PyTorch_course_1.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyM+l+JkH5rAVL1sPRIEqYwk",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    },
    "accelerator": "GPU",
    "gpuClass": "standard"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/andysingal/PyTorch-ML/blob/main/PyTorch_course_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#What is PyTorch ?\n",
        "PyTorch is a python library for scientific computing that offers flexibility and speed. It's two main offerings are a high level tensor library with strong GPU acceleration and a automatic differentiation system for computational graphs.\n",
        "\n",
        "Reasons to use:\n",
        "\n",
        "Deep python integration with minimal framework overhead and links with external libraries like NVIDIA (CuDNN, etc.).\n",
        "\n",
        "Imperative style makes it very flexible and transparent. You see exactly what is going to be run.\n",
        "\n",
        "Dynamic computation graphs makes a a graph for each instance (or minibatch) and is efficient for tasks with variable amounts of work per sample.\n",
        "\n"
      ],
      "metadata": {
        "id": "Vju1I8aZrr9i"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!pip install d2l==1.0.0b0\n"
      ],
      "metadata": {
        "id": "KLx230rpTEXz"
      },
      "execution_count": 77,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "%%capture\n",
        "!pip install pycrayon"
      ],
      "metadata": {
        "id": "eqo5VHbTsr_1"
      },
      "execution_count": 78,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 79,
      "metadata": {
        "id": "ibndmllRrXLi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f7030a68-4709-436c-dab5-ef5bdffd5514"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "ERROR:root:File `'plot_conf.py'` not found.\n"
          ]
        }
      ],
      "source": [
        "import sys\n",
        "import os\n",
        "import sys\n",
        "import random\n",
        "import time\n",
        "import math\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pylab as pl\n",
        "\n",
        "%matplotlib inline\n",
        "from matplotlib_inline import backend_inline\n",
        "from d2l import torch as d2l\n",
        "\n",
        "\n",
        "from pycrayon import (\n",
        "    CrayonClient,\n",
        ")\n",
        "\n",
        "from IPython import (\n",
        "    display,\n",
        ")\n",
        "\n",
        "from IPython.display import (\n",
        "    Image,\n",
        "    clear_output,\n",
        ")\n",
        "\n",
        "sys.path.insert(0, '..')\n",
        "# get matplotlib configuration\n",
        "%matplotlib inline\n",
        "%run plot_conf.py"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.utils.data\n",
        "import torch.nn as nn\n",
        "import torch.nn.functional as F\n",
        "import torch.optim as optim\n",
        "from torch.autograd import (\n",
        "    Variable,\n",
        ")\n",
        "from torch.nn import (\n",
        "    init,\n",
        ")"
      ],
      "metadata": {
        "id": "5OPk8TPmrdxU"
      },
      "execution_count": 80,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#PyTorch basics\n",
        "http://pytorch.org/docs/\n",
        "\n",
        "Tensors"
      ],
      "metadata": {
        "id": "bXPRg2PbuUFq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.arange(12, dtype=torch.float32)\n",
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-jDN9g3gslGM",
        "outputId": "a30fea09-da1f-481e-f23b-e1baaf641980"
      },
      "execution_count": 81,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11.])"
            ]
          },
          "metadata": {},
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Each of these values is called an element of the tensor. The tensor x contains 12 elements. We can inspect the total number of elements in a tensor via its numel method."
      ],
      "metadata": {
        "id": "EQbJLojftAI6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x.numel()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QmgWuSsAtB7u",
        "outputId": "d0f92cb2-aad6-4025-b392-65c3eb5c0e69"
      },
      "execution_count": 82,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {},
          "execution_count": 82
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = x.reshape(3, 4)"
      ],
      "metadata": {
        "id": "-qPtxd1XtEzo"
      },
      "execution_count": 83,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#SLICING"
      ],
      "metadata": {
        "id": "VynDte-lwzfT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X[-1],X[1:3]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5kHksPtJwkvS",
        "outputId": "6fe742a2-7511-434d-ff59-4e648f3781ec"
      },
      "execution_count": 84,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([ 8.,  9., 10., 11.]), tensor([[ 4.,  5.,  6.,  7.],\n",
              "         [ 8.,  9., 10., 11.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 84
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X[1, 2] = 17\n",
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wfIPOpx1wwyH",
        "outputId": "0d3a3521-a485-4582-8ce6-e91d2a24799b"
      },
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.,  1.,  2.,  3.],\n",
              "        [ 4.,  5., 17.,  7.],\n",
              "        [ 8.,  9., 10., 11.]])"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.zeros((2, 3, 4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PoGDIkPLt8iT",
        "outputId": "ed62b884-ee46-45fe-d275-cebb33b14a3c"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[0., 0., 0., 0.],\n",
              "         [0., 0., 0., 0.],\n",
              "         [0., 0., 0., 0.]],\n",
              "\n",
              "        [[0., 0., 0., 0.],\n",
              "         [0., 0., 0., 0.],\n",
              "         [0., 0., 0., 0.]]])"
