Efl5TOF8oje2ju3rfrvi1itQ3FDoiM5wr995775lr165dM/F9991nYv97Mnjw4KTt56NWUjVyl8vFiCgKHOyIKAo18xgb3m4DnZe2eO+8807S9ltR+8cEv8wqjdPJi1FoK2o/ZYZqk89tH/vSSfgY60sdftmkn77ktxirlp5us16O30ne2RFRFDjYEVEUONgRURRqpmbnl674qSd++Um4jZP/OH7WrFkmrmQdw29tM3r0aBOH9Zj9+/eba35Lbd9PfyQk1Sa/TNDn8vXr100cHnnop4v4Gl6aue1r4WFu+yNEm5ub8/7sSuQ67+yIKAoc7IgoChzsiCgKNVOz89vc+C2ezpw5Y+JwSZjfXrqStS5fxxgzxu79OGfOHBMfPXo0ab/99tvmmj8+LtyOG+i8bTvVpkuXLpnY17fyLa3y8898rpdTodwOj0IA7LGOfq6r3xrN99tvRVUOvLMjoihwsCOiKHCwI6Io1EzNztcLfOyPMAxreL624I9DLIWvmfjj5PxaRT+n6vXXX0/aGzduNNf8sYt+ex6/7pFqk1/76mNfw8u39ZevbZfC57Y/6tPX6PyxAf/4xz+Stj/S8erVqybOd6xCufDOjoiiwMGOiKLAwY6IolCzNTvP1znCuUn+75YyF8nX+3xNzq9VvHjxoon9NtpbtmxJ2n4+VXiEI9C5ZpLmNtpUPeU80jAfn9t+Tqiv0fncfuONN0y8evWXB7OdO3fOXPM1Ol9X97XtcuCdHRFFgYMdEUWBgx0RRaFmanaF+DpceByir235OXkTJkwwsa9dhPOH/NwjXys8f/68icMjHQFg06ZNJr5y5UrSnj9/vrnm18JSnPx8yzC3fT76dbZhfgGda2Ph+mpff/a5vWfPHhO/9dZbJv7nP/9p4iFDhiTtu+66y1yrRm7zzo6IosDBjoii0GceY/2WMOHH5BcuXDDXwq1ngM7LbwYMGGDi8Ng3v8zFL+XZsWOHif2tv19SE34Ez8fWOPnHRc9P8ZgyZUrS9ksIC+VQvlz3W4qFy70A4LXXXjNxuI0a0Plx+ytf+UrSnjRpUt5+pYF3dkQUBQ52RBSFgoOdiEwWkY0i0iIizSKyLPd6g4isE5HW3NcRhX4WUZYwt+NSTM3uOoCfq+o2ERkC4AMRWQfgPwFsUNUVIrIcwHIAz1aqo/4jdF8781vbNDY2Jm1/JKHnayY3btwwcbiFtK9TXL58Oe/PCj9+BzofAVnO7aaoxzKR2z6XfeyFdWBfX/Y1OX98wfHjx038wQcfJO3w+FEA+Oijj0zsa9/+WAAfV2Jr9VIUvLNT1XZV3ZZrXwLQAmAigIUAVuW+bRWARRXqI1FFMLfj0qOanYhMAzAfwBYAY1W1HehIGgBjuvk7z4hIk4g0+bszoqxgbvd9RQ92IjIYwJ8A/FRVLxb6/n9T1RdUtVFVG+vr63vTR6KKYm7Hoah5diLSHx3J8JKqvpl7+YSIjFfVdhEZD+BkpToJdJ5r5Oev1dXVmfihhx5K2n45mK9btLe3m7i5udnE4Tw7vxzHJ/ngwYPzXq/EdtPUe1nIbb+1V1tbm4lPnTpl4rBufOzYMXPN564/YnTXrl0m/vDDD5O2r8n5raXuv/9+E/saXdZzu5hPYwXA7wG0qOqvg0trACzJtZcAWO3/LlGWMbfjUsyd3SMA/gPAJyKyPffa/wBYAeA1EVkK4BCA71akh0SVw9yOSMHBTlXfBdDdNsFPlLc7ROlhbselZtbG+q2TfG3Cb10T8nOPfH3P1+H82tlQoaMTw+13iIrh67p+zqhfsxpupbR+/foevZff7iycC+e3GJs9e7aJaz23uVyMiKLAwY6IosDBjoiiUDM1O79e1c9F8jU9v7dWPv6oRV/XGD58eLc/19f/iHrKHyng10/79dXhXM7du3eba/7IAb8+debMmSYO930cN26cudbXcpt3dkQUBQ52RBSFmnmM9fxjrV9S4+N8/DZL3HaJqsk/1vrljmG8YMGCVPrUF/DOjoiiwMGOiKLAwY6IosDBjoiiwMGOiKLAwY6IosDBjoiiIP7ov4q+mcgpAAcBjAJwusC3V0NM/ZqqqqPL/DOjlcvty4gnf8oh1bxOdbBL3lSkSVUbC39nutgvKkVW/53Yrw58jCWiKHCwI6IoVGuwe6FK71sI+0WlyOq/E/uFKtXsiIjSxsdYIooCBzsiikKqg52IPCUiu0Vkr4gsT/O9u+jLShE5KSI7gtcaRGSdiLTmvha/t3t5+jRZRDaKSIuINIvIsiz0iwrLSm5nMa9zfah6bqc22IlIPwDPA3gawFwAi0Vkbv6/VVEvAnjKvbYcwAZVnQlgQy5O03UAP1fVOwE8BOC/cv8bVbtflEfGcvtFZC+vgQzkdpp3dg8A2Kuqbar6OYBXACxM8f0NVf07gLPu5YUAVuXaqwAsSrlP7aq6Lde+BKAFwMRq94sKykxuZzGvgWzkdpqD3UQAh4P4SO61LBmrqu1Axz8OgDHV6oiITAMwH8CWLPWLupT13M5U/lQrt9Mc7KSL1zjvpQsiMhjAnwD8VFUvVrs/VBBzu0jVzO00B7sjACYH8SQAx1J8/2KcEJHxAJD7ejLtDohIf3Qkw0uq+mZW+kV5ZT23M5E/1c7tNAe7rQBmisjtIjIAwPcBrEnx/YuxBsCSXHsJgNVpvrl0nNb9ewAtqvrrrPSLCsp6blc9fzKR26qa2h8A3wSwB8A+AP+b5nt30ZeXAbQD+AId/8+8FMBIdHwi1Jr72pBynx5Fx+PPxwC25/58s9r94p+i/u0ykdtZzOtcv6qe21wuRkRR4AoKIooCBzsiikJJg11WlsgQlRtzu+/pdc0ut0RmD4AF6CiEbgWwWFV3dvd3Bg4cqIMGDerV+1F5nT179rTyDIou9Sa36+rqmNsZcPnyZVy7dq2reY+4tYSfmyyRAQAR+fcSmW4TYtCgQXj66adLeEsql5deeulgtfuQYb3K7SeeeCKl7lF3NmzY0O21Uh5ji1oiIyLPiEiTiDR99tlnJbwdUWp6nNvXrl1LrXPUO6UMdkUtkVHVF1S1UVUbBw4cWMLbEaWmx7ldV1eXQreoFKUMdllfIkPUW8ztPqiUwS7rS2SIeou53Qf1+gMKVb0uIv8NYC2AfgBWqmpz2XpGVCXM7b6plE9joapvA3i7TH0hygzmdt9T0mBHnQ0dOtTEU6ZMMfHEifZDvaNHjybtQ4cOmWsXL3IrO0rP8OHDTTx9+nQTT5482cSHDx82cVtbm4nPnz9ftr6VA5eLEVEUONgRURT4GFuiSZMmmXjBggV5v3/r1q0mvn79etKeNWuWudbU1FRi74jyGzZsWNKeO9ceiHbp0iUT+zLLI488YuKHH37YxH/84x+TdhYeaXlnR0RR4GBHRFHgYEdEUWDNrofmzZtn4h//+Mcm/vjjj0383nvvmdhvhhBuC7R9+3ZzzU8F8FNRbt68WbC/RKERI0aYePbs2Ul7z5495pqvIZ87d87E77zzjon9ri8/+clPkvbzzz9vrp0968/xrjze2RFRFDjYEVEUONgRURRYs+tCv379TBzOP3r22WfNtTfffNPEn376qYnHjh1rYj/f6JVXXkna999/v7k2Z84cEx8/ftzEBw4cAFHo1lvtr3Q4jw7ovATs4MEvN6y+4447zDVfw/P16n379uX9/m984xtJO6zfAcAvf/lLE6dRf+adHRFFgYMdEUWBgx0RRYE1O3Su0T311FMmXrx4cdJevXq1ueZrdDdu3Mh73c+ze+ihh5L2qFGjzDVfoztz5kynvhOFfF3Nz9X0dbZwbXdYvwOA++67z8S+/uzPlPHz7kKLFi0ycWNjo4n9OvBK1PB4Z0dEUeBgR0RR4GBHRFGIsmbna3RPPvmkiR977DETv/7660nb19z8ekFfE/F1OL+1dbif3d69e821+vp6E/v9xYh8Te7EiRN5v3/GjBkm3rJlS9IeOXKkueZrcv5n++vjxo0z8caNG5P2gAEDzLVwTS7Q+feotbW1U99LxTs7IooCBzsiikKUj7F+6/RwWQsArFu3zsRffPFF0va31x988IGJv/3tb5t4zRp7trLf8unuu+9O2mPGjDHX2tvbTTx69GgTX7t2zcQ8jSwO+bZS9/lZaPpS+BjsSy5vvPGGif11/97+UTUsu/hlbLfcYu+z/LK2SuCdHRFFgYMdEUWBgx0RRSGKmp3fXnrhwoUm/tvf/mbiK1eumPiTTz5J2n5JzA9/+EMTv//++yZ+9913Tfyd73zHxGGdzi81C6eldBU3NDSYmDW7vmnw4MEmDnPGb6s0bdo0E4e5CwAzZ840cTh9xC/Z8nW0o0eP5u2nr+GF+bp582ZzbdmyZT362eXAOzsiigIHOyKKQsHBTkRWishJEdkRvNYgIutEpDX3dUS+n0GURcztuBRTs3sRwHMA/i94bTmADaq6QkSW5+Jnu/i7VTNhwoSk7etqvjbhj3Vbv369icN5d34eXXNzs4nb2tpM7LeL8nW5fDW7w4cPm9jXUPwcKuqxF5HB3PbLGX0dLpz3OWTIEHPNHxPgt/b3PzvMOb/t0tq1a03cv39/E/ulatu2bTPxbbfdlrR9Te6jjz4ysd+ayv+O+uMMeqPgnZ2q/h2AP+RxIYBVufYqAItK7glRypjbceltzW6sqrYDQO7rmO6+UUSeEZEmEWnyi+iJMqhXue1Xs1D2VPwDClV9QVUbVbXR75JAVMvC3K6rq6t2d6iA3s6zOyEi41W1XUTGAzhZzk71hq9dPP3000n75EnbPT83aeXKlSb2W6k/+OCDSdvPwfPbR4fbXPeUXy/ot4Py/eadckVUPbd9Lvuacji/MtyiCbDb/AOd68A7d+40cTg3zm/h5Ld88vw27j1R6DgDf6yjr+H1Rm/v7NYAWJJrLwGwOs/3EtUS5nYfVczUk5cBvAdgtogcEZGlAFYAWCAirQAW5GKimsLcjkvBx1hVXdzNpSfK3BeiVDG341Kza2N9fcsf+zZ16tSkvWnTJnPtueeeM7Gfv+bnG12+fDlpp/khSzhPCWCNLha+7nvkyBETnzp1Kmn7XPW1sClTppj4888/N3E4N86vwS2ViBT9vVevXjWxz/1y4HIxIooCBzsiikLNPsYOHTrUxE88Ycss4XKUDRs