pytorch_basics.ipynb

{
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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XpmMgAzW-_Pz"
      },
      "source": [
        "**Note**: Some of the PyTorch code examples are digested from \n",
        "\n",
        "1. [Deep Learning with PyTorch: A 60 Minute Blitz](https://pytorch.org/tutorials/beginner/deep_learning_60min_blitz.html) \n",
        "2. [Github repo](https://github.com/deep-learning-with-pytorch/dlwpt-code) for \"Deep Learning with PyTorch\""
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DJ_eVZoImlZW"
      },
      "source": [
        "# Google Colab Basics\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nZP4FMTtmxEA"
      },
      "source": [
        "## Check the resources obtained from Collab"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9uMuftEImym3"
      },
      "source": [
        "Google colab is a free to use Jupyter notebook , that allows you to use free Tesla T4 GPU it also gives you a total of 12 GB of ram , and you can use it up to 12 hours in row"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BvTz5fe2m8cf"
      },
      "source": [
        "!lsb_release -a"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AnbX1PwPnDXl"
      },
      "source": [
        "!uname -r"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IfxfE5VQnExV"
      },
      "source": [
        "!lscpu | grep 'Model name'\n",
        "!lscpu | grep 'Socket(s):'\n",
        "!lscpu | grep 'Thread(s) per core'\n",
        "!lscpu | grep \"L3 cache\""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ORILkenqnIFX"
      },
      "source": [
        "!cat /proc/meminfo | grep 'MemAvailable'"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R7ClJ_wNnK7z"
      },
      "source": [
        "!df -h / | awk '{print $4}'"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bEjLUGTXnNaa"
      },
      "source": [
        "!nvidia-smi"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sPt5y71ynZTc"
      },
      "source": [
        "## Check the libs in Colab"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cLX4sEYbnaXo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "dfca4291-230d-48ba-bfd9-9effbc1eb146"
      },
      "source": [
        "import sys\n",
        "print('The python version is', sys.version)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The python version is 3.7.12 (default, Sep 10 2021, 00:21:48) \n",
            "[GCC 7.5.0]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r22pYH7zYqZm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a369deb-0f10-44fb-8381-fdd9b8e9ac4a"
      },
      "source": [
        "from __future__ import print_function\n",
        "import torch\n",
        "print(torch.__version__)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.10.0+cu111\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GXer5iQhvrV5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2521692-38ab-434d-8d5b-58dd82cca29e"
      },
      "source": [
        "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
        "print(device)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda:0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0UodTj2pdi1O"
      },
      "source": [
        "# Tensor Basics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WseF3aond2hV"
      },
      "source": [
        "### Initialization "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lRWYc7QpZL8X",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "3802b38e-f93e-4bfa-ad73-fae8d04de09e"
      },
      "source": [
        "# Construct a 5x3 matrix, uninitialized\n",
        "x = torch.empty(5, 3)\n",
        "print(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[1.0178e-35, 0.0000e+00, 0.0000e+00],\n",
            "        [0.0000e+00, 0.0000e+00, 0.0000e+00],\n",
            "        [0.0000e+00, 0.0000e+00, 2.8026e-45],\n",
            "        [0.0000e+00, 1.1210e-44, 0.0000e+00],\n",
            "        [1.4013e-45, 0.0000e+00, 0.0000e+00]])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WJDiat4XZ46Z",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "944dfa2d-a923-44e2-d7c1-594a4ac78441"
      },
      "source": [
        "x.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 3])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_2Y1mToyY2i-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "43924a99-ad25-41c3-91ec-37ad5e301f70"
      },
      "source": [
