PyTorch_Basics.ipynb

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  "metadata": {
    "colab": {
      "name": "PyTorch-Basics.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/anujdutt9/PyTorch-DeepLearning/blob/master/PyTorch_Basics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Al-MNGd_pXCp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Import Dependencies\n",
        "import torch\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cnVXpmAdpbvr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ed217902-a22a-445f-a0de-cfc59bc70d2d"
      },
      "source": [
        "v = torch.tensor([1,2,3,4,5,6])\n",
        "print(v)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([1, 2, 3, 4, 5, 6])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7qpA9AWppine",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e558d280-6215-4d58-fd32-3446ad37df78"
      },
      "source": [
        "print(v.dtype)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "torch.int64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nzQGDXW_plCr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d6365244-bb43-47a4-a936-0a90cfe4865a"
      },
      "source": [
        "v[4:]"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([5, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p5wnwC81pn12",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bd3ea877-1d77-47fc-a66d-84552bc699b1"
      },
      "source": [
        "v[1:5]"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 3, 4, 5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P_pM3ag2ps6d",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6d9be87b-50a1-4f95-87be-8d8d112893b6"
      },
      "source": [
        "v[0]"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kxG2_hAMpvdl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "548bd2fc-2046-4ed5-ebeb-e8ad5569c273"
      },
      "source": [
        "f = torch.FloatTensor([1,2,3,4,5,6])\n",
        "print(f)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "tensor([1., 2., 3., 4., 5., 6.])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cRuIPDhOp1Z2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "20fe0720-5519-47e1-8788-d3a5eccdc3e0"
      },
      "source": [
        "f.size()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6sZTikW1p3gy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "b7066160-15f4-477d-e1ec-88ce8744a3a6"
      },
      "source": [
        "# Reshaping Tensor to (6,1)\n",
        "v.view(6,1)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1],\n",
              "        [2],\n",
              "        [3],\n",
              "        [4],\n",
              "        [5],\n",
              "        [6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "g7DXD7VEp6MC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "24f8f75e-0bab-4837-8b02-f9659b87407b"
      },
      "source": [
        "# Reshaping Tensor to (3,2)\n",
        "f.view(3,2)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2.],\n",
              "        [3., 4.],\n",
              "        [5., 6.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cC17hwbaqDwz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "b87d4c65-4809-4e38-bc77-dd7a24c72567"
      },
      "source": [
        "# -1: Column size inferred from size of tensor array\n",
        "v.view(3, -1)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 2],\n",
              "        [3, 4],\n",
              "        [5, 6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5XJkVNfBqTJP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "26832f03-8511-404a-dd12-c9e31011347d"
      },
      "source": [
        "a = np.array([1,2,3,4,5,6])\n",
        "a"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wt_o2ogbwKcH",
        "colab_type": "text"
      },
      "source": [
        "**Numpy to PyTorch Tensor**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eR_wbCA8qVoe",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6aa8cdf5-59ce-4a70-8d2e-ed9aef9c0d55"
      },
      "source": [
        "a_tensor = torch.from_numpy(a)\n",
        "a_tensor"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1, 2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dBINjvXlqjsj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "8221c19d-7f89-4fe9-a29a-1cae9c02d56f"
      },
      "source": [
        "a_tensor.dtype"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JDCDALUSquak",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7b134909-f67b-4543-cbde-ef01b2b33322"
      },
      "source": [
        "a_tensor.type()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'torch.LongTensor'"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F8nUOAw6wOEg",
        "colab_type": "text"
      },
      "source": [
        "**PyTorch to Numpy**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gR0ttvouqwSc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d606dd70-5e00-4423-cb66-fba424e4f5dc"
      },
      "source": [
        "a_np = a_tensor.numpy()\n",
