ti-72_lab_03_var_04_VasinaEO.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "!pip install -Uqq fastbook\n",
    "import fastbook\n",
    "fastbook.setup_book()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "from fastai.vision.all import *\n",
    "from fastbook import *\n",
    "\n",
    "matplotlib.rc('image', cmap='Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = untar_data(URLs.MNIST_SAMPLE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "Path.BASE_PATH = path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(#3) [Path('labels.csv'),Path('valid'),Path('train')]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path.ls()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(#2) [Path('train/7'),Path('train/3')]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(path/'train').ls()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(#6131) [Path('train/3/10.png'),Path('train/3/10000.png'),Path('train/3/10011.png'),Path('train/3/10031.png'),Path('train/3/10034.png'),Path('train/3/10042.png'),Path('train/3/10052.png'),Path('train/3/1007.png'),Path('train/3/10074.png'),Path('train/3/10091.png')...]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threes = (path/'train'/'3').ls().sorted()\n",
    "sevens = (path/'train'/'7').ls().sorted()\n",
    "threes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABwAAAAcCAAAAABXZoBIAAAA9ElEQVR4nM3Or0sDcRjH8c/pgrfBVBjCgibThiKIyTWbWF1bORhGwxARxH/AbtW0JoIGwzXRYhJhtuFY2q1ocLgbe3sGReTuuWbwkx6+r+/zQ/pncX6q+YOldSe6nG3dn8U/rTQ70L8FCGJUewvxl7NTmezNb8xIkvKugr1HSeMP6SrWOVkoTEuSyh0Gm2n3hQyObMnXnxkempRrvgD+gokzwxFAr7U7YXHZ8x4A/Dl7rbu6D2yl3etcw/F3nZgfRVI7rXM7hMUUqzzBec427x26rkmlkzEEa4nnRqnSOH2F0UUx0ePzlbuqMXAHgN6GY9if5xP8dmtHFfwjuQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=L size=28x28 at 0x7F33FDE7ADF0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im3_path = threes[1]\n",
    "im3 = Image.open(im3_path)\n",
    "im3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   0,   0,   0,   0,   0],\n",
       "       [  0,   0,   0,   0,   0,  29],\n",
       "       [  0,   0,   0,  48, 166, 224],\n",
       "       [  0,  93, 244, 249, 253, 187],\n",
       "       [  0, 107, 253, 253, 230,  48],\n",
       "       [  0,   3,  20,  20,  15,   0]], dtype=uint8)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array(im3)[4:10,4:10]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[  0,   0,   0,   0,   0,   0],\n",
       "        [  0,   0,   0,   0,   0,  29],\n",
       "        [  0,   0,   0,  48, 166, 224],\n",
       "        [  0,  93, 244, 249, 253, 187],\n",
       "        [  0, 107, 253, 253, 230,  48],\n",
       "        [  0,   3,  20,  20,  15,   0]], dtype=torch.uint8)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tensor(im3)[4:10,4:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row4_col14{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #767676;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col1{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #fcfcfc;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col2,#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col3{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #f6f6f6;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col4,#T_4370dfec_38dc_11eb_b398_0242ac110002row7_col7{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #f8f8f8;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col10,#T_4370dfec_38dc_11eb_b398_0242ac110002row10_col7{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #e8e8e8;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col11{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #222222;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col13,#T_4370dfec_38dc_11eb_b398_0242ac110002row6_col12{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #090909;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row5_col14{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #d0d0d0;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row6_col10,#T_4370dfec_38dc_11eb_b398_0242ac110002row7_col11,#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col6{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #060606;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row6_col13{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #979797;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row7_col8{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #b6b6b6;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row7_col9{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #252525;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row7_col12{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #999999;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row8_col5{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #f9f9f9;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row8_col7{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #101010;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row8_col9,#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col9{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #020202;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row8_col11{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #545454;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row8_col12{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #f1f1f1;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col5{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #f7f7f7;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col7{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #030303;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col12{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #181818;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col13{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #303030;\n",
       "            color:  #f1f1f1;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col14{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #a9a9a9;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row9_col15{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #fefefe;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row10_col8,#T_4370dfec_38dc_11eb_b398_0242ac110002row10_col9{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #bababa;\n",
       "            color:  #000000;\n",
       "        }#T_4370dfec_38dc_11eb_b398_0242ac110002row10_col10{\n",
       "            font-size:  6pt;\n",
       "            background-color:  #393939;\n",
       "            color:  #f1f1f1;\n",
       "        }</style><table id=\"T_4370dfec_38dc_11eb_b398_0242ac110002\" ><thead>    <tr>        <th class=\"blank level0\" ></th>        <th class=\"col_heading level0 col0\" >0</th>        <th class=\"col_heading level0 col1\" >1</th>        <th class=\"col_heading level0 col2\" >2</th>        <th class=\"col_heading level0 col3\" >3</th>        <th class=\"col_heading level0 col4\" >4</th>        <th class=\"col_heading level0 col5\" >5</th>        <th class=\"col_heading level0 col6\" >6</th>        <th class=\"col_heading level0 col7\" >7</th>        <th class=\"col_heading level0 col8\" >8</th>        <th class=\"col_heading level0 col9\" >9</th>        <th class=\"col_heading level0 col10\" >10</th>        <th class=\"col_heading level0 col11\" >11</th>        <th class=\"col_heading level0 col12\" >12</th>        <th class=\"col_heading level0 col13\" >13</th>        <th class=\"col_heading level0 col14\" >14</th>        <th class=\"col_heading level0 col15\" >15</th>        <th class=\"col_heading level0 col16\" >16</th>        <th class=\"col_heading level0 col17\" >17</th>    </tr></thead><tbody>\n",
