Tensor_Operations.ipynb

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    "accelerator": "GPU"
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  "cells": [
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        "<a href=\"https://colab.research.google.com/github/smlra-kjsce/Pytorch-101-2023/blob/main/Tensor_Operations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Tensor Operations\n",
        "This section covers:\n",
        "* Indexing and slicing\n",
        "* Reshaping tensors (tensor views)\n",
        "* Shifting tensors between CPU and GPU\n",
        "* Tensor arithmetic and basic operations\n",
        "* Dot products\n",
        "* Matrix multiplication\n",
        "* Element-wise multiplication\n",
        "* Broadcasting\n",
        "\n",
        "## Perform standard imports"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c1YWkgLDB4JE"
      },
      "source": [
        "import torch\n",
        "import numpy as np"
      ],
      "execution_count": 1,
      "outputs": []
    },
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      "source": [
        "## Indexing and slicing\n",
        "Extracting specific values from a tensor works just the same as with NumPy arrays<br><br>\n",
        "\n",
        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)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "95Te7_qvB4JF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c7ecd4f6-64f4-47b6-ddb1-8dafadbaa465"
      },
      "source": [
        "x = torch.arange(20).reshape(5,4)\n",
        "print(x)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[ 0,  1,  2,  3],\n",
            "        [ 4,  5,  6,  7],\n",
            "        [ 8,  9, 10, 11],\n",
            "        [12, 13, 14, 15],\n",
            "        [16, 17, 18, 19]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zNZSSs6PB4JF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4798d735-511c-4fe4-c985-96bec7890987"
      },
      "source": [
        "print(x[0][1])\n",
        "print(x[2][1])"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor(1)\n",
            "tensor(9)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pwbwNtM2B4JF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f4eae6c6-7e1f-4429-bd02-a17eade13e38"
      },
      "source": [
        "# Grabbing the right hand column values\n",
        "x[1:4,1:] # x[start:end:step, start:end:step]"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 5,  6,  7],\n",
              "        [ 9, 10, 11],\n",
              "        [13, 14, 15]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "16TRklnSB4JG"
      },
      "source": [
        "## Reshape tensors\n",
        "<a href='https://pytorch.org/docs/master/tensors.html#torch.Tensor.view'><strong><tt>view()</tt></strong></a> and <a href='https://pytorch.org/docs/master/torch.html#torch.reshape'><strong><tt>reshape()</tt></strong></a> do essentially the same thing by returning a reshaped tensor without changing the original tensor in place.<br>\n",
        "There's a good discussion of the differences <a href='https://stackoverflow.com/questions/49643225/whats-the-difference-between-reshape-and-view-in-pytorch'>here</a>.\n",
        "\n",
        "Also learn about <a href='https://pytorch.org/docs/stable/generated/torch.squeeze.html'><strong><tt>squeeze()</tt></strong></a> and <a href='https://pytorch.org/docs/stable/generated/torch.unsqueeze.html'><strong><tt>unsqueeze()</tt></strong></a> "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lUF-FnstB4JG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "84a6083c-1a05-44af-e47e-4e62eef91b91"
      },
      "source": [
        "x = torch.arange(10)\n",
        "print(x)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pYCEKlRdB4JG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c5361826-cb14-4e87-f654-81095dcacd56"
      },
      "source": [
        "x.view(2,5)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1, 2, 3, 4],\n",
              "        [5, 6, 7, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Efq3v9AfB4JG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2469d456-9014-4a29-e09f-f02e023401ff"
      },
      "source": [
        "x.view(5,2)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1],\n",
              "        [2, 3],\n",
              "        [4, 5],\n",
              "        [6, 7],\n",