            ]
          },
          "metadata": {},
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# tensor of ones\n",
        "x= torch.ones(4,3)\n",
        "print(x.size(),x.size(0),x.size(1),x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P2V1nOljuGDO",
        "outputId": "19c19f0c-77f1-4a23-bcb6-f8d25313b8ad"
      },
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([4, 3]) 4 3 tensor([[1., 1., 1.],\n",
            "        [1., 1., 1.],\n",
            "        [1., 1., 1.],\n",
            "        [1., 1., 1.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# random tensors\n",
        "w = torch.rand(3, 2)\n",
        "print(w)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_Pi_H5gSvgWy",
        "outputId": "175860c5-e25f-4439-f4cb-81745eabd2d9"
      },
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[0.5544, 0.5574],\n",
            "        [0.1269, 0.5309],\n",
            "        [0.9862, 0.6265]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.randn(3, 4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9vWUwT2awSrI",
        "outputId": "31bc53a8-4f7e-4410-94a2-3221e3a99add"
      },
      "execution_count": 89,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.1969, -1.4121,  0.1466,  0.2291],\n",
              "        [ 0.0720,  0.1270,  0.7452, -0.8531],\n",
              "        [ 1.1145,  0.8279,  1.5421,  0.1909]])"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = torch.tensor([[2, 1, 4, 3], [1, 2, 3, 4], [4, 3, 2, 1]])\n",
        "a.ndim,a.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "10nWoF5DwXw1",
        "outputId": "71546b4e-de94-4431-8685-7f7815219015"
      },
      "execution_count": 90,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(2, torch.Size([3, 4]))"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.arange(start=1, end=11,step=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W2CWIt9VIRfP",
        "outputId": "92a9719b-f6f0-4984-c4b5-26ddc9e7cb78"
      },
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "float_tensor = torch.tensor([3.0,6.0,9.0],\n",
        "                            dtype=None, device=None,requires_grad=False)\n"
      ],
      "metadata": {
        "id": "7Ub_ppP8LvTK"
      },
      "execution_count": 92,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Tensor aggregation"
      ],
      "metadata": {
        "id": "38oaMKxB4MPg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a tensor\n",
        "x1 = torch.arange(0, 100, 10)\n",
        "x1"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "miRNYxIW4PIM",
        "outputId": "e0b4ee47-268d-4942-abf8-4737ac4a8796"
      },
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0, 10, 20, 30, 40, 50, 60, 70, 80, 90])"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.max()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4BsaUVRy5g7c",
        "outputId": "35bcd697-816e-4188-a1a1-0164e2b89734"
      },
      "execution_count": 94,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x.type(torch.float32).mean()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I_F91zq05rMs",
        "outputId": "61b9ec1d-54ee-4ef5-a563-624e63f8b6fb"
      },
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#position \n",
        "x.argmin(),x.argmax()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PLdKjOSL936q",
        "outputId": "c95bdfcd-c569-4e28-d22a-ff1f0f935b5c"
      },
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0), tensor(0))"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x2 = torch.arange(1,10)\n",
        "x2, x2.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b78VZ1WFDIw_",
        "outputId": "e76d84a5-f5e1-4374-c9e7-ae6dd2519e84"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([1, 2, 3, 4, 5, 6, 7, 8, 9]), torch.Size([9]))"
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_reshaped = x2.reshape(1,9)\n",
        "x_reshaped.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jVYZEQZjFMG9",
        "outputId": "8adec552-2dad-42ab-ca53-b107e6f1663a"
      },
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([1, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_squeezed = x_reshaped.squeeze()"
      ],
      "metadata": {
        "id": "wwavQ_qsKDi6"
      },
      "execution_count": 99,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"Previous tensor: {x_squeezed}\")\n",
        "print(f\"Previous shape: {x_squeezed.shape}\")\n",
        "\n",
        "## Add an extra dimension with unsqueeze\n",
        "x_unsqueezed = x_squeezed.unsqueeze(dim=0)\n",
        "print(f\"\\nNew tensor: {x_unsqueezed}\")\n",
        "print(f\"New shape: {x_unsqueezed.shape}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "snP2BD_DLXZy",
        "outputId": "31212610-3b85-41f8-f0f4-b311b38cffbe"
      },
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Previous tensor: tensor([1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
            "Previous shape: torch.Size([9])\n",
            "\n",
            "New tensor: tensor([[1, 2, 3, 4, 5, 6, 7, 8, 9]])\n",
            "New shape: torch.Size([1, 9])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Create tensor with specific shape\n",
        "x_original = torch.rand(size=(224, 224, 3))\n",
        "\n",
        "# Permute the original tensor to rearrange the axis order\n",
        "x_permuted = x_original.permute(2, 0, 1) # shifts axis 0->1, 1->2, 2->0\n",
        "\n",
        "print(f\"Previous shape: {x_original.shape}\")\n",
        "print(f\"New shape: {x_permuted.shape}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rb7S3wF1LlGV",
        "outputId": "c27a7d2c-c012-479e-fd28-97dbeeb99f16"
      },
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Previous shape: torch.Size([224, 224, 3])\n",
            "New shape: torch.Size([3, 224, 224])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_original[0,0,0],x_permuted[0,0,0]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2JDkFKt1Npfy",
        "outputId": "820fd035-9a46-40aa-c326-58aa2ddcc685"
      },
      "execution_count": 102,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.7741), tensor(0.7741))"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x3 = torch.arange(1,10).reshape(1,3,3)\n",
        "x3, x3.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RwJSulrAO9rs",
        "outputId": "0142c994-01d3-4a39-f273-e7a8462beeb0"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[[1, 2, 3],\n",
              "          [4, 5, 6],\n",
              "          [7, 8, 9]]]), torch.Size([1, 3, 3]))"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x3[0][2][2]\n",
        "\n",
        "x3[:,:,2]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rvfLy9nOP4m8",
        "outputId": "795dd471-92ba-4203-daf5-7aa267ea86d2"
      },
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[3, 6, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "array = np.arange(1.0,8.0)\n",
        "tensor = torch.from_numpy(array)\n",
        "array,tensor"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cU7tau4fRdMD",
        "outputId": "bbabc489-063f-4030-df36-0181f6870ce4"
      },
      "execution_count": 105,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([1., 2., 3., 4., 5., 6., 7.]),\n",
              " tensor([1., 2., 3., 4., 5., 6., 7.], dtype=torch.float64))"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Tensor operations"
      ],
      "metadata": {
        "id": "UMjWU2x6yMUo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "torch.exp(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IFPXoK7sxAaX",
        "outputId": "1d2c7e91-5892-42ae-919a-cd4382715802"
      },
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[2.7183, 2.7183, 2.7183],\n",
              "        [2.7183, 2.7183, 2.7183],\n",
              "        [2.7183, 2.7183, 2.7183],\n",
              "        [2.7183, 2.7183, 2.7183]])"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.tensor([1.0, 2, 4, 8])\n",
        "y = torch.tensor([2, 2, 2, 2])\n",
        "x + y, x - y, x * y, x / y, x ** y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sWBQ8GaXxYam",
        "outputId": "a9017285-fa45-462e-b55c-31d531d7add6"
      },
      "execution_count": 107,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([ 3.,  4.,  6., 10.]),\n",
              " tensor([-1.,  0.,  2.,  6.]),\n",
              " tensor([ 2.,  4.,  8., 16.]),\n",
              " tensor([0.5000, 1.0000, 2.0000, 4.0000]),\n",
              " tensor([ 1.,  4., 16., 64.]))"