        "a = torch.ones(3, dtype=torch.long)\n",
        "a"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1, 1, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qc3LEFROeNry",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "191cd1d6-35ab-4b04-db02-ed8696ac2d96"
      },
      "source": [
        "x = torch.tensor([5.5, 3])\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([5.5000, 3.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PvKlP8QteWR0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "622bd522-913c-4649-e6dc-3eb108afbe5a"
      },
      "source": [
        "# Creating a tensor based on an existing tensor. These methods will reuse properties of the input tensor, e.g. dtype\n",
        "x = x.new_ones(5, 3, dtype=torch.double) # new_* methods take in sizes\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 1., 1.],\n",
              "        [1., 1., 1.],\n",
              "        [1., 1., 1.],\n",
              "        [1., 1., 1.],\n",
              "        [1., 1., 1.]], dtype=torch.float64)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rJiKyA52erYM",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "c990863a-beb5-4f31-a40c-5bb49733545d"
      },
      "source": [
        "x = torch.randn_like(x, dtype=torch.float)    # override dtype!\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-0.6125, -0.3408, -0.1856],\n",
              "        [ 0.3077,  0.0066,  1.3437],\n",
              "        [-0.8480,  0.8010, -0.1335],\n",
              "        [-1.0343,  0.1071,  0.4825],\n",
              "        [-0.0091, -0.4897, -2.8141]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5tMPFXiQfHZt"
      },
      "source": [
        "y = torch.rand(5, 3)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "96duNhqce_fX"
      },
      "source": [
        "### Operations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LODj3Hkje-2r",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "2bbadc96-a2e9-4758-82dd-895dc9d6e991"
      },
      "source": [
        "x + y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.1954,  0.3325,  0.7218],\n",
              "        [ 0.3231,  0.1257,  1.5167],\n",
              "        [ 0.1278,  1.7324,  0.3735],\n",
              "        [-0.9547,  0.9870,  1.1708],\n",
              "        [ 0.2119,  0.1096, -2.0860]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vmWkEqslfMGf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "58440cb0-a98f-4e5d-a527-36cbcda77356"
      },
      "source": [
        "torch.add(x, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.1954,  0.3325,  0.7218],\n",
              "        [ 0.3231,  0.1257,  1.5167],\n",
              "        [ 0.1278,  1.7324,  0.3735],\n",
              "        [-0.9547,  0.9870,  1.1708],\n",
              "        [ 0.2119,  0.1096, -2.0860]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gBO68XDUfQJ9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "00060c97-7111-48b0-c7f7-c790e30b3fbf"
      },
      "source": [
        "result = torch.empty(5, 3)\n",
        "torch.add(x, y, out=result)\n",
        "result"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.1954,  0.3325,  0.7218],\n",
              "        [ 0.3231,  0.1257,  1.5167],\n",
              "        [ 0.1278,  1.7324,  0.3735],\n",
              "        [-0.9547,  0.9870,  1.1708],\n",
              "        [ 0.2119,  0.1096, -2.0860]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qf4MQlrHfYXL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "eb4fa9bd-6d9a-4261-ee69-0c32bbf0aea5"
      },
      "source": [
        "y.add_(x)\n",
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.1954,  0.3325,  0.7218],\n",
              "        [ 0.3231,  0.1257,  1.5167],\n",
              "        [ 0.1278,  1.7324,  0.3735],\n",
              "        [-0.9547,  0.9870,  1.1708],\n",
              "        [ 0.2119,  0.1096, -2.0860]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NJ96AorCkMVY"
      },
      "source": [
        "### Numpy Interchangability"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "64_O4HBCjcML",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bfab6b30-1f04-4aa3-fe86-1d43e8accf06"
      },
      "source": [
        "a = torch.ones(5)\n",
        "a"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1., 1., 1., 1., 1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WFkfqzZVkTgc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3f8daa6f-65d8-4c13-f0ba-8e69bd0dfbf2"