              "        [8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0YvK0ih7B4JH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "169b96d2-6184-45d9-8494-f572fbdbea55"
      },
      "source": [
        "# x is unchanged\n",
        "x"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aaMkaZqLB4JH"
      },
      "source": [
        "### Views reflect the most current data"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "z = x.view(2,5)\n",
        "x[0]=1\n",
        "print(z)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N-1g9TJ45Tl9",
        "outputId": "73e5fe4c-0928-4738-fa11-5433c8d9211c"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[1, 1, 2, 3, 4],\n",
            "        [5, 6, 7, 8, 9]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RKMh0gGsB4JH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7acb1525-8cd0-4b59-957e-a7165c05fc2a"
      },
      "source": [
        "z = x.view(2,5).clone()\n",
        "x[0]=1\n",
        "print(z)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[1, 1, 2, 3, 4],\n",
            "        [5, 6, 7, 8, 9]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3HZIxhTvB4JH"
      },
      "source": [
        "### Views can infer the correct size\n",
        "By passing in <tt>-1</tt> PyTorch will infer the correct value from the given tensor, when you are aware of fixing all dimensions except one while reshaping."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Awr1LZDitbs0",
        "outputId": "f7b4a8b3-e3ea-41f7-87bb-8886e984977c"
      },
      "source": [
        "y = torch.Tensor([[1,2,3,4,5,6,7,8,9,10], [11,12,13,14,15,16,17,18,19,20]])\n",
        "print(y.shape)\n",
        "y = y.view(2,2,-1)\n",
        "print(y)\n",
        "print(y.shape)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([2, 10])\n",
            "tensor([[[ 1.,  2.,  3.,  4.,  5.],\n",
            "         [ 6.,  7.,  8.,  9., 10.]],\n",
            "\n",
            "        [[11., 12., 13., 14., 15.],\n",
            "         [16., 17., 18., 19., 20.]]])\n",
            "torch.Size([2, 2, 5])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lQWVxviFB4JI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f364468d-15c0-4c90-a985-5193e4798f4f"
      },
      "source": [
        "y.view(4,-1)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.,  2.,  3.,  4.,  5.],\n",
              "        [ 6.,  7.,  8.,  9., 10.],\n",
              "        [11., 12., 13., 14., 15.],\n",
              "        [16., 17., 18., 19., 20.]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UUcDN9EnB4JI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "71835d85-732b-452e-bc39-35289500a7bd"
      },
      "source": [
        "y.view(-1,5)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.,  2.,  3.,  4.,  5.],\n",
              "        [ 6.,  7.,  8.,  9., 10.],\n",
              "        [11., 12., 13., 14., 15.],\n",
              "        [16., 17., 18., 19., 20.]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jim9POU9B4JI"
      },
      "source": [
        "### Adopt another tensor's shape with <tt>.view_as()</tt>\n",
        "<a href='https://pytorch.org/docs/master/tensors.html#torch.Tensor.view_as'><strong><tt>view_as(input)</tt></strong></a> only works with tensors that have the same number of elements."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q3X7UZgyB4JI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eced8700-cb36-48e1-8485-6514a3ebe414"
      },
      "source": [
        "x1 = torch.rand(5,4)\n",
        "x2 = torch.rand(2,10)\n",
        "print(x1)\n",
        "print()\n",
        "print(x2)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[0.0117, 0.7000, 0.3742, 0.9361],\n",
            "        [0.1188, 0.3239, 0.6452, 0.5105],\n",
            "        [0.8339, 0.6292, 0.7103, 0.5491],\n",
            "        [0.4954, 0.4763, 0.9559, 0.3393],\n",
            "        [0.2325, 0.7498, 0.7296, 0.1382]])\n",
            "\n",
            "tensor([[0.8693, 0.1949, 0.9626, 0.0965, 0.1385, 0.7827, 0.6018, 0.6016, 0.0083,\n",
            "         0.6733],\n",
            "        [0.9647, 0.6824, 0.9955, 0.1162, 0.0558, 0.9848, 0.0596, 0.5633, 0.9978,\n",
            "         0.9781]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DPOMio2JB4JI"
      },
      "source": [