       "                <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row0\" class=\"row_heading level0 row0\" >0</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col0\" class=\"data row0 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col1\" class=\"data row0 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col2\" class=\"data row0 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col3\" class=\"data row0 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col4\" class=\"data row0 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col5\" class=\"data row0 col5\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col6\" class=\"data row0 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col7\" class=\"data row0 col7\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col8\" class=\"data row0 col8\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col9\" class=\"data row0 col9\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col10\" class=\"data row0 col10\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col11\" class=\"data row0 col11\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col12\" class=\"data row0 col12\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col13\" class=\"data row0 col13\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col14\" class=\"data row0 col14\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col15\" class=\"data row0 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col16\" class=\"data row0 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row0_col17\" class=\"data row0 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row1\" class=\"row_heading level0 row1\" >1</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col0\" class=\"data row1 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col1\" class=\"data row1 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col2\" class=\"data row1 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col3\" class=\"data row1 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col4\" class=\"data row1 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col5\" class=\"data row1 col5\" >29</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col6\" class=\"data row1 col6\" >150</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col7\" class=\"data row1 col7\" >195</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col8\" class=\"data row1 col8\" >254</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col9\" class=\"data row1 col9\" >255</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col10\" class=\"data row1 col10\" >254</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col11\" class=\"data row1 col11\" >176</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col12\" class=\"data row1 col12\" >193</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col13\" class=\"data row1 col13\" >150</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col14\" class=\"data row1 col14\" >96</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col15\" class=\"data row1 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col16\" class=\"data row1 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row1_col17\" class=\"data row1 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row2\" class=\"row_heading level0 row2\" >2</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col0\" class=\"data row2 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col1\" class=\"data row2 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col2\" class=\"data row2 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col3\" class=\"data row2 col3\" >48</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col4\" class=\"data row2 col4\" >166</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col5\" class=\"data row2 col5\" >224</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col6\" class=\"data row2 col6\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col7\" class=\"data row2 col7\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col8\" class=\"data row2 col8\" >234</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col9\" class=\"data row2 col9\" >196</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col10\" class=\"data row2 col10\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col11\" class=\"data row2 col11\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col12\" class=\"data row2 col12\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col13\" class=\"data row2 col13\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col14\" class=\"data row2 col14\" >233</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col15\" class=\"data row2 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col16\" class=\"data row2 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row2_col17\" class=\"data row2 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row3\" class=\"row_heading level0 row3\" >3</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col0\" class=\"data row3 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col1\" class=\"data row3 col1\" >93</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col2\" class=\"data row3 col2\" >244</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col3\" class=\"data row3 col3\" >249</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col4\" class=\"data row3 col4\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col5\" class=\"data row3 col5\" >187</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col6\" class=\"data row3 col6\" >46</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col7\" class=\"data row3 col7\" >10</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col8\" class=\"data row3 col8\" >8</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col9\" class=\"data row3 col9\" >4</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col10\" class=\"data row3 col10\" >10</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col11\" class=\"data row3 col11\" >194</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col12\" class=\"data row3 col12\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col13\" class=\"data row3 col13\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col14\" class=\"data row3 col14\" >233</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col15\" class=\"data row3 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col16\" class=\"data row3 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row3_col17\" class=\"data row3 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row4\" class=\"row_heading level0 row4\" >4</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col0\" class=\"data row4 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col1\" class=\"data row4 col1\" >107</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col2\" class=\"data row4 col2\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col3\" class=\"data row4 col3\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col4\" class=\"data row4 col4\" >230</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col5\" class=\"data row4 col5\" >48</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col6\" class=\"data row4 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col7\" class=\"data row4 col7\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col8\" class=\"data row4 col8\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col9\" class=\"data row4 col9\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col10\" class=\"data row4 col10\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col11\" class=\"data row4 col11\" >192</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col12\" class=\"data row4 col12\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col13\" class=\"data row4 col13\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col14\" class=\"data row4 col14\" >156</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col15\" class=\"data row4 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col16\" class=\"data row4 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row4_col17\" class=\"data row4 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row5\" class=\"row_heading level0 row5\" >5</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col0\" class=\"data row5 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col1\" class=\"data row5 col1\" >3</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col2\" class=\"data row5 col2\" >20</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col3\" class=\"data row5 col3\" >20</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col4\" class=\"data row5 col4\" >15</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col5\" class=\"data row5 col5\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col6\" class=\"data row5 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col7\" class=\"data row5 col7\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col8\" class=\"data row5 col8\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col9\" class=\"data row5 col9\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col10\" class=\"data row5 col10\" >43</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col11\" class=\"data row5 col11\" >224</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col12\" class=\"data row5 col12\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col13\" class=\"data row5 col13\" >245</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col14\" class=\"data row5 col14\" >74</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col15\" class=\"data row5 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col16\" class=\"data row5 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row5_col17\" class=\"data row5 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row6\" class=\"row_heading level0 row6\" >6</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col0\" class=\"data row6 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col1\" class=\"data row6 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col2\" class=\"data