      },
      "source": [
        "b = a.numpy()\n",
        "b"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 1., 1., 1., 1.], dtype=float32)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4vIm7NjHka4m",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "9b0fee00-2d1f-4ac7-c5ad-085d03dbf585"
      },
      "source": [
        "a.add_(1)\n",
        "print(a)\n",
        "print(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([2., 2., 2., 2., 2.])\n",
            "[2. 2. 2. 2. 2.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lW5FKZKvknd3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "acbd8619-7e16-4fbc-be0f-fb6557fa9c2b"
      },
      "source": [
        "import numpy as np\n",
        "a = np.ones(5)\n",
        "b = torch.from_numpy(a)\n",
        "np.add(a, 1, out=a)\n",
        "print(a)\n",
        "print(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[2. 2. 2. 2. 2.]\n",
            "tensor([2., 2., 2., 2., 2.], dtype=torch.float64)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I2-kqdv_dwkq"
      },
      "source": [
        "### Storage and Views"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0WITOHsvZRNm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "0eb46a37-d034-419a-a5ee-4b5b71655fb2"
      },
      "source": [
        "points = torch.FloatTensor([[4.0, 1.0], [5.0, 3.0], [2.0, 1.0]])\n",
        "points"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[4., 1.],\n",
              "        [5., 3.],\n",
              "        [2., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9wyoLlUHaqmg",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 136
        },
        "outputId": "43cc1742-2e19-457c-e495-500d26a1ccb6"
      },
      "source": [
        "points.storage()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 4.0\n",
              " 1.0\n",
              " 5.0\n",
              " 3.0\n",
              " 2.0\n",
              " 1.0\n",
              "[torch.FloatStorage of size 6]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uriuYNIvaxUS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "167e6f3c-8363-4a3b-8f68-b58a5fa16eeb"
      },
      "source": [
        "points_storage = points.storage()\n",
        "points_storage[0] = 2.0\n",
        "points"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[2., 1.],\n",
              "        [5., 3.],\n",
              "        [2., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7RMtISBYa5_n",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "3d5c7023-353e-4216-e5d8-e7b8c430cf52"
      },
      "source": [
        "points = torch.tensor([[4.0, 1.0], [5.0, 3.0], [2.0, 1.0]])\n",
        "second_point = points[1]\n",
        "second_point.storage_offset()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xsdW47Pabbra",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8b583fd1-012b-4d90-dbb8-460bb020d859"
      },
      "source": [
        "second_point.size()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u_R7wBGjbed_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "0832e59e-175e-4268-ef78-e5d3bdbf9641"
      },
      "source": [
        "second_point.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HRgKv1qbbhBe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "49c59ef3-e197-49e7-e83e-a4d0e4484cf6"
      },
      "source": [
        "# Stride is a tuple indicating the number of elements in the storage that have to be skipped when the index is increased by 1 in each dimension\n",
        "points.stride()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uHzwUYQkbjxF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7dd32a4a-d37d-4105-b35a-b2e7a2e12ced"
      },
      "source": [
        "second_point.stride()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4IIiyEPWcrZL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "33cc3f40-a7b6-4391-bd32-8e388b99a821"
      },
      "source": [
        "points = torch.tensor([[4.0, 1.0], [5.0, 3.0], [2.0, 1.0]])\n",
        "second_point = points[1].clone()\n",
        "second_point[0] = 10.0\n",
        "points"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[4., 1.],\n",
              "        [5., 3.],\n",
              "        [2., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xt1mYisncxVw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "31141767-e010-4773-eb31-283609905158"
      },
      "source": [