        "x2 = x2.view_as(x1)"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FJCYL-sDmdVK",
        "outputId": "baa7e097-6a07-410f-aeff-05cdd11adc7c"
      },
      "source": [
        "x2 #= x2.reshape(x1.shape)\n",
        "# unchanged"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0.8693, 0.1949, 0.9626, 0.0965],\n",
              "        [0.1385, 0.7827, 0.6018, 0.6016],\n",
              "        [0.0083, 0.6733, 0.9647, 0.6824],\n",
              "        [0.9955, 0.1162, 0.0558, 0.9848],\n",
              "        [0.0596, 0.5633, 0.9978, 0.9781]])"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4lwQqFM4tBP1"
      },
      "source": [
        "### squeeze() and unsqueeze()"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pAAgCoHWmwgJ",
        "outputId": "98db4cfe-1b10-4797-c8af-6985b0e42ca4"
      },
      "source": [
        "y = torch.Tensor([[1,2,3,4,5,6,7,8,9,10], [11,12,13,14,15,16,17,18,19,20]])\n",
        "print(\"Original size: \", y.shape)\n",
        "y_row = torch.unsqueeze(y,0) # unsqueeze about row as axis=0\n",
        "print(\"Unsqueezed size:\", y_row.shape) \n",
        "print(y_row)\n",
        "y_col = torch.unsqueeze(y,1) # unsqueeze about col as axis=1\n",
        "print(y_col.shape)\n",
        "print(y_col)\n",
        "y_axis2 = torch.unsqueeze(y,2) # unsqueeze about axis=2\n",
        "print(y_axis2.shape)\n",
        "print(y_axis2)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original size:  torch.Size([2, 10])\n",
            "Unsqueezed size: torch.Size([1, 2, 10])\n",
            "tensor([[[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.],\n",
            "         [11., 12., 13., 14., 15., 16., 17., 18., 19., 20.]]])\n",
            "torch.Size([2, 1, 10])\n",
            "tensor([[[ 1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.]],\n",
            "\n",
            "        [[11., 12., 13., 14., 15., 16., 17., 18., 19., 20.]]])\n",
            "torch.Size([2, 10, 1])\n",
            "tensor([[[ 1.],\n",
            "         [ 2.],\n",
            "         [ 3.],\n",
            "         [ 4.],\n",
            "         [ 5.],\n",
            "         [ 6.],\n",
            "         [ 7.],\n",
            "         [ 8.],\n",
            "         [ 9.],\n",
            "         [10.]],\n",
            "\n",
            "        [[11.],\n",
            "         [12.],\n",
            "         [13.],\n",
            "         [14.],\n",
            "         [15.],\n",
            "         [16.],\n",
            "         [17.],\n",
            "         [18.],\n",
            "         [19.],\n",
            "         [20.]]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JenP1UVWu0yu",
        "outputId": "38f593bf-e424-40bd-abb4-47bca060a544"
      },
      "source": [
        "y = torch.Tensor([4])\n",
        "print(\"Original size: \", y.shape)\n",
        "print(y)\n",
        "y_row = torch.unsqueeze(y,0) #added another dimension across row\n",
        "print(y_row.shape)\n",
        "print(y_row)\n",
        "y_col= torch.unsqueeze(y,1) #added another dimension across column\n",
        "print(y_col.shape)\n",
        "print(y_col)\n",
        "y_restored = torch.squeeze(y_row,0) #added another dimension across row\n",
        "print(y_restored.shape)\n",
        "print(y_restored)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Original size:  torch.Size([1])\n",
            "tensor([4.])\n",
            "torch.Size([1, 1])\n",
            "tensor([[4.]])\n",
            "torch.Size([1, 1])\n",
            "tensor([[4.]])\n",
            "torch.Size([1])\n",
            "tensor([4.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MlcBWfzXwEYG",
        "outputId": "bcff2b6a-029e-4c7a-8779-ce166cecc940"
      },
      "source": [
        "y = torch.zeros(2, 1, 2, 1, 2)\n",
        "print(y.shape)\n",
        "y_sq = torch.squeeze(y)\n",
        "print(y_sq)\n",
        "print(y_sq.shape)\n",
        "print(torch.squeeze(y,0).shape) # won't change as axis=0 is not equal to 1\n",
        "print(torch.squeeze(y,1).shape)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "torch.Size([2, 1, 2, 1, 2])\n",
            "tensor([[[0., 0.],\n",
            "         [0., 0.]],\n",
            "\n",
            "        [[0., 0.],\n",
            "         [0., 0.]]])\n",
            "torch.Size([2, 2, 2])\n",
