lec_7_v6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "13efbcd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "import torch, gzip, pickle\n",
    "import torchvision.transforms.functional as TF\n",
    "import torch.nn.functional as F\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from datasets import load_dataset\n",
    "\n",
    "mpl.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b03f58d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "with gzip.open('./data/mnist.pkl.gz', 'rb') as f:\n",
    "    data = pickle.load(f, encoding='latin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "619ed7bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "((x_train, y_train),(x_val, y_val), _) = data\n",
    "(x_train, y_train, x_val, y_val) = map(torch.tensor, (x_train, y_train, x_val, y_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0899c6df",
   "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": 16,
   "id": "2e10644b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "label:3\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "im3  = x_imgs[7]\n",
    "plt.imshow(im3); print(f'label:{y_train[7]}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a02cbf33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17341af10>"
      ]
     },
     "execution_count": 17,
     "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": [
    "top_edges = torch.tensor([\n",
    "    [-1, -1, -1],\n",
    "    [0, 0, 0],\n",
    "    [1, 1, 1]\n",
    "]).float()\n",
    "\n",
    "plt.imshow(top_edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f8634e9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "27c264e4",
   "metadata": {},
   "outputs": [
    {
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       "      <td id=\"T_610aa_row0_col9\" class=\"data row0 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col10\" class=\"data row0 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col11\" class=\"data row0 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col12\" class=\"data row0 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col13\" class=\"data row0 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col14\" class=\"data row0 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col15\" class=\"data row0 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col16\" class=\"data row0 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col17\" class=\"data row0 col17\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col18\" class=\"data row0 col18\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col19\" class=\"data row0 col19\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col20\" class=\"data row0 col20\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col21\" class=\"data row0 col21\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col22\" class=\"data row0 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col23\" class=\"data row0 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col24\" class=\"data row0 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col25\" class=\"data row0 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row0_col26\" class=\"data row0 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "      <td id=\"T_610aa_row1_col0\" class=\"data row1 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col1\" class=\"data row1 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col2\" class=\"data row1 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col3\" class=\"data row1 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col4\" class=\"data row1 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col5\" class=\"data row1 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col6\" class=\"data row1 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col7\" class=\"data row1 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col8\" class=\"data row1 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col9\" class=\"data row1 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col10\" class=\"data row1 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col11\" class=\"data row1 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col12\" class=\"data row1 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col13\" class=\"data row1 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col14\" class=\"data row1 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col15\" class=\"data row1 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col16\" class=\"data row1 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col17\" class=\"data row1 col17\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col18\" class=\"data row1 col18\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col19\" class=\"data row1 col19\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col20\" class=\"data row1 col20\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col21\" class=\"data row1 col21\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col22\" class=\"data row1 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col23\" class=\"data row1 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col24\" class=\"data row1 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col25\" class=\"data row1 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row1_col26\" class=\"data row1 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "      <td id=\"T_610aa_row2_col0\" class=\"data row2 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col1\" class=\"data row2 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col2\" class=\"data row2 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col3\" class=\"data row2 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col4\" class=\"data row2 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col5\" class=\"data row2 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col6\" class=\"data row2 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col7\" class=\"data row2 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col8\" class=\"data row2 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col9\" class=\"data row2 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col10\" class=\"data row2 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col11\" class=\"data row2 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col12\" class=\"data row2 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col13\" class=\"data row2 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col14\" class=\"data row2 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col15\" class=\"data row2 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col16\" class=\"data row2 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col17\" class=\"data row2 col17\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col18\" class=\"data row2 col18\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col19\" class=\"data row2 col19\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col20\" class=\"data row2 col20\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col21\" class=\"data row2 col21\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col22\" class=\"data row2 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col23\" class=\"data row2 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col24\" class=\"data