row6 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col3\" class=\"data row6 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col4\" class=\"data row6 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col5\" class=\"data row6 col5\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col6\" class=\"data row6 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col7\" class=\"data row6 col7\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col8\" class=\"data row6 col8\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col9\" class=\"data row6 col9\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col10\" class=\"data row6 col10\" >249</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col11\" class=\"data row6 col11\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col12\" class=\"data row6 col12\" >245</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col13\" class=\"data row6 col13\" >126</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col14\" class=\"data row6 col14\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col15\" class=\"data row6 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col16\" class=\"data row6 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row6_col17\" class=\"data row6 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row7\" class=\"row_heading level0 row7\" >7</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col0\" class=\"data row7 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col1\" class=\"data row7 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col2\" class=\"data row7 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col3\" class=\"data row7 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col4\" class=\"data row7 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col5\" class=\"data row7 col5\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col6\" class=\"data row7 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col7\" class=\"data row7 col7\" >14</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col8\" class=\"data row7 col8\" >101</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col9\" class=\"data row7 col9\" >223</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col10\" class=\"data row7 col10\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col11\" class=\"data row7 col11\" >248</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col12\" class=\"data row7 col12\" >124</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col13\" class=\"data row7 col13\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col14\" class=\"data row7 col14\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col15\" class=\"data row7 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col16\" class=\"data row7 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row7_col17\" class=\"data row7 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row8\" class=\"row_heading level0 row8\" >8</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col0\" class=\"data row8 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col1\" class=\"data row8 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col2\" class=\"data row8 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col3\" class=\"data row8 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col4\" class=\"data row8 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col5\" class=\"data row8 col5\" >11</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col6\" class=\"data row8 col6\" >166</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col7\" class=\"data row8 col7\" >239</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col8\" class=\"data row8 col8\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col9\" class=\"data row8 col9\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col10\" class=\"data row8 col10\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col11\" class=\"data row8 col11\" >187</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col12\" class=\"data row8 col12\" >30</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col13\" class=\"data row8 col13\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col14\" class=\"data row8 col14\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col15\" class=\"data row8 col15\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col16\" class=\"data row8 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row8_col17\" class=\"data row8 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row9\" class=\"row_heading level0 row9\" >9</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col0\" class=\"data row9 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col1\" class=\"data row9 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col2\" class=\"data row9 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col3\" class=\"data row9 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col4\" class=\"data row9 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col5\" class=\"data row9 col5\" >16</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col6\" class=\"data row9 col6\" >248</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col7\" class=\"data row9 col7\" >250</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col8\" class=\"data row9 col8\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col9\" class=\"data row9 col9\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col10\" class=\"data row9 col10\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col11\" class=\"data row9 col11\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col12\" class=\"data row9 col12\" >232</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col13\" class=\"data row9 col13\" >213</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col14\" class=\"data row9 col14\" >111</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col15\" class=\"data row9 col15\" >2</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col16\" class=\"data row9 col16\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row9_col17\" class=\"data row9 col17\" >0</td>\n",
       "            </tr>\n",
       "            <tr>\n",
       "                        <th id=\"T_4370dfec_38dc_11eb_b398_0242ac110002level0_row10\" class=\"row_heading level0 row10\" >10</th>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col0\" class=\"data row10 col0\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col1\" class=\"data row10 col1\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col2\" class=\"data row10 col2\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col3\" class=\"data row10 col3\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col4\" class=\"data row10 col4\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col5\" class=\"data row10 col5\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col6\" class=\"data row10 col6\" >0</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col7\" class=\"data row10 col7\" >43</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col8\" class=\"data row10 col8\" >98</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col9\" class=\"data row10 col9\" >98</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col10\" class=\"data row10 col10\" >208</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col11\" class=\"data row10 col11\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col12\" class=\"data row10 col12\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col13\" class=\"data row10 col13\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col14\" class=\"data row10 col14\" >253</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col15\" class=\"data row10 col15\" >187</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col16\" class=\"data row10 col16\" >22</td>\n",
       "                        <td id=\"T_4370dfec_38dc_11eb_b398_0242ac110002row10_col17\" class=\"data row10 col17\" >0</td>\n",
       "            </tr>\n",
       "    </tbody></table>"
      ],
      "text/plain": [
       "<pandas.io.formats.style.Styler at 0x7f3335029af0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im3_t = tensor(im3)\n",
    "df = pd.DataFrame(im3_t[4:15,4:22])\n",
    "df.style.set_properties(**{'font-size':'6pt'}).background_gradient('Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6131, 6265)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seven_tensors = [tensor(Image.open(o)) for o in sevens]\n",
    "three_tensors = [tensor(Image.open(o)) for o in threes]\n",