        "a_np"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_MrLvseIrACo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "813f7e54-4ecc-44cb-c550-caedb3dd1d75"
      },
      "source": [
        "type(a_np)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sqj8pkDVwSGM",
        "colab_type": "text"
      },
      "source": [
        "**Vector Operations**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PN1OPKrjrOR5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Two random Tensors\n",
        "t_one = torch.tensor([1,2,3])\n",
        "t_two = torch.tensor([1,2,3])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VaAGqgGIrdEn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "14616e1e-6caa-4012-c623-c708bc86150e"
      },
      "source": [
        "# Addition operation\n",
        "t_one + t_two"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2, 4, 6])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rjBAKlKWrfxU",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a07d7edc-8997-4235-c69b-4dfe8408a039"
      },
      "source": [
        "# Multiplication operation\n",
        "t_one * t_two"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1, 4, 9])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4owdvNm6rjQV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "29e28615-186a-48fa-8115-69e7618bee4b"
      },
      "source": [
        "t_one * 3"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([3, 6, 9])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b3G3xLhWrpO1",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "e92e29d8-3de3-412b-8904-83983d04c7ed"
      },
      "source": [
        "# Dot Product\n",
        "dot_prod = torch.dot(t_one, t_two)\n",
        "dot_prod"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(14)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dX8ae04Br1dI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "outputId": "a00246f1-d79e-4090-fe1b-7ba88d679649"
      },
      "source": [
        "# Linspace\n",
        "x = torch.linspace(0, 10, 100)\n",
        "y = torch.exp(x)\n",
        "x"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0000,  0.1010,  0.2020,  0.3030,  0.4040,  0.5051,  0.6061,  0.7071,\n",
              "         0.8081,  0.9091,  1.0101,  1.1111,  1.2121,  1.3131,  1.4141,  1.5152,\n",
              "         1.6162,  1.7172,  1.8182,  1.9192,  2.0202,  2.1212,  2.2222,  2.3232,\n",
              "         2.4242,  2.5253,  2.6263,  2.7273,  2.8283,  2.9293,  3.0303,  3.1313,\n",
              "         3.2323,  3.3333,  3.4343,  3.5354,  3.6364,  3.7374,  3.8384,  3.9394,\n",
              "         4.0404,  4.1414,  4.2424,  4.3434,  4.4444,  4.5455,  4.6465,  4.7475,\n",
              "         4.8485,  4.9495,  5.0505,  5.1515,  5.2525,  5.3535,  5.4545,  5.5556,\n",
              "         5.6566,  5.7576,  5.8586,  5.9596,  6.0606,  6.1616,  6.2626,  6.3636,\n",
              "         6.4646,  6.5657,  6.6667,  6.7677,  6.8687,  6.9697,  7.0707,  7.1717,\n",
              "         7.2727,  7.3737,  7.4747,  7.5758,  7.6768,  7.7778,  7.8788,  7.9798,\n",
              "         8.0808,  8.1818,  8.2828,  8.3838,  8.4848,  8.5859,  8.6869,  8.7879,\n",
              "         8.8889,  8.9899,  9.0909,  9.1919,  9.2929,  9.3939,  9.4949,  9.5960,\n",
              "         9.6970,  9.7980,  9.8990, 10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JM0UAFUFr-rQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 306
        },
        "outputId": "15fdd320-f4af-43a0-f498-7c3232e233bf"
      },
      "source": [
        "y"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1.0000e+00, 1.1063e+00, 1.2239e+00, 1.3540e+00, 1.4979e+00, 1.6571e+00,\n",
              "        1.8332e+00, 2.0280e+00, 2.2436e+00, 2.4821e+00, 2.7459e+00, 3.0377e+00,\n",
              "        3.3606e+00, 3.7178e+00, 4.1130e+00, 4.5501e+00, 5.0337e+00, 5.5688e+00,\n",
              "        6.1606e+00, 6.8154e+00, 7.5398e+00, 8.3412e+00, 9.2278e+00, 1.0209e+01,\n",
              "        1.1294e+01, 1.2494e+01, 1.3822e+01, 1.5291e+01, 1.6916e+01, 1.8714e+01,\n",
              "        2.0704e+01, 2.2904e+01, 2.5338e+01, 2.8032e+01, 3.1011e+01, 3.4307e+01,\n",
              "        3.7954e+01, 4.1988e+01, 4.6450e+01, 5.1387e+01, 5.6849e+01, 6.2892e+01,\n",
              "        6.9576e+01, 7.6971e+01, 8.5153e+01, 9.4203e+01, 1.0422e+02, 1.1529e+02,\n",
              "        1.2755e+02, 1.4110e+02, 1.5610e+02, 1.7269e+02, 1.9105e+02, 2.1135e+02,\n",
              "        2.3382e+02, 2.5867e+02, 2.8616e+02, 3.1658e+02, 3.5023e+02, 3.8745e+02,\n",
              "        4.2864e+02, 4.7419e+02, 5.2459e+02, 5.8035e+02, 6.4204e+02, 7.1028e+02,\n",
              "        7.8577e+02, 8.6929e+02, 9.6168e+02, 1.0639e+03, 1.1770e+03, 1.3021e+03,\n",
              "        1.4405e+03, 1.5936e+03, 1.7630e+03, 1.9503e+03, 2.1576e+03, 2.3870e+03,\n",
              "        2.6407e+03, 2.9213e+03, 3.2318e+03, 3.5753e+03, 3.9554e+03, 4.3758e+03,\n",
              "        4.8409e+03, 5.3554e+03, 5.9246e+03, 6.5543e+03, 7.2510e+03, 8.0216e+03,\n",