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# tensor addition\n",
        "print(torch.add(x, x))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pA5CTqtAx9tE",
        "outputId": "b4342330-bfa0-447b-fcd6-c660d78921fd"
      },
      "execution_count": 108,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([ 2.,  4.,  8., 16.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# # matrix multiplication\n",
        "# z = x.mm(w) \n",
        "# print(z)"
      ],
      "metadata": {
        "id": "kZ2OzLBFypC2"
      },
      "execution_count": 109,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.arange(12,dtype=torch.float32).reshape(3,4)\n",
        "Y = torch.tensor([[2.0, 1, 4, 3], [1, 2, 3, 4], [4, 3, 2, 1]])\n",
        "torch.cat((X, Y), dim=0), torch.cat((X, Y), dim=1)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fG7f7VoGxkZO",
        "outputId": "37031473-1281-4382-89c4-ed76a5568ef8"
      },
      "execution_count": 110,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[ 0.,  1.,  2.,  3.],\n",
              "         [ 4.,  5.,  6.,  7.],\n",
              "         [ 8.,  9., 10., 11.],\n",
              "         [ 2.,  1.,  4.,  3.],\n",
              "         [ 1.,  2.,  3.,  4.],\n",
              "         [ 4.,  3.,  2.,  1.]]),\n",
              " tensor([[ 0.,  1.,  2.,  3.,  2.,  1.,  4.,  3.],\n",
              "         [ 4.,  5.,  6.,  7.,  1.,  2.,  3.,  4.],\n",
              "         [ 8.,  9., 10., 11.,  4.,  3.,  2.,  1.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = torch.arange(3).reshape((3,1))\n",
        "b = torch.arange(2).reshape((1,2))\n",
        "a, b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xHWOubV8ybEK",
        "outputId": "4dcdce3c-a8ff-47e7-ffe8-3db3cd3abd9d"
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0],\n",
              "         [1],\n",
              "         [2]]), tensor([[0, 1]]))"
            ]
          },
          "metadata": {},
          "execution_count": 111
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#RANDOMNESS"
      ],
      "metadata": {
        "id": "LoP9ByykkawA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "torch.rand(3,3)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8WlnpHMyjmns",
        "outputId": "a05e4e85-6659-4963-be1e-4f5be1280373"
      },
      "execution_count": 112,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.8033, 0.6779, 0.1668],\n",
              "        [0.6201, 0.0718, 0.9028],\n",
              "        [0.1886, 0.9134, 0.6592]])"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "random_tensor_A = torch.rand(3,4)\n",
        "random_tensor_B = torch.rand(3,4)\n",
        "random_tensor_A == random_tensor_B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ntHfCdEjkcqK",
        "outputId": "9f84be18-0f1b-4ae2-ecad-2653ff18bbcc"
      },
      "execution_count": 113,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[False, False, False, False],\n",
              "        [False, False, False, False],\n",
              "        [False, False, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Run the code in this section. Change the conditional statement X == Y to X < Y or X > Y, and then see what kind of tensor you can get."
      ],
      "metadata": {
        "id": "39LrDQ8K1He4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.arange(15).reshape(5,3)\n",
        "\n",
        "Y = torch.arange(15, 0, -1).reshape(5,3)\n",
        "\n",
        "X == Y, X > Y, X < Y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "42G9wymvzEyN",
        "outputId": "74e84604-b9e4-4f90-f085-5227a144245c"
      },
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[False, False, False],\n",
              "         [False, False, False],\n",
              "         [False, False, False],\n",
              "         [False, False, False],\n",
              "         [False, False, False]]), tensor([[False, False, False],\n",
              "         [False, False, False],\n",
              "         [False, False,  True],\n",
              "         [ True,  True,  True],\n",
              "         [ True,  True,  True]]), tensor([[ True,  True,  True],\n",
              "         [ True,  True,  True],\n",
              "         [ True,  True, False],\n",
              "         [False, False, False],\n",
              "         [False, False, False]]))"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Replace the two tensors that operate by element in the broadcasting mechanism with other shapes, e.g., 3-dimensional tensors. Is the result the same as expected?"
      ],
      "metadata": {
        "id": "Fxr7xJ741Qk5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.arange(8).reshape(4, 2, 1)\n",
        "Y = torch.arange(8).reshape(1, 2 ,4)\n",
        "\n",
        "print(f\"{X}, \\n\\n\\n{Y}, \\n\\n\\n{X + Y}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ibt0ywiJz_zS",
        "outputId": "fa44ddd2-22c0-44ac-ef20-d09f944f19c4"
      },
      "execution_count": 115,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[[0],\n",
            "         [1]],\n",
            "\n",
            "        [[2],\n",
            "         [3]],\n",
            "\n",
            "        [[4],\n",
            "         [5]],\n",
            "\n",
            "        [[6],\n",
            "         [7]]]), \n",
            "\n",
            "\n",
            "tensor([[[0, 1, 2, 3],\n",
            "         [4, 5, 6, 7]]]), \n",
            "\n",
            "\n",
            "tensor([[[ 0,  1,  2,  3],\n",
            "         [ 5,  6,  7,  8]],\n",
            "\n",
            "        [[ 2,  3,  4,  5],\n",
            "         [ 7,  8,  9, 10]],\n",
            "\n",
            "        [[ 4,  5,  6,  7],\n",
            "         [ 9, 10, 11, 12]],\n",
            "\n",
            "        [[ 6,  7,  8,  9],\n",
            "         [11, 12, 13, 14]]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#LINEAR ALGEBRA\n",
        "https://medium.com/codex/tensor-basics-in-pytorch-252a34288f2"
      ],
      "metadata": {
        "id": "1Oq1_EYjBsP6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.tensor(3.0)\n",
        "y = torch.tensor(2.0)\n",
        "x + y, x * y, x / y, x**y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CxEXcWS7BuyI",
        "outputId": "194dd842-03f8-4253-b102-729c5974dd94"
      },
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(5.), tensor(6.), tensor(1.5000), tensor(9.))"
            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Vectors\n",
        "For our purposes, you can think of vectors as fixed-length arrays of scalars. As with their code counterparts, we call these values the elements of the vector (synonyms include entries and components). When vectors represent examples from real-world datasets, their values hold some real-world significance. For example, if we were training a model to predict the risk of a loan defaulting, we might associate each applicant with a vector whose components correspond to quantities like their income, length of employment, or number of previous defaults. If we were studying heart attack risk, each vector might represent a patient and its components might correspond to their most recent vital signs, cholesterol levels, minutes of exercise per day, etc. We denote vectors by bold lowercase letters, (e.g., \n",
        ", \n",
        ", and \n",
        ").\n",
        "\n",
        "Vectors are implemented as \n",
        "-order tensors. In general, such tensors can have arbitrary lengths, subject to memory limitations. Caution: in Python, like in most programming languages, vector indices start at \n",
        ", also known as zero-based indexing, whereas in linear algebra subscripts begin at \n",
        " (one-based indexing)."
      ],
      "metadata": {
        "id": "-P1uYPc5Chgc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.arange(3)\n",
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uXOzdF3vCa9t",
        "outputId": "27c5d322-05b6-4f39-8d91-3965ce8c1ad6"
      },
      "execution_count": 117,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0, 1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#MATRICES"
      ],
      "metadata": {
        "id": "ZibOGfXQCzcF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = torch.arange(6).reshape(3,2)\n",
        "A"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "12ju596zC1SS",
        "outputId": "ba6f58f8-cdde-4d77-a41c-f2091c60a879"
      },
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1],\n",
              "        [2, 3],\n",
              "        [4, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 118
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kbVMeLWbDCve",
        "outputId": "d9388db0-292e-4e5c-fcf6-d66828014a34"
      },
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 2, 4],\n",
              "        [1, 3, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Tensors\n",
        "While you can go far in your machine learning journey with only scalars, vectors, and matrices, eventually you may need to work with higher-order tensors. Tensors give us a generic way to describe extensions to \n",
        "-order arrays. We call software objects of the tensor class “tensors” precisely because they too can have arbitrary numbers of axes. While it may be confusing to use the word tensor for both the mathematical object and its realization in code, our meaning should usually be clear from context. We denote general tensors by capital letters with a special font face (e.g., \n",
        ", \n",
        ", and \n",
        ") and their indexing mechanism (e.g., \n",
        " and \n",
        ") follows naturally from that of matrices.\n",
        "\n",
        "Tensors will become more important when we start working with images. Each image arrives as a \n",
        "-order tensor with axes corresponding to the height, width, and channel. At each spatial location, the intensities of each color (red, green, and blue) are stacked along the channel. Moreover a collection of images is represented in code by a \n",
        "-order tensor, where distinct images are indexed along the first axis. Higher-order tensors are constructed analogously to vectors and matrices, by growing the number of shape components."
