coursera_deep_neural_network/Week 1 - Tensor and Datasets.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "physical-gothic",
   "metadata": {},
   "source": [
    "# Tensors 1D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "contained-archives",
   "metadata": {},
   "source": [
    "## The basics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lonely-scanner",
   "metadata": {},
   "source": [
    "### tensors, dtype, type()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "related-haiti",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:42:49.791221Z",
     "start_time": "2021-07-07T11:42:49.776317Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "a=torch.tensor([7,4,3,2,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "severe-helping",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:42:55.398591Z",
     "start_time": "2021-07-07T11:42:55.381271Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([7, 4, 3, 2, 6])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "confidential-pizza",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:43:05.297654Z",
     "start_time": "2021-07-07T11:43:05.280774Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(6)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "regional-index",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:43:20.769460Z",
     "start_time": "2021-07-07T11:43:20.761022Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "moderate-working",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:43:35.016861Z",
     "start_time": "2021-07-07T11:43:35.007961Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'torch.LongTensor'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.type()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "monthly-cincinnati",
   "metadata": {},
   "source": [
    "### tensors of float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "normal-riding",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:44:01.946934Z",
     "start_time": "2021-07-07T11:44:01.944504Z"
    }
   },
   "outputs": [],
   "source": [
    "a=torch.tensor([0.0, 1.0, 2.1, 3.0, 4.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "arctic-gross",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:44:03.432519Z",
     "start_time": "2021-07-07T11:44:03.407325Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.0000, 1.0000, 2.1000, 3.0000, 4.0000])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "about-defensive",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:44:12.144492Z",
     "start_time": "2021-07-07T11:44:12.133845Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.float32"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bibliographic-joseph",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:44:17.220449Z",
     "start_time": "2021-07-07T11:44:17.213889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'torch.FloatTensor'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.type()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "collectible-price",
   "metadata": {},
   "source": [
    "### force tensor type"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "amino-participant",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:44:52.182231Z",
     "start_time": "2021-07-07T11:44:52.176377Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-d6616eab2e34>:1: DeprecationWarning: an integer is required (got type float).  Implicit conversion to integers using __int__ is deprecated, and may be removed in a future version of Python.\n",
      "  a=torch.tensor([0.0,1.0,2.0,3.0,4.0], dtype=torch.int32)\n"
     ]
    }
   ],
   "source": [
    "a=torch.tensor([0.0,1.0,2.0,3.0,4.0], dtype=torch.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dedicated-morning",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:45:23.678614Z",
     "start_time": "2021-07-07T11:45:23.675911Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.int32"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "frequent-friday",
   "metadata": {},
   "source": [
    "### FloatTensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "radio-vegetation",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:45:57.806179Z",
     "start_time": "2021-07-07T11:45:57.803734Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "a=torch.FloatTensor([0,1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "worst-profile",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:45:59.955952Z",
     "start_time": "2021-07-07T11:45:59.945381Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1., 2., 3., 4.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "contained-amazon",
   "metadata": {},
   "source": [
    "### Convert with .type()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "hungry-representation",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:49:56.808212Z",
     "start_time": "2021-07-07T11:49:56.803033Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "a=torch.tensor([0,1,2,3,4])\n",
    "a=a.type(torch.FloatTensor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "proved-surgeon",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:50:06.899707Z",
     "start_time": "2021-07-07T11:50:06.890437Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'torch.FloatTensor'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.type()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "smaller-indonesian",
   "metadata": {},
   "source": [
    "### size(), ndimension()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "important-replacement",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:55:16.768878Z",
     "start_time": "2021-07-07T11:55:16.763610Z"
    }
   },
   "outputs": [],
   "source": [
    "a=torch.Tensor([0,1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "recognized-hayes",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:55:23.865982Z",
     "start_time": "2021-07-07T11:55:23.860192Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([5])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "prime-small",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:55:33.908730Z",
     "start_time": "2021-07-07T11:55:33.900025Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ndimension()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "military-terry",
   "metadata": {},