        "points_t = points.t()\n",
        "points_t"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[4., 5., 2.],\n",
              "        [1., 3., 1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WRMf946Gc1tQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "54410f8d-d714-46d4-919d-1a4267c825b1"
      },
      "source": [
        "id(points.storage()) == id(points_t.storage())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r6NfsY4Wc6Rk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e873a107-b852-4500-a431-75d171cd0cda"
      },
      "source": [
        "points.stride()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, 1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "heWqLO2gc8bY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1931745e-132b-4d67-b7b7-08269a6b8ccc"
      },
      "source": [
        "points_t.stride()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r2wyM55jc-hK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "35664a50-0146-4f55-a3a4-313a798f4c0a"
      },
      "source": [
        "points.is_contiguous()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r119HXjEdEx8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e033b4c9-efe2-4d87-c439-92f9853e47e1"
      },
      "source": [
        "points_t.is_contiguous()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Wbwyt4Q2jsOC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9365ad34-638b-44f1-8515-535c8eee978e"
      },
      "source": [
        "x = torch.randn(4, 4)\n",
        "y = x.view(16)\n",
        "z = x.view(-1, 8)  # the size -1 is inferred from other dimensions\n",
        "print(x.size(), y.size(), z.size())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.Size([4, 4]) torch.Size([16]) torch.Size([2, 8])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cCudreKkkzuZ"
      },
      "source": [
        "### CUDA Tensors"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h8t2zwPAdG5e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "04438fea-fd78-4367-a3ba-839dd3cab93b"
      },
      "source": [
        "if torch.cuda.is_available():\n",
        "    device = torch.device(\"cuda\")          # a CUDA device object\n",
        "    y = torch.ones_like(x, device=device)  # directly create a tensor on GPU\n",
        "    x = x.to(device)                       # or just use strings ``.to(\"cuda\")``\n",
        "    z = x + y\n",
        "    print(z)\n",
        "    print(z.to(\"cpu\", torch.double))       # ``.to`` can also change dtype together!"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([[-0.3412,  1.6253,  0.8647,  0.8041],\n",
            "        [ 0.4846, -0.0901,  1.0045, -0.0930],\n",
            "        [ 1.6945,  1.5010,  2.3046,  0.8209],\n",
            "        [ 1.3585,  1.1518,  1.9489,  0.4589]], device='cuda:0')\n",
            "tensor([[-0.3412,  1.6253,  0.8647,  0.8041],\n",
            "        [ 0.4846, -0.0901,  1.0045, -0.0930],\n",
            "        [ 1.6945,  1.5010,  2.3046,  0.8209],\n",
            "        [ 1.3585,  1.1518,  1.9489,  0.4589]], dtype=torch.float64)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y7v33EK7mRkm"
      },
      "source": [
        "# Autograd"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3PBoWP_Kmzxx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "45b65f0b-fad8-4dd6-f169-6b1382dc25fa"
      },
      "source": [
        "a = torch.randn(2, 2)\n",
        "a = ((a * 3) / (a - 1))\n",
        "print(a.requires_grad)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "False\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DgW5AJApnNCS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "90e759a2-3cfa-4a0e-9713-434ffe3591d1"
      },
      "source": [
        "a.requires_grad_(True)\n",
        "print(a.requires_grad)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "umBswn4DnPoO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f567acf5-ffc6-4701-c6e6-c9c964585cbb"
      },
      "source": [
        "b = (a * a).sum()\n",
        "print(b)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(11.7610, grad_fn=<SumBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1-78hYueoYDt"
      },
      "source": [
        "### Example for scaler-valued function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CKYqi3wjmTkA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "479e3494-d182-450a-c434-34862cf55449"
      },
      "source": [