              "        8.8742e+03, 9.8175e+03, 1.0861e+04, 1.2015e+04, 1.3292e+04, 1.4705e+04,\n",
              "        1.6268e+04, 1.7997e+04, 1.9910e+04, 2.2026e+04])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dJqrGkzWsFsf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "89e92799-c321-4c89-8641-6fe6988a380c"
      },
      "source": [
        "plt.plot(x.numpy(), y.numpy())"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f5d20afd1d0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dfXskIpICz20/SszhvmUVF++cgRQOIiKXqDfm/HB7DcvnlnDllKKwy0kKhYOIyCV6eX8D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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GDl7IUVBsIik",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "outputId": "c311fd58-a53d-48fa-b991-694296cea63a"
      },
      "source": [
        "x = torch.linspace(0, 10, 100)\n",
        "y = torch.sin(x)\n",
        "x"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0000,  0.1010,  0.2020,  0.3030,  0.4040,  0.5051,  0.6061,  0.7071,\n",
              "         0.8081,  0.9091,  1.0101,  1.1111,  1.2121,  1.3131,  1.4141,  1.5152,\n",
              "         1.6162,  1.7172,  1.8182,  1.9192,  2.0202,  2.1212,  2.2222,  2.3232,\n",
              "         2.4242,  2.5253,  2.6263,  2.7273,  2.8283,  2.9293,  3.0303,  3.1313,\n",
              "         3.2323,  3.3333,  3.4343,  3.5354,  3.6364,  3.7374,  3.8384,  3.9394,\n",
              "         4.0404,  4.1414,  4.2424,  4.3434,  4.4444,  4.5455,  4.6465,  4.7475,\n",
              "         4.8485,  4.9495,  5.0505,  5.1515,  5.2525,  5.3535,  5.4545,  5.5556,\n",
              "         5.6566,  5.7576,  5.8586,  5.9596,  6.0606,  6.1616,  6.2626,  6.3636,\n",
              "         6.4646,  6.5657,  6.6667,  6.7677,  6.8687,  6.9697,  7.0707,  7.1717,\n",
              "         7.2727,  7.3737,  7.4747,  7.5758,  7.6768,  7.7778,  7.8788,  7.9798,\n",
              "         8.0808,  8.1818,  8.2828,  8.3838,  8.4848,  8.5859,  8.6869,  8.7879,\n",
              "         8.8889,  8.9899,  9.0909,  9.1919,  9.2929,  9.3939,  9.4949,  9.5960,\n",
              "         9.6970,  9.7980,  9.8990, 10.0000])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iCrfbIIBsQe7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 238
        },
        "outputId": "7fbfb479-4304-4ecb-88a4-f026d4bbabff"
      },
      "source": [
        "y"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.0000,  0.1008,  0.2006,  0.2984,  0.3931,  0.4839,  0.5696,  0.6496,\n",
              "         0.7230,  0.7889,  0.8469,  0.8962,  0.9364,  0.9670,  0.9878,  0.9985,\n",
              "         0.9990,  0.9893,  0.9696,  0.9399,  0.9007,  0.8523,  0.7952,  0.7300,\n",
              "         0.6574,  0.5781,  0.4928,  0.4026,  0.3082,  0.2107,  0.1111,  0.0103,\n",
              "        -0.0906, -0.1906, -0.2886, -0.3837, -0.4748, -0.5612, -0.6418, -0.7158,\n",
              "        -0.7826, -0.8414, -0.8916, -0.9327, -0.9643, -0.9861, -0.9978, -0.9994,\n",
              "        -0.9908, -0.9720, -0.9434, -0.9051, -0.8576, -0.8014, -0.7370, -0.6651,\n",
              "        -0.5864, -0.5017, -0.4120, -0.3180, -0.2207, -0.1213, -0.0206,  0.0804,\n",
              "         0.1805,  0.2787,  0.3742,  0.4658,  0.5526,  0.6338,  0.7086,  0.7761,\n",
              "         0.8358,  0.8869,  0.9289,  0.9615,  0.9843,  0.9971,  0.9997,  0.9921,\n",
              "         0.9744,  0.9467,  0.9094,  0.8629,  0.8075,  0.7439,  0.6727,  0.5947,\n",
              "         0.5106,  0.4213,  0.3277,  0.2308,  0.1315,  0.0308, -0.0701, -0.1703,\n",
              "        -0.2688, -0.3646, -0.4566, -0.5440])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHdlFIwUsQ5L",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "583bdc28-8212-4938-f0bc-1d7a864ede5d"
      },
      "source": [
        "plt.plot(x.numpy(), y.numpy())"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f5d1e2840b8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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nsP2od67R4JeJoX8JPi0jjb4l2QleXWv1NYdqT3O8vk3f+26wJDuB7l7Dewe8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\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcJLF1aXwXTK",
        "colab_type": "text"
      },
      "source": [
        "**Dimensional Tensors**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tlYvsPIFsdNC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "83e725c4-e01f-47af-d880-b1eb32ff53fa"
      },
      "source": [
        "one_d = torch.arange(0,9)\n",
        "one_d"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0, 1, 2, 3, 4, 5, 6, 7, 8])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "375Y0toOsjdn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "0c77252b-c93d-4cfc-9177-7e7cf4b909d4"
      },
      "source": [
        "two_d = one_d.view(3,3)\n",
        "two_d"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1, 2],\n",
              "        [3, 4, 5],\n",
