lec_7_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "9a89d655",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch, gzip, matplotlib as mpl, pickle\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "mpl.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d43caceb",
   "metadata": {},
   "outputs": [],
   "source": [
    "data = None\n",
    "with gzip.open('data/mnist.pkl.gz', 'rb') as f:\n",
    "    data = pickle.load(f, encoding='latin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7c222e45",
   "metadata": {},
   "outputs": [],
   "source": [
    "((x_train, y_train), (x_val, y_val), _) = data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8fb51e5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50000, 784), (50000,), (10000, 784), (10000,))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b76c551b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([50000, 784]),\n",
       " torch.Size([50000]),\n",
       " torch.Size([10000, 784]),\n",
       " torch.Size([10000]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x_train, y_train, x_val, y_val) = map(torch.tensor, (x_train, y_train, x_val, y_val))\n",
    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "16162940",
   "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": 15,
   "id": "8e05c015",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([50000, 28, 28])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_imgs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "02942dbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x13c6c4510>"
      ]
     },
     "execution_count": 18,
     "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(x_imgs[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "87c500d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "img3 = x_imgs[7]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5216cde9",
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams['figure.dpi'] = 80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "80e0ee01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x13cfab050>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(img3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "b74542c7",
   "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": 37,
   "id": "777415f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x140253050>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS0AAAEXCAYAAAD4AhIlAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAAxOAAAMTgF/d4wjAAAOYElEQVR4nO3bYYxldXnH8e+PbBVwRa2NYHpddg2UamlSjW9spJI0NrGhGGATQ0JSk9W4FWOajUmrTWqjfaVhXxghuCyBpCZQdIPBhmo1arAiqAFWikmXXR2WCS3EtEIosRb79MWcqeMwszvLnJl7n9nvJ7nZe8/899wnZ8mXe8+ck6pCkro4Y9oDSNKpMFqSWjFakloxWpJaMVqSWjFakloxWpJaGSVaSc5OcluSo0mOJLnyBGsryQ+SPDQ8LhljBkmnh20j7efDwH9X1QVJdgHfSfKNqvrPVdb/flU9O9J7SzqNjPX18N3A9QBV9WPgHuBdI+1bkv7fWNHaATy25PXcsG0130xyOMn+JC8baQZJp4E1fT1M8i3gDav8+E3Dn0tvYswJdnd+VR0fYnUj8CngA6u87z5g35JNv7mWeSXNrqo6UR9OKmPcMJ3kEeA9VfW94fUdwN1VdetJ/t5bgQNV9btrfB/v7paaW2+0xvp6+HngWoDhRPzbgbuWL0ryqiRnD8/PYOFc2IMjzSDpNDBWtD4FnJXkKPAV4Nqq+g+AJHuTfHxY99vAfUkOAw8Drwb+fKQZJJ0GRvl6uFn8eij1NytfDyVpUxgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrYwarSQXJrk3yZEk303yxlXW7UnyaJJjSQ4k2TbmHJK2rrE/aX0WOFBVvwV8Erh5+YIku4BPAG8DLgDOA/aMPIekLWq0aCV5DfBm4HPDpkPAriQ7ly3dDdxZVU9WVQE3AlePNYekrW3MT1qvA56oqucBhiAdB3YsW7cDeGzJ67kV1kjSisb+eljLXmcN61ZbQ5J9SeYXH+ueTlJ7Y0brcWCyeFI9SVj49HV82brjwM4lr89fYQ0AVbW/qiaLjxFnldTUaNGqqqeAB4Frhk1XAXNVNbds6SHgiiTnDmHbC9w+1hyStrYsnHoaaWfJRcCtwKuBZ4A/rapHkhwE7qqqu4Z17wP+goVofh34s6r6nzXsf7xhJU1FVa16SmgtRo3WRjNaUn/rjZZXxEtqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJamXUaCW5MMm9SY4k+W6SN66w5tIkzyV5aMnjrDHnkLR1bRt5f58FDlTVrUl2AzcDb11h3Q+r6i0jv7ek08Bon7SSvAZ4M/C5YdMhYFeSnWO9hySN+UnrdcATVfU8QFVVkuPADmBu2dqLkjwA/AK4papuWGmHSfYB+xZfv/SlL+UjH/nIiCNL2kzXXXfduvcx9tfDWvY6K6x5AJhU1dNJJsDdSX5SVXe8YGdV+4H9i6/POeec5fuXdJoZ80T848AkyTaAJGHh09fxpYuq6pmqenp4Pg/cBlwy4hyStrDRolVVTwEPAtcMm64C5qpqbum6JK9Ncsbw/OXAZcPfk6STGvs6rfcD709yBPhLYA9AkoNJLh/WXAU8nOQwcB/wVeCWkeeQtEWNek6rqv6VFS5xqKr3Lnn+GeAzY76vpNOHV8RLasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJasVoSWrFaElqxWhJamW0aCX5dJK5JJXk4hOs25Pk0STHkhxIsm2sGSRtfWN+0voC8DbgsdUWJNkFfGJYdwFwHrBnxBkkbXGjRauq7qmq+ZMs2w3cWVVPVlUBNwJXjzWDpK1vs89p7eBXP4nNDdtWlGRfkvnFx89//vONnk/SjJvGifha8jwnXFi1v6omi4+XvOQlGzyapFm32dE6Duxc8vr8YZskrclmR+sQcEWSc5ME2AvcvskzSGpszEserk8yD0yAryU5Omw/mORygKr6EfAx4NvAMeAp4OaxZpC09Y12jVRVXQtcu8L29y57fRNw01jvK+n04hXxkloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloZLVpJPp1kLkkluXiVNZcmeS7JQ0seZ401g6Stb9uI+/oC8Engn0+y7odV9ZYR31fSaWS0aFXVPQBJxtqlJL1AqmrcHSZzwGVV9S8r/OxS4EvAo8AvgFuq6oa17nsymdT8/Pw4g0radJPJhPn5+XV9shnz6+FaPABMqurpJBPg7iQ/qao7VlqcZB+wb/H1K17xik0aU9Ks2tTfHlbVM1X19PB8HrgNuOQE6/dX1WTxsX379s0aVdKM2tRoJXltkjOG5y8HLgMe3MwZJPU25iUP1yeZBybA15IcHbYfTHL5sOwq4OEkh4H7gK8Ct4w