        "x = torch.ones(2, 2, requires_grad=True)\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 1.],\n",
              "        [1., 1.]], requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sjWIsKf9mbUx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "78fe616a-cf55-44f8-81e7-2ef5fcd29759"
      },
      "source": [
        "y = x + 2\n",
        "print(y)\n",
        "print(y.grad_fn) # .grad_fn attribute that references a Function"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[3., 3.],\n",
            "        [3., 3.]], grad_fn=<AddBackward0>)\n",
            "<AddBackward0 object at 0x7f91db0c1250>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_vpNilJ_ofXm"
      },
      "source": [
        "$$ z = \\frac{1}{N} \\sum_{i=1}^N 3(x_i + 2)^2 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SE6WYqPimhJy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7a23e9e6-70f2-45ad-be96-9b95f5d891a0"
      },
      "source": [
        "z = y * y * 3\n",
        "out = z.mean()\n",
        "print(z)\n",
        "print(out)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[27., 27.],\n",
            "        [27., 27.]], grad_fn=<MulBackward0>)\n",
            "tensor(27., grad_fn=<MeanBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y4yRQN5hpnd9"
      },
      "source": [
        "$$ \\frac{\\partial z}{\\partial x_i} = \\frac{3}{2} (x_i + 2) $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "39CLLcbBnSFB"
      },
      "source": [
        "out.backward()  # same as out.backward(torch.tensor(1.))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XCZNmjaCnqsw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "de5e0159-7d64-4f2e-92a6-9b32aa4b2969"
      },
      "source": [
        "x.grad # = d(out)/dx"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[4.5000, 4.5000],\n",
              "        [4.5000, 4.5000]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J8hAcWHgq6oV"
      },
      "source": [
        "### Example of non-scalar-output function"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MVn0pKxnrosP"
      },
      "source": [
        "NOTE: `torch.autograd` is an engine for computing vector-Jacobian product:\n",
        "\n",
        "It means: if we have $\\vec{y}=f(\\vec{x})$, given any vector $v=\\left(\\begin{array}{ccc}\\frac{\\partial l}{\\partial y_{1}} & \\cdots & \\frac{\\partial l}{\\partial y_{m}}\\end{array}\\right)^{T}$, it can compute the gradient of $l$ with respect of $\\vec{x}$:\n",
        "\n",
        "$$\\begin{split}J^{T}\\cdot v=\\left(\\begin{array}{ccc}\n",
        " \\frac{\\partial y_{1}}{\\partial x_{1}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{1}}\\\\\n",
        " \\vdots & \\ddots & \\vdots\\\\\n",
        " \\frac{\\partial y_{1}}{\\partial x_{n}} & \\cdots & \\frac{\\partial y_{m}}{\\partial x_{n}}\n",
        " \\end{array}\\right)\\left(\\begin{array}{c}\n",
        " \\frac{\\partial l}{\\partial y_{1}}\\\\\n",
        " \\vdots\\\\\n",
        " \\frac{\\partial l}{\\partial y_{m}}\n",
        " \\end{array}\\right)=\\left(\\begin{array}{c}\n",
        " \\frac{\\partial l}{\\partial x_{1}}\\\\\n",
        " \\vdots\\\\\n",
        " \\frac{\\partial l}{\\partial x_{n}}\n",
        " \\end{array}\\right)\\end{split} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r7uP-QMrrKGk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "29282074-9dbc-4039-86e4-9c95770bdbee"
      },
      "source": [
        "x = torch.randn(3, requires_grad=True)\n",
        "y = x * 2\n",
        "while y.data.norm() < 1000:\n",
        "    y = y * 2\n",
        "print(x)\n",
        "print(y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([ 0.3952, -0.1307, -0.2266], requires_grad=True)\n",
            "tensor([1618.8090, -535.5025, -928.0955], grad_fn=<MulBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uhpBhZ4su50G",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b715df59-eb27-4663-9131-fd0040cacfc3"
      },
      "source": [
        "v = torch.tensor([0.1, 1.0, 0.0001], dtype=torch.float)\n",
        "y.backward(v)\n",
        "print(x.grad)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([4.0960e+02, 4.0960e+03, 4.0960e-01])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AmWG9fo6vms0"
      },
      "source": [
        "### Stop autograd if needed"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KuBRBNhsu8th",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8f9e9c4a-b07a-42c5-a139-1b2ef035263f"