   "source": [
    "### tensor vs Tensor\n",
    "\n",
    "https://stackoverflow.com/questions/51911749/what-is-the-difference-between-torch-tensor-and-torch-tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "stopped-baseball",
   "metadata": {},
   "source": [
    "torch.tensor infers the dtype automatically, while torch.Tensor returns a torch.FloatTensor. I would recommend to stick to torch.tensor, which also has arguments like dtype, if you would like to change the type."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "coastal-johnston",
   "metadata": {},
   "source": [
    "### convert 1D to 2D using view"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "affiliated-emphasis",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:57:12.263508Z",
     "start_time": "2021-07-07T11:57:12.261101Z"
    }
   },
   "outputs": [],
   "source": [
    "a=torch.Tensor([0,1,2,3,4])\n",
    "a_col = a.view(5,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "pretty-administrator",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:57:15.728261Z",
     "start_time": "2021-07-07T11:57:15.724990Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.],\n",
       "        [1.],\n",
       "        [2.],\n",
       "        [3.],\n",
       "        [4.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "raised-demographic",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:57:32.729426Z",
     "start_time": "2021-07-07T11:57:32.716177Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0.],\n",
       "        [1.],\n",
       "        [2.],\n",
       "        [3.],\n",
       "        [4.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_col = a.view(-1,1)\n",
    "b_col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "running-student",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:58:00.738154Z",
     "start_time": "2021-07-07T11:58:00.732722Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_col.ndimension()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "derived-steal",
   "metadata": {},
   "source": [
    "### create torch tensors from numpy arrays: from_numpy, numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "lasting-burden",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T11:59:53.177963Z",
     "start_time": "2021-07-07T11:59:53.172361Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "numpy_array = np.array([0.0, 1.0, 2.0, 3.0, 4.0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "foster-person",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:00:34.537042Z",
     "start_time": "2021-07-07T12:00:34.534285Z"
    }
   },
   "outputs": [],
   "source": [
    "torch_tensor = torch.from_numpy(numpy_array)\n",
    "back_to_numpy = torch_tensor.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "periodic-baltimore",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:00:37.755102Z",
     "start_time": "2021-07-07T12:00:37.741308Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1., 2., 3., 4.], dtype=torch.float64)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch_tensor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "virgin-excellence",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:00:41.917347Z",
     "start_time": "2021-07-07T12:00:41.901960Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 1., 2., 3., 4.])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "back_to_numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "educational-promise",
   "metadata": {},
   "source": [
    "### pandas series to torch tensors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "bound-ukraine",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:03:51.329121Z",
     "start_time": "2021-07-07T12:03:51.317481Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     0.1\n",
       "1     2.0\n",
       "2     0.3\n",
       "3    10.1\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "pandas_series = pd.Series([0.1, 2, 0.3, 10.1])\n",
    "pandas_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "indie-characterization",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:04:18.866685Z",
     "start_time": "2021-07-07T12:04:18.861964Z"
    }
   },
   "outputs": [],
   "source": [
    "pandas_to_torch = torch.from_numpy(pandas_series.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "healthy-marsh",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:04:22.924113Z",
     "start_time": "2021-07-07T12:04:22.918297Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.1000,  2.0000,  0.3000, 10.1000], dtype=torch.float64)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pandas_to_torch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "elegant-breakdown",
   "metadata": {},
   "source": [
    "### tensor to list: tolist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "intermediate-husband",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:05:34.488918Z",
     "start_time": "2021-07-07T12:05:34.485797Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "this_tensor = torch.tensor([0, 1, 2, 3])\n",
    "torch_to_list = this_tensor.tolist()\n",
    "torch_to_list"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "proud-bowling",
   "metadata": {},
   "source": [
    "### item to return a number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "stuck-republican",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:06:43.065018Z",
     "start_time": "2021-07-07T12:06:43.062102Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(5)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_tensor = torch.tensor([5, 2, 6, 1])\n",
    "new_tensor[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "comfortable-chemical",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:06:50.941904Z",
     "start_time": "2021-07-07T12:06:50.935579Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_tensor[0].item()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "framed-foster",
   "metadata": {},
   "source": [
    "### indexing and slicing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "crucial-texas",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:17:30.407803Z",
     "start_time": "2021-07-07T12:17:30.401464Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([20,  1,  2,  3,  4])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c=torch.tensor([20, 1, 2, 3, 4])\n",