1g6Stb/QT8RvJE/FSb2OciPeKeEmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtGC1JrRgtSa0YLUmtjBatJGcm+WKSI0keSvLlJDtXWbsnyaNJjiU5kGTbWHNI2trG/qR1ALioqn4P+Ifh9a9Isgv4BPA24ALgPGDPyHNI2qJGi1ZV/ayq7q6qGjbdB7x+haW7gTur6slh7Y3A1WPNIWlr28hzWh8CvrTC9h3AY0tezw3bJOmkNiRaST4KXAj81SpLaunyE+xnX5L5xcezzz475piSGho9Wkk+DFwJvLOqnlthyXFg55LX5w/bXqCq9lfVZPGxffv2sceV1Myo0Uqyj4XzU++oqp+usuwQcEWSc5ME2AvcPuYckrauMS95mADXAa8EvjFc9nD/8LODSS4HqKofAR8Dvg0cA54Cbh5rDklb22jXR1XVPKucn6qq9y57fRNw01jvLen04RXxkloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaMVqSWjFakloxWpJaGS1aSc5M8sUkR5I8lOTLSXausO7SJM8NaxYfZ401h6StbdvI+zsA/GNVVZIPDq//aIV1P6yqt4z83pJOA6N90qqqn1XV3VVVw6b7gNePtX9JgvE/aS31IeBLq/zsoiQPAL8AbqmqG1ZalGQfsG/Jpv9N8m/jjjmq7cCz0x7iBGZ9Ppj9GZ1vfc5b7w7yyw9G40nyUeBPgD+squeW/eyc4X2fTjIB7gb+tqruWMN+56tqMvrAI3G+9Zv1GZ1vfcaYb/TfHib5MHAl8M7lwQKoqmeq6unh+TxwG3DJ2HNI2ppGjdbwde5q4B1V9dNV1rw2yRnD85cDlwEPjjmHpK1rzEseJsB1wCuBbwyXMtw//OxgksuHpVcBDyc5zMLJ+q8Ct6zxbfaPNe8Gcb71m/UZnW991j3fhpzTkqSN4hXxkloxWpJamdloJTk7yW1Jjg63Bl15grWV5AdLbgvasN9GJrkwyb3DTN9N8sZV1u1J8miSY0kOJNnIa+JOab5p3kqV5NNJ5oZ/s4tPsG5ax++k8035+K3pdrlh7aYfw025na+qZvIB/DVw6/B8F/DvwKtWWVvA9k2a6+vAe4bnu4HvrLBmF/AEcC4Q4C7g/TM036XA96f07/oHwASYAy5eZc00j99a5pvm8TsT+GN+eT76g8A/zcoxPIX5XvQxnNlPWsC7gesBqurHwD3Au6Y5UJLXAG8GPjdsOgTsWuH/JLuBO6vqyVr4F7qRhUtBZmW+qamqe2rh+rwTmcrxgzXPNzW19tvlpnIMT2G+F22Wo7UDeGzJ67lh22q+meRwkv1JXrZBM70OeKKqngcY/mGOrzDXqc6+2fPBcCtVku8l+cAmzHYqpnX8TsWsHL/VbpeblWN40tv5TvUYbsp5gpUk+RbwhlV+/Kbhz6XXY+QEuzu/qo4PsboR+BSwUf8hLb9GZLW51jr72NYy3wPApJbcSpXkJ7WGW6k20bSO31rMxPEbbpe7ENi7ypKpHsOTzPeij+HUPmlV1SVV9RurPB5n4RPCziV/5fxh20r7Oj78+V/ADWzcbUGPA5PFE5pJwsKnm+VzrXn2acxXs38r1bSO35rMwvE72e1yTPkYbuTtfLP89fDzwLUASXYBb2fhZOKvSPKqJGcPz89g4VzYhtwWVFVPDfu+Zth0FTBXVXPLlh4Crkhy7hCOvcDtGzHTi5kvs38r1VSO31pN+/hlDbfLMcVjuJb51nUMN/q3Cev4LcTLgL8HjgJHgN1LfrYX+Pjw/K3AD4DDwCPA3wG/voFzXQR8Z5jp+8DvDNsPApcvWfe+YfYfDT/7tU06biedj4Xf6Dyy5Jj9DcNvezZhvuuBeeB5Fn4jfHTGjt9J55vy8Zuw8LXvGPDQ8Lh/Vo7hWudbzzH0Nh5Jrczy10NJegGjJakVoyWpFaMlqRWjJakVoyWpFaMlqRWjJakVoyWplf8DQUWq0GwWUkkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "230a7047",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td id=\"T_6f983_row7_col7\" class=\"data row7 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row7_col8\" class=\"data row7 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row7_col9\" class=\"data row7 col9\" >0.695312</td>\n",
       "      <td id=\"T_6f983_row7_col10\" class=\"data row7 col10\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col11\" class=\"data row7 col11\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col12\" class=\"data row7 col12\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col13\" class=\"data row7 col13\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col14\" class=\"data row7 col14\" >0.988281</td>\n",
       "      <td id=\"T_6f983_row7_col15\" class=\"data row7 col15\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col16\" class=\"data row7 col16\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col17\" class=\"data row7 col17\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col18\" class=\"data row7 col18\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col19\" class=\"data row7 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col20\" class=\"data row7 col20\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col21\" class=\"data row7 col21\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row7_col22\" class=\"data row7 col22\" >0.230469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6f983_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_6f983_row8_col0\" class=\"data row8 col0\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col1\" class=\"data row8 col1\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col2\" class=\"data row8 col2\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col3\" class=\"data row8 col3\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col4\" class=\"data row8 col4\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col5\" class=\"data row8 col5\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col6\" class=\"data row8 col6\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col7\" class=\"data row8 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col8\" class=\"data row8 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row8_col9\" class=\"data row8 col9\" >0.425781</td>\n",
       "      <td id=\"T_6f983_row8_col10\" class=\"data row8 col10\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col11\" class=\"data row8 col11\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col12\" class=\"data row8 col12\" >0.898438</td>\n",
       "      <td id=\"T_6f983_row8_col13\" class=\"data row8 col13\" >0.515625</td>\n",
       "      <td id=\"T_6f983_row8_col14\" class=\"data row8 col14\" >0.519531</td>\n",