      ],
      "metadata": {
        "id": "cx_vPtQiDKv-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "torch.arange(24).reshape(2, 3, 4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WMS6At2ADEff",
        "outputId": "4ae686a9-5e0c-4f10-f273-a93b65867e2c"
      },
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[ 0,  1,  2,  3],\n",
              "         [ 4,  5,  6,  7],\n",
              "         [ 8,  9, 10, 11]],\n",
              "\n",
              "        [[12, 13, 14, 15],\n",
              "         [16, 17, 18, 19],\n",
              "         [20, 21, 22, 23]]])"
            ]
          },
          "metadata": {},
          "execution_count": 120
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A = torch.arange(6, dtype=torch.float32).reshape(2, 3)\n",
        "B = A.clone()  # Assign a copy of `A` to `B` by allocating new memory\n",
        "A, A + B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LcvNFs1tDg3C",
        "outputId": "ceb6e404-0afc-4100-c7f3-f94625dbe2e7"
      },
      "execution_count": 121,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0., 1., 2.],\n",
              "         [3., 4., 5.]]), tensor([[ 0.,  2.,  4.],\n",
              "         [ 6.,  8., 10.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 121
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.arange(3,dtype=torch.float32)\n",
        "x, x.sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8sOzihISDvzi",
        "outputId": "2fe395c8-0137-4669-b123-5628aeb0910d"
      },
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([0., 1., 2.]), tensor(3.))"
            ]
          },
          "metadata": {},
          "execution_count": 122
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.shape, A.sum(axis=0).shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nB7xktk6EIeI",
        "outputId": "4c49206b-ed27-4912-9cd7-176e4f201c83"
      },
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([2, 3]), torch.Size([3]))"
            ]
          },
          "metadata": {},
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.mean(), A.sum()/A.numel()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i85fRk5fETG2",
        "outputId": "2d70adbb-23aa-4078-d7ae-cb82a1d60250"
      },
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(2.5000), tensor(2.5000))"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Non-Reduction Sum"
      ],
      "metadata": {
        "id": "8Vojl5doEldb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sum_A = A.sum(axis=1, keepdims=True)\n",
        "sum_A, sum_A.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dUyEZyLTEm2N",
        "outputId": "f558a7a6-7472-42b6-8bd7-313a741ff75d"
      },
      "execution_count": 125,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[ 3.],\n",
              "         [12.]]), torch.Size([2, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#DOT"
      ],
      "metadata": {
        "id": "b0xoYlM7E719"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y = torch.ones(3, dtype = torch.float32)\n",
        "x,y,torch.dot(x,y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "89B7naamE-X5",
        "outputId": "b86706f4-02f2-4244-e660-4a506b38f2e9"
      },
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([0., 1., 2.]), tensor([1., 1., 1.]), tensor(3.))"
            ]
          },
          "metadata": {},
          "execution_count": 126
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.sum(x * y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iQtH9ag-FJ0t",
        "outputId": "81ffe69f-b0e8-43e5-9967-18570c571a0f"
      },
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(3.)"
            ]
          },
          "metadata": {},
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Matrix-Vector Products¶\n",
        "PyTorch has a convenience operator @ that can execute both matrix-vector and matrix-matrix products (depending on its arguments). Thus we can write A@x.\n",
        "\n"
      ],
      "metadata": {
        "id": "9_SZaphlFW21"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A.shape, x.shape, torch.mv(A, x), A@x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5N5LGnJNFYKa",
        "outputId": "06a807e3-0563-492b-9318-40f87aa142f9"
      },
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([2, 3]), torch.Size([3]), tensor([ 5., 14.]), tensor([ 5., 14.]))"
            ]
          },
          "metadata": {},
          "execution_count": 128
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "B = torch.ones(3, dtype = torch.float32)\n",
        "torch.mv(A,B), A@B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TDUD692RFYNg",
        "outputId": "ccd82a87-409c-4948-cd32-596c75898669"
      },
      "execution_count": 129,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([ 3., 12.]), tensor([ 3., 12.]))"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.matmul(torch.rand(3,2),torch.rand(2,3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Bb8zTKLMlex5",
        "outputId": "4672ca7c-0cfa-45e5-f149-d2b5b0f101dc"
      },
      "execution_count": 130,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.3699, 0.4396, 0.2878],\n",
              "        [0.3016, 0.5181, 0.5665],\n",
              "        [0.2613, 0.5800, 0.7632]])"
            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tensor_A = torch.tensor([[1, 2],\n",
        "                         [3, 4],\n",
        "                         [5, 6]], dtype=torch.float32)\n",
        "\n",
        "tensor_B = torch.tensor([[7, 10],\n",
        "                         [8, 11], \n",
        "                         [9, 12]], dtype=torch.float32)\n",
        "print(tensor_B.T)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zdrH7gTO4G8R",
        "outputId": "a2e985fd-a1fe-4f3a-84ef-ede3b2f896be"
      },
      "execution_count": 131,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ 7.,  8.,  9.],\n",
            "        [10., 11., 12.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "output = torch.matmul(tensor_A, tensor_B.T)\n",
        "print(output) \n",
        "print(f\"\\nOutput shape: {output.shape}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YiMJh7Wp497N",
        "outputId": "b339a068-af57-4db0-f153-0d55bb7a1f2d"
      },
      "execution_count": 132,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ 27.,  30.,  33.],\n",
            "        [ 61.,  68.,  75.],\n",
            "        [ 95., 106., 117.]])\n",
            "\n",
            "Output shape: torch.Size([3, 3])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Norms\n",
        "Some of the most useful operators in linear algebra are norms. Informally, the norm of a vector tells us how big it is. For instance, the \n",
        " norm measures the (Euclidean) length of a vector. Here, we are employing a notion of size that concerns the magnitude of a vector’s components (not its dimensionality)."
