lec_1_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "958d6fcf",
   "metadata": {},
   "outputs": [],
   "source": [
    "import gzip, pickle\n",
    "from pathlib import Path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01f921d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "DATA_DOWNLOAD_PATH = 'https://github.com/mnielsen/neural-networks-and-deep-learning/blob/master/data/mnist.pkl.gz?raw=true'\n",
    "DATA_FOLDER = Path('data')\n",
    "DATA_FOLDER.mkdir(exist_ok=True)\n",
    "DATA_FILE  = DATA_FOLDER/'mnist.pkl.gz'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "aa789c5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from urllib.request import urlretrieve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "80d3c6b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "if not DATA_FILE.exists():\n",
    "    urlretrieve(DATA_DOWNLOAD_PATH, DATA_FILE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5a6fb48b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total 34560\r\n",
      "-rw-r--r--@ 1 arun  staff  17051982 Apr 24 09:43 mnist.pkl.gz\r\n"
     ]
    }
   ],
   "source": [
    "!ls -l data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bbf02ecd",
   "metadata": {},
   "outputs": [],
   "source": [
    "with gzip.open(DATA_FILE, 'rb') as f:\n",
    "    data = pickle.load(f, encoding='latin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2b301b4b",
   "metadata": {},
   "outputs": [],
   "source": [
    "((x_train, y_train), (x_val, y_val), _) = data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0ace5805",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50000, 784), (50000,), (10000, 784), (10000,))"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "806b14c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1d671dc8",
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train, x_val, y_val) = map(lambda x: torch.tensor(x), (x_train, y_train, x_val, y_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c1933d60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([50000, 784]),\n",
       " torch.Size([50000]),\n",
       " torch.Size([10000, 784]),\n",
       " torch.Size([10000]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape, x_val.shape, y_val.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "c213f011",
   "metadata": {},
   "outputs": [],
   "source": [
    "def chunks(x, sz):\n",
    "    for i in range(0, len(x), sz):\n",
    "        yield x[i:i+sz]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "15cdee7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "chnkls = chunks(x_val, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "3a3435f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<generator object chunks at 0x17e0305e0>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chnkls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "302f017b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 784])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(chnkls).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "7397cf61",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "35f99874",
   "metadata": {},
   "outputs": [],
   "source": [
    "mpl.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "abb203e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = x_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "a0d5ebc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([784])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "3915d483",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls1 = list(chunks(list(ls), 28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "c3227578",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0.])"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls1[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "1c2a9141",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.),\n",
       " tensor(0.)]"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls1[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "d370d7f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(ls1[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "4df5bce5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17e131210>"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(ls1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d130fbfd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79214ddb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9b3dfb1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7b031d2c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e7d9c18d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "8f5bb191",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = [1, 2, 3, 4, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "8761f8f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "tt = iter(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "id": "27e71172",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<list_iterator at 0x17e1c74c0>"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "id": "dbef4c76",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = tt.__iter__()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "d3f62fea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<list_iterator at 0x17e1c74c0>"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "id": "46010e17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k == tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "39bd0438",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "id": "0b186f95",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: '_', 1: '_', 2: '_', 3: '_', 4: '_'}"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t =  {i:'_' for i in range(5)}\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "id": "6473c512",
   "metadata": {},
   "outputs": [],
   "source": [
    "tt = iter(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "c46dfc98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<dict_keyiterator at 0x17e28a570>"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "14fdfc50",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[167], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m tt\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__next__\u001b[39m()\n",
      "\u001b[0;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "tt.__next__()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "301cb71c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    for i in x:\n",
    "        yield i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "baa01e43",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = [1, 2, 3, 4, 5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "5ec87bb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "tt = g(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "7a0d532c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<generator object g at 0x17e274380>"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "id": "e2f5baf4",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[153], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m tt\u001b[38;5;241m.\u001b[39m\u001b[38;5;21m__next__\u001b[39m()\n",
      "\u001b[0;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "tt.__next__()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "id": "eb210219",
   "metadata": {},
   "outputs": [
    {
     "ename": "StopIteration",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStopIteration\u001b[0m                             Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[154], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28mnext\u001b[39m(tt)\n",
      "\u001b[0;31mStopIteration\u001b[0m: "
     ]
    }
   ],
   "source": [
    "next(tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "3fea46de",
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import islice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "id": "bad9ffd1",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [1, 2, 3, 4, 5, 6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "id": "917c0cc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "xl = [list(x_train[0])[i: i+28] for i in islice(range(len(x_train[0])), 0, len(x_train[0]), 28)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "id": "3c0451d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "id": "2e241a20",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 263,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(xl[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "45cca5ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17e3cda10>"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(xl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "id": "9bc9b049",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(x_train[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "b39fe21b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(xl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "4f134746",