       "      <td id=\"T_6f983_row8_col15\" class=\"data row8 col15\" >0.515625</td>\n",
       "      <td id=\"T_6f983_row8_col16\" class=\"data row8 col16\" >0.515625</td>\n",
       "      <td id=\"T_6f983_row8_col17\" class=\"data row8 col17\" >0.738281</td>\n",
       "      <td id=\"T_6f983_row8_col18\" class=\"data row8 col18\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col19\" class=\"data row8 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col20\" class=\"data row8 col20\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col21\" class=\"data row8 col21\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row8_col22\" class=\"data row8 col22\" >0.230469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6f983_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_6f983_row9_col0\" class=\"data row9 col0\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col1\" class=\"data row9 col1\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col2\" class=\"data row9 col2\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col3\" class=\"data row9 col3\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col4\" class=\"data row9 col4\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col5\" class=\"data row9 col5\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col6\" class=\"data row9 col6\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col7\" class=\"data row9 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col8\" class=\"data row9 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col9\" class=\"data row9 col9\" >0.015625</td>\n",
       "      <td id=\"T_6f983_row9_col10\" class=\"data row9 col10\" >0.113281</td>\n",
       "      <td id=\"T_6f983_row9_col11\" class=\"data row9 col11\" >0.113281</td>\n",
       "      <td id=\"T_6f983_row9_col12\" class=\"data row9 col12\" >0.093750</td>\n",
       "      <td id=\"T_6f983_row9_col13\" class=\"data row9 col13\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col14\" class=\"data row9 col14\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col15\" class=\"data row9 col15\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col16\" class=\"data row9 col16\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row9_col17\" class=\"data row9 col17\" >0.054688</td>\n",
       "      <td id=\"T_6f983_row9_col18\" class=\"data row9 col18\" >0.882812</td>\n",
       "      <td id=\"T_6f983_row9_col19\" class=\"data row9 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row9_col20\" class=\"data row9 col20\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row9_col21\" class=\"data row9 col21\" >0.671875</td>\n",
       "      <td id=\"T_6f983_row9_col22\" class=\"data row9 col22\" >0.027344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6f983_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "      <td id=\"T_6f983_row10_col0\" class=\"data row10 col0\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col1\" class=\"data row10 col1\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col2\" class=\"data row10 col2\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col3\" class=\"data row10 col3\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col4\" class=\"data row10 col4\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col5\" class=\"data row10 col5\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col6\" class=\"data row10 col6\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col7\" class=\"data row10 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col8\" class=\"data row10 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col9\" class=\"data row10 col9\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col10\" class=\"data row10 col10\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col11\" class=\"data row10 col11\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col12\" class=\"data row10 col12\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col13\" class=\"data row10 col13\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col14\" class=\"data row10 col14\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col15\" class=\"data row10 col15\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col16\" class=\"data row10 col16\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row10_col17\" class=\"data row10 col17\" >0.332031</td>\n",
       "      <td id=\"T_6f983_row10_col18\" class=\"data row10 col18\" >0.949219</td>\n",
       "      <td id=\"T_6f983_row10_col19\" class=\"data row10 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row10_col20\" class=\"data row10 col20\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row10_col21\" class=\"data row10 col21\" >0.562500</td>\n",