      ],
      "metadata": {
        "id": "Cq-gs9LFGCq-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "u = torch.tensor([3.0, -4.0])\n",
        "torch.norm(u)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DN598avyFYQ6",
        "outputId": "7734bc3f-abb2-4cb3-9003-323badeda37f"
      },
      "execution_count": 133,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5.)"
            ]
          },
          "metadata": {},
          "execution_count": 133
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "torch.abs(u).sum()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BwDwdCd7FYTw",
        "outputId": "27d98f27-978f-46f9-aef6-9c7b2389a38a"
      },
      "execution_count": 134,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(7.)"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#EXERCISE:\n",
        "(A.T).T = A"
      ],
      "metadata": {
        "id": "07gb2hpjGiEB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = torch.arange(6).reshape(3, 2)\n",
        "A.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "34RUhAOAGn4a",
        "outputId": "f94532bd-3e4c-486f-d5c3-3e43ca634f54"
      },
      "execution_count": 135,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([3, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 135
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(A.T).T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zr_ReW6LGpa3",
        "outputId": "f0668d1c-be49-4134-e17c-3748d50c6e6b"
      },
      "execution_count": 136,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1],\n",
              "        [2, 3],\n",
              "        [4, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 136
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "B = torch.ones(3, 2)\n",
        "B.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7rDM6OEcG3VN",
        "outputId": "0108dffb-2a79-4c50-e7f4-4247796499cf"
      },
      "execution_count": 137,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([3, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 137
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.T,B.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dEeeY_E2G5jq",
        "outputId": "aae69e1e-e692-4f06-d004-9d70c5980f69"
      },
      "execution_count": 138,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0, 2, 4],\n",
              "         [1, 3, 5]]), tensor([[1., 1., 1.],\n",
              "         [1., 1., 1.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 138
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A.T + B.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "brHOBUgqHOyh",
        "outputId": "9f6d67ba-de27-4958-fa8c-6186fef8acfc"
      },
      "execution_count": 139,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 3., 5.],\n",
              "        [2., 4., 6.]])"
            ]
          },
          "metadata": {},
          "execution_count": 139
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A + B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QveV5_liG-ca",
        "outputId": "9f7ef9a6-6d79-4bd2-97da-4c0ebf891e3d"
      },
      "execution_count": 140,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2.],\n",
              "        [3., 4.],\n",
              "        [5., 6.]])"
            ]
          },
          "metadata": {},
          "execution_count": 140
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(A + B).T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ciO0G5tyHSv2",
        "outputId": "f0d1705b-5891-4524-a920-1bac4968c84f"
      },
      "execution_count": 141,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 3., 5.],\n",
              "        [2., 4., 6.]])"
            ]
          },
          "metadata": {},
          "execution_count": 141
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We defined the tensor $ \\mathsf{X} $ of shape (2, 3, 4) in this section. What is the output of len(X)? Write your answer without implementing any code, then check your answer using code."
      ],
      "metadata": {
        "id": "ZYH1xy8qIHnK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = torch.tensor([2,3,4])\n",
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ped7C6rzHNKk",
        "outputId": "a200c422-8ce1-448e-c550-126b78f661eb"
      },
      "execution_count": 142,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 142
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# A / A.sum(axis=1)"
      ],
      "metadata": {
        "id": "gB48yrbPKMxi"
      },
      "execution_count": 143,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# distances of avenues and streets\n",
        "\n",
        "dist_ave = 30.0\n",
        "\n",
        "dist_str = 40.0\n",
        "\n",
        "dis_2pt = torch.tensor([dist_ave, dist_str])\n",
        "\n",
        "torch.abs(dis_2pt).sum()\n",
        "\n",
        "#Can. Fly straightly and diagonally.the â„“2 norm\n",
        "\n",
        "\n",
        "torch.norm(dis_2pt)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mLCUUL3LOdd2",
        "outputId": "b6051b31-2f6d-4716-e8db-1696c10478f3"
      },
      "execution_count": 144,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(50.)"
            ]
          },
          "metadata": {},
          "execution_count": 144
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Define three large matrices, say $ \\mathbf{A} \\in \\mathbb{R}^{2^{10} \\times 2^{16}} $ , $ \\mathbf{B} \\in \\mathbb{R}^{2^{16} \\times 2^{5}} $ and $ \\mathbf{C} \\in \\mathbb{R}^{2^{5} \\times 2^{16}} $. Is there any difference in speed depending on whether you compute $ \\mathbf{A} \\mathbf{B} $ or $ \\mathbf{A} \\mathbf{C}^\\top $? Why? What changes if you initialize $ \\mathbf{C} = \\mathbf{B}^\\top $ without cloning memory? Why?"
      ],
      "metadata": {
        "id": "YADBIXQHQ-eb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import timeit\n",
        "A = torch.randn(2**10,2**16)\n",
        "B = torch.randn(2**16,2**5)\n",
        "C = torch.randn(2**5,2**16)\n"
      ],
      "metadata": {
        "id": "ZMgvqenhRBPu"
      },
      "execution_count": 145,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "C.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lqD2plMbRrNs",
        "outputId": "54ec91fc-beab-499b-f998-11b6c154eb9e"
      },
      "execution_count": 146,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-0.7765,  1.1304, -1.1058,  ...,  1.3564,  0.5840, -0.1606],\n",
              "        [-0.1731, -0.9823,  0.2417,  ...,  1.2117,  1.3935, -1.5320],\n",
              "        [ 0.3956, -0.7942, -0.7254,  ..., -0.0590, -0.3692, -0.0904],\n",
              "        ...,\n",
              "        [-0.7175,  1.5627, -1.2257,  ...,  0.8239,  1.0217, -0.5860],\n",
              "        [-0.8871,  1.1626,  0.7529,  ..., -0.4630, -0.4176, -2.3187],\n",
              "        [-0.1881,  1.1722,  0.4419,  ..., -1.1727,  1.1701, -2.4888]])"
            ]
          },
          "metadata": {},
          "execution_count": 146
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%timeit A@B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cN57UsVZRc_f",
        "outputId": "0d811fe7-ef72-428e-c942-7ec887989537"
      },
      "execution_count": 147,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "65.5 ms ± 5.04 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%timeit A@C.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hXGueZZzRuHV",
        "outputId": "2096bec9-d959-4af7-abeb-dcae5d957a1e"
      },
      "execution_count": 148,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "82.6 ms ± 8.73 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Y= torch.arange(24,dtype = torch.float32).reshape(2, 3, 4)\n",
        "\n",
        "torch.norm(Y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Dn8unGM9O0NN",
        "outputId": "ece08e4f-0a62-4935-9c1c-107189b50907"
      },
      "execution_count": 149,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(65.7571)"
            ]
          },
          "metadata": {},
          "execution_count": 149
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "%timeit C = B.T"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ke8jrjchR3zH",
        "outputId": "a0a28560-c851-4907-9ef2-68fe5570387f"
      },
      "execution_count": 150,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.57 µs ± 1.14 µs per loop (mean ± std. dev. of 7 runs, 1000000 loops each)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "A = torch.randn( (100, 200) )\n",
        "B = torch.randn( (100, 200) )\n",
        "C = torch.randn( (100, 200) )\n",
        "\n",
        "stacked = torch.stack([ A, B, C ])\n",
        "print(f\"{stacked.shape = }\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "L8TsDwbXSYmO",
        "outputId": "20fbad79-3760-48a2-a473-fbf623b84767"
      },
      "execution_count": 151,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "stacked.shape = torch.Size([3, 100, 200])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "v3pwB40phcJ9"
      },
      "execution_count": 151,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Cuda"
      ],
      "metadata": {
        "id": "hCVW7Mu4zBJF"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "4JF-FSuVG470"
      },
      "execution_count": 151,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# running on GPU\n",
        "# if torch.cuda.is_available():\n",
        "#     x = x.cuda()\n",
        "#     w = w.cuda()\n",
        "#     print(x.mm(w))"
      ],
      "metadata": {
        "id": "XvdiKCGCy511"
      },
      "execution_count": 152,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Automatic differentiation\n",
        "\n",
        "\n",
        "\n",
        "The autograd package is a key package for working with our computational graphs. It provides automatic differentiation for operations on tensors. Variable is the core class in the package and it wraps around our tensors. Once we defined our computations in the graph, we can call .backward() on our objective to calculate all the gradients automatically! We can always access the values in raw tensors with .data and the gradient w.r.t to our objective with .grad."