    "len(three_tensors),len(seven_tensors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAABECAYAAAA4E5OyAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAJHElEQVR4nO2bXXMSZxuAL1jYXYQsiCYxIWIIjImJ0TaVTu2H41FnnGmPPOtMf0NP+i/6H9oDx+OOOtMjW6cdGz/Sk1ZqxkRDhCTQEAjfsLDsvgeWbbMmxgrEzDtcR5ln+bi5eJ5n7/t+iM0wDPr8g/1tB3DY6Aux0BdioS/EQl+IBcc+1/+fb0G23Qb7M8RCX4iFvhALfSEW+kIs9IVY6Aux0BdiYb/ErGMMw6DVatFsNqlUKmiaRrPZpNls0mg0Xnq8LMtIkoSu6+i6jtPpxOFw4HQ6EQQBWZZxOHoXds+FaJpGvV4nHo/zww8/kMlkSKVSxONxnjx5wr/7MTabjffee4+pqSmq1SqqqjIyMsKxY8eIRCIMDw8zOzuLz+frWbxdF6LrujkDisUilUqFbDbLn3/+yeLiIoVCgfX1dTKZDJVKBVEUEUWRer1OrVZjZWUFh8NhCqlUKmxublIulzl+/DgTExM9FWLbp2P2n2sZVVXZ3t5mdXWV77//nlQqxaNHj8jlcqTTaQzDwDAMZFnG7XYzODhIIBDgyZMnPH/+HLvdjt1uN2eOzWbDZrPh8/nwer1cv36daDT6hh93B7vWMh3PEE3TqNVq1Go1UqkUlUqFVCrFysoKT58+pVQqIQgCExMTRKNRnE4nkiQhiiIulwtFUfB6vczOzpLJZFheXubZs2eUy2VqtZr5Po1GA1VV0XW905BfScdCVFUlFovx22+/8c0331CpVGg2m7RaLRqNBoFAgGg0ysWLF7l69Soejwe3220+3263Y7PZ0HUdwzC4ceMG165dIxaLkUwmOw3vP9OxEMMwaDQaVKtVSqUS1WoVXdex2+2IokggEGBubo5z587h8/lwOp04nU7z+e0l8e+lJAgCNtvOGe33+wkGg8iy3GnIr6QrQqrVKrVaDVVV0TQNAFEUOXr0KHNzc3zxxRf4fD4URXnpg7ZpjzudTux2+0vXpqenmZmZQVGUTkN+JR0LcTqdhEIhRFEkn8/TbDaBF0Lcbjdzc3N4vV5EUdxTBrzYizRNI5/Pk8/nzRzFZrMhCALDw8OEw2FcLlenIb+SjoVIksTp06cJh8N88MEH5nh7KQiCgCiK+75Oo9GgVCqxtrZGMpmkWq0CmM+PRCJEo9Ed+08v6FhI+1sXBGHH3tC+Zp3+e7G+vs7PP//M77//TqlUQtM0BEEgHA4zPj7OzMwMJ06ceOk9uk1XErP2bHidmbAXd+7c4auvvkLTNHRdx+FwIIoiFy9eJBqN8u6773LixIluhPtKep66WzEMA13XqdfrlMtlM2FbWFgwN2S73U4kEiESifDhhx8SjUZ7vpm2OXAhuq6jaRrZbJbHjx/z448/cvPmTbLZrHm7djgcXLhwgY8//phPP/2UkydPHlh8B1LtGoZBsVhkdXXVrGWSySSrq6ssLS2Ry+Wo1+vAi3zD7/dz+vRpzp8/z8DAQK9D3MGBlf/JZJLvvvuO5eVlHjx4gKqqO1LzNkNDQ0xPT3PhwgUmJyd7fpu1ciBLRtd1CoUCjx49Yn19HVVVzXzFSiaTIRaLcevWLeLxOMeOHcPj8TA2NobX62VwcLCnkg5syWxtbfHgwQM0TTM31t3IZDJkMhnW19dxu90oioLH4+HKlSucP3+eS5cuIcvyK5O8Tuh6+f/SC/y9ZDY2Nrh9+zblcplCoUCxWCSXy5mPi8fjLC0tmT0UURRxOp1mv2RqaorR0VE++ugjzpw5w9mzZ/F6vQiC8Nq5joVdjfZciJVarWbKWFtbM8d/+uknfvnlF1ZXV0mn07s+t91Ri0QifP3110xOTiJJEoIgvEkovemH/FecTieKoiDL8o7O19DQEJcuXWJtbY10Ok0mkyGXy3H//n3i8TjwYrYlEgmq1SrPnz9ncHCQ48ePv6mQXTlwIQ6HA4fDgcvlwuv1muPDw8NMT09TrVbNW/TKygrZbNYUArC5uUkulyMejxMKhTh69Gh34+vqq3VAuxBsd9VlWSYYDBKPx/nrr79IJBJsb28DL2bKxsYG8XicU6dOdTWOQ3Mu0y4EJUkye63BYJDZ2VmmpqZ2pO6GYZgzR1XVrsZxaITsRbtwtI55vd6eVL+HXgjAbndCt9uN3+/v6oYKh2gPsVIsFtne3mZhYYGHDx/uyFlsNhunTp0iEol01HLYjUMppF0MJpNJEokEiURiR2YrCAJDQ0P4/f6uH2seOiHVapVKpcK9e/e4c+cOf/zxh3lEATA5Ocn4+DiBQABZlt80S92TQyOk/YHr9TrZbJZYLMb8/DypVMq8ZrfbCQaDRCIRvF4vDoej6zXNoRFSKBRIp9Pcvn2bu3fv8vjxY5LJpNknGRgYwO12c/XqVS5fvszo6Oiu5zed8laFtCthwzDI5/M8ffqUhw8fcuPGDbO3Ci820SNHjjA4OMi5c+cIhUI9kQFvUYiqqqiqysbGBktLS9y9e5f5+XkSiQTNZtNcJi6XC1mW+fLLL/nkk08Ih8M9kwFdFvLvb9yaULXH2383Gg0KhQLxeJz5+XkWFha4d++e+fj2me/AwACKonD27FneeecdPB5Pz2RAF4Vomka1WqVcLrO2toaiKIyMjJiH3pVKha2tLUqlEpubmywvL7O4uGjWKfl8HvgnM41EIoTDYa5cuUI0GiUUCqEoSk9/PQRdFNJqtSiVSmxtbRGLxRgdHUWSJPMXRLlcjuXlZba2tsxl0u6tqqq645RPFEXGx8cJh8NEo1FmZmbMhlGv6ZqQfD7Pt99+SzKZ5P79++Zhd6vVotVqmecwqqqaM6ZSqZgb5/DwMGNjY7z//vtmk/nkyZMoioIkSV3PN/aia0IajQaJRIJnz56xuLj4Wj9ssdlsSJKEJEmMjY0RiUQ4c+YM0WiUiYkJ/H5/t8J7bbomxOPxcPnyZTweD7/++uu+QmRZ5siRI3z++ed89tlnhEIhRkZGcLlcB7Y8dqNrQhwOB8FgkHQ6TSAQMI8l98LlcuHz+ZicnGR2dpahoaEdHbS3RdeazK1WyzxvKRaL+7/x3w0ht9ttdsm6XcrvF8KugwfddT9E9P+j6nXoC7HQF2KhL8TCfrfd3lVRh5T+DLHQF2KhL8RCX4iFvhALfSEW/gcMlBno19ugeQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_image(three_tensors[1]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([6131, 28, 28])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stacked_sevens = torch.stack(seven_tensors).float()/255\n",
    "stacked_threes = torch.stack(three_tensors).float()/255\n",
    "stacked_threes.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(stacked_threes.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stacked_threes.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean3 = stacked_threes.mean(0)\n",
    "show_image(mean3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean7 = stacked_sevens.mean(0)\n",
    "show_image(mean7);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_3 = stacked_threes[1]\n",
    "show_image(a_3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.1114), tensor(0.2021))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_3_abs = (a_3 - mean3).abs().mean()\n",
    "dist_3_sqr = ((a_3 - mean3)**2).mean().sqrt()\n",
    "dist_3_abs,dist_3_sqr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.1586), tensor(0.3021))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dist_7_abs = (a_3 - mean7).abs().mean()\n",
    "dist_7_sqr = ((a_3 - mean7)**2).mean().sqrt()\n",
    "dist_7_abs,dist_7_sqr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.1586), tensor(0.3021))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F.l1_loss(a_3.float(),mean7), F.mse_loss(a_3,mean7).sqrt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = [[1,2,3],[4,5,6]]\n",
    "arr = array (data)\n",
    "tns = tensor(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr  # numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1, 2, 3],\n",
       "        [4, 5, 6]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns  # pytorch\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([4, 5, 6])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2, 5])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([5, 6])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns[1,1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2, 3, 4],\n",
       "        [5, 6, 7]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns+1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'torch.LongTensor'"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns.type()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1.5000, 3.0000, 4.5000],\n",
       "        [6.0000, 7.5000, 9.0000]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tns*1.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1010, 28, 28]), torch.Size([1028, 28, 28]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valid_3_tens = torch.stack([tensor(Image.open(o)) \n",
    "                            for o in (path/'valid'/'3').ls()])\n",
    "valid_3_tens = valid_3_tens.float()/255\n",
    "valid_7_tens = torch.stack([tensor(Image.open(o)) \n",
    "                            for o in (path/'valid'/'7').ls()])\n",
    "valid_7_tens = valid_7_tens.float()/255\n",
    "valid_3_tens.shape,valid_7_tens.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.1114)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mnist_distance(a,b): return (a-b).abs().mean((-1,-2))\n",
    "mnist_distance(a_3, mean3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([0.1290, 0.1223, 0.1380,  ..., 0.1337, 0.1132, 0.1097]),\n",
       " torch.Size([1010]))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "valid_3_dist = mnist_distance(valid_3_tens, mean3)\n",
    "valid_3_dist, valid_3_dist.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2, 3, 4])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tensor([1,2,3]) + tensor([1,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1010, 28, 28])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(valid_3_tens-mean3).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_3(x): return mnist_distance(x,mean3) < mnist_distance(x,mean7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(True), tensor(1.))"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_3(a_3), is_3(a_3).float()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([True, True, True,  ..., True, True, True])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_3(valid_3_tens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(0.9168), tensor(0.9854), tensor(0.9511))"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_3s =      is_3(valid_3_tens).float() .mean()\n",
    "accuracy_7s = (1 - is_3(valid_7_tens).float()).mean()\n",
    "\n",
    "accuracy_3s,accuracy_7s,(accuracy_3s+accuracy_7s)/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
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   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x): return x**2"
   ]
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   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/envs/fastai/lib/python3.8/site-packages/fastbook/__init__.py:73: UserWarning: Not providing a value for linspace's steps is deprecated and will throw a runtime error in a future release. This warning will appear only once per process. (Triggered internally at  /opt/conda/conda-bld/pytorch_1603729096996/work/aten/src/ATen/native/RangeFactories.cpp:23.)\n",