       "      <td id=\"T_6f983_row10_col22\" class=\"data row10 col22\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6f983_level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "      <td id=\"T_6f983_row11_col0\" class=\"data row11 col0\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col1\" class=\"data row11 col1\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col2\" class=\"data row11 col2\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col3\" class=\"data row11 col3\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col4\" class=\"data row11 col4\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col5\" class=\"data row11 col5\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col6\" class=\"data row11 col6\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col7\" class=\"data row11 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col8\" class=\"data row11 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col9\" class=\"data row11 col9\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col10\" class=\"data row11 col10\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col11\" class=\"data row11 col11\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col12\" class=\"data row11 col12\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col13\" class=\"data row11 col13\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col14\" class=\"data row11 col14\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col15\" class=\"data row11 col15\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row11_col16\" class=\"data row11 col16\" >0.343750</td>\n",
       "      <td id=\"T_6f983_row11_col17\" class=\"data row11 col17\" >0.738281</td>\n",
       "      <td id=\"T_6f983_row11_col18\" class=\"data row11 col18\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row11_col19\" class=\"data row11 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row11_col20\" class=\"data row11 col20\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row11_col21\" class=\"data row11 col21\" >0.054688</td>\n",
       "      <td id=\"T_6f983_row11_col22\" class=\"data row11 col22\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_6f983_level0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "      <td id=\"T_6f983_row12_col0\" class=\"data row12 col0\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col1\" class=\"data row12 col1\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col2\" class=\"data row12 col2\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col3\" class=\"data row12 col3\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col4\" class=\"data row12 col4\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col5\" class=\"data row12 col5\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col6\" class=\"data row12 col6\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col7\" class=\"data row12 col7\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col8\" class=\"data row12 col8\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col9\" class=\"data row12 col9\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col10\" class=\"data row12 col10\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col11\" class=\"data row12 col11\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col12\" class=\"data row12 col12\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col13\" class=\"data row12 col13\" >0.000000</td>\n",
       "      <td id=\"T_6f983_row12_col14\" class=\"data row12 col14\" >0.355469</td>\n",
       "      <td id=\"T_6f983_row12_col15\" class=\"data row12 col15\" >0.828125</td>\n",
       "      <td id=\"T_6f983_row12_col16\" class=\"data row12 col16\" >0.964844</td>\n",
       "      <td id=\"T_6f983_row12_col17\" class=\"data row12 col17\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row12_col18\" class=\"data row12 col18\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row12_col19\" class=\"data row12 col19\" >0.984375</td>\n",
       "      <td id=\"T_6f983_row12_col20\" class=\"data row12 col20\" >0.796875</td>\n",
       "      <td id=\"T_6f983_row12_col21\" class=\"data row12 col21\" >0.035156</td>\n",
       "      <td id=\"T_6f983_row12_col22\" class=\"data row12 col22\" >0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x179c62bd0>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(img3[:13, :23])\n",
    "df.style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "b1c4a537",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(img3[3:6, 14:17] * top_edges).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "bc5ffed7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-2.9570)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(img3[7:10, 14:17] * top_edges).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "4651ccba",