      ],
      "metadata": {
        "id": "PBc7ME1kzJWE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Image(filename='/content/AD.png', width=300) "
      ],
      "metadata": {
        "id": "9Q4WWNZLzFf0"
      },
      "execution_count": 153,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating a Variable\n",
        "x = Variable(torch.ones(3, 3), requires_grad=True)\n",
        "print(x)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hlrrNT4y2W0o",
        "outputId": "d98151e0-3b44-4172-9b80-67e67ac6a390"
      },
      "execution_count": 154,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[1., 1., 1.],\n",
            "        [1., 1., 1.],\n",
            "        [1., 1., 1.]], requires_grad=True)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# + operation\n",
        "y = x + 4\n",
        "print(y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GcJrkqYR2Xz6",
        "outputId": "65f562c1-0ef8-4504-80af-a97706dc838f"
      },
      "execution_count": 155,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[5., 5., 5.],\n",
            "        [5., 5., 5.],\n",
            "        [5., 5., 5.]], grad_fn=<AddBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# * and mean\n",
        "z = y * 3\n",
        "o = z.mean()\n",
        "print(o)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TrBLYHbk4O5B",
        "outputId": "dc608ff2-8a48-447e-cf61-9f5b469c4354"
      },
      "execution_count": 156,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(15., grad_fn=<MeanBackward0>)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Backward pass\n",
        "o.backward()"
      ],
      "metadata": {
        "id": "jPAcL_TB4TmC"
      },
      "execution_count": 157,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Gradients w.r.t o\n",
        "print(x.grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OsmFRfv04aLV",
        "outputId": "ebc59090-9cd0-4c6a-e500-257091f449ab"
      },
      "execution_count": 158,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[0.3333, 0.3333, 0.3333],\n",
            "        [0.3333, 0.3333, 0.3333],\n",
            "        [0.3333, 0.3333, 0.3333]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# see the data and creator\n",
        "print (x.data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sZd_8q7q4dAE",
        "outputId": "ca7e151e-8b58-44ca-cb1b-a39507e77431"
      },
      "execution_count": 159,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[1., 1., 1.],\n",
            "        [1., 1., 1.],\n",
            "        [1., 1., 1.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#CALCULUS"
      ],
      "metadata": {
        "id": "HXDg1cLVOekM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def f(x):\n",
        "  return 3 * x ** 2 - 4 * x"
      ],
      "metadata": {
        "id": "BRyVq_jn4iXh"
      },
      "execution_count": 160,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for h in 10.0**np.arange(-1, -6, -1):\n",
        "    print(f'h={h:.5f}, numerical limit={(f(1+h)-f(1))/h:.5f}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Aq6I8OxBPMaM",
        "outputId": "92bc927f-6d84-41cc-bd3c-46259a32b233"
      },
      "execution_count": 161,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "h=0.10000, numerical limit=2.30000\n",
            "h=0.01000, numerical limit=2.03000\n",
            "h=0.00100, numerical limit=2.00300\n",
            "h=0.00010, numerical limit=2.00030\n",
            "h=0.00001, numerical limit=2.00003\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2.4.2. Visualization Utilities\n",
        "We can visualize the slopes of functions using the matplotlib library. We need to define a few functions. As its name indicates, use_svg_display tells matplotlib to output graphics in SVG format for crisper images. The comment #@save is a special modifier that allows us to save any function, class, or other code block to the d2l package so that we can invoke it later without repeating the code, e.g., via d2l.use_svg_display().\n",
        "\n"
      ],
      "metadata": {
        "id": "Rn0SAJy7P6ON"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def use_svg_display():  \n",
        "    \"\"\"Use the svg format to display a plot in Jupyter.\"\"\"\n",
        "    backend_inline.set_matplotlib_formats('svg')"
      ],
      "metadata": {
        "id": "pK0wNnYbPM9x"
      },
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def set_figsize(figsize=(3.5, 2.5)):  \n",
        "    \"\"\"Set the figure size for matplotlib.\"\"\"\n",
        "    use_svg_display()\n",
        "    d2l.plt.rcParams['figure.figsize'] = figsize"
      ],
      "metadata": {
        "id": "SXRIKW30TZvL"
      },
      "execution_count": 163,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):\n",
        "    \"\"\"Set the axes for matplotlib.\"\"\"\n",
        "    axes.set_xlabel(xlabel), axes.set_ylabel(ylabel)\n",
        "    axes.set_xscale(xscale), axes.set_yscale(yscale)\n",
        "    axes.set_xlim(xlim),     axes.set_ylim(ylim)\n",
        "    if legend:\n",
        "        axes.legend(legend)\n",
        "    axes.grid()"
      ],
      "metadata": {
        "id": "1M5yCAGhTinl"
      },
      "execution_count": 164,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot(X, Y=None, xlabel=None, ylabel=None, legend=[], xlim=None,\n",
        "         ylim=None, xscale='linear', yscale='linear',\n",
        "         fmts=('-', 'm--', 'g-.', 'r:'), figsize=(3.5, 2.5), axes=None):\n",
        "    \"\"\"Plot data points.\"\"\"\n",
        "\n",
        "    def has_one_axis(X):  # True if `X` (tensor or list) has 1 axis\n",