              "        [6, 7, 8]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bSL62q-EsrAd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b9b52b28-88ff-45fd-9fbf-02e9ffe5c595"
      },
      "source": [
        "# Dimensions of Tensor\n",
        "two_d.dim()"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tEdoTnjlsvh4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ad0d73f3-0b69-4b2b-a6c6-9edbc1be9a39"
      },
      "source": [
        "# Indexing\n",
        "two_d[1, 2]"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v5dTxQnEs4Ia",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "ba4fb98c-d97e-4ae9-dd1a-a96ef733cbcb"
      },
      "source": [
        "x = torch.arange(0, 18).view(3,2,3)\n",
        "x"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[ 0,  1,  2],\n",
              "         [ 3,  4,  5]],\n",
              "\n",
              "        [[ 6,  7,  8],\n",
              "         [ 9, 10, 11]],\n",
              "\n",
              "        [[12, 13, 14],\n",
              "         [15, 16, 17]]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "81x0MQx9wbfP",
        "colab_type": "text"
      },
      "source": [
        "**Slicing 3D Tensor**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mq6BMgHvtOlY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "86085923-307a-4beb-c352-7e4d94c9cb96"
      },
      "source": [
        "x[1, 1, 1]"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(10)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wcW1xEe0tV7U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "99bccc09-c50b-4b33-da2d-857ed72bb710"
      },
      "source": [
        "x[1, : , :]"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 6,  7,  8],\n",
              "        [ 9, 10, 11]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1zTljw_lweoJ",
        "colab_type": "text"
      },
      "source": [
        "**Matrix Multiplication**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K0AAXKbItr-I",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "9d70c68c-56c5-421a-fd9b-cdf216b320eb"
      },
      "source": [
        "# Matrix A\n",
        "mat_a = torch.tensor([0,3, 5, 5, 5, 2]).view(2,3)\n",
        "mat_a"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 3, 5],\n",
              "        [5, 5, 2]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_-nF5hYbuGkY",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "cdd87138-35a2-4c9b-e1e6-3981e3b61003"
      },
      "source": [
        "# Matrix B\n",
        "mat_b = torch.tensor([3,4, 3, -2, 4, -2]).view(3, 2)\n",
        "mat_b"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 3,  4],\n",
              "        [ 3, -2],\n",
              "        [ 4, -2]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DDkDmbqtuPCh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "b67d301a-f754-4e48-eee2-18907baa22db"
      },
      "source": [
        "mul_op = torch.matmul(mat_a, mat_b)\n",
        "mul_op"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 29, -16],\n",
              "        [ 38,   6]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ymmxUy-PuYVa",
        "colab_type": "text"
      },
      "source": [
        "**Gradient With PyTorch**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZBgaBf8Auawf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "549f0558-6369-4206-b4bb-e0e2bd17c652"
      },
      "source": [
        "x = torch.tensor(2.0, requires_grad=True)\n",
        "y = 9*x**4 + 2*x**3 + 3*x**2 + 6*x + 1\n",
        "y"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(185., grad_fn=<AddBackward0>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "onHr90N4uk1l",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Derivative of y at x = 2\n",
        "y.backward() "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K8dPmdzwu7AS",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f7888697-143b-417d-b9e0-1245d76613f7"
      },
      "source": [
        "# Access value of derivative\n",
        "x.grad"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(330.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EW7mfGydu8FF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x = torch.tensor(1.0, requires_grad=True)\n",
        "z = torch.tensor(2.0, requires_grad=True)\n",
        "y = x**2 + z**3"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CV5Vp4AbviPy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y.backward()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1P3TxNsHvkXa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a2b07958-b347-4265-d9b5-f109740f39e4"
      },
      "source": [
        "x.grad"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(2.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lchWbLPCvlsu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f5e2d852-03a2-425c-918c-e3084c328997"
      },
      "source": [
        "z.grad"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(12.)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    }
  ]
}