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yWCqdEtq4HafJOLVgUKSIzBSRHBEpEpE1IjKhgbZTRKTGu0ZE3TbOiZxOunp4Kh1iI/n759vdjmKMOU2zvtpFdY2H28c132k1fHGqBxEG7AbOAxKAB4DXRSS9gfZLvWtE1G0LnYnpnKjwUKaN7c5X2w+zJveo23GMMafoaEkl85bu4geDOjXLKb1PxKkFg0pU9SFV3aWqHlV9D8gGhjux/2B13chutIsO56kF1oswprl6YXE2JZU13HVBL7ejNDlXxiBEJAXoA2xsoMkwETksIlki8oCI+LygWESmiUimiGTm5eUFLG+gxESGMXV0dxZsOcSGvYVuxzHGNNKx8ipeWLKLiwd0pG/HeLfjNDnHC4SIhAMvAXNUdYuPJouAgUAyMBGYBPza1+9S1RmqmqGqGUlJSYGKHFA3jkonPiqMpxZsczuKMaaR5izeRVF5dYvsPYDDBUJEQoB5QCVwl682qrpTVbO9p6LWA9OBqxyM6aj4qHCmnNudjzceZPP+Y27HMcb4qbiimpmLsxnfN5mBXRLcjhMQjhUIERFgJpACTFRVfxdGUKD5zpfrh5vPTScmIpSn7YomY5qNF5flUFBaxc/G93Y7SsA42YN4BugHXKKqDa69KSITvGMUiEhfaq94eseZiO5oGx3BjaPS+WD9frYdLHI7jjHmJEorq3lu0U7G9O7A0K5t3Y4TME7dB9ENuA0YChyod3/DdSKS5n1cN/XheGCdiJQAHwDzgcecyOmmW8f0oE14KH/7zMYijAl285bmcKSkkru/13J7D1B7f0LAqWoOJz5NFFuv7b3AvQEPFWQSYyK4aVQ6z36xg58fLKJPSpzbkYwxPpRWVvNPb+9heLdEt+MElE21EURuHdOD6PBQnrRehDFBa+7SHPJLKrn7e33cjhJwViCCSF0v4v31+8mysQhjgk5JRTUzFu1kbJ8khndr53acgLMCEWTqehE2FmFM8PlP76Fljz3UsQIRZNrFRDDl3NormrYcsPsijAkWxRXVzFi0g7F9kjgzreX3HsAKRFC6dUwPYiPC+OunWW5HMcZ4vfBVNkdLq/jV91v+2EMdKxBBqG10BFPH1N5dvX6PzdFkjNsKS6uY8eVOvtcvhSEt+L6H41mBCFI3j+5O2+hw/vLpVrejGNPqPfflTorKq/llK+o9gBWIoBUfFc5tY3uycGseq3Js1Tlj3HKkuIJZi7P54eBO9O/c8mZsPRG/CoSIRIvIMBH5zt1bInJu08cyADeN6kaH2Aj+8omNRRjjln8u2kl5VQ33tJIrl+o7aYEQkRFADrAQOCgi/++4Jh8GIJcBoiPCuHNcL5bsOMLi7YfdjmNMq3OgsJw5S3Zx+dAu9EpufbMb+NOD+AvwO1VNAEYB14vIs/Xeb9Ezrbpt8sg0OidE8fhHW1BVt+MY06o8uWAbHlXuaWVjD3X8KRADgecBVPVrYDTQV0Tmedd3MAEUFR7K3d/vw9o9hXy88YDbcYxpNbIPl/Dayt1MHpFG18Rot+O4wp8v+FLgm+XaVPUYcLH3tTexHkTAXTmsCz2TYvjzJ1lU13jcjmNMq/DEp1lEhIZw1wWtb+yhjj8F4gtgcv0XVLUcuBQIB9oEIJepJyw0hHsvPIPth4qZv2av23GMafE27C3k3bX7uHl0OklxkW7HcY0/BeIX+FiwR1UrgSuA85s6lPmuiwd2ZHBqAv/7aRblVTVuxzGmRfvzJ1tJaBPOtLE93Y7iqpMWCFXNAwbXPReRS+u9V62qi072O0QkUkRmikiOiBSJyBoRmXCC9veIyAERKRSRWSLSeku4l4jwm4v7sq+wnBeX5bgdx5gWa+mOIyzcmscd43qS0Cbc7Tiu8neQOVlEbhaRm6hdU7qxwoDdwHlAArXLiL4uIunHNxSRi4D7qF1ZLh3oATx8Cvtscc7t1YExvTvw1ILtFJb6u6S3McZfHo/yxw830ykhiimj0t2O4zp/7oMYC2wDbgFuBbK8r/lNVUtU9SFV3aWqHlV9D8gGhvtofhMwU1U3qupR4BFgSmP215LdN6Evx8qr+McX292OYkyL8/76/azbU8ivLjyDqPBQt+O4zp8eRHegG7WD0dHex91PZ6cikgL0ATb6eHsAsLbe87VAioi09/F7polIpohk5uXlnU6kZmNA5wSuGNqFFxbvYl9BmdtxjGkxKqs9/OnjrfTtGMcVw7q4HSco+DMGMQcoBF70bse8r50SEQkHXgLmqOoWH01ivfurU/f4O7cxquoMVc1Q1YykpKTj326xfnlh7U07T9h04MY0mZeX55CbX8pvJvQlNMSu3gf/xyCSgP8FnqTePRGN5b2xbh5QCdzVQLNioP6MWHWPbQ1Or9R20UwZlc6/Vu9h835bVMiY03WsvIonF2znnB7tGden9fyxeTL+FgjhPzfEnVJpFREBZlI7yD1RVRsaZd0IDKn3fAhwUFWPnMp+W6qfjutFQptw/vD+ZpuCw5jT9I/Pd5BfUsnvftCP2q8qA/4XiDxq74f4GXDoFPf1DNAPuERVT3TyfC4wVUT6i0g74H5g9inus8VKiA7n5xf05qvth1m4tXWMvxgTCLvzS5m1OJsrh3VhUGqC23GCij9XMd1I7Wme671bvPc1v4lIN+A2YChwQESKvdt1IpLmfZwGoKofAY8Dn1M7i2wO8GBj9tdaXH92N7p3iOEPH2y2KTiMOUWPf7yVEIF7LzrD7ShBx58eRA6wi9o5mcr4z5e231Q1R1VFVaNUNbbe9pKq5nof59Zr/4SqpqhqvKr+RFUrGrO/1iIiLIT7JvRl+6FiXlm52+04xjQ7a3KP8u7afUwb04PObW3WoOP5cxXTF9Rekvq8d+vjfc0EgQv7pzCieyL/+2kWx8rt5jlj/KWqPPr+ZpLiIrntvNY9pUZDGjMGsVNVZ3sff0NEJjV1KOM/EeGBH/bnSEklf19gN88Z46/31u1nVc5RfvX9PsREhrkdJyj5VSBU9W3gTRH5H+B9ABFpKyKvYdNguG5QagJXD09l1uJssg+XuB3HmKBXVlnDf3+4hQGd47k6o6vbcYJWYxb8GULtIPNKEZkKrAcKgGFNH8s01q8vPoOI0BD+8P5mt6MYE/RmLNrJ3oIyHrxkgN0UdwJ+FwhV3Qdc7v2ZGcCHqnqbqtqfrEEgOS6Kuy7ozf9tPsiX2+yyV2Masq+gjGe+2M4PB3diRPdEt+MENb8LhIgMBTKBncBlwAUi8oqItA1MNNNYN49Op1v7aKa/u8kuezWmAf/94RZU4bcT+rodJeg15hTTZ8ATqnq5dzbWIdRe+ro+IMlMo0WGhfL7H/Rj26Fi5tmaEcZ8x8pd+fx77T5uO68nqe1a5zrTjdGYAnGWqs6se+Kdwnsq8NOmj2VO1ff7pzCmdwee+DSLw8V2+4gxdaprPDzw9gY6J0Rx+3k93I7TLDRmDGJnA6//u+nimNMlIjx06QDKq2r4nw99TZZrTOv00vJcthwo4oEf9Sc6wi5r9UdjehCmmeiZFMvNo7vzxqo9rM496nYcY1x3uLiCv3yyldG9OnDxwI5ux2k2rEC0UD+/oDcp8ZE8+M5Gajw226tp3f700VZKK2t46NL+NltrI1iBaKFiIsP4/Q/7s35vIa+syD35DxjTQq3JPcprmbuZOro7vZK/s+6YOQErEC3YJYM7Mapnex7/aIsNWJtWqbrGw+/f2kDH+Ch+Nr6323GaHSsQLZiIMP2ygZRV1fCY3WFtWqE5S3PYtP8YD17Sn1ibb6nRrEC0cL2SY7ltbE/mr9nLkh2H3Y5jjGMOFJbzxCdbGXdGkg1MnyLHCoSI3CUimSJSISKzT9BuiojU1FtUqFhExjmVsyW664JepCVG88DbG6istjusTevwyHubqPYo0y8daAPTp8jJHsQ+4FFglh9tlx63sNDCwEZr2aLCQ3n4sgHsyCthxqIdbscxJuAWbj3E++v387MLepHW3u6YPlWOFQhVne+dNvyIU/s0/3H+Gcn8cFAnnlywnZ15xW7HMSZgSiuruf/tDfRKjuXWsXbH9OkI1jGIYSJyWESyROQBEfE5uiQi07ynrTLz8mwG05N58JL+RIaF8Lu31qNq90aYlumJT7LYc7SMP145iMiwULfjNGvBWCAWAQOBZGAiMAn4ta+GqjpDVTNUNSMpKcnBiM1TcnwUv/tBP5btzOeNzD1uxzGmya3fU8isxdlMHpnGWek2lffpCroCoao7VTVbVT2quh6YDlzldq6W4tqMroxIT+QPH2wmr8jujTAtR3WNh/vmr6NDbCS/udim8m4KQVcgfFDALkFoIiEhwmNXDqKssoaH3t3odhxjmszzX2Wzcd8xHr50AAltwt2O0yI4eZlrmIhEAaFAqIhE+RpbEJEJIpLifdwXeAB4x6mcrUGv5Fh+Pr4X76/bz0cbDrgdx5jTtiOvmCc+zeLC/il2z0MTcrIHcT9QBtwHXO99fL+IpHnvdUjzthsPrBOREuADYD7wmIM5W4XbzutJ/07xPPDOBgpKK92OY8wpq/Eo/+/NdbQJD+XRy+2eh6bk5GWuD6mqHLc9pKq53nsdcr3t7lXVFFWNUdUeqvpfqlrlVM7WIjw0hD9dPZijJZVMf2+T23GMOWVzl+5iVc5R/utH/UmOj3I7TovSHMYgTIAM6JzAHeN6Mn/1Xj7fcsjtOMY0Wu6RUh7/qHY6jSvP7OJ2nBbHCkQrd9cFveidHMtv56+nsNQ6aqb58HiUX7+5ltAQ4bErBtmppQCwAtHKRYaF8pdrhpBXXGFXNZlm5YUlu1ienc9/XdKfzm3buB2nRbICYRic2pafnt+Lt9bs5aMN+92OY8xJbT9UzOMfbWF832SuHp7qdpwWywqEAeCu83sxoHM8v39rgy0uZIJadY2HX72xljYRofzxSju1FEhWIAwAEWEhPHHNUIrKq/m9zdVkgtgzC3ewdncBj14+0K5aCjArEOYbZ3SM41cX9uHjjQdtriYTlNbuLuBvn23jkiGd+dHgzm7HafGsQJhvuWVMD87ukchD724k50iJ23GM+UZpZTV3v/Y1yXGRPHrZQLfjtApWIMy3hIYIT1wzlLAQ4e7Xvqa6xlagM8Hhkfc2s+tICX+5ZigJ0TbXkhOsQJjv6Ny2DX+4YhBrcgt4asF2t+MYw6ebDvLKilymje3BOT3bux2n1bACYXy6ZEhnrhzWhacWbGNFdr7bcUwrdqCwnP/35lr6d4rnl9/v43acVsUKhGnQ9MsHkpYYzS9eXWMT+hlX1HiUX7y6hopqD09NHmYrxDnMCoRpUGxkGE9NOpPDxRX8+s11dumrcdzTC7azPDuf6ZcNpGdSrNtxWh0rEOaEBqUm8JuL+/LppoPMW5bjdhzTiqzIzudvn2VxxbAuTLSJ+Fzh5IJBd4lIpohUiMjsk7S9R0QOiEihiMwSkUiHYhofpo7uzgV9k3n0vc2s31PodhzTChwpruDnr6whLTGaR2yNB9c42YPYBzwKzDpRIxG5iNpFhcYD6UAP4OFAhzMNExH+fPUQ2sdGcOfLq2zWVxNQNR7l7te+Jr+0kr9fdyaxkd9ZeNI4xMkFg+ar6tvAkZM0vQmYqaobVfUo8AgwJcDxzEkkxkTw9OQz2V9Qzr1vrrXxCBMwTy3YxpfbDvPwpQMY0DnB7TitWjCOQQwA1tZ7vhZIERG7+Nllw7u147c/6Menmw7y3Jc73Y5jWqCvth3mb59t48phXfjxWV3djtPqBWOBiAXqn+iuexx3fEMRmeYd18jMy8tzJFxrd/O56UwY2JH/+WgrS3ecrDNojP/2FpTx81fX0CsplkevsHGHYBCMBaIYiK/3vO5x0fENVXWGqmaoakZSUpIj4Vo7EeHxqwaT3j6au15ezb6CMrcjmRagvKqG2+etoqraw7M3DCc6wsYdgkEwFoiNwJB6z4cAB1XV/lwNEnFR4fzzhgwqqj3c8eIqyqtq3I5kmjFV5f63N7B+byFPXDvU7ncIIk5e5homIlFAKBAqIlEi4uvPhLnAVBHpLyLtgPuB2U7lNP7plRzLX64Zwto9hfzXOxts0NqcsheX5fDmqj38fHxvvt8/xe04ph4nexD3A2XUXsJ6vffx/SKSJiLFIpIGoKofAY8DnwM53u1BB3MaP100oCM/u6AXr2fuYc6SXW7HMc3Q0h1HePjdTVzQN5m7x/d2O445jrSUv/wyMjI0MzPT7Ritjsej3PbiKj7bfJDZPxnB2D42FmT8k3uklEv//hUdYiOZf+co4qNsCm83iMgqVc3w9V4wjkGYZiQkRPjrtUPpkxLHT19ezY68YrcjmWagqLyKqXNWAvD8jRlWHIKUFQhz2mIjw3juxgwiQkO4dU6mzfxqTqh2htavyT5cwj+uO5P0DjFuRzINsAJhmkTXxGievWE4e46Wcdu8VVRU25VN5rtUlYff3ciCLYd46NIBjOrZwe1I5gSsQJgmc1Z6In+6ejDLs/O571/r7com8x0zv8pm7tIcpo3twfVnd3M7jjkJuxvFNKnLhnZhd34pf/4ki66J0bYCmPnGRxsO8IcPNjNhYEfuu7iv23GMH6xAmCb30/N7kZtfypOfbaNL2yiuPSvN7UjGZaty8vnFq2sY2rUtf712KCEhNo1Gc2AFwjQ5EeEPVwziUFEFv52/nnbREVw4oKPbsYxLsg4WcfPsTDq3bcPzN2YQFW7LhjYXNgZhAiI8NIR/XHcmg1Lb8rNX1rAiO9/tSMYFewvKuHHmCiLDQph78wjax9raX82JFQgTMNERYbww5Sy6tGvD1Dkr2bz/mNuRjIOOFFdw48zllFRUM+fmEXRNjHY7kmkkKxAmoBJjIph78whiI8O4YeZyu5GulSgsq+LGWSvYc7SM52/KoF+n+JP/kAk6ViBMwKW2i+bFW0YCcP3zy9mdX+pyIhNIJRXV3Dx7JVkHi3j2huGM7GFrfTVXViCMI3omxTJv6khKK2u47vnlHCgsdzuSCYDyqhqmzcvk690FPDVpGOefkex2JHMarEAYx/TrFM+cm0eQX1LJpOeWWZFoYcqrarh1biZLdhzhT1cN5uKBndyOZE6TFQjjqKFd2zLn5hHkFVVYkWhB6orDV9sP8/jEwVx5ZqrbkUwTsAJhHDe8W7tvisSPZyxlf6EtW9qclVXWcMuc2uLwp6uGcHVGV7cjmSbi5IpyiSLyloiUiEiOiExuoN0UEanxLiJUt41zKqdxxvBu7Zg7dQRHiiu5+tml5BwpcTuSOQVF5VXcNGsFi3fUFoerhlvPoSVxsgfxd6ASSAGuA54RkQENtF2qqrH1toVOhTTOOTOtHS/fejYlFdVc/exSth0scjuSaYSjJZVc9/xyVuce5ckfD7Pi0AI5UiBEJAaYCDygqsWq+hXwb+AGJ/Zvgteg1AReu+0cAK7551LW7SlwN5Dxy8Fj5Vw7YylbDhTxzxuGc8mQzm5HMgHgVA+iD1Cjqln1XlsLNNSDGCYih0UkS0QeEBGfc0aJyDQRyRSRzLy8vKbObBzSJyWON24/h5jIMH48YxkLtx5yO5I5ge2HirjyH0vYc7SM2VPOYny/FLcjmQBxqkDEAoXHvVYIxPlouwgYCCRT2+uYBPza1y9V1RmqmqGqGUlJthZyc9atfQzz7xhFevsYbpmTyZur9rgdyfiQuSufic8spaLaw2vTzmFUL1vwpyVzqkAUA8ffax8PfOeks6ruVNVsVfWo6npgOnCVAxmNy5Ljo3jttrM5u0d77n1jLU9+ts0WHQoiH67fz3XPLycxJoL5d4xiUGqC25FMgDlVILKAMBHpXe+1IcBGP35WAZs8vpWIiwpn1pSzuHJYF574NIu7X/ua8ipbvtRNqsrTC7Zxx0urGdA5nn/dMYq09jbxXmvgyHoQqloiIvOB6SJyCzAUuAwYdXxbEZkArFbVgyLSF3gAeMOJnCY4RISF8JdrhtAzOZY/fbyV3PxSZtyQQVKcTRXttPKqGn47fz1vrdnL5UM7898TB9t6Dq2Ik5e53gm0AQ4BrwB3qOpGEUnz3utQt+zYeGCdiJQAHwDzgccczGmCgIjw0/N78cx1Z7J5/zEuffor1uQedTtWq7KvoIxr/7mUt9bs5d4L+/DXa4dacWhlpKWc483IyNDMzEy3Y5gA2LC3kNtfXMWhYxU8fNkAJo2wJUwDbcmOw/zs5TVUVHv489VDuHigrQjYUonIKlXN8PWeTbVhgt7ALgm8e9doRvZI5Lfz1/PrN9ZSWlntdqwWyeNRnlm4g+ufX07b6HDe/um5VhxaMVuT2jQL7WIimP2TEfz10yz+vnA7a3YX8PTkYfTtaAvRNJW8ogp++frXfLntMD8c1In/uWowsZH2FdGaWQ/CNBuhIcK9F53BvJtHUlBaxWVPL2beshy7FLYJLMrKY8LfvmRFdj6PXTGIpycPs+JgrECY5md07w58+IsxjOzRngfe3sBNL6y0acNPUWllNfe/vZ4bZ62gXXQ479x1LpNHpiFiV5YbKxCmmUqKi2T2lLN45LIBrMzO58K/fsFba/ZYb6IRVu7KZ8LfvuSl5bncMro77/5stJ2yM99iBcI0WyEhwg3npPPBL8bQOyWOe15by00vrCT3iK15fSKFpVX8dv56rn52KTUe5ZVbz+b+H/W3S1jNd9hlrqZFqPEo85bu4k8fb6VGlV+M78PU0d2JCLO/geqoKu+u28/0dzeRX1LB1NHduef7fYiOsLGG1uxEl7lagTAtyr6CMh7890Y+3XSQ7h1i+P0P+jG+X3KrP6e+fk8h09/byMpdRxnUJYE/XjmIgV1sLiVjBcK0Qp9vPcQj721iZ14JY3p34DcX922VX4h7C8r430+zeHP1HhKjI7j3ojO4JqMroSGtu2Ca/7ACYVqlqhoPc5fm8ORn2ygsq+KHgzrxywv70DMp1u1oAXe4uIJ/fL6DF5flAHDjOd34+fd6Ex8V7nIyE2ysQJhW7Vh5Fc8v2snzX2VTXlXDDwd35vbzejCgc8vrUewrKOO5L3fy6ordVFTXcNXwVH7xvT50advG7WgmSFmBMIbav6qf+3InLy3LpbiimnFnJHHzud0Z3asDIc38lMuGvYXMXrKLd77ei0fhsqGduXNcL3olt/zekjk9ViCMqaewtIp5y3Yxe8kuDhdX0r1DDNef3Y0rh3WhXUyE2/H8VlZZw8cbDzB36S5W5xbQJjyUazJSuXVsD1Lb2XoNxj9WIIzxoaK6hg/XH2DO0l2syS0gPFQ4/4xkrjyzC+POSA7K+wJqPMqK7HzeWrOHD9YfoLiimvT20dxwTjpXDU8loY2NMZjGOVGBsAugTasVGRbK5cO6cPmwLmzad4z5q/fw9tf7+GTTQaIjQhl3RhIX9u/I2D5JJLrYsyitrGbZziN8vOEg/7f5IEdKKomJCGXCoE5cOawLZ/do3+xPkZng5FgPQkQSgZnAhcBh4Leq+nIDbe8BfkPtAkP/onZxoYoT/X7rQZimUF3jYcmOI3y88QCfbDpIXlHtx65/p3hG9+5ARrd2DOnalpT4qIBlKCytYt3eAlbnFLB4x2HW5B6lqkaJjQzj/L7JXNg/hfH9ku0GN9MkguIUk4i8Qu3UHlOpXXL0fWCUqm48rt1FwFzgAmAf8BawTFXvO9HvtwJhmprHo6zdU8Di7YdZvP0Iq3KOUlnjAaBjfBR9O8XRKymWnsmxdG0XTceESFLio4jz41LS8qoaDh4r50BhOXsLytiRV8yOQyVsPVhE9uESAERgYOcERvVqz7k9OzCyRyKRYcF32ss0b64XCBGJAY4CA1U1y/vaPGDv8V/8IvIysEtVf+d9Ph54SVVPuGqJFQgTaOVVNWzaf4yvcwtYu6eArIPF7MwrpqLa8612EaEhxEaFERMZSmRYKHUnf6pqPBRX1FBcUUV51bd/JixE6NY+ml7JsQxObcvQrm0ZlJpg9y2YgAuGMYg+QE1dcfBaC5zno+0A4J3j2qWISHtVPVK/oYhMA6YBpKXZMpQmsKLCQzkzrR1nprX75jWPR9lbUMbegrJvegRHS6sorqiipKKGiuqab9qGhYQQExlGXFQY8VFhpMRH0TEhik4JbejWPprwUJs3ygQXpwpELFB43GuFQJwfbesexwHfKhCqOgOYAbU9iCZJakwjhIQIXROj6Zpol5WalsepP1mKgeMnmo8HivxoW/fYV1tjjDEB4lSByALCRKR3vdeGABt9tN3ofa9+u4PHn14yxhgTWI4UCFUtAeYD00UkRkTOBS4D5vloPheYKiL9RaQdcD8w24mcxhhj/sPJUbE7qb2v4RDwCrX3NmwUkTQRKRaRNABV/Qh4HPgcyPFuDzqY0xhjDA7eSa2q+cDlPl7PpXZguv5rTwBPOJPMGGOML3ZdnTHGGJ+sQBhjjPHJCoQxxhifWsx03yKSR+2A9qnoQO0EgsEmWHNB8GazXI1juRqnJebqpqpJvt5oMQXidIhIZkNzkbgpWHNB8GazXI1juRqnteWyU0zGGGN8sgJhjDHGJysQtWa4HaABwZoLgjeb5Wocy9U4rSqXjUEYY4zxyXoQxhhjfLICYYwxxicrEMYYY3xqdQVCRCJFZKaI5IhIkYisEZEJJ/mZe0TkgIgUisgsEYkMULa7RCRTRCpEZPZJ2k4RkRrvTLh12zi3c3nbO3W8EkXkLREp8f7/nHyCtgE9Xo3M4sjxaUwuJz9P3v015rPu5PHyK5fD//4a9Z3VlMer1RUIamew3U3tetgJwAPA6yKS7quxiFwE3AeMB9KBHsDDAcq2D3gUmOVn+6WqGltvW+h2LoeP19+BSiAFuA54RkQGnKB9II+XX1kcPj5+5/Jy6vMEfn6mXDhejfk36NTx8vs7q8mPl6q2+g1YB0xs4L2XgcfqPR8PHAhwnkeB2SdpMwX4yuHj5E8uR44XEEPtF1+feq/NA/7b6ePVmCxOfp4amcvxz5M/nyk3/v35mcuV41Vv/z6/s5r6eLXGHsS3iEgK0Affy58CDADW1nu+FkgRkfaBzuaHYSJyWESyROQBEXFsfY8TcOp49QFqVDXruH2dqAcRqOPVmCxOfp4ae4xa8+fpVLhyvE7yndWkxysYPgCuEZFw4CVgjqpuaaBZLFBY73nd4zjAzXWyFwEDqZ2gcADwGlAN/NHFTODc8Tp+P3X7imugfSCPV2OyOPl5akyu1v55aixXjpcf31lNerxaXA9CRBaKiDawfVWvXQi13e1K4K4T/MpiIL7e87rHRYHI5S9V3amq2arqUdX1wHTgqsb+nqbOhXPH6/j91O3L536a6ng1oDFZmuT4NHWuAB+f0+Hk8fKbG8fLz++sJj1eLa5AqOo4VZUGttEAIiLATGoH7iaqatUJfuVGYEi950OAg6raqGrsT67TpIA0+oeaPpdTxysLCBOR3sftq6FThd/ZBadwvBrQmCxNcnwCkOt4TXl8ToeTx+t0BPR4NeI7q0mPV4srEH56BugHXKKqZSdpOxeYKiL9RaQdcD8wOxChRCRMRKKAUCBURKIaOq8pIhO85yIRkb7UXtnwjtu5cOh4qWoJMB+YLiIxInIucBm1f2H5+m8I2PFqZBbHPk+NyeXk58m7D38/U44dr8bkcvp44f93VtMeL7dG4d3agG7UVvtyartjddt13vfTvM/T6v3ML4GDwDHgBSAyQNke8marvz3kKxfwZ2+mEmAntV3ccLdzOXy8EoG3vccgF5hc7z1Hj1dDWdw8Po3J5eTn6USfqSA4Xn7lcvjfX4PfWYE+XjZZnzHGGJ9a6ykmY4wxJ2EFwhhjjE9WIIwxxvhkBcIYY4xPViCMMcb4ZAXCGGOMT1YgjDHG+GQFwhhjjE9WIIwxxvhkBcKYABCRniKSLyJnep939q4dMM7dZMb4z6baMCZARORWaufFGQ68BaxX1XvdTWWM/6xAGBNAIvJvoDu1k62dpaoVLkcyxm92ismYwHqO2pXHnrLiYJob60EYEyAiEkvtmsCfAxOAQaqa724qY/xnBcKYABGRmUCcql4jIjOAtqp6jdu5jPGXnWIyJgBE5DLgYuB270u/BM4UkevcS2VM41gPwhhjjE/WgzDGGOOTFQhjjDE+WYEwxhjjkxUIY4wxPlmBMMYY45MVCGOMMT5ZgTDGGOOTFQhjjDE+/X/6O4mYueruKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(f, 'x', 'x**2')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(f, 'x', 'x**2')\n",
    "plt.scatter(-1.5, f(-1.5), color='red');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "xt = tensor(3.).requires_grad_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(9., grad_fn=<PowBackward0>)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yt = f(xt)\n",
    "yt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "yt.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(6.)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xt.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 3.,  4., 10.], requires_grad=True)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xt = tensor([3.,4.,10.]).requires_grad_()\n",
    "xt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(125., grad_fn=<SumBackward0>)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(x): return (x**2).sum()\n",
    "\n",
    "yt = f(xt)\n",
    "yt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 6.,  8., 20.])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yt.backward()\n",
    "xt.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19.])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time = torch.arange(0,20).float(); time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "speed = torch.randn(20)*3 + 0.75*(time-9.5)**2 + 1\n",
    "plt.scatter(time,speed);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, params):\n",
    "    a,b,c = params\n",
    "    return a*(t**2) + (b*t) + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse(preds, targets): return ((preds-targets)**2).mean().sqrt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = torch.randn(3).requires_grad_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "orig_params = params.clone()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = f(time, params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_preds(preds, ax=None):\n",
    "    if ax is None: ax=plt.subplots()[1]\n",
    "    ax.scatter(time, speed)\n",
    "    ax.scatter(time, to_np(preds), color='red')\n",
    "    ax.set_ylim(-300,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_preds(preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(160.6979, grad_fn=<SqrtBackward>)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss = mse(preds, speed)\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-165.5151,  -10.6402,   -0.7900])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss.backward()\n",
    "params.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-1.6552e-03, -1.0640e-04, -7.8996e-06])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params.grad * 1e-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-0.7658, -0.7506,  1.3525], requires_grad=True)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 1e-5\n",
    "params.data -= lr * params.grad.data\n",
    "params.grad = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(160.4228, grad_fn=<SqrtBackward>)"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = f(time,params)\n",
    "mse(preds, speed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_preds(preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "def apply_step(params, prn=True):\n",
    "    preds = f(time, params)\n",
    "    loss = mse(preds, speed)\n",
    "    loss.backward()\n",
    "    params.data -= lr * params.grad.data\n",
    "    params.grad = None\n",
    "    if prn: print(loss.item())\n",
    "    return preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "160.42279052734375\n",
      "160.14772033691406\n",
      "159.87269592285156\n",
      "159.59768676757812\n",
      "159.3227081298828\n",
      "159.04774475097656\n",
      "158.7728271484375\n",
      "158.4979248046875\n",
      "158.22305297851562\n",
      "157.9481964111328\n"
     ]
    }
   ],
   "source": [
    "for i in range(10): apply_step(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "params = orig_params.detach().requires_grad_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x216 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_,axs = plt.subplots(1,4,figsize=(12,3))\n",
    "for ax in axs: show_preds(apply_step(params, False), ax)\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
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   "source": [
    "gv('''\n",
    "init->predict->loss->gradient->step->stop\n",
    "step->predict[label=repeat]\n",
    "''')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x = torch.cat([stacked_threes, stacked_sevens]).view(-1, 28*28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([12396, 784]), torch.Size([12396, 1]))"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_y = tensor([1]*len(threes) + [0]*len(sevens)).unsqueeze(1)\n",
    "train_x.shape,train_y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([784]), tensor([1]))"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dset = list(zip(train_x,train_y))\n",
    "x,y = dset[0]\n",
    "x.shape,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_x = torch.cat([valid_3_tens, valid_7_tens]).view(-1, 28*28)\n",
    "valid_y = tensor([1]*len(valid_3_tens) + [0]*len(valid_7_tens)).unsqueeze(1)\n",
    "valid_dset = list(zip(valid_x,valid_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_params(size, std=1.0): return (torch.randn(size)*std).requires_grad_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = init_params((28*28,1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "bias = init_params(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([20.2336], grad_fn=<AddBackward0>)"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(train_x[0]*weights.T).sum() + bias\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[20.2336],\n",
       "        [17.0644],\n",
       "        [15.2384],\n",
       "        ...,\n",
       "        [18.3804],\n",
       "        [23.8567],\n",
       "        [28.6816]], grad_fn=<AddBackward0>)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def linear1(xb): return xb@weights + bias\n",
    "preds = linear1(train_x)\n",
    "preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ True],\n",
       "        [ True],\n",
       "        [ True],\n",
       "        ...,\n",
       "        [False],\n",