            "torch.Size([2, 1, 2, 1, 2])\n",
            "torch.Size([2, 2, 1, 2])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1uXv5av2r-Ju"
      },
      "source": [
        "## Shifting tensors between CPU and GPU"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N8qZo6XPsEHo"
      },
      "source": [
        "# Tensor loading into GPU, back to CPU, detach(), etc.\n",
        "# Check device (first) = cuda, if i want to perform a non-gpu task then first i have to bring the tensors from gpu memory to cpu one.\n",
        "# if gradient is attached to tensor in cpu or gpu, so call detach (if cpu) and detach().cpu() (if gpu)"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FT88A8Q6cPSD"
      },
      "source": [
        "t = torch.Tensor([1,2,3])"
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "xDVh5x461yLo",
        "outputId": "b1568e94-ae1f-41ad-dbe7-80513ea3432b"
      },
      "source": [
        "t.type()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'torch.FloatTensor'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QdiyHOGjbBm7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d66541b7-d086-4702-a8a0-ece05a63edb6"
      },
      "source": [
        "# To check where a particular tensor is located\n",
        "t.device"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "device(type='cpu')"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xv5mLa2kcrGi",
        "outputId": "cf606d2c-ad29-4a88-f06f-665c3724d846"
      },
      "source": [
        "dev = torch.device(\"cuda\") if torch.cuda.is_available() else torch.device(\"cpu\")\n",
        "print(dev)"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "cuda\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "kCHCHc4jdJeN",
        "outputId": "972b4b10-6cb2-432a-9336-d80600d0088d"
      },
      "source": [
        "# For now, let's assume dev = 'gpu', you can shift tensors or models from gpu to cpu or vice versa using tensor_name.to(dev) / model.to(dev)\n",
        "t.to(dev)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1., 2., 3.], device='cuda:0')"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "TzTZnb391ul5",
        "outputId": "be25fb9a-9d81-413c-cf82-030c51154880"
      },
      "source": [
        "t.type()"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'torch.FloatTensor'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3jjZT-IQdwdP",
        "outputId": "53b81ad0-a555-46ce-a946-851b593ce165"
      },
      "source": [
        "# You can also use tensor_name.cpu()\n",
        "t.cpu()"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1., 2., 3.])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6xdNkHPZB4JI"
      },
      "source": [
        "## Tensor Arithmetic\n",
        "Adding tensors can be performed a few different ways depending on the desired result.<br>\n",
        "\n",
        "As a simple expression:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dAlIO1CcB4JJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b36e7196-8c5d-4785-bc0c-09e9550fea1e"
      },
      "source": [
        "a = torch.tensor([1,2,3], dtype=torch.float32)\n",
        "b = torch.tensor([4,5,6], dtype=torch.float32)\n",
        "print(a + b)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([5., 7., 9.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U1E05lSwB4JJ"
      },
      "source": [
        "As arguments passed into a torch operation:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V3_7JsZoB4JJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d981bf2-71ee-4caa-8390-e8f38b96882b"
      },
      "source": [
        "print(torch.add(a, b))\n",
        "print(a)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([5., 7., 9.])\n",
            "tensor([1., 2., 3.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pCL7y9x6B4JJ"
      },
      "source": [
        "Changing a tensor in-place"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jU5J3c8sB4JJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "41839b82-f640-4fc4-d2ba-65f8e7eaf144"
      },
      "source": [
        "a.add_(b)  # equivalent to a=torch.add(a,b)\n",
        "print(a)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([5., 7., 9.])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cKt8jB09B4JK"
      },
      "source": [