        "        return (hasattr(X, \"ndim\") and X.ndim == 1 or isinstance(X, list)\n",
        "                and not hasattr(X[0], \"__len__\"))\n",
        "\n",
        "    if has_one_axis(X): X = [X]\n",
        "    if Y is None:\n",
        "        X, Y = [[]] * len(X), X\n",
        "    elif has_one_axis(Y):\n",
        "        Y = [Y]\n",
        "    if len(X) != len(Y):\n",
        "        X = X * len(Y)\n",
        "\n",
        "    set_figsize(figsize)\n",
        "    if axes is None: axes = d2l.plt.gca()\n",
        "    axes.cla()\n",
        "    for x, y, fmt in zip(X, Y, fmts):\n",
        "        axes.plot(x,y,fmt) if len(x) else axes.plot(y,fmt)\n",
        "    set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)"
      ],
      "metadata": {
        "id": "evjlo9UWT4vX"
      },
      "execution_count": 165,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.arange(0, 3, 0.1)\n",
        "plot(x, [f(x), 2 * x - 3], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 262
        },
        "id": "H0RBuLMJ3-Yw",
        "outputId": "9098037f-83e7-42b7-eb9b-228c9ae2119d"
      },
      "execution_count": 166,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 252x180 with 1 Axes>"
            ],
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    {
      "cell_type": "code",
      "source": [
        "x = np.arange(0, 3, 0.1)\n",
        "plot(x, [f(x),  x**3 - 1/x], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "NJD6G4IB4ZsM",
        "outputId": "a1a5600c-51b1-4740-a7fc-79db32d60ac1"
      },
      "execution_count": 167,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-167-bc5ae5cc3bd7>:2: RuntimeWarning: divide by zero encountered in true_divide\n",
            "  plot(x, [f(x),  x**3 - 1/x], 'x', 'f(x)', legend=['f(x)', 'Tangent line (x=1)'])\n"
          ]
        },
        {
          "output_type": "display_data",
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    {
      "cell_type": "markdown",
      "source": [
        "let’s use a simple tensor and set the requires_grad parameter to true. This allows us to perform automatic differentiation and lets PyTorch evaluate the derivatives using the given value which, in this case, is 3.0."
      ],
      "metadata": {
        "id": "iPD9sCJ7k_ka"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.tensor(3.0, requires_grad=True )\n",
        "x"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E_X0Q8-FmnoD",
        "outputId": "e73eb067-61b7-4195-a2d1-f56712b83bd5"
      },
      "execution_count": 168,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(3., requires_grad=True)"
            ]
          },
          "metadata": {},
          "execution_count": 168
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y = 3 * x ** 2\n",
        "print(\"Result of the equation is: \", y)\n",
        "y.backward()\n",
        "print(\"Dervative of the equation at x = 3 is: \", x.grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8J0ZCcvin7nX",
        "outputId": "1d426c0f-9ea5-4bdf-cc2a-f5f8da985a76"
      },
      "execution_count": 169,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result of the equation is:  tensor(27., grad_fn=<MulBackward0>)\n",
            "Dervative of the equation at x = 3 is:  tensor(18.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Computational Graph\n",
        "PyTorch generates derivatives by building a backwards graph behind the scenes, while tensors and backwards functions are the graph’s nodes. In a graph, PyTorch computes the derivative of a tensor depending on whether it is a leaf or not.\n",
        "\n",
        "PyTorch will not evaluate a tensor’s derivative if its leaf attribute is set to True. We won’t go into much detail about how the backwards graph is created and utilized, because the goal here is to give you a high-level knowledge of how PyTorch makes use of the graph to calculate derivatives.\n",
        "\n",
        "So, let’s check how the tensors x and y look internally once they are created. For x:"
      ],
      "metadata": {
        "id": "rtcgTK8YoRWL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "print('data attribute of the tensor:',x.data)\n",
        "print('grad attribute of the tensor::',x.grad)\n",
        "print('grad_fn attribute of the tensor::',x.grad_fn)\n",
        "print(\"is_leaf attribute of the tensor::\",x.is_leaf)\n",
        "print(\"requires_grad attribute of the tensor::\",x.requires_grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PU-CRv62oSEx",
        "outputId": "aa03ab74-1dfd-4e21-cf01-d3ef61d6d8ba"
      },
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "data attribute of the tensor: tensor(3.)\n",
            "grad attribute of the tensor:: tensor(18.)\n",
            "grad_fn attribute of the tensor:: None\n",
            "is_leaf attribute of the tensor:: True\n",
            "requires_grad attribute of the tensor:: True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.tensor(3.0, requires_grad = True)\n",
        "y = 6 * x ** 2 + 2 * x + 4\n",
        "print(\"Result of the equation is: \", y)\n",
        "y.backward()\n",
        "print(\"Derivative of the equation at x = 3 is: \", x.grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "U3iiehonoXpz",
        "outputId": "a64ddec2-deda-43aa-dbf5-def23e003820"
      },
      "execution_count": 171,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result of the equation is:  tensor(64., grad_fn=<AddBackward0>)\n",
            "Derivative of the equation at x = 3 is:  tensor(38.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Implementing Partial Derivatives of Functions\n",
        "PyTorch also allows us to calculate partial derivatives of functions."