row2 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col25\" class=\"data row2 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row2_col26\" class=\"data row2 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "      <td id=\"T_610aa_row3_col0\" class=\"data row3 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col1\" class=\"data row3 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col2\" class=\"data row3 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col3\" class=\"data row3 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col4\" class=\"data row3 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col5\" class=\"data row3 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col6\" class=\"data row3 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col7\" class=\"data row3 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col8\" class=\"data row3 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col9\" class=\"data row3 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col10\" class=\"data row3 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col11\" class=\"data row3 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col12\" class=\"data row3 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col13\" class=\"data row3 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col14\" class=\"data row3 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col15\" class=\"data row3 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col16\" class=\"data row3 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col17\" class=\"data row3 col17\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col18\" class=\"data row3 col18\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col19\" class=\"data row3 col19\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col20\" class=\"data row3 col20\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col21\" class=\"data row3 col21\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col22\" class=\"data row3 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col23\" class=\"data row3 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col24\" class=\"data row3 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col25\" class=\"data row3 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row3_col26\" class=\"data row3 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "      <td id=\"T_610aa_row4_col0\" class=\"data row4 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col1\" class=\"data row4 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col2\" class=\"data row4 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col3\" class=\"data row4 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col4\" class=\"data row4 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col5\" class=\"data row4 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col6\" class=\"data row4 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col7\" class=\"data row4 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col8\" class=\"data row4 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col9\" class=\"data row4 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col10\" class=\"data row4 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col11\" class=\"data row4 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col12\" class=\"data row4 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col13\" class=\"data row4 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col14\" class=\"data row4 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col15\" class=\"data row4 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col16\" class=\"data row4 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col17\" class=\"data row4 col17\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col18\" class=\"data row4 col18\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col19\" class=\"data row4 col19\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col20\" class=\"data row4 col20\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col21\" class=\"data row4 col21\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col22\" class=\"data row4 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col23\" class=\"data row4 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col24\" class=\"data row4 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col25\" class=\"data row4 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row4_col26\" class=\"data row4 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "      <td id=\"T_610aa_row5_col0\" class=\"data row5 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col1\" class=\"data row5 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col2\" class=\"data row5 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col3\" class=\"data row5 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col4\" class=\"data row5 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col5\" class=\"data row5 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col6\" class=\"data row5 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col7\" class=\"data row5 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col8\" class=\"data row5 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col9\" class=\"data row5 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col10\" class=\"data row5 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col11\" class=\"data row5 col11\" >0.148438</td>\n",
       "      <td id=\"T_610aa_row5_col12\" class=\"data row5 col12\" >0.167969</td>\n",
       "      <td id=\"T_610aa_row5_col13\" class=\"data row5 col13\" >0.410156</td>\n",
       "      <td id=\"T_610aa_row5_col14\" class=\"data row5 col14\" >0.996094</td>\n",
       "      <td id=\"T_610aa_row5_col15\" class=\"data row5 col15\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row5_col16\" class=\"data row5 col16\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row5_col17\" class=\"data row5 col17\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row5_col18\" class=\"data row5 col18\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row5_col19\" class=\"data row5 col19\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row5_col20\" class=\"data row5 col20\" >0.679688</td>\n",
       "      <td id=\"T_610aa_row5_col21\" class=\"data row5 col21\" >0.023438</td>\n",
       "      <td id=\"T_610aa_row5_col22\" class=\"data row5 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col23\" class=\"data row5 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col24\" class=\"data row5 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col25\" class=\"data row5 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row5_col26\" class=\"data row5 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "      <td id=\"T_610aa_row6_col0\" class=\"data row6 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col1\" class=\"data row6 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col2\" class=\"data row6 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col3\" class=\"data row6 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col4\" class=\"data row6 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col5\" class=\"data row6 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col6\" class=\"data row6 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col7\" class=\"data row6 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col8\" class=\"data row6 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col9\" class=\"data row6 col9\" >0.167969</td>\n",