    "c\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "adverse-allowance",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:17:37.938095Z",
     "start_time": "2021-07-07T12:17:37.921194Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([100,   1,   2,   3,   4])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0]=100\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "thrown-occasion",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:17:45.006849Z",
     "start_time": "2021-07-07T12:17:45.003883Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([100,   1,   2,   3,   0])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[4]=0\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "regulated-bench",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:18:10.949223Z",
     "start_time": "2021-07-07T12:18:10.946530Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1, 2, 3])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#from 1 to 3\n",
    "d=c[1:4]\n",
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "transparent-opening",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:19:02.322431Z",
     "start_time": "2021-07-07T12:19:02.316467Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([100,   1,   2, 300,   4])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[3:5]=torch.tensor([300.0, 4.0])\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "least-shelf",
   "metadata": {},
   "source": [
    "## Basic Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "through-phoenix",
   "metadata": {},
   "source": [
    "### vector addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "warming-eating",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:21:14.056400Z",
     "start_time": "2021-07-07T12:21:14.043537Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 1.])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = torch.tensor([1.0, 0.0])\n",
    "v = torch.tensor([0.0, 1.0])\n",
    "z=u+v\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lasting-religious",
   "metadata": {},
   "source": [
    "### Vector multiplication with a scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "metric-letter",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:22:58.450336Z",
     "start_time": "2021-07-07T12:22:58.443690Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2, 4])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.tensor([1, 2])\n",
    "z = 2*y\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "female-juice",
   "metadata": {},
   "source": [
    "### hadamard product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "vertical-separation",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:25:04.655817Z",
     "start_time": "2021-07-07T12:25:04.643830Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([3, 8])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = torch.tensor([1, 2])\n",
    "v = torch.tensor([3, 4])\n",
    "z = u*v\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cardiovascular-venture",
   "metadata": {},
   "source": [
    "### dot product (produit scalaire)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "widespread-burton",
   "metadata": {},
   "source": [
    "gives an indication about how similar these vectors are"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "geographic-richardson",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:27:20.078172Z",
     "start_time": "2021-07-07T12:27:20.060898Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(5)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = torch.tensor([1, 2])\n",
    "v = torch.tensor([3, 1])\n",
    "result = torch.dot(u, v)\n",
    "result"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loving-alert",
   "metadata": {},
   "source": [
    "### adding constant to a tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "extended-martial",
   "metadata": {},
   "source": [
    "it uses broadcasting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "specified-guitar",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:28:32.066376Z",
     "start_time": "2021-07-07T12:28:32.061103Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2, 3, 4, 0])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = torch.tensor([1, 2, 3, -1])\n",
    "z = u + 1\n",
    "z\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "international-weapon",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "collect-gibraltar",
   "metadata": {},
   "source": [
    "### universal functions: mean, max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "historic-problem",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:31:28.007019Z",
     "start_time": "2021-07-07T12:31:28.003755Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = torch.tensor([1, -1, 1, -1.0])\n",
    "a.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "involved-disabled",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:32:17.675736Z",
     "start_time": "2021-07-07T12:32:17.670479Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(5)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = torch.tensor([1, -2, 3, 4, 5])\n",
    "b.max()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "timely-gothic",
   "metadata": {},
   "source": [
    "### mathematical functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "suspected-leisure",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:33:50.755591Z",
     "start_time": "2021-07-07T12:33:50.752945Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "swiss-clinic",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:34:14.669316Z",
     "start_time": "2021-07-07T12:34:14.663359Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.0000, 1.5708, 3.1416])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x= torch.tensor([0, np.pi/2, np.pi])\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "fleet-canberra",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:34:26.793788Z",
     "start_time": "2021-07-07T12:34:26.784075Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 0.0000e+00,  1.0000e+00, -8.7423e-08])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y=torch.sin(x)\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ecological-dynamics",
   "metadata": {},
   "source": [