2mGv+UdQvx/Efg6f16Opv+1U17/f708b8lAWqDf5ULr9M0E9BCh89x44da675ePfu3Sb2p3iFy8f8o2Spwvz1ue2Xf/mlZ5XAOzsiigIHOyKKAgc7IopCzdbsHnvsMRPv2LHDxGHdw390n8axbcUKaxl+iczWrVtNfODAARP7xef+lHWqDeFUEqBz3W3v3r0mvvPOO5O236rfH1l4+vTpcnSxS367KJ9/4dI0v2Tz2LFjFetXd3hnR0RR4GBHRFHgYEdEUaiZmt3o0aNN7Je9hFtVA8ChQ4eStl9aNmJE9Y4V8DWVJ598Mmnv2rXLXGtpaTGx3+LJzy2k2uTndfqtlnzuT5w4MWn7LcfSrNH5GrP/75g+fXrS9nVHfwyo37a9vr6+1/3sDu/siCgKHOyIKAoc7IgoCjVTs/P1Ar9u1M85C2sXvpaQ5nkBvj64dOlSE4f9/vOf/2yu/fa3vzXx17/+dRP7/02ob/D56ufhhds6+TWnfr5pKfx81LAGB3ReS+vrbp988knS/upXv2qu+a2ofA3PH8tYDryzI6IocLAjoihwsCOiKNRMza4QX8ML1975Ldv9Or1yuueee0z8ve99z8R+PuCKFV+e5/L888+ba+EcPAAYNWpUObpIGVNo+/L58+ebOMxfvw9cKVv3+3lzfo2u34PuzJkzJvY1u7Dfvl9+vun+/ftN7Nf8lgPv7IgoChzsiCgKHOyIKAo1W7PzdQ6/nnDevHlJ29ca5syZY2Jfa/B1tbAuMmHCBHPt4YcfNrE/ui48CwMA/vCHP5j4rbfeSto/+MEPQPEpdNaIPzfiZz/7WdJ++eWXzTV/BKGfv+bPswjPcvF7zPl9IP0a8/CIUQCYNWuWicPf0ZkzZ5pr77//PtLGOzsiigIHOyKKQs0+xvpbf/8xeVtbW9L2H6n7R+C7777bxH6JVzjlY+TIkebazZs3Tfzqq6+aePPmzSZeu3atiR9//HEQ5eOXQobbly1btsxcW7lypYn9siz/6Bn+bH9kqD/S0W/TdO+995rY/970798/aVfjsdXjnR0RRYGDHRFFoeBgJyKTRWSjiLSISLOILMu93iAi60SkNfe1etv/EvUCczsuxdTsrgP4uapuE5EhAD4QkXUA/hPABlVdISLLASwH8Gzlupqf324m3Mra1+j8Ehtf7xs/fryJw2ktx48fN9e2bNli4qamJhP74w8fffTRvH2hVGUit/3UEp+v4TbsgN2+39eu/bQqv9W/P87g448/TtoXL1401/w0Fr980ef2gAEDTOz/u6qt4J2dqrar6rZc+xKAFgATASwEsCr3basALKpQH4kqgrkdlx7V7ERkGoD5ALYAGKuq7UBH0gAY083feUZEmkSkqZRFykSVVGpu+09MKXuKHuxEZDCAPwH4qapeLPT9/6aqL6hqo6o2+o+2ibKgHLmd5u7X1DtFzbMTkf7oSIaXVPXN3MsnRGS8qraLyHgAlds3qQsXLlwwcb6jFX0tYty4cSb2dY/W1lYTh/OLNm7caK75JTW+/sfjDrMtC7nta2ObNm0ysZ8rF27Lvnv3bnPND7p+CdjOnTtNHObrpEmTzDW/jNLPu/O57o/+zJpiPo0VAL8H0KKqvw4urQGwJNdeAmB1+btHVDnM7bgUc2f3CID/APCJiGzPvfY/AFYAeE1ElgI4BOC7FekhUeUwtyNScLBT1XcBdLeVKp/RqGYxt+NSM2tj/TZNvu7maxNh7cLP/9mwYUPe9/JrAMPtp/120o888kjen0VUiP/g7sEHHzTx+vXrTRzm+gMPPJD3Z8+YMcPEvi7na98hP78vPBoR6HzEY9ZxuRgRRYGDHRFFgYMdEUWhZmp2fvVFvvlCgK3T7du3L+/PPnjwoIn9XKW77roradfX1xfuLFEJ/Hrpb33rWyZub29P2nv27DHX/Nbo4b6OADB9+nQTDxs2LGn7GpyfQ1rreGdHRFHgYEdEUaiZx1jPLw/zS1l6YurUqaV2h6hifFll2rRpRf9dvxSyUEmnL+OdHRFFgYMdEUWBgx0RRYGDHRFFgYMdEUWBgx0RRYGDHRFFQfw8nIq+mcgpAAcBjAJwOrU3Ll5M/ZqqqqMLfxsVI5fblxFP/pRDqnmd6mCXvKlIk6o2Fv7OdLFfVIqs/juxXx34GEtEUeBgR0RRqNZg90KV3rcQ9otKkdV/J/YLVarZERGljY+xRBQFDnZEFIVUBzsReUpEdovIXhFZnuZ7d9GXlSJyUkR2BK81iMg6EWnNfR2Rcp8mi8hGEWkRkWYRWZaFflFhWcntLOZ1rg9Vz+3UBjsR6QfgeQBPA5gLYLGIzE3r/bvwIoCn3GvLAWxQ1ZkANuTiNF0H8HNVvRPAQwD+K/e/UbX7RXlkLLdfRPbyGshAbqd5Z/cAgL2q2qaqnwN4BcDCFN/fUNW/AzjrXl4IYFWuvQrAopT71K6q23LtSwBaAEysdr+ooMzkdhbzGshGbqc52E0EEO6dfiT3WpaMVdV2oOMfB8CYanVERKYBmA9gS5b6RV3Kem5nKn+qldtpDnbSxWuc99IFERkM4E8AfqqqF6vdHyqIuV2kauZ2moPdEQCTg3gSgGMpvn8xTojIeADIfT2ZdgdEpD86kuElVX0zK/2ivLKe25nIn2rndpqD3VYAM0XkdhEZAOD7ANak+P7FWANgSa69BMDqNN9cRATA7wG0qOqvs9IvKijruV31/MlEbqtqan8AfBPAHgD7APxvmu/dRV9eBtAO4At0/D/zUgAj0fGJUGvua0PKfXoUHY8/HwPYnvvzzWr3i3+K+rfLRG5nMa9z/ap6bnO5GBFFgSsoiCgKHOyIKAoc7IgoChzsiCgKHOyIKAoc7IgoChzsiCgK/w8ThTxvsuS+dAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(2, 2, 1)\n",