       "      <td id=\"T_610aa_row6_col10\" class=\"data row6 col10\" >0.542969</td>\n",
       "      <td id=\"T_610aa_row6_col11\" class=\"data row6 col11\" >0.875000</td>\n",
       "      <td id=\"T_610aa_row6_col12\" class=\"data row6 col12\" >0.882812</td>\n",
       "      <td id=\"T_610aa_row6_col13\" class=\"data row6 col13\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col14\" class=\"data row6 col14\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row6_col15\" class=\"data row6 col15\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col16\" class=\"data row6 col16\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col17\" class=\"data row6 col17\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col18\" class=\"data row6 col18\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col19\" class=\"data row6 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col20\" class=\"data row6 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row6_col21\" class=\"data row6 col21\" >0.617188</td>\n",
       "      <td id=\"T_610aa_row6_col22\" class=\"data row6 col22\" >0.054688</td>\n",
       "      <td id=\"T_610aa_row6_col23\" class=\"data row6 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col24\" class=\"data row6 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col25\" class=\"data row6 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row6_col26\" class=\"data row6 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "      <td id=\"T_610aa_row7_col0\" class=\"data row7 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col1\" class=\"data row7 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col2\" class=\"data row7 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col3\" class=\"data row7 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col4\" class=\"data row7 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col5\" class=\"data row7 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col6\" class=\"data row7 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col7\" class=\"data row7 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col8\" class=\"data row7 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col9\" class=\"data row7 col9\" >0.695312</td>\n",
       "      <td id=\"T_610aa_row7_col10\" class=\"data row7 col10\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col11\" class=\"data row7 col11\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col12\" class=\"data row7 col12\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col13\" class=\"data row7 col13\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col14\" class=\"data row7 col14\" >0.988281</td>\n",
       "      <td id=\"T_610aa_row7_col15\" class=\"data row7 col15\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col16\" class=\"data row7 col16\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col17\" class=\"data row7 col17\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col18\" class=\"data row7 col18\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col19\" class=\"data row7 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col20\" class=\"data row7 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col21\" class=\"data row7 col21\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row7_col22\" class=\"data row7 col22\" >0.230469</td>\n",
       "      <td id=\"T_610aa_row7_col23\" class=\"data row7 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col24\" class=\"data row7 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col25\" class=\"data row7 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row7_col26\" class=\"data row7 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "      <td id=\"T_610aa_row8_col0\" class=\"data row8 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col1\" class=\"data row8 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col2\" class=\"data row8 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col3\" class=\"data row8 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col4\" class=\"data row8 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col5\" class=\"data row8 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col6\" class=\"data row8 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col7\" class=\"data row8 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col8\" class=\"data row8 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col9\" class=\"data row8 col9\" >0.425781</td>\n",
       "      <td id=\"T_610aa_row8_col10\" class=\"data row8 col10\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col11\" class=\"data row8 col11\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col12\" class=\"data row8 col12\" >0.898438</td>\n",
       "      <td id=\"T_610aa_row8_col13\" class=\"data row8 col13\" >0.515625</td>\n",
       "      <td id=\"T_610aa_row8_col14\" class=\"data row8 col14\" >0.519531</td>\n",
       "      <td id=\"T_610aa_row8_col15\" class=\"data row8 col15\" >0.515625</td>\n",
       "      <td id=\"T_610aa_row8_col16\" class=\"data row8 col16\" >0.515625</td>\n",
       "      <td id=\"T_610aa_row8_col17\" class=\"data row8 col17\" >0.738281</td>\n",
       "      <td id=\"T_610aa_row8_col18\" class=\"data row8 col18\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col19\" class=\"data row8 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col20\" class=\"data row8 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col21\" class=\"data row8 col21\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row8_col22\" class=\"data row8 col22\" >0.230469</td>\n",
       "      <td id=\"T_610aa_row8_col23\" class=\"data row8 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col24\" class=\"data row8 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col25\" class=\"data row8 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row8_col26\" class=\"data row8 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "      <td id=\"T_610aa_row9_col0\" class=\"data row9 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col1\" class=\"data row9 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col2\" class=\"data row9 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col3\" class=\"data row9 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col4\" class=\"data row9 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col5\" class=\"data row9 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col6\" class=\"data row9 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col7\" class=\"data row9 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col8\" class=\"data row9 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col9\" class=\"data row9 col9\" >0.015625</td>\n",
       "      <td id=\"T_610aa_row9_col10\" class=\"data row9 col10\" >0.113281</td>\n",
       "      <td id=\"T_610aa_row9_col11\" class=\"data row9 col11\" >0.113281</td>\n",
       "      <td id=\"T_610aa_row9_col12\" class=\"data row9 col12\" >0.093750</td>\n",