    "### to plot math function: linspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "waiting-debut",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:35:34.820132Z",
     "start_time": "2021-07-07T12:35:34.808147Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-2., -1.,  0.,  1.,  2.])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# evenly spaced numbers into a specified interval\n",
    "torch.linspace(-2, 2, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "union-longitude",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:36:10.405076Z",
     "start_time": "2021-07-07T12:36:10.401536Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([-2.0000, -1.5000, -1.0000, -0.5000,  0.0000,  0.5000,  1.0000,  1.5000,\n",
       "         2.0000])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.linspace(-2, 2, 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "faced-moisture",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T12:38:10.935127Z",
     "start_time": "2021-07-07T12:38:10.673759Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe87c52b580>]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x = torch.linspace(0, 2 * np.pi, 100)\n",
    "y = torch.sin(x)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.plot(x.numpy(), y.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "miniature-problem",
   "metadata": {},
   "source": [
    "# Tensors 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "derived-bangkok",
   "metadata": {},
   "source": [
    "## Tensor creation in 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "rapid-peripheral",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:56:05.569618Z",
     "start_time": "2021-07-07T16:56:05.562718Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[11, 12, 13],\n",
       "        [21, 22, 23],\n",
       "        [31, 32, 33]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [ [11, 12, 13], [21, 22, 23], [31, 32, 33] ]\n",
    "A = torch.tensor(a)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "scheduled-activation",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:56:18.389963Z",
     "start_time": "2021-07-07T16:56:18.387221Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.ndimension()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "isolated-theology",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:56:22.788714Z",
     "start_time": "2021-07-07T16:56:22.786230Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 3])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "american-marine",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:56:30.096184Z",
     "start_time": "2021-07-07T16:56:30.090515Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 3])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "unknown-leadership",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:56:51.946819Z",
     "start_time": "2021-07-07T16:56:51.943866Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#number of elements\n",
    "A.numel()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "backed-chrome",
   "metadata": {},
   "source": [
    "## Indexing and slicing in 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "hindu-joshua",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:59:44.081356Z",
     "start_time": "2021-07-07T16:59:44.073815Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[11, 12, 13],\n",
       "        [21, 22, 23],\n",
       "        [31, 32, 33]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = [ [11, 12, 13], [21, 22, 23], [31, 32, 33] ]\n",
    "A = torch.tensor(a)\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "incident-utilization",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T16:59:44.450085Z",
     "start_time": "2021-07-07T16:59:44.445835Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([11, 12])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0, 0:2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "alike-passion",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:00:05.186009Z",
     "start_time": "2021-07-07T17:00:05.182826Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([23, 33])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1:3,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "executed-charlotte",
   "metadata": {},
   "source": [
    "## Basic operations in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "discrete-service",
   "metadata": {},
   "source": [
    "### addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "interstate-emphasis",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:02:12.218625Z",
     "start_time": "2021-07-07T17:02:12.209796Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[3, 1],\n",
       "        [1, 3]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1,0], [0,1]])\n",
    "Y = torch.tensor([[2,1], [1,2]])\n",
    "Z = X+Y\n",
    "Z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "frozen-instruction",
   "metadata": {},
   "source": [
    "### hadamard product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "handmade-journalist",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:04:17.171624Z",
     "start_time": "2021-07-07T17:04:17.165599Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[2, 0],\n",
       "        [0, 2]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z = X*Y\n",
    "Z"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "medium-cotton",
   "metadata": {},
   "source": [
    "### matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "fixed-position",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:07:41.520309Z",
     "start_time": "2021-07-07T17:07:41.507736Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[0, 2],\n",
       "        [0, 2]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = torch.tensor([ [0, 1, 1], [1, 0, 1]])\n",
    "B = torch.tensor([ [1, 1], [1, 1], [-1, 1]])\n",
    "C = torch.mm(A, B)\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "phantom-gothic",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:07:49.531218Z",
     "start_time": "2021-07-07T17:07:49.521697Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([2, 3])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "automatic-prince",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:07:56.815331Z",