    "plt.imshow(batch_features[1, 0])\n",
    "\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.imshow(batch_features[1, 1])\n",
    "\n",
    "plt.subplot(2, 2, 3)\n",
    "plt.imshow(batch_features[1, 2])\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.imshow(batch_features[1, 3])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9516ca67",
   "metadata": {},
   "source": [
    "#### creating cnn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "d1b76488",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "42d66e0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Dataset():\n",
    "    def __init__(self, x, y): self.x,self.y = x,y\n",
    "    def __len__(self): return len(self.x)\n",
    "    def __getitem__(self, i): return self.x[i],self.y[i]\n",
    "    \n",
    "    \n",
    "class DataLoader():\n",
    "    def __init__(self, ds, batch_size): self.ds,self.bs = ds,bs\n",
    "    def __iter__(self):\n",
    "        for i in range(0, len(self.ds), self.bs): yield self.ds[i:i+self.bs]\n",
    "     \n",
    "    \n",
    "def get_dls(train_ds, valid_ds, bs, **kwargs):\n",
    "    return (DataLoader(train_ds, batch_size=bs, **kwargs),\n",
    "            DataLoader(valid_ds, batch_size=bs*2, **kwargs))\n",
    "\n",
    "def accuracy(out, yb): return (out.argmax(dim=1)==yb).float().mean()\n",
    "\n",
    "def fit(epochs, model, loss_func, opt, train_dl, valid_dl):\n",
    "    for epoch in range(epochs):\n",
    "        model.train()\n",
    "        for xb,yb in train_dl:\n",
    "            loss = loss_func(model(xb), yb)\n",
    "            loss.backward()\n",
    "            opt.step()\n",
    "            opt.zero_grad()\n",
    "\n",
    "        model.eval()\n",
    "        with torch.no_grad():\n",
    "            tot_loss,tot_acc,count = 0.,0.,0\n",
    "            for xb,yb in valid_dl:\n",
    "                pred = model(xb)\n",
    "                n = len(xb)\n",
    "                count += n\n",
    "                tot_loss += loss_func(pred,yb).item()*n\n",
    "                tot_acc  += accuracy (pred,yb).item()*n\n",
    "        print(epoch, tot_loss/count, tot_acc/count)\n",