       "      <td id=\"T_610aa_row9_col13\" class=\"data row9 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col14\" class=\"data row9 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col15\" class=\"data row9 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col16\" class=\"data row9 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col17\" class=\"data row9 col17\" >0.054688</td>\n",
       "      <td id=\"T_610aa_row9_col18\" class=\"data row9 col18\" >0.882812</td>\n",
       "      <td id=\"T_610aa_row9_col19\" class=\"data row9 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row9_col20\" class=\"data row9 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row9_col21\" class=\"data row9 col21\" >0.671875</td>\n",
       "      <td id=\"T_610aa_row9_col22\" class=\"data row9 col22\" >0.027344</td>\n",
       "      <td id=\"T_610aa_row9_col23\" class=\"data row9 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col24\" class=\"data row9 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col25\" class=\"data row9 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row9_col26\" class=\"data row9 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "      <td id=\"T_610aa_row10_col0\" class=\"data row10 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col1\" class=\"data row10 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col2\" class=\"data row10 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col3\" class=\"data row10 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col4\" class=\"data row10 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col5\" class=\"data row10 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col6\" class=\"data row10 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col7\" class=\"data row10 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col8\" class=\"data row10 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col9\" class=\"data row10 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col10\" class=\"data row10 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col11\" class=\"data row10 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col12\" class=\"data row10 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col13\" class=\"data row10 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col14\" class=\"data row10 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col15\" class=\"data row10 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col16\" class=\"data row10 col16\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col17\" class=\"data row10 col17\" >0.332031</td>\n",
       "      <td id=\"T_610aa_row10_col18\" class=\"data row10 col18\" >0.949219</td>\n",
       "      <td id=\"T_610aa_row10_col19\" class=\"data row10 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row10_col20\" class=\"data row10 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row10_col21\" class=\"data row10 col21\" >0.562500</td>\n",
       "      <td id=\"T_610aa_row10_col22\" class=\"data row10 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col23\" class=\"data row10 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col24\" class=\"data row10 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col25\" class=\"data row10 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row10_col26\" class=\"data row10 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row11\" class=\"row_heading level0 row11\" >11</th>\n",
       "      <td id=\"T_610aa_row11_col0\" class=\"data row11 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col1\" class=\"data row11 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col2\" class=\"data row11 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col3\" class=\"data row11 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col4\" class=\"data row11 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col5\" class=\"data row11 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col6\" class=\"data row11 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col7\" class=\"data row11 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col8\" class=\"data row11 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col9\" class=\"data row11 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col10\" class=\"data row11 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col11\" class=\"data row11 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col12\" class=\"data row11 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col13\" class=\"data row11 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col14\" class=\"data row11 col14\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col15\" class=\"data row11 col15\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col16\" class=\"data row11 col16\" >0.343750</td>\n",
       "      <td id=\"T_610aa_row11_col17\" class=\"data row11 col17\" >0.738281</td>\n",
       "      <td id=\"T_610aa_row11_col18\" class=\"data row11 col18\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row11_col19\" class=\"data row11 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row11_col20\" class=\"data row11 col20\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row11_col21\" class=\"data row11 col21\" >0.054688</td>\n",
       "      <td id=\"T_610aa_row11_col22\" class=\"data row11 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col23\" class=\"data row11 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col24\" class=\"data row11 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col25\" class=\"data row11 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row11_col26\" class=\"data row11 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th id=\"T_610aa_level0_row12\" class=\"row_heading level0 row12\" >12</th>\n",
       "      <td id=\"T_610aa_row12_col0\" class=\"data row12 col0\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col1\" class=\"data row12 col1\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col2\" class=\"data row12 col2\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col3\" class=\"data row12 col3\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col4\" class=\"data row12 col4\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col5\" class=\"data row12 col5\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col6\" class=\"data row12 col6\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col7\" class=\"data row12 col7\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col8\" class=\"data row12 col8\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col9\" class=\"data row12 col9\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col10\" class=\"data row12 col10\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col11\" class=\"data row12 col11\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col12\" class=\"data row12 col12\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col13\" class=\"data row12 col13\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col14\" class=\"data row12 col14\" >0.355469</td>\n",
       "      <td id=\"T_610aa_row12_col15\" class=\"data row12 col15\" >0.828125</td>\n",
       "      <td id=\"T_610aa_row12_col16\" class=\"data row12 col16\" >0.964844</td>\n",
       "      <td id=\"T_610aa_row12_col17\" class=\"data row12 col17\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row12_col18\" class=\"data row12 col18\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row12_col19\" class=\"data row12 col19\" >0.984375</td>\n",