       "        [False],\n",
       "        [False]])"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrects = (preds>0.0).float() == train_y\n",
    "corrects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4912068545818329"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrects.float().mean().item()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights[0] *= 1.0001\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4912068545818329"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = linear1(train_x)\n",
    "((preds>0.0).float() == train_y).float().mean().item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "trgts  = tensor([1,0,1])\n",
    "prds   = tensor([0.9, 0.4, 0.2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mnist_loss(predictions, targets):\n",
    "    return torch.where(targets==1, 1-predictions, predictions).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.4000, 0.8000])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.where(trgts==1, 1-prds, prds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.4333)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist_loss(prds,trgts)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.2333)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist_loss(tensor([0.9, 0.4, 0.8]),trgts)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x): return 1/(1+torch.exp(-x))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(torch.sigmoid, title='Sigmoid', min=-4, max=4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mnist_loss(predictions, targets):\n",
    "    predictions = predictions.sigmoid()\n",
    "    return torch.where(targets==1, 1-predictions, predictions).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([ 3, 12,  8, 10,  2]),\n",
       " tensor([ 9,  4,  7, 14,  5]),\n",
       " tensor([ 1, 13,  0,  6, 11])]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "coll = range(15)\n",
    "dl = DataLoader(coll, batch_size=5, shuffle=True)\n",
    "list(dl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(#26) [(0, 'a'),(1, 'b'),(2, 'c'),(3, 'd'),(4, 'e'),(5, 'f'),(6, 'g'),(7, 'h'),(8, 'i'),(9, 'j')...]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds = L(enumerate(string.ascii_lowercase))\n",
    "ds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(tensor([17, 18, 10, 22,  8, 14]), ('r', 's', 'k', 'w', 'i', 'o')),\n",
       " (tensor([20, 15,  9, 13, 21, 12]), ('u', 'p', 'j', 'n', 'v', 'm')),\n",
       " (tensor([ 7, 25,  6,  5, 11, 23]), ('h', 'z', 'g', 'f', 'l', 'x')),\n",
       " (tensor([ 1,  3,  0, 24, 19, 16]), ('b', 'd', 'a', 'y', 't', 'q')),\n",
       " (tensor([2, 4]), ('c', 'e'))]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dl = DataLoader(ds, batch_size=6, shuffle=True)\n",
    "list(dl)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights = init_params((28*28,1))\n",
    "bias = init_params(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([256, 784]), torch.Size([256, 1]))"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dl = DataLoader(dset, batch_size=256)\n",
    "xb,yb = first(dl)\n",
    "xb.shape,yb.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "valid_dl = DataLoader(valid_dset, batch_size=256)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([4, 784])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch = train_x[:4]\n",
    "batch.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-2.1876],\n",
       "        [-8.3973],\n",
       "        [ 2.5000],\n",
       "        [-4.9473]], grad_fn=<AddBackward0>)"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = linear1(batch)\n",
    "preds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.7419, grad_fn=<MeanBackward0>)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss = mnist_loss(preds, train_y[:4])\n",
    "loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([784, 1]), tensor(-0.0061), tensor([-0.0420]))"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loss.backward()\n",
    "weights.grad.shape,weights.grad.mean(),bias.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_grad(xb, yb, model):\n",
    "    preds = model(xb)\n",
    "    loss = mnist_loss(preds, yb)\n",
    "    loss.backward()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(-0.0121), tensor([-0.0840]))"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_grad(batch, train_y[:4], linear1)\n",
    "weights.grad.mean(),bias.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor(-0.0182), tensor([-0.1260]))"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calc_grad(batch, train_y[:4], linear1)\n",
    "weights.grad.mean(),bias.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "weights.grad.zero_()\n",
    "bias.grad.zero_();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_epoch(model, lr, params):\n",
    "    for xb,yb in dl:\n",
    "        calc_grad(xb, yb, model)\n",
    "        for p in params:\n",
    "            p.data -= p.grad*lr\n",
    "            p.grad.zero_()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[False],\n",
       "        [False],\n",
       "        [ True],\n",
       "        [False]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(preds>0.0).float() == train_y[:4]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "def batch_accuracy(xb, yb):\n",
    "    preds = xb.sigmoid()\n",
    "    correct = (preds>0.5) == yb\n",
    "    return correct.float().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.2500)"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "batch_accuracy(linear1(batch), train_y[:4])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "def validate_epoch(model):\n",
    "    accs = [batch_accuracy(model(xb), yb) for xb,yb in valid_dl]\n",
    "    return round(torch.stack(accs).mean().item(), 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5263"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "validate_epoch(linear1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6663"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr = 1.\n",
    "params = weights,bias\n",
    "train_epoch(linear1, lr, params)\n",
    "validate_epoch(linear1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8265 0.8899 0.9182 0.9275 0.9397 0.9466 0.9505 0.9525 0.9559 0.9578 0.9598 0.9608 0.9613 0.9618 0.9632 0.9637 0.9647 0.9657 0.9672 0.9677 "
     ]
    }
   ],
   "source": [
    "for i in range(20):\n",
    "    train_epoch(linear1, lr, params)\n",
    "    print(validate_epoch(linear1), end=' ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_model = nn.Linear(28*28,1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1, 784]), torch.Size([1]))"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w,b = linear_model.parameters()\n",
    "w.shape,b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "class BasicOptim:\n",
    "    def __init__(self,params,lr): self.params,self.lr = list(params),lr\n",
    "\n",
    "    def step(self, *args, **kwargs):\n",
    "        for p in self.params: p.data -= p.grad.data * self.lr\n",
    "\n",
    "    def zero_grad(self, *args, **kwargs):\n",
    "        for p in self.params: p.grad = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = BasicOptim(linear_model.parameters(), lr)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_epoch(model):\n",
    "    for xb,yb in dl:\n",
    "        calc_grad(xb, yb, model)\n",
    "        opt.step()\n",
    "        opt.zero_grad()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4608"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "validate_epoch(linear_model)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_model(model, epochs):\n",
    "    for i in range(epochs):\n",
    "        train_epoch(model)\n",
    "        print(validate_epoch(model), end=' ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4932 0.7685 0.8554 0.9135 0.9345 0.9482 0.957 0.9633 0.9658 0.9677 0.9697 0.9716 0.9736 0.9746 0.976 0.977 0.9775 0.9775 0.978 0.9785 "
     ]
    }
   ],
   "source": [
    "train_model(linear_model, 20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4932 0.8179 0.8496 0.914 0.9345 0.9482 0.957 0.9619 0.9658 0.9672 0.9692 0.9712 0.9741 0.9751 0.976 0.9775 0.9775 0.978 0.9785 0.979 "
     ]
    }
   ],
   "source": [
    "linear_model = nn.Linear(28*28,1)\n",
    "opt = SGD(linear_model.parameters(), lr)\n",
    "train_model(linear_model, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "dls = DataLoaders(dl, valid_dl)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn = Learner(dls, nn.Linear(28*28,1), opt_func=SGD,\n",
    "                loss_func=mnist_loss, metrics=batch_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>batch_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.636709</td>\n",
       "      <td>0.503144</td>\n",
       "      <td>0.495584</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.429828</td>\n",