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_kernel(row, col, kernel):\n",
    "    return (img3[row-1:row+2, col-1:col+2] * kernel).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b569bf7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "apply_kernel(4, 15, top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "3b4efe3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[(0, 0), (0, 1), (0, 2)],\n",
       " [(1, 0), (1, 1), (1, 2)],\n",
       " [(2, 0), (2, 1), (2, 2)],\n",
       " [(3, 0), (3, 1), (3, 2)]]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[[(i, j) for j in range(3)] for i in range(4)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "ab3bfc9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = range(1, 27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "66985a7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "top_edge3 = [[apply_kernel(i, j, top_edges) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "ba1ea722",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17612b9d0>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(top_edge3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "e7ce1beb",
   "metadata": {},
   "outputs": [],
   "source": [
    "left_edge = torch.tensor([\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "83bdefa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x179fcf990>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j6G08klrZzF8PJekFjJakVoyWpFaMlqRWjJakVoyWpFaMlqRWjJakVoyWpFb+H4M+l8aoyMzqAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(left_edge)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "aeb6f3f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "left_edge3 = [[apply_kernel(i, j, left_edge) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "d824c9d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17a078b90>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(left_edge3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "28146f24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([28, 28])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "00d77111",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1, 28, 28])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = img3[None,None,:,:]\n",
    "inp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "e142432f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9, 676])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp_unf = F.unfold(inp, (3, 3))[0]\n",
    "inp_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "806ac166",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-1,  0,  1],\n",
       "        [-1,  0,  1],\n",
       "        [-1,  0,  1]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left_edge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "dc4e505b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = left_edge.view(-1).float()\n",
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "f0701ac7",
   "metadata": {},
   "outputs": [],
   "source": [
    "out_unf = w@inp_unf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "a054f8dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([676])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "528cd623",
   "metadata": {},
   "outputs": [],
   "source": [
    "out = out_unf.view(26, 26)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "c236940e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([26, 26])"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e3628b1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17b6d8b90>"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 480x320 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "133d1197",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pdb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "72de97a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fnx(n):\n",
    "#     pdb.set_trace()\n",
    "    for i in range(n):\n",
    "        print(f'hello {i+1}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "2aa5af33",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hello 1\n",
      "hello 2\n",
      "hello 3\n",
      "hello 4\n",
      "hello 5\n"
     ]
    }
   ],
   "source": [
    "fnx(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49ee61fa",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c5783985",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5f23ba66",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fcfec0a1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f706a5c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4e72e2c4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24cb4870",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:python_main] *",
   "language": "python",
   "name": "conda-env-python_main-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}