      },
      "source": [
        "print(x.requires_grad)\n",
        "print((x ** 2).requires_grad)\n",
        "\n",
        "with torch.no_grad():\n",
        "    print((x ** 2).requires_grad)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "True\n",
            "False\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X4y7-PdFvrLb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "761e6e24-babc-4496-ede0-c54e134ec8ec"
      },
      "source": [
        "print(x.requires_grad)\n",
        "y = x.detach()\n",
        "print(y.requires_grad)\n",
        "print(x.eq(y).all())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n",
            "False\n",
            "tensor(True)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9qflSNcBSqxP"
      },
      "source": [
        "### Using autograd to solve an optimization problem"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZRomBJY1S0GV"
      },
      "source": [
        "import numpy as np\n",
        "import torch"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yz-mOc6g4TF2"
      },
      "source": [
        "import torch.optim as optim\n",
        "dir(optim)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ehDdplUCTkRH"
      },
      "source": [
        "We want to solve the minumum value of the function $$ f(x) = a x^2 + b x + c $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X_HTkBoSTOb1"
      },
      "source": [
        "def f(x):\n",
        "    result = a*torch.pow(x,2) + b*x + c\n",
        "    return(result)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "py8gwzF5S4cL"
      },
      "source": [
        "x = torch.tensor(0.0,requires_grad = True)\n",
        "a = torch.tensor(2.0)\n",
        "b = torch.tensor(-5.0)\n",
        "c = torch.tensor(3.0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eN0lRzGVTJun"
      },
      "source": [
        "optimizer = torch.optim.SGD(params=[x],lr = 0.01)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KFIwN626TLnD"
      },
      "source": [
        "for i in range(500):\n",
        "    optimizer.zero_grad()\n",
        "    y = f(x)\n",
        "    y.backward()\n",
        "    optimizer.step()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XoObnvBlTbIN",
        "outputId": "8556d217-8ddb-473a-a199-ec735a937ec4"
      },
      "source": [
        "print(\"y=\",f(x).data,\";\",\"x=\",x.data)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y= tensor(-0.1250) ; x= tensor(1.2500)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xiSmJJTA2cnx"
      },
      "source": [
        "# Neural Networks\n",
        "\n",
        "Fahrenheit-Celsius Conversion Problem as illustration"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ih3_30yh2qHC"
      },
      "source": [
        "## Data preparation\n",
        "\n",
        "Assuming we collected the following data over the weeks:\n",
        "\n",
        "*   `t_c`: known temperature in Celsius\n",
        "*   `t_u`: 1 wall-mounted analog thermometer without unit"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HOwz-Z6S2nEF"
      },
      "source": [
        "t_c = [0.5,  14.0, 15.0, 28.0, 11.0,  8.0,  3.0, -4.0,  6.0, 13.0, 21.0]\n",
        "t_u = [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mBllXQqUNlL4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "outputId": "621aaa53-0b2b-42a0-f8a5-6e36d5849e0e"
      },
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "t_u_range = np.linspace(20., 90.)\n",
        "t_c_range = (t_u_range -32) * 5/9\n",
        "\n",
        "fig = plt.figure(dpi=150)\n",
        "plt.xlabel(\"Fahrenheit\")\n",
        "plt.ylabel(\"Celsius\")\n",
        "plt.plot(t_u, t_c, 'o', label='Collected Data')\n",
        "plt.plot(t_u_range, t_c_range, '--', label='True relation')\n",
        "plt.legend(loc='best')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3f1c0263c8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 900x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l3twByb1OIYi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 255
        },
        "outputId": "1d522c6c-4bca-4ab2-afad-5f49f37f7f99"
      },
      "source": [
        "print('t_u as Numpy list:', t_u)\n",
        "\n",
        "t_c = torch.tensor(t_c).unsqueeze(1) \n",
        "t_u = torch.tensor(t_u).unsqueeze(1) \n",
        "t_c = t_c.to(device)\n",
        "t_u = t_u.to(device)\n",
        "\n",
        "print(\"t_u after unsqueeze:\\n\", t_u)\n",