   "metadata": {},
   "outputs": [],
   "source": [
    "islice??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "8fc52f93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "3\n",
      "5\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "id": "fc170867",
   "metadata": {},
   "outputs": [],
   "source": [
    "ls = list(x_train[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "8df3f212",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([tensor(0.), tensor(0.), tensor(0.), tensor(0.), tensor(0.)], 784)"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls[:5], len(ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "84d98638",
   "metadata": {},
   "outputs": [],
   "source": [
    "lstr = iter(ls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "id": "e71e88de",
   "metadata": {},
   "outputs": [],
   "source": [
    "img1 = [list(islice(lstr, 28)) for _ in range(28)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "id": "ce9bec8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 284,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(img1), len(img1[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "id": "ae2aac22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17e607550>"
      ]
     },
     "execution_count": 285,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(img1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "id": "dad63a7b",
   "metadata": {},
   "outputs": [],
   "source": [
    "iter??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 287,
   "id": "fd9047cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [1, 2, 3, 4, 5, 6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "id": "468c1028",
   "metadata": {},
   "outputs": [],
   "source": [
    "lx = iter(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 299,
   "id": "6676a90b",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[299], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28mlist\u001b[39m(ls)\n",
      "Cell \u001b[0;32mIn[298], line 1\u001b[0m, in \u001b[0;36m<lambda>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m ls \u001b[38;5;241m=\u001b[39m \u001b[38;5;28miter\u001b[39m(\u001b[38;5;28;01mlambda\u001b[39;00m: \u001b[38;5;28mnext\u001b[39m(\u001b[38;5;28miter\u001b[39m(x)), [])\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "iter(lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 310,
   "id": "b6ea2ed5",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [1, 2, 3, 4, 5, 6]\n",
    "xl = iter(list(x_train[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 311,
   "id": "81b4ff12",
   "metadata": {},
   "outputs": [],
   "source": [
    "img1 = list(iter(lambda: list(islice(xl, 28)), []))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 312,
   "id": "029cb754",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 312,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(img1), len(img1[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 313,
   "id": "f60b28a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17e236250>"
      ]
     },
     "execution_count": 313,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(img1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9c2ad70",
   "metadata": {},
   "source": [
    "#### matrix and tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 331,
   "id": "a995c7f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Matrix():\n",
    "    def __init__(self, xs):\n",
    "        self.xs = xs\n",
    "    def __getitem__(self, idx):\n",
    "        return self.xs[idx[0]][idx[1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "id": "99e37b89",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = Matrix(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "id": "a7ea54bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.9883)"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m[14, 17]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "750231e2",
   "metadata": {},
   "source": [
    "#### tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "id": "3f134e10",
   "metadata": {},
   "outputs": [],
   "source": [
    "imgs = x_train.reshape(-1, 28, 28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "id": "520dcebe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([50000, 28, 28])"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imgs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "id": "9c91525d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([50000, 784])"
      ]
     },
     "execution_count": 338,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "id": "e4bd222b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x17e342910>"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(imgs[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "id": "561323a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.)"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "imgs[0,0,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa43348d",
   "metadata": {},
   "source": [
    "#### matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "id": "b2eef17f",
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.manual_seed(1)\n",
    "weights = torch.randn(784, 10)\n",
    "bias = torch.randn(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 345,
   "id": "956623f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 784])"
      ]
     },
     "execution_count": 345,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m1 = x_val[:5]\n",
    "m1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "id": "f608e4b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([784, 10])"
      ]
     },
     "execution_count": 346,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2 = weights\n",
    "m2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "id": "b402b458",
   "metadata": {},
   "outputs": [],
   "source": [
    "ar, ac = m1.shape\n",
    "br, bc = m2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "id": "fe24ffec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 10])"
      ]
     },
     "execution_count": 348,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = torch.zeros(ar, bc)\n",
    "t.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "id": "40492b12",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(ar):\n",
    "    for j in range(bc):\n",
    "        for k in range(ac):\n",
    "            t[i, j] += m1[i, k] * m2[k, j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "id": "7bb7aa3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5, 10])"
      ]
     },
     "execution_count": 351,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "id": "87c1d7e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.set_printoptions(precision=2, sci_mode=False, linewidth=140)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "id": "87b77355",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
       "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
       "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
       "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
       "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "id": "9920a794",
   "metadata": {},
   "outputs": [],
   "source": [
    "def matmul(m1, m2):\n",
    "    ar, ac = m1.shape\n",
    "    br, bc = m2.shape\n",
    "    c = torch.zeros(ar, bc)\n",
    "    for i in range(ar):\n",
    "        for j in range(bc):\n",
    "            for k in range(ac):\n",
    "                c[i, j] += m1[i, k] * m2[k, j]\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "id": "8c512d2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 688 ms, sys: 8.46 ms, total: 696 ms\n",
      "Wall time: 701 ms\n"
     ]
    }
   ],
   "source": [
    "%time _ = matmul(x_val[:5], weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "id": "581aecdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39200"
      ]
     },
     "execution_count": 366,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ar*bc*ac"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07722e43",
   "metadata": {},
   "source": [
    "#### elementwise operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "id": "5e18ad75",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = torch.tensor([10., 6, -4])\n",
    "b = torch.tensor([2, 8, 7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "id": "72bf6a5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([12., 14.,  3.])"