     "start_time": "2021-07-07T17:07:56.809428Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3, 2])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "champion-finance",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-07T17:08:12.502884Z",
     "start_time": "2021-07-07T17:08:12.499799Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([3])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0,:].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "humanitarian-consultancy",
   "metadata": {},
   "source": [
    "# Derivatives in PyTorch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "revolutionary-particle",
   "metadata": {},
   "source": [
    "## Derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "endless-block",
   "metadata": {},
   "source": [
    "$$y(x)=x^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "helpful-fault",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T06:29:32.258894Z",
     "start_time": "2021-07-08T06:29:32.251191Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(4.)"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "x = torch.tensor(2., requires_grad=True)\n",
    "y = x ** 2\n",
    "\n",
    "y.backward()\n",
    "\n",
    "x.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "owned-point",
   "metadata": {},
   "source": [
    "$$z(x)=x^2+2x+1$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "understood-settlement",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:13:51.683533Z",
     "start_time": "2021-07-08T07:13:51.669663Z"
    }
   },
   "outputs": [
    {
     "ename": "RuntimeError",
     "evalue": "Only Tensors of floating point and complex dtype can require gradients",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-92-979d0f10c1e7>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtensor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrequires_grad\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      4\u001b[0m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mz\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbackward\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mRuntimeError\u001b[0m: Only Tensors of floating point and complex dtype can require gradients"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "x = torch.tensor(2, requires_grad=True)\n",
    "z = x**2 + 2*x + 1\n",
    "z.backward()\n",
    "x.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "straight-princeton",
   "metadata": {},
   "source": [
    "## Partial derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "seasonal-gamma",
   "metadata": {},
   "source": [
    "$$f(u, v)=uv+u^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "municipal-level",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial f(u,v)}{\\partial u} = v+2u$$\n",
    "\n",
    "$$\\frac{\\partial f(u,v)}{\\partial v} = u$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "cloudy-composition",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T06:34:16.765981Z",
     "start_time": "2021-07-08T06:34:16.763388Z"
    }
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "u = torch.tensor(1., requires_grad=True)\n",
    "v = torch.tensor(2., requires_grad=True)\n",
    "\n",
    "f = u*v + u**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "anonymous-billion",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T06:35:04.716970Z",
     "start_time": "2021-07-08T06:35:04.708392Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1.)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f.backward()\n",
    "v.grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "regulation-alarm",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T06:35:12.303031Z",
     "start_time": "2021-07-08T06:35:12.299579Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(4.)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u.grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "falling-weekend",
   "metadata": {},
   "source": [
    "# Simple Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protective-rachel",
   "metadata": {},
   "source": [
    "## Build a Dataset Class and Object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "healthy-harvard",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:23:22.849381Z",
     "start_time": "2021-07-08T07:23:22.838765Z"
    }
   },
   "outputs": [],
   "source": [
    "from torch.utils.data import Dataset\n",
    "\n",
    "class toy_set(Dataset):\n",
    "    def __init__(self, length=100, transform=None):\n",
    "        self.x = 2*torch.ones(length, 2)\n",
    "        self.y = torch.ones(length, 1)\n",
    "        self.len = length\n",
    "        self.transform = transform\n",
    "    def __getitem__(self, index):\n",
    "        sample=self.x[index], self.y[index]\n",
    "        if self.transform:\n",
    "            sample = self.transform(sample)\n",
    "        return sample\n",
    "    def __len__(self):\n",
    "        return self.len"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "liked-greeting",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:23:30.773729Z",
     "start_time": "2021-07-08T07:23:30.766989Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = toy_set()\n",
    "len(dataset)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "upset-oxygen",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:23:51.987546Z",
     "start_time": "2021-07-08T07:23:51.981526Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([2., 2.]), tensor([1.]))"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "infrared-opening",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:26:19.101950Z",
     "start_time": "2021-07-08T07:26:19.096655Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 x:tensor([2., 2.]), y:tensor([1.])\n",
      "1 x:tensor([2., 2.]), y:tensor([1.])\n",
      "2 x:tensor([2., 2.]), y:tensor([1.])\n"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    x, y = dataset[i]\n",
    "    print(f'{i} x:{x}, y:{y}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apparent-bulgaria",
   "metadata": {},
   "source": [
    "## Build a Dataset Transform (e.g. normalize or standardize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "modular-husband",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:29:56.220500Z",
     "start_time": "2021-07-08T07:29:56.208773Z"
    }
   },
   "outputs": [],