        "<div class=\"alert alert-info\"><strong>NOTE:</strong> Any operation that changes a tensor in-place is post-fixed with an underscore _.\n",
        "    <br>In the above example: <tt>a.add_(b)</tt> changed <tt>a</tt>.</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s2EJjZPYB4JK"
      },
      "source": [
        "### Basic Tensor Operations\n",
        "<table style=\"display: inline-block\">\n",
        "<caption style=\"text-align: center\"><strong>Arithmetic</strong></caption>\n",
        "<tr><th>OPERATION</th><th>FUNCTION</th><th>DESCRIPTION</th></tr>\n",
        "<tr><td>a + b</td><td>a.add(b)</td><td>element wise addition</td></tr>\n",
        "<tr><td>a - b</td><td>a.sub(b)</td><td>subtraction</td></tr>\n",
        "<tr><td>a * b</td><td>a.mul(b)</td><td>multiplication</td></tr>\n",
        "<tr><td>a / b</td><td>a.div(b)</td><td>division</td></tr>\n",
        "<tr><td>a % b</td><td>a.fmod(b)</td><td>modulo (remainder after division)</td></tr>\n",
        "<tr><td>a<sup>b</sup></td><td>a.pow(b)</td><td>power</td></tr>\n",
        "<tr><td>&nbsp;</td><td></td><td></td></tr>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PbReIs_KB4JK"
      },
      "source": [
        "<table style=\"display: inline-block\">\n",
        "<caption style=\"text-align: center\"><strong>Monomial Operations</strong></caption>\n",
        "<tr><th>OPERATION</th><th>FUNCTION</th><th>DESCRIPTION</th></tr>\n",
        "<tr><td>|a|</td><td>torch.abs(a)</td><td>absolute value</td></tr>\n",
        "<tr><td>1/a</td><td>torch.reciprocal(a)</td><td>reciprocal</td></tr>\n",
        "<tr><td>$\\sqrt{a}$</td><td>torch.sqrt(a)</td><td>square root</td></tr>\n",
        "<tr><td>log(a)</td><td>torch.log(a)</td><td>natural log</td></tr>\n",
        "<tr><td>e<sup>a</sup></td><td>torch.exp(a)</td><td>exponential</td></tr>\n",
        "<tr><td>12.34  ==>  12.</td><td>torch.trunc(a)</td><td>truncated integer</td></tr>\n",
        "<tr><td>12.34  ==>  0.34</td><td>torch.frac(a)</td><td>fractional component</td></tr>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G6ilCs3kB4JK"
      },
      "source": [
        "<table style=\"display: inline-block\">\n",
        "<caption style=\"text-align: center\"><strong>Summary Statistics</strong></caption>\n",
        "<tr><th>OPERATION</th><th>FUNCTION</th><th>DESCRIPTION</th></tr>\n",
        "<tr><td>$\\sum a$</td><td>torch.sum(a)</td><td>sum</td></tr>\n",
        "<tr><td>$\\bar a$</td><td>torch.mean(a)</td><td>mean</td></tr>\n",
        "<tr><td>a<sub>max</sub></td><td>torch.max(a)</td><td>maximum</td></tr>\n",
        "<tr><td>a<sub>min</sub></td><td>torch.min(a)</td><td>minimum</td></tr>\n",
        "<tr><td colspan=\"3\">torch.max(a,b) returns a tensor of size a<br>containing the element wise max between a and b</td></tr>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AsikSU_EB4JK"
      },
      "source": [
        "<div class=\"alert alert-info\"><strong>NOTE:</strong> Most arithmetic operations require float values. Those that do work with integers return integer tensors.<br>\n",
        "For example, <tt>torch.div(a,b)</tt> performs floor division (truncates the decimal) for integer types, and classic division for floats.</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mWtCOyCxB4JL"
      },
      "source": [
        "## Dot products\n",
        "A <a href='https://en.wikipedia.org/wiki/Dot_product'>dot product</a> is the sum of the products of the corresponding entries of two 1D tensors. If the tensors are both vectors, the dot product is given as:<br>\n",
        "\n",
        "$\\begin{bmatrix} a & b & c \\end{bmatrix} \\;\\cdot\\; \\begin{bmatrix} d & e & f \\end{bmatrix} = ad + be + cf$\n",
        "\n",
        "If the tensors include a column vector, then the dot product is the sum of the result of the multiplied matrices. For example:<br>\n",
        "$\\begin{bmatrix} a & b & c \\end{bmatrix} \\;\\cdot\\; \\begin{bmatrix} d \\\\ e \\\\ f \\end{bmatrix} = ad + be + cf$<br><br>\n",
        "Dot products can be expressed as <a href='https://pytorch.org/docs/stable/torch.html#torch.dot'><strong><tt>torch.dot(a,b)</tt></strong></a> or `a.dot(b)` or `b.dot(a)`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "DJhnV8cyB4JL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5a00d170-067e-4c11-dce9-a4b8f3d412ab"
      },
      "source": [
        "a = torch.tensor([1,2,3], dtype=torch.float)\n",