    "    return tot_loss/count, tot_acc/count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "f0ab8459",
   "metadata": {},
   "outputs": [],
   "source": [
    "m,n = x_train.shape\n",
    "nh  = 50\n",
    "c  = y_train.max() + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "ac56882f",
   "metadata": {},
   "outputs": [],
   "source": [
    "broken_cnn = nn.Sequential(\n",
    "    nn.Conv2d(1, 30, kernel_size=3, padding=1),\n",
    "    nn.ReLU(),\n",
    "    nn.Conv2d(30, 10, kernel_size=3, padding=1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "a4a8833c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sequential(\n",
       "  (0): Conv2d(1, 30, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       "  (1): ReLU()\n",
       "  (2): Conv2d(30, 10, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
       ")"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "broken_cnn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "7284ce98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16, 10, 28, 28])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "broken_cnn(xb).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "fb82161a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16, 1, 28, 28])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xb.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "4f7e010f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def conv(ni, nf, ks=3, stride=2, act=True):\n",
    "    res = nn.Conv2d(ni, nf, kernel_size=ks, stride=stride, padding=ks//2)\n",
    "    if act:\n",
    "        res = nn.Sequential(res, nn.ReLU())\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "65faee73",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_cnn = nn.Sequential(\n",
    "    conv(1, 4),\n",
    "    conv(4, 8),\n",
    "    conv(8, 16),\n",
    "    conv(16, 16),\n",
    "    conv(16, 10, act=False),\n",
    "    nn.Flatten()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "ac8fb020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([16, 10])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_cnn(xb).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "8288b227",
   "metadata": {},
   "outputs": [],
   "source": [
    "def_device = 'mps' if torch.backends.mps.is_available() else 'cuda' if torch.cuda.is_available() else 'cpu'\n",
    "\n",
    "def to_device(x, device=def_device):\n",
    "    if isinstance(x, torch.Tensor): return x.to(device)\n",
    "    if isinstance(x, Mapping): return {k:v.to(device) for k,v in x.items()}\n",
    "    return type(x)(to_device(o, device) for o in x)\n",