   "source": [
    "class add_mult(object):\n",
    "    def __init__(self, addx=1, muly=1):\n",
    "        self.addx = addx\n",
    "        self.muly = muly\n",
    "    def __call__(self, sample):\n",
    "        x=sample[0]\n",
    "        y=sample[1]\n",
    "        x=x+self.addx\n",
    "        y=y*self.muly\n",
    "        sample=x, y\n",
    "        return sample\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "illegal-brush",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:31:46.888628Z",
     "start_time": "2021-07-08T07:31:46.884002Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([3., 3.]), tensor([1.]))"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# applying the transform directly to the dataset\n",
    "dataset = toy_set()\n",
    "a_m = add_mult()\n",
    "x_, y_ = a_m(dataset[0])\n",
    "x_, y_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "polish-bridge",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:34:20.088291Z",
     "start_time": "2021-07-08T07:34:20.082888Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([3., 3.]), tensor([1.]))"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# automatically apply the transform\n",
    "a_m = add_mult()\n",
    "dataset_ = toy_set(transform=a_m)\n",
    "dataset_[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "first-remainder",
   "metadata": {},
   "source": [
    "## Compose Transforms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "liked-evanescence",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:36:43.774485Z",
     "start_time": "2021-07-08T07:36:43.768346Z"
    }
   },
   "outputs": [],
   "source": [
    "class mult(object):\n",
    "    def __init__(self, mul=100):\n",
    "        self.mul = mul\n",
    "\n",
    "    def __call__(self, sample):\n",
    "        x = sample[0]\n",
    "        y = sample[1]\n",
    "        x = x * self.mul\n",
    "        y = y * self.mul\n",
    "        sample = x, y\n",
    "        return sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "disabled-bouquet",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:37:46.897428Z",
     "start_time": "2021-07-08T07:37:46.839541Z"
    }
   },
   "outputs": [],
   "source": [
    "from torchvision import transforms\n",
    "\n",
    "data_transform = transforms.Compose([add_mult(), mult()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "empty-northern",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:38:45.785863Z",
     "start_time": "2021-07-08T07:38:45.776258Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([300., 300.]), tensor([100.]))"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#applying composed transform on data directly\n",
    "x_, y_ = data_transform(dataset[0])\n",
    "x_, y_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "neither-seating",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T07:39:56.136377Z",
     "start_time": "2021-07-08T07:39:56.132383Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([300., 300.]), tensor([100.]))"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#or directly in dataset\n",
    "dataset_tr = toy_set(transform=data_transform)\n",
    "dataset_tr[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "decent-mother",
   "metadata": {},
   "source": [
    "# Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "animated-speaker",
   "metadata": {},
   "source": [
    "## Dataset Class for images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "super-customer",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-08T08:05:00.020172Z",
     "start_time": "2021-07-08T08:05:00.017623Z"
    }
   },
   "outputs": [],
   "source": [
    "from PIL import Image\n",
    "import pandas as pd\n",
    "import os\n",
    "from matplotlib.pyplot import imshow\n",
    "from torch.utils.data import Dataset, DataLoader"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "optical-bumper",
   "metadata": {},
   "source": [
    "Download MNIST fashion dataset (only first 100 images)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "intense-collective",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:05:27.011320Z",
     "start_time": "2021-07-09T07:05:19.382724Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2021-07-09 09:05:19--  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/labs/Week1/data/img.tar.gz\n",
      "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104\n",
      "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n",
      "HTTP request sent, awaiting response... 304 Not Modified\n",
      "File ‘./resources/data/img.tar.gz’ not modified on server. Omitting download.\n",
      "\n",
      "--2021-07-09 09:05:20--  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/labs/Week1/data/index.csv\n",
      "Resolving cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)... 169.63.118.104\n",
      "Connecting to cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud (cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud)|169.63.118.104|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 1680905 (1,6M) [text/csv]\n",
      "Saving to: ‘index.csv’\n",
      "\n",
      "index.csv           100%[===================>]   1,60M   281KB/s    in 5,6s    \n",
      "\n",
      "2021-07-09 09:05:26 (292 KB/s) - ‘index.csv’ saved [1680905/1680905]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "!wget -N https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/labs/Week1/data/img.tar.gz -P ./resources/data/\n",
    "!tar -xf ./resources/data/img.tar.gz -C ./resources/data\n",
    "!wget  https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0110EN-SkillsNetwork/labs/Week1/data/index.csv -O index.csv\n",
    "!mv index.csv ./resources/data/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "technological-pearl",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:06:02.661933Z",
     "start_time": "2021-07-09T07:06:02.625452Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>category</th>\n",
       "      <th>image</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Ankle boot</td>\n",
       "      <td>img/fashion0.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>T-shirt</td>\n",
       "      <td>img/fashion1.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>T-shirt</td>\n",