        "b = torch.tensor([4,5,6], dtype=torch.float)\n",
        "print(a.mul(b)) # for reference\n",
        "print()\n",
        "print(a.dot(b))"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([ 4., 10., 18.])\n",
            "\n",
            "tensor(32.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XzHSC2EjB4JL"
      },
      "source": [
        "<div class=\"alert alert-info\"><strong>NOTE:</strong> There's a slight difference between <tt>torch.dot()</tt> and <tt>numpy.dot()</tt>. While <tt>torch.dot()</tt> only accepts 1D arguments and returns a dot product, <tt>numpy.dot()</tt> also accepts 2D arguments and performs matrix multiplication. We show matrix multiplication below.</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SYUtYD8TB4JM"
      },
      "source": [
        "## Matrix multiplication\n",
        "2D <a href='https://en.wikipedia.org/wiki/Matrix_multiplication'>Matrix multiplication</a> is possible when the number of columns in tensor <strong><tt>A</tt></strong> matches the number of rows in tensor <strong><tt>B</tt></strong>. In this case, the product of tensor <strong><tt>A</tt></strong> with size $(x,y)$ and tensor <strong><tt>B</tt></strong> with size $(y,z)$ results in a tensor of size $(x,z)$\n",
        "\n",
        "<br>\n",
        "\n",
        "$\\begin{bmatrix} a & b & c \\\\\n",
        "d & e & f \\end{bmatrix} \\;\\times\\; \\begin{bmatrix} m & n \\\\ p & q \\\\ r & s \\end{bmatrix} = \\begin{bmatrix} (am+bp+cr) & (an+bq+cs) \\\\\n",
        "(dm+ep+fr) & (dn+eq+fs) \\end{bmatrix}$\n",
        "\n",
        "<br>\n",
        "\n",
        "Matrix multiplication can be computed using <a href='https://pytorch.org/docs/stable/torch.html#torch.mm'><strong><tt>torch.mm(a,b)</tt></strong></a> or `a.mm(b)` or `a @ b`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uA6WZW-oB4JM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8c19b152-eccc-43fd-b4a0-4636daf4e5cb"
      },
      "source": [
        "a = torch.tensor([[0,2,4],[1,3,5]], dtype=torch.float)\n",
        "b = torch.tensor([[6,7],[8,9],[10,11]], dtype=torch.float)\n",
        "\n",
        "print('a: ',a.size())\n",
        "print('b: ',b.size())\n",
        "print('a x b: ',torch.mm(a,b).size())"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "a:  torch.Size([2, 3])\n",
            "b:  torch.Size([3, 2])\n",
            "a x b:  torch.Size([2, 2])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jDzrDElNB4JN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "57ec6117-35dd-4f6a-be95-e4a512bbef39"
      },
      "source": [
        "print(torch.mm(a,b))"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[56., 62.],\n",
            "        [80., 89.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zquvOOQOB4JN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2c6842e0-516a-42aa-e5ab-7b656dd403ca"
      },
      "source": [
        "print(a.mm(b))"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[56., 62.],\n",
            "        [80., 89.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M1vM6HXkB4JN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3af26cd7-d0a5-4f09-d87b-3044bdd93381"
      },
      "source": [
        "print(a @ b)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[56., 62.],\n",
            "        [80., 89.]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zCkV5LEG1YT2"
      },
      "source": [
        "## Element-Wise Multiplication"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XbJSBSM81a4E"
      },
      "source": [
        "#TODO: Show usage of mul() operator. A.mul(B) or torch.mul(A,B)\n",
        "a = torch.tensor([[1,2,4],[1,3,5]])\n",
        "b = torch.tensor([[6,8,9],[2,10,11]])"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4fMUP8RTO6yP",
        "outputId": "93de0387-7dc2-4d3b-d3d6-deeef5b1d554"
      },
      "source": [
        "a.mul(b) # Use mul_ to store the output matrix in 'a' itself"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 6, 16, 36],\n",
              "        [ 2, 30, 55]])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iMtaI2xvQnhw",
        "outputId": "c38100e6-0e72-4d03-d56f-f40372686ad2"
      },
      "source": [
        "b.mul(a)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 6, 16, 36],\n",
              "        [ 2, 30, 55]])"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lujdtMhhQZzh",