        "t_u.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "t_u as Numpy list: [35.7, 55.9, 58.2, 81.9, 56.3, 48.9, 33.9, 21.8, 48.4, 60.4, 68.4]\n",
            "t_u after unsqueeze:\n",
            " tensor([[35.7000],\n",
            "        [55.9000],\n",
            "        [58.2000],\n",
            "        [81.9000],\n",
            "        [56.3000],\n",
            "        [48.9000],\n",
            "        [33.9000],\n",
            "        [21.8000],\n",
            "        [48.4000],\n",
            "        [60.4000],\n",
            "        [68.4000]], device='cuda:0')\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([11, 1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kyH9Jkf-3B8q",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d5c3e573-afa8-4868-f78e-dea0e881dde9"
      },
      "source": [
        "n_samples = t_u.shape[0]\n",
        "n_val = int(0.2 * n_samples)\n",
        "\n",
        "shuffled_indices = torch.randperm(n_samples)\n",
        "\n",
        "train_indices = shuffled_indices[:-n_val]\n",
        "val_indices = shuffled_indices[-n_val:]\n",
        "\n",
        "train_indices, val_indices"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([ 7,  5,  1,  6,  8, 10,  9,  4,  2]), tensor([3, 0]))"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tui3iHOA3IMd"
      },
      "source": [
        "t_u_train = t_u[train_indices]\n",
        "t_c_train = t_c[train_indices]\n",
        "\n",
        "t_u_val = t_u[val_indices]\n",
        "t_c_val = t_c[val_indices]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XeqZJtRjW6Mv"
      },
      "source": [
        "**Watch out** for the scales of weights and biases. If they are in the different scaled space, one learning rate that is large for one enough to meaningfully update one will be so large as to be unstable for the other. \n",
        "\n",
        "The common way is to do the normalization to the data. But here it seems that a simple rescaling by a factor of ten can make the gradients of both weights and biases in the same magnitudes. That would be good enough for our demonstration."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YZ_kyP8rTijZ"
      },
      "source": [
        "t_un_train = 0.1 * t_u_train\n",
        "t_un_val = 0.1 * t_u_val"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f1mgkEsXJmXq"
      },
      "source": [
        "## Using Neural Network model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_1hkkwRw3gfj"
      },
      "source": [
        "import torch.nn as nn\n",
        "dir(nn)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ryUmQUQDJ3Q-"
      },
      "source": [
        "We use the simplest linear NN model with one hidden layer.\n",
        "<img src=\"https://huqy.github.io/deep_learning_workshops/nn_c2f.svg\" alt=\"Linear NN model\" style=\"width: 500px;\"/>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zdTM7yd_3yRO",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        },
        "outputId": "652c18ef-3e0b-4d22-cf14-b8fa2742bc81"
      },
      "source": [
        "from collections import OrderedDict\n",
        "\n",
        "seq_model = nn.Sequential(OrderedDict([\n",
        "    ('hidden_linear', nn.Linear(1, 8)),\n",
        "    ('hidden_activation', nn.Tanh()),\n",
        "    ('output_linear', nn.Linear(8, 1))\n",
        "]))\n",
        "\n",
        "seq_model.to(device)\n",
        "\n",
        "seq_model"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Sequential(\n",
              "  (hidden_linear): Linear(in_features=1, out_features=8, bias=True)\n",
              "  (hidden_activation): Tanh()\n",
              "  (output_linear): Linear(in_features=8, out_features=1, bias=True)\n",
              ")"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cF0lU1Cg39jA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        },
        "outputId": "ca427a15-23b7-42c2-87c2-3f29002ba720"
      },
      "source": [
        "for name, param in seq_model.named_parameters():\n",
        "    print(name, param.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "hidden_linear.weight torch.Size([8, 1])\n",
            "hidden_linear.bias torch.Size([8])\n",
            "output_linear.weight torch.Size([1, 8])\n",
            "output_linear.bias torch.Size([1])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SIfs08P64C7X",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "93eaffb0-5919-4a0a-eedc-ea07d75f4f26"