    "\n",
    "def collate_device(b): return to_device(default_collate(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "0a5832cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_imgs = x_train.view(-1, 1, 28, 28)\n",
    "xval_imgs = x_val.view(-1, 1, 28, 28)\n",
    "train_ds, val_ds = Dataset(x_imgs, y_train), Dataset(xval_imgs, y_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "35c000e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "0a46aaef",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.4\n",
    "bs = 256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "e0d55bde",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_dl, val_dl = get_dls(train_ds, val_ds, bs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "ce253dfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = optim.SGD(simple_cnn.parameters(), lr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "c1582f45",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 2.2360411514282226 0.2893\n",
      "1 0.2510062300205231 0.9272\n",
      "2 0.1556034809887409 0.9515\n",
      "3 0.17306179146766662 0.9449\n",
      "4 0.14703145915716886 0.9544\n"
     ]
    }
   ],
   "source": [
    "loss, acc =  fit(5, simple_cnn.to(def_device), F.cross_entropy, opt, train_dl, val_dl)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a29e8d4b",
   "metadata": {},
   "source": [
    "#### understanding convolution arithmetic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b8fcf519",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Conv2d(1, 4, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_cnn[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "d9cd9a99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Conv2d(1, 4, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv1 = simple_cnn[0][0]\n",
    "conv1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "f7c6de54",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 1, 3, 3])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv1.weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "1c171ca0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conv1.bias.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43b90609",
   "metadata": {},
   "source": [
    "#### color images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "0c1eaf10",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e1b5d12a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6a0f9dfb",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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