        "outputId": "fa9e9ebf-6678-405a-c0b9-f1c340127df0"
      },
      "source": [
        "torch.mul(a,b)"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 6, 16, 36],\n",
              "        [ 2, 30, 55]])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q_5J_7zzQcwd",
        "outputId": "71b32547-b83d-4366-9977-999fb11fe85d"
      },
      "source": [
        "a \n",
        "# unchanged"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 2, 4],\n",
              "        [1, 3, 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yjjdxebmxul0"
      },
      "source": [
        "## Broadcasting\n",
        "\n",
        "Two tensors are “broadcastable” if the following rules hold:\n",
        "\n",
        "* Each tensor has at least one dimension.\n",
        "\n",
        "* When iterating over the dimension sizes, starting at the trailing dimension (last dimension in the list), the dimension sizes must either be equal, one of them is 1, or one of them does not exist."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bRnwB8itxq2n",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2954fcee-db13-4def-ad42-50918a2cefca"
      },
      "source": [
        "t1 = torch.randn(3, 4)\n",
        "t2 = torch.randn(1, 4)\n",
        "\n",
        "print(t1,t2,sep='\\n\\n')"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[-1.8285,  1.5425, -1.4791,  0.9434],\n",
            "        [-0.0147,  0.2155,  1.1475, -0.5443],\n",
            "        [ 0.4971,  1.1518,  0.7871, -0.9881]])\n",
            "\n",
            "tensor([[-0.7777,  1.5015, -1.3785, -0.2593]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2HjVrXAdZLXJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7fcdaf2c-2e44-441b-b0dc-8ea6dae6a126"
      },
      "source": [
        "# Notice how the two tensors dont have the same dimensions but we can still perform arithmetic operations. Why?\n",
        "t1 + t2"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-2.6062,  3.0440, -2.8576,  0.6841],\n",
              "        [-0.7924,  1.7170, -0.2310, -0.8036],\n",
              "        [-0.2805,  2.6533, -0.5914, -1.2473]])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0G37JNv1ZOPL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "881bc918-094d-4c92-ca4a-62ad0d1cf059"
      },
      "source": [
        "t1 - t2"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1.0508,  0.0410, -0.1006,  1.2027],\n",
              "        [ 0.7630, -1.2860,  2.5260, -0.2850],\n",
              "        [ 1.2748, -0.3497,  2.1656, -0.7288]])"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-mpoax8XZaIr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "916fbfc4-5aa6-4a6f-931c-eed1108f0134"
      },
      "source": [
        "t1 = torch.randn(3, 1, 4, 1)\n",
        "t2 = torch.randn(   3, 4, 1)\n",
        "\n",
        "print(t1,t2,sep='\\n\\n')"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "tensor([[[[-0.6851],\n",
            "          [-0.3240],\n",
            "          [-0.7711],\n",
            "          [ 0.1193]]],\n",
            "\n",
            "\n",
            "        [[[-2.2631],\n",
            "          [ 0.2476],\n",
            "          [-0.0523],\n",
            "          [-0.0991]]],\n",
            "\n",
            "\n",
            "        [[[ 0.4461],\n",
            "          [ 1.4291],\n",
            "          [-0.7044],\n",
            "          [ 0.9454]]]])\n",
            "\n",
            "tensor([[[ 0.0805],\n",
            "         [-1.0933],\n",
            "         [-1.1993],\n",
            "         [-0.9187]],\n",
            "\n",
            "        [[-0.4285],\n",
            "         [-1.4204],\n",
            "         [-0.1731],\n",
            "         [-0.2208]],\n",
            "\n",
            "        [[ 0.4331],\n",
            "         [ 1.1109],\n",
            "         [ 0.9169],\n",
            "         [ 0.3299]]])\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XPfNO1ayZPgZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "42e4bad8-a7ef-4dc9-c0b0-87c8c92b3772"
      },
      "source": [
        "(t1 + t2).size()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([3, 3, 4, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wV8PxbSPB4JN"
      },
      "source": [
        "## Great work!"
      ]
    }
  ]
}