      ],
      "metadata": {
        "id": "XfvRdmAPpQTR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "u = torch.tensor(3., requires_grad=True)\n",
        "v = torch.tensor(4., requires_grad=True)\n",
        " \n",
        "f = u**3 + v**2 + 4*u*v\n",
        " \n",
        "print(u)\n",
        "print(v)\n",
        "print(f)\n",
        " \n",
        "f.backward()\n",
        "print(\"Partial derivative with respect to u: \", u.grad)\n",
        "print(\"Partial derivative with respect to v: \", v.grad)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "j9BF9w_2pDz0",
        "outputId": "5ef0edae-37c8-4fc5-cb06-a28ab185950a"
      },
      "execution_count": 172,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(3., requires_grad=True)\n",
            "tensor(4., requires_grad=True)\n",
            "tensor(91., grad_fn=<AddBackward0>)\n",
            "Partial derivative with respect to u:  tensor(43.)\n",
            "Partial derivative with respect to v:  tensor(20.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Derivative of Functions with Multiple Values\n",
        "What if we have a function with multiple values and we need to calculate the derivative with respect to its multiple values? For this, we’ll make use of the sum attribute to (1) produce a scalar-valued function, and then (2) take the derivative. This is how we can see the ‘function vs. derivative’ plot:\n",
        "\n",
        "Source:\n",
        "-- https://machinelearningmastery.com/calculating-derivatives-in-pytorch/\n",
        "\n",
        "-- https://androidkt.com/create-numpy-array-from-pytorch-tensor-using-detach-numpy/\n",
        "\n",
        "--- https://medium.com/@pranav.kushare2001/solving-calculus-problems-using-pytorchs-automatic-differentiation-c672df970fda\n"
      ],
      "metadata": {
        "id": "Jh1eathrppb_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = torch.linspace(-20, 20, 20, requires_grad = True)\n",
        "Y = x ** 2\n",
        "y = torch.sum(Y)\n",
        "y.backward()\n",
        "\n",
        "# ploting the function and derivative\n",
        "function_line, = plt.plot(x.detach().numpy(), Y.detach().numpy(), label = 'Function')\n",
        "function_line.set_color(\"red\")\n",
        "derivative_line, = plt.plot(x.detach().numpy(), x.grad.detach().numpy(), label = 'Derivative')\n",
        "derivative_line.set_color(\"green\")\n",
        "plt.xlabel('x')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 262
        },
        "id": "ZhE73xWnpcka",
        "outputId": "abc1faa6-e720-438b-abe1-ff243a5e1922"
      },
      "execution_count": 173,
      "outputs": [
        {
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    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "-2R2umu9rk2R"
      },
      "execution_count": 173,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "gVnN-fgxsotI"
      },
      "execution_count": 173,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        " a= torch.tensor(1,requires_grad=True,dtype=float)\n",
        " y = (1/torch.cos(torch.atan(a)))\n",
        " y.backward()\n",
        " a.grad\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BGZNToNLso2h",
        "outputId": "d77245e8-509a-4fed-cde8-44ce40bfa28f"
      },
      "execution_count": 174,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.7071, dtype=torch.float64)"
            ]
          },
          "metadata": {},
          "execution_count": 174
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "\n",
        "X = torch.rand(size=(7,7))\n",
        "x.shape\n",
        "\n",
        "Y = torch.rand(size=(1,7))\n",
        "Y.T\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zyzEMOXmAAdG",
        "outputId": "fb1a9d7e-1eaf-42f4-c6a7-0b0693484a1b"
      },
      "execution_count": 182,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.9785],\n",
              "        [0.9495],\n",
              "        [0.2643],\n",
              "        [0.2797],\n",
              "        [0.3577],\n",
              "        [0.4719],\n",
              "        [0.4709]])"
            ]
          },
          "metadata": {},
          "execution_count": 182
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Z = torch.matmul(X, Y.T) # no error because of transpose\n",
        "Z, Z.shape\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jeoGpaAdAA9J",
        "outputId": "321272c3-cea8-45b4-af6f-35a37e8147ac"
      },
      "execution_count": 183,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[2.0203],\n",
              "         [1.3354],\n",
              "         [2.8562],\n",
              "         [2.7670],\n",
              "         [1.3645],\n",
              "         [2.0234],\n",
              "         [1.1493]]), torch.Size([7, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 183
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Set manual seed\n",
        "torch.manual_seed(0)\n",
        "\n",
        "# Create two random tensors\n",
        "X = torch.rand(size=(7, 7))\n",
        "Y = torch.rand(size=(1, 7))\n",
        "\n",
        "# Matrix multiply tensors\n",
        "Z = torch.matmul(X, Y.T)\n",
        "Z, Z.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NYbgdD1FGHg6",
        "outputId": "d84a1fb5-4bfc-4d7d-b8ee-a8e5730bea15"
      },
      "execution_count": 184,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[1.8542],\n",
              "         [1.9611],\n",
              "         [2.2884],\n",
              "         [3.0481],\n",
              "         [1.7067],\n",
              "         [2.5290],\n",
              "         [1.7989]]), torch.Size([7, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 184
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Set random seed\n",
        "torch.manual_seed(1234)\n",
        "\n",
        "# Check for access to GPU\n",
        "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n",
        "print(f\"Device: {device}\")\n",
        "\n",
        "# Create two random tensors on GPU\n",
        "tensor_A = torch.rand(size=(2,3)).to(device)\n",
        "tensor_B = torch.rand(size=(2,3)).to(device)\n",
        "tensor_A, tensor_B"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lukYFP_OF72p",
        "outputId": "f0d39539-eca9-4aca-896b-34c2802c1478"
      },
      "execution_count": 185,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Device: cuda\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0.0290, 0.4019, 0.2598],\n",
              "         [0.3666, 0.0583, 0.7006]], device='cuda:0'),\n",
              " tensor([[0.0518, 0.4681, 0.6738],\n",
              "         [0.3315, 0.7837, 0.5631]], device='cuda:0'))"
            ]
          },
          "metadata": {},
          "execution_count": 185
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "tensor_C = torch.matmul(tensor_A, tensor_B.T)\n",
        "tensor_C, tensor_C.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fATpIhpdGRMG",
        "outputId": "57ca7c1f-6c7b-4b59-fbc2-f9480eceb499"
      },
      "execution_count": 186,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[0.3647, 0.4709],\n",
              "         [0.5184, 0.5617]], device='cuda:0'), torch.Size([2, 2]))"
            ]
          },
          "metadata": {},
          "execution_count": 186
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "max = torch.max(tensor_C)\n",
        "min = torch.min(tensor_C)\n",
        "max, min"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Uxud-jb0GjVv",
        "outputId": "d1b79f04-e7e5-4347-be6b-01b9eb22780c"
      },
      "execution_count": 188,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0.5617, device='cuda:0'), tensor(0.3647, device='cuda:0'))"
            ]
          },
          "metadata": {},
          "execution_count": 188
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Find arg max\n",
        "arg_max = torch.argmax(tensor_C)\n",
        "\n",
        "# Find arg min\n",
        "arg_min = torch.argmin(tensor_C)\n",
        "arg_max, arg_min"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IfHfJmIoG_z8",
        "outputId": "d0e4a112-609a-48b3-d407-bfcdca50daf8"
      },
      "execution_count": 189,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(3, device='cuda:0'), tensor(0, device='cuda:0'))"
            ]
          },
          "metadata": {},
          "execution_count": 189
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Set seed\n",
        "torch.manual_seed(7)\n",
        "\n",
        "# Create random tensor\n",
        "tensor_D = torch.rand(size=(1, 1, 1, 10))\n",
        "\n",
        "# Remove single dimensions\n",
        "tensor_E = tensor_D.squeeze()\n",
        "\n",
        "# Print out tensors\n",
        "print(tensor_D, tensor_D.shape)\n",
        "print(tensor_E, tensor_E.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3YoFlSICHCc6",
        "outputId": "e26fee62-3fb0-4ce0-c4e4-068f7f004dc5"
      },
      "execution_count": 190,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[[[0.5349, 0.1988, 0.6592, 0.6569, 0.2328, 0.4251, 0.2071, 0.6297,\n",
            "           0.3653, 0.8513]]]]) torch.Size([1, 1, 1, 10])\n",
            "tensor([0.5349, 0.1988, 0.6592, 0.6569, 0.2328, 0.4251, 0.2071, 0.6297, 0.3653,\n",
            "        0.8513]) torch.Size([10])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "c_A6Od6SHOwz"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}