      ]
     },
     "execution_count": 371,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "id": "f0477b08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.67)"
      ]
     },
     "execution_count": 376,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(a < b).float().mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "id": "36b4a586",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 20.,  48., -28.])"
      ]
     },
     "execution_count": 379,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "id": "ce1fbdd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = torch.tensor([\n",
    "    [1, 2, 3],\n",
    "    [4, 5, 6],\n",
    "    [7, 8, 9]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "id": "a94d5572",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 3])"
      ]
     },
     "execution_count": 378,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "id": "4bd89880",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 1,  4,  9],\n",
       "        [16, 25, 36],\n",
       "        [49, 64, 81]])"
      ]
     },
     "execution_count": 380,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m * m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "id": "ed93d763",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(16.88)"
      ]
     },
     "execution_count": 382,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(m*m).sum().sqrt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 387,
   "id": "393c387d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([7, 8, 9]), tensor([3, 6, 9]))"
      ]
     },
     "execution_count": 387,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m[2,:], m[:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 388,
   "id": "05330609",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([7, 8, 9])"
      ]
     },
     "execution_count": 388,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "id": "046b4c59",
   "metadata": {},
   "outputs": [],
   "source": [
    "def matmul(m1, m2):\n",
    "    (ar, ac), (br, bc) = m1.shape, m2.shape\n",
    "    c = torch.zeros(ar, bc)\n",
    "    for i in range(ar):\n",
    "        for j in range(bc):\n",
    "            c[i, j] = (m1[i,:] * m2[:,j]).sum()\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "id": "f17315b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "t2 = matmul(m1, m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 393,
   "id": "29487656",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
       "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
       "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
       "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
       "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
      ]
     },
     "execution_count": 393,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "id": "b6ea861e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 395,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.allclose(t, t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "id": "e3ba213c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.05 ms, sys: 4.14 ms, total: 9.18 ms\n",
      "Wall time: 7 ms\n"
     ]
    }
   ],
   "source": [
    "%time _= matmul(m1, m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "id": "75c1b86b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "933 µs ± 140 µs per loop (mean ± std. dev. of 7 runs, 50 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit -n 50 _= matmul(m1, m2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bec480de",
   "metadata": {},
   "source": [
    "#### broadcasting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "27557c0a",
   "metadata": {},
   "source": [
    "#### broadcasting with a scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "id": "81a83823",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([10.,  6., -4.])"
      ]
     },
     "execution_count": 398,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 399,
   "id": "213ba37a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3])"
      ]
     },
     "execution_count": 399,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 400,
   "id": "7a73dd46",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ True,  True, False])"
      ]
     },
     "execution_count": 400,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "id": "267064dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 2,  4,  6],\n",
       "        [ 8, 10, 12],\n",
       "        [14, 16, 18]])"
      ]
     },
     "execution_count": 401,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2*m"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "970a205b",
   "metadata": {},
   "source": [
    "#### broadcasting a vector to a matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "id": "364d6309",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3])"
      ]
     },
     "execution_count": 403,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    " c = torch.tensor([10, 20, 30]);c.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "id": "e9060b4c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1, 2, 3],\n",
       "        [4, 5, 6],\n",
       "        [7, 8, 9]])"
      ]
     },
     "execution_count": 404,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "id": "420277fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 3])"
      ]
     },
     "execution_count": 405,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "id": "3fa4fcb2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([3, 3]), torch.Size([3]))"
      ]
     },
     "execution_count": 406,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.shape, c.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "id": "dd7b1b8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[11, 22, 33],\n",
       "        [14, 25, 36],\n",
       "        [17, 28, 39]])"
      ]
     },
     "execution_count": 407,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m + c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "id": "cb491518",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[11, 22, 33],\n",
       "        [14, 25, 36],\n",
       "        [17, 28, 39]])"
      ]
     },
     "execution_count": 408,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c + m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "id": "ff19b30e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 20, 30],\n",
       "        [10, 20, 30],\n",
       "        [10, 20, 30]])"
      ]
     },
     "execution_count": 415,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = c.expand_as(m)\n",
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "id": "bde0f036",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[11, 22, 33],\n",
       "        [14, 25, 36],\n",
       "        [17, 28, 39]])"
      ]
     },
     "execution_count": 416,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m + l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "id": "5a5351ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8k/07c2mpg56x7c31_26k0qj2y00000gn/T/ipykernel_44474/2651326052.py:1: UserWarning: TypedStorage is deprecated. It will be removed in the future and UntypedStorage will be the only storage class. This should only matter to you if you are using storages directly.  To access UntypedStorage directly, use tensor.untyped_storage() instead of tensor.storage()\n",