       "      <td>0.248517</td>\n",
       "      <td>0.777233</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.161680</td>\n",
       "      <td>0.155361</td>\n",
       "      <td>0.861629</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.072948</td>\n",
       "      <td>0.097722</td>\n",
       "      <td>0.917566</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.040128</td>\n",
       "      <td>0.073205</td>\n",
       "      <td>0.936212</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.027210</td>\n",
       "      <td>0.059466</td>\n",
       "      <td>0.950442</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.021837</td>\n",
       "      <td>0.050799</td>\n",
       "      <td>0.957802</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.019398</td>\n",
       "      <td>0.044980</td>\n",
       "      <td>0.964181</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.018122</td>\n",
       "      <td>0.040853</td>\n",
       "      <td>0.966143</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.017330</td>\n",
       "      <td>0.037788</td>\n",
       "      <td>0.968106</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit(10, lr=lr)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simple_net(xb): \n",
    "    res = xb@w1 + b1\n",
    "    res = res.max(tensor(0.0))\n",
    "    res = res@w2 + b2\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "w1 = init_params((28*28,30))\n",
    "b1 = init_params(30)\n",
    "w2 = init_params((30,1))\n",
    "b2 = init_params(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_function(F.relu)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_net = nn.Sequential(\n",
    "    nn.Linear(28*28,30),\n",
    "    nn.ReLU(),\n",
    "    nn.Linear(30,1)\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "learn = Learner(dls, simple_net, opt_func=SGD,\n",
    "                loss_func=mnist_loss, metrics=batch_accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>batch_accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.333021</td>\n",
       "      <td>0.396112</td>\n",
       "      <td>0.512267</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.152461</td>\n",
       "      <td>0.235238</td>\n",
       "      <td>0.797350</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.083573</td>\n",
       "      <td>0.117471</td>\n",
       "      <td>0.911678</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.054309</td>\n",
       "      <td>0.078720</td>\n",
       "      <td>0.940628</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.040829</td>\n",
       "      <td>0.061228</td>\n",
       "      <td>0.956330</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.034006</td>\n",
       "      <td>0.051490</td>\n",
       "      <td>0.963690</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.030123</td>\n",
       "      <td>0.045381</td>\n",
       "      <td>0.966634</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.027619</td>\n",
       "      <td>0.041218</td>\n",
       "      <td>0.968106</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.025825</td>\n",
       "      <td>0.038200</td>\n",
       "      <td>0.969087</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.024441</td>\n",
       "      <td>0.035901</td>\n",
       "      <td>0.969578</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>0.023321</td>\n",
       "      <td>0.034082</td>\n",
       "      <td>0.971541</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>0.022387</td>\n",
       "      <td>0.032598</td>\n",
       "      <td>0.972031</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>0.021592</td>\n",
       "      <td>0.031353</td>\n",
       "      <td>0.974485</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>0.020904</td>\n",
       "      <td>0.030284</td>\n",
       "      <td>0.975466</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>0.020300</td>\n",
       "      <td>0.029352</td>\n",
       "      <td>0.975466</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>0.019766</td>\n",
       "      <td>0.028526</td>\n",
       "      <td>0.975466</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>0.019288</td>\n",
       "      <td>0.027788</td>\n",
       "      <td>0.976448</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>17</td>\n",
       "      <td>0.018857</td>\n",
       "      <td>0.027124</td>\n",
       "      <td>0.977429</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>18</td>\n",
       "      <td>0.018465</td>\n",
       "      <td>0.026523</td>\n",
       "      <td>0.978410</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>19</td>\n",
       "      <td>0.018107</td>\n",
       "      <td>0.025977</td>\n",
       "      <td>0.978901</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>20</td>\n",
       "      <td>0.017777</td>\n",
       "      <td>0.025479</td>\n",
       "      <td>0.978901</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>21</td>\n",
       "      <td>0.017473</td>\n",
       "      <td>0.025022</td>\n",
       "      <td>0.979392</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>0.017191</td>\n",
       "      <td>0.024601</td>\n",
       "      <td>0.980373</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>0.016927</td>\n",
       "      <td>0.024213</td>\n",
       "      <td>0.980373</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>0.016680</td>\n",
       "      <td>0.023855</td>\n",
       "      <td>0.981354</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25</td>\n",
       "      <td>0.016449</td>\n",
       "      <td>0.023521</td>\n",
       "      <td>0.981354</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>26</td>\n",
       "      <td>0.016230</td>\n",
       "      <td>0.023211</td>\n",
       "      <td>0.981354</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>27</td>\n",
       "      <td>0.016023</td>\n",
       "      <td>0.022922</td>\n",
       "      <td>0.981354</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>28</td>\n",
       "      <td>0.015827</td>\n",
       "      <td>0.022653</td>\n",
       "      <td>0.981845</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>29</td>\n",
       "      <td>0.015641</td>\n",
       "      <td>0.022401</td>\n",
       "      <td>0.981845</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>30</td>\n",
       "      <td>0.015463</td>\n",
       "      <td>0.022165</td>\n",
       "      <td>0.981845</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>31</td>\n",
       "      <td>0.015294</td>\n",
       "      <td>0.021944</td>\n",
       "      <td>0.983317</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>32</td>\n",
       "      <td>0.015132</td>\n",
       "      <td>0.021736</td>\n",
       "      <td>0.982826</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>33</td>\n",
       "      <td>0.014977</td>\n",
       "      <td>0.021541</td>\n",
       "      <td>0.982826</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>34</td>\n",
       "      <td>0.014828</td>\n",
       "      <td>0.021357</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>35</td>\n",
       "      <td>0.014686</td>\n",
       "      <td>0.021184</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>36</td>\n",
       "      <td>0.014549</td>\n",
       "      <td>0.021019</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>37</td>\n",
       "      <td>0.014417</td>\n",
       "      <td>0.020864</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>38</td>\n",
       "      <td>0.014290</td>\n",
       "      <td>0.020716</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>39</td>\n",
       "      <td>0.014168</td>\n",
       "      <td>0.020576</td>\n",
       "      <td>0.982336</td>\n",
       "      <td>00:00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn.fit(40, 0.1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(L(learn.recorder.values).itemgot(2));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98233562707901"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn.recorder.values[-1][2]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: left;\">\n",
       "      <th>epoch</th>\n",
       "      <th>train_loss</th>\n",
       "      <th>valid_loss</th>\n",
       "      <th>accuracy</th>\n",
       "      <th>time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.069314</td>\n",
       "      <td>0.011416</td>\n",
       "      <td>0.996075</td>\n",
       "      <td>00:19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dls = ImageDataLoaders.from_folder(path)\n",
    "learn = cnn_learner(dls, resnet18, pretrained=False,\n",
    "                    loss_func=F.cross_entropy, metrics=accuracy)\n",
    "learn.fit_one_cycle(1, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}