       "      <td id=\"T_610aa_row12_col20\" class=\"data row12 col20\" >0.796875</td>\n",
       "      <td id=\"T_610aa_row12_col21\" class=\"data row12 col21\" >0.035156</td>\n",
       "      <td id=\"T_610aa_row12_col22\" class=\"data row12 col22\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col23\" class=\"data row12 col23\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col24\" class=\"data row12 col24\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col25\" class=\"data row12 col25\" >0.000000</td>\n",
       "      <td id=\"T_610aa_row12_col26\" class=\"data row12 col26\" >0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x179b05a10>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(im3[:13, :27])\n",
    "df.style.background_gradient(cmap='PuBu').set_properties(**{'font-size': '7pt'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "20331583",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = (top_edges * im3[3:6, 14:17]).sum()\n",
    "t1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "0d3efe01",
   "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": 73,
   "id": "400636aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(2.9727)"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2 = apply_kernel(4, 15, top_edges)\n",
    "t2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "8c9a0fb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[(1, 1), (1, 2), (1, 3), (1, 4)],\n",
       " [(2, 1), (2, 2), (2, 3), (2, 4)],\n",
       " [(3, 1), (3, 2), (3, 3), (3, 4)],\n",
       " [(4, 1), (4, 2), (4, 3), (4, 4)]]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = range(1, 5)\n",
    "[[(i, j) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "a719ee5e",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = range(1, 27)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "7636b612",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x179c84590>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zOzBhW6eZvWlmR4vbpn4Iaooenzez08Xjuc/MHmtmj0VPd5jZH81swMwOmtn3iu2t9nhO1ectPaZNeU9vZnMkHZH0t5JOSXpf0pPufqjhzQTMbFBSn7u31IkaZvbXki5K+qW7319s+2dJ5939heIX6TJ3/8cW6/F5SRdbaR2G4pTyrolrRkh6QtLfq7Uez6n6/DvdwmParGf6bZKOufsJd78q6deSHm9SLzOSu78t6fyXNj8uaXdxf7fG/0M0zRQ9thx3H3L3D4r7I5JurhnRao/nVH3ekmaFfp2kkxO+P6XWXZjDJf3ezPaY2c5mNxNYXSx6cnPxk/iCeM3RsuswfGnNiJZ9PGtZ26JZobdJtrXqscPt7v6gpG9I+m7xkhXTV2odhmaYZM2IljTdtS1ualboT0m6Y8L36yWdaVIvSe5+prgdlvSqplg3oEWcvfmR5+J2uMn9fEXZdRgabbI1I9SCj2cta1vc1KzQvy9po5ndZWZtkr4t6fUm9TIlM1tY/MFEZrZQ0tfV2usGvC5pR3F/h6TXmtjLpFpxHYap1oxQiz2ela1t4e5N+ZL0mMb/gn9c0j81q4+gx7sl/XfxdbCV+pT0isZfyl3T+CunpyQtl/SWpKPFbWcL9vjvkj6UtF/joepqgcfyrzT+9nK/pH3F12Mt+HhO1ectPaachgtkhjPygMwQeiAzhB7IDKEHMkPogcwQeiAzhB7IzP8CmJDXqaYaX2oAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "top_edge3 = [[apply_kernel(i, j, top_edges) for j in rng] for i in rng]\n",
    "plt.imshow(top_edge3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "f3d9d839",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x179e0b510>"
      ]
     },
     "execution_count": 77,
     "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": [
    "left_edges = torch.tensor([\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1],\n",
    "    [-1, 0, 1]\n",
    "]).float()\n",
    "left_edge3 = [[apply_kernel(i, j, left_edges) for j in rng] for i in rng]\n",
    "plt.imshow(left_edge3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "31bba7ee",
   "metadata": {},
   "outputs": [],
   "source": [
    "inp = im3[None,None,:,:].float()\n",
    "inp_unf = F.unfold(inp, (3,3))[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "00becafc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 1, 28, 28])"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "22de6f2b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9, 676])"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "90d0e7d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([9])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w = left_edges.view(-1)\n",
    "w.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "614c5407",
   "metadata": {},
   "outputs": [],
   "source": [
    "out_unf = w@inp_unf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "5f7bfa96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([676])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "out_unf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "03f63c71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17ada8890>"
      ]
     },
     "execution_count": 125,
     "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_unf.view(26, 26))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "dc749d1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "13.3 ms ± 6.68 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 1 [[apply_kernel(i, j, left_edges) for j in rng] for i in rng]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "192aba55",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "88.5 µs ± 27.6 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 100 (w@F.unfold(inp, (3,3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "18c4e240",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 7.82 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "87.1 µs ± 99.5 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, top_edges[None,None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "id": "1331645f",
   "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": 134,
   "id": "cb366129",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_simple_cnn():\n",
    "    return nn.Sequential(\n",
    "        *[\n",
    "            conv(1, 4),\n",
    "            conv(4, 8),\n",
    "            conv(8, 16),\n",
    "            conv(16, 32),\n",
    "            conv(16, 16),\n",
    "            conv(16, 10, act=False),\n",
    "            nn.Flatten()\n",
    "        ]\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "id": "438b3a47",
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_cnn = get_simple_cnn()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "id": "acf8fc9f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Conv2d(1, 4, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1))"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_cnn[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "3cb368be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 1, 3, 3])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_cnn[0][0].weight.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "cfbea074",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4])"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simple_cnn[0][0].bias.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "78c1d339",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(1.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "688ad2ee",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "589597fe",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d7c6ecba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "229afe4a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ad824392",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "python_main",
   "language": "python",
   "name": "python_main"
  },
  "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
}