      "  l.storage()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " 10\n",
       " 20\n",
       " 30\n",
       "[torch.storage.TypedStorage(dtype=torch.int64, device=cpu) of size 3]"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l.storage()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "id": "60202fcf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8k/07c2mpg56x7c31_26k0qj2y00000gn/T/ipykernel_44474/1226304414.py:1: UserWarning: TypedStorage is deprecated. It will be removed in the future and UntypedStorage will be the only storage class. This should only matter to you if you are using storages directly.  To access UntypedStorage directly, use tensor.untyped_storage() instead of tensor.storage()\n",
      "  c.storage()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " 10\n",
       " 20\n",
       " 30\n",
       "[torch.storage.TypedStorage(dtype=torch.int64, device=cpu) of size 3]"
      ]
     },
     "execution_count": 421,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.storage()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "id": "d33de96c",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/8k/07c2mpg56x7c31_26k0qj2y00000gn/T/ipykernel_44474/1122607061.py:1: UserWarning: TypedStorage is deprecated. It will be removed in the future and UntypedStorage will be the only storage class. This should only matter to you if you are using storages directly.  To access UntypedStorage directly, use tensor.untyped_storage() instead of tensor.storage()\n",
      "  m.storage()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       " 1\n",
       " 2\n",
       " 3\n",
       " 4\n",
       " 5\n",
       " 6\n",
       " 7\n",
       " 8\n",
       " 9\n",
       "[torch.storage.TypedStorage(dtype=torch.int64, device=cpu) of size 9]"
      ]
     },
     "execution_count": 422,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.storage()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "id": "99ae6ed9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((0, 1), torch.Size([3, 3]))"
      ]
     },
     "execution_count": 425,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l.stride(), l.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "id": "f8ab86c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((3, 1), torch.Size([3, 3]))"
      ]
     },
     "execution_count": 426,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.stride(), m.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "id": "2b7fc423",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(18, 3, 1)"
      ]
     },
     "execution_count": 433,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k = torch.zeros(5, 6, 3)\n",
    "k.stride()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "id": "e1fc53e5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 20, 30]])"
      ]
     },
     "execution_count": 448,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.unsqueeze(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25cac831",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "id": "0e7337b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 20, 30]])"
      ]
     },
     "execution_count": 441,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "id": "c0515287",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([3]), torch.Size([1, 3]))"
      ]
     },
     "execution_count": 442,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.shape,c[None].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "id": "92dc58a1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 20, 30]])"
      ]
     },
     "execution_count": 447,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "id": "bb6ca1b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([3]), torch.Size([3, 1]))"
      ]
     },
     "execution_count": 446,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.shape, c[...,None].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "id": "6bef45ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[10],\n",
       "         [20],\n",
       "         [30]]),\n",
       " torch.Size([3, 1]))"
      ]
     },
     "execution_count": 451,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,None], c[:,None].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "id": "cf428abe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1, 2, 3],\n",
       "        [4, 5, 6],\n",
       "        [7, 8, 9]])"
      ]
     },
     "execution_count": 452,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "id": "3b1ab2e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([3, 1, 3]), torch.Size([3, 3]))"
      ]
     },
     "execution_count": 456,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m[:,None].shape, m.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "id": "fd710db9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 10, 10],\n",
       "        [20, 20, 20],\n",
       "        [30, 30, 30]])"
      ]
     },
     "execution_count": 460,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,None].expand_as(m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10b38986",
   "metadata": {},
   "source": [
    "#### broadcasting rules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "id": "97681950",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 1])"
      ]
     },
     "execution_count": 463,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,None].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "id": "4adb23e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 3])"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[None,:].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "id": "13c0e900",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10, 20, 30]])"
      ]
     },
     "execution_count": 465,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[None,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "id": "e61a704a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[10],\n",
       "        [20],\n",
       "        [30]])"
      ]
     },
     "execution_count": 466,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "id": "f4b57bbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([3, 1]), torch.Size([3, 1]))"
      ]
     },
     "execution_count": 468,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,None].shape, c[:,None].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "id": "05360190",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[100, 200, 300],\n",
       "        [200, 400, 600],\n",
       "        [300, 600, 900]])"
      ]
     },
     "execution_count": 467,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[None,:] * c[:,None]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d62318f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "eee667d6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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