       "      <td>img/fashion2.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Dress</td>\n",
       "      <td>img/fashion3.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>T-shirt</td>\n",
       "      <td>img/fashion4.png</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     category             image\n",
       "0  Ankle boot  img/fashion0.png\n",
       "1     T-shirt  img/fashion1.png\n",
       "2     T-shirt  img/fashion2.png\n",
       "3       Dress  img/fashion3.png\n",
       "4     T-shirt  img/fashion4.png"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "directory = \"./resources/data\"\n",
    "csv_file = \"index.csv\"\n",
    "csv_path = os.path.join(directory, csv_file)\n",
    "\n",
    "data_name = pd.read_csv(csv_path)\n",
    "data_name.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "id": "colored-guess",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T06:43:08.722434Z",
     "start_time": "2021-07-09T06:43:08.715138Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60000"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_name)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "id": "political-clothing",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:06:48.606071Z",
     "start_time": "2021-07-09T07:06:48.502545Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random image path ./resources/data/img/fashion93.png\n"
     ]
    },
    {
     "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": [
    "import random\n",
    "index_image = random.randint(0,99)\n",
    "image_path = os.path.join(directory, data_name.iloc[index_image]['image'])\n",
    "print(f'Random image path {image_path}')\n",
    "image = Image.open(image_path)\n",
    "plt.imshow(image, cmap='gray', vmin=0, vmax=255)\n",
    "plt.title(data_name.iloc[index_image]['category'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "intelligent-aaron",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:17:16.349993Z",
     "start_time": "2021-07-09T07:17:16.343748Z"
    }
   },
   "outputs": [],
   "source": [
    "class Dataset(Dataset):\n",
    "    def __init__(self, csv_file, data_dir, transform=None):\n",
    "        self.transform = transform\n",
    "        self.data_dir = data_dir\n",
    "        data_dir_csv_file = os.path.join(self.data_dir, csv_file)\n",
    "        self.data_name = pd.read_csv(data_dir_csv_file)\n",
    "        self.len = self.data_name.shape[0]\n",
    "    def __len__(self):\n",
    "        return self.len\n",
    "    def __getitem__(self, idx):\n",
    "        img_name=os.path.join(self.data_dir, self.data_name.iloc[idx, 1])\n",
    "        image = Image.open(img_name)\n",
    "        y = self.data_name.iloc[idx, 0]\n",
    "        if self.transform:\n",
    "            image = self.transform(image)\n",
    "        return image, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "different-example",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:17:18.064372Z",
     "start_time": "2021-07-09T07:17:18.034894Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<PIL.PngImagePlugin.PngImageFile image mode=L size=28x28 at 0x7FE8A766E6D0>,\n",
       " 'Ankle boot')"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset = Dataset(csv_file=csv_file, data_dir=directory)\n",
    "dataset[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "sophisticated-cambridge",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:17:18.648142Z",
     "start_time": "2021-07-09T07:17:18.640100Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=L size=28x28 at 0x7FE8A766E550>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "painful-ideal",
   "metadata": {},
   "source": [
    "## Torch Vision Transforms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "id": "least-psychiatry",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:17:19.753840Z",
     "start_time": "2021-07-09T07:17:19.719772Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1, 20, 20])"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torchvision.transforms as transforms\n",
    "transforms.CenterCrop(20)\n",
    "transforms.ToTensor()\n",
    "croptensor_data_transform = transforms.Compose( [ transforms.CenterCrop(20), transforms.ToTensor() ] )\n",
    "dataset = Dataset(csv_file=csv_file, data_dir=directory, transform=croptensor_data_transform)\n",
    "dataset[0][0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "historic-necessity",
   "metadata": {},
   "source": [
    "## Torch Vision Datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "id": "widespread-clearing",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-09T07:24:42.258821Z",
     "start_time": "2021-07-09T07:19:05.187131Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz to ./data/MNIST/raw/train-images-idx3-ubyte.gz\n"
     ]
    },
    {
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     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/train-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
      "Downloading http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz to ./data/MNIST/raw/train-labels-idx1-ubyte.gz\n"
     ]
    },
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/train-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw/t10k-images-idx3-ubyte.gz\n"
     ]
    },
    {
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       "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/t10k-images-idx3-ubyte.gz to ./data/MNIST/raw\n",
      "Downloading http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "de8339cf62654949bab3b5684c334f8f",
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       "version_minor": 0
      },
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       "HBox(children=(FloatProgress(value=1.0, bar_style='info', max=1.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracting ./data/MNIST/raw/t10k-labels-idx1-ubyte.gz to ./data/MNIST/raw\n",
      "Processing...\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "import torchvision.datasets as dsets\n",
    "dataset = dsets.MNIST(root='./data', train = False, download = True, transform = transforms.ToTensor())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bulgarian-review",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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