      },
      "source": [
        "seq_model.output_linear.bias"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Parameter containing:\n",
              "tensor([-0.2060], device='cuda:0', requires_grad=True)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U5bO7FujOap_"
      },
      "source": [
        "## Training"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cmjdNO6r4bYB"
      },
      "source": [
        "def training_loop(n_epochs, optimizer, model, loss_fn, t_u_train, t_u_val, t_c_train, t_c_val):\n",
        "    for epoch in range(1, n_epochs + 1):\n",
        "\n",
        "        t_p_train = model(t_u_train) \n",
        "        loss_train = loss_fn(t_p_train, t_c_train)\n",
        "\n",
        "        t_p_val = model(t_u_val) \n",
        "        loss_val = loss_fn(t_p_val, t_c_val)\n",
        "        \n",
        "        optimizer.zero_grad()\n",
        "        loss_train.backward() \n",
        "        optimizer.step()\n",
        "\n",
        "        if epoch == 1 or epoch % 1000 == 0:\n",
        "            print('Epoch {}, Training loss {}, Validation loss {}'.format(\n",
        "                epoch, float(loss_train), float(loss_val)))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JCsYuvb24GyK",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 323
        },
        "outputId": "d237e37a-5efe-4ef9-f6f3-890a6e262b39"
      },
      "source": [
        "optimizer = optim.SGD(seq_model.parameters(), lr=1e-3) \n",
        "\n",
        "training_loop(\n",
        "    n_epochs = 5000, \n",
        "    optimizer = optimizer,\n",
        "    model = seq_model,\n",
        "    loss_fn = nn.MSELoss(),\n",
        "    t_u_train = t_un_train,\n",
        "    t_u_val = t_un_val, \n",
        "    t_c_train = t_c_train,\n",
        "    t_c_val = t_c_val)\n",
        "    \n",
        "print('output', seq_model(t_un_val))\n",
        "print('answer', t_c_val)\n",
        "print('hidden', seq_model.hidden_linear.weight.grad)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Epoch 1, Training loss 168.82614135742188, Validation loss 430.9350891113281\n",
            "Epoch 1000, Training loss 5.3353681564331055, Validation loss 56.425514221191406\n",
            "Epoch 2000, Training loss 3.143742322921753, Validation loss 27.245527267456055\n",
            "Epoch 3000, Training loss 2.550266981124878, Validation loss 17.77342987060547\n",
            "Epoch 4000, Training loss 2.2472312450408936, Validation loss 12.695697784423828\n",
            "Epoch 5000, Training loss 2.3520495891571045, Validation loss 9.433873176574707\n",
            "output tensor([[23.6293],\n",
            "        [ 2.1584]], device='cuda:0', grad_fn=<AddmmBackward>)\n",
            "answer tensor([[28.0000],\n",
            "        [ 0.5000]], device='cuda:0')\n",
            "hidden tensor([[ 1.8398e+00],\n",
            "        [ 1.7023e+00],\n",
            "        [ 2.3202e+01],\n",
            "        [-1.2213e+01],\n",
            "        [-1.1468e-02],\n",
            "        [-1.9977e+01],\n",
            "        [-2.1008e+00],\n",
            "        [ 8.6864e-01]], device='cuda:0')\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m5knIqr04hVS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 579
        },
        "outputId": "c2bda5b0-ac1f-426e-91db-a0d774645619"
      },
      "source": [
        "from matplotlib import pyplot as plt\n",
        "\n",
        "t_range = torch.arange(20., 90.).unsqueeze(1)\n",
        "t_range = t_range.to(device)\n",
        "\n",
        "t_u_range = np.linspace(20., 90.)\n",
        "t_c_range = (t_u_range -32) * 5/9\n",
        "\n",
        "fig = plt.figure(dpi=150)\n",
        "plt.xlabel(\"Fahrenheit\")\n",
        "plt.ylabel(\"Celsius\")\n",
        "plt.plot(t_u.cpu().numpy(), t_c.cpu().numpy(), 'o', label=\"Collected data\")\n",
        "plt.plot(t_range.cpu().numpy(), seq_model(0.1 * t_range).detach().cpu().numpy(), 'c-', label=\"Prediction curve from NN\")\n",
        "plt.plot(t_u.cpu().numpy(), seq_model(0.1 * t_u).detach().cpu().numpy(), 'kx', label=\"Predicted data from NN\")\n",
        "plt.plot(t_u_range, t_c_range, '--', label=\"Known truth\")\n",
        "plt.legend(loc='best')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3f15309e48>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 900x600 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}