Copy_of_01_matmul.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/alimoradi296/DeepLearning/blob/main/Copy_of_01_matmul.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Ty6mGmfHWuX"
      },
      "source": [
        "## Matrix multiplication from foundations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VTBBWx-CHWuZ"
      },
      "source": [
        "The *foundations* we'll assume throughout this course are:\n",
        "\n",
        "- Python\n",
        "- matplotlib\n",
        "- The Python standard library\n",
        "- Jupyter notebooks and nbdev"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "W__63KXWHWua"
      },
      "outputs": [],
      "source": [
        "from pathlib import Path\n",
        "import pickle, gzip, math, os, time, shutil, matplotlib as mpl, matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BvpaPiK-HWub"
      },
      "source": [
        "## Get data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "q-XJ0BHXHWuc"
      },
      "outputs": [],
      "source": [
        "MNIST_URL='https://github.com/mnielsen/neural-networks-and-deep-learning/blob/master/data/mnist.pkl.gz?raw=true'\n",
        "path_data = Path('data')\n",
        "path_data.mkdir(exist_ok=True)\n",
        "path_gz = path_data/'mnist.pkl.gz'"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D6lx7q7fHWuc"
      },
      "source": [
        "[urlretrieve](https://docs.python.org/3/library/urllib.request.html#urllib.request.urlretrieve) - (read the docs!)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N2K52lLlHWud"
      },
      "outputs": [],
      "source": [
        "from urllib.request import urlretrieve\n",
        "if not path_gz.exists(): urlretrieve(MNIST_URL, path_gz)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aZMQf3iaHWud",
        "outputId": "2641b8be-0258-49b0-f996-8c962512e764"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "total 16656\n",
            "-rw-r--r-- 1 root root 17051982 Oct  3 10:56 mnist.pkl.gz\n"
          ]
        }
      ],
      "source": [
        "!ls -l data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1TyPLX5THWue"
      },
      "outputs": [],
      "source": [
        "with gzip.open(path_gz, 'rb') as f: ((x_train, y_train), (x_valid, y_valid), _) = pickle.load(f, encoding='latin-1')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ISC9brs_HWuf",
        "outputId": "5e8c17fe-e1a1-412f-ec90-ba807cee61d7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0,\n",
              " 0.0,\n",
              " 0.0,\n",
              " 0.19140625,\n",
              " 0.9296875,\n",
              " 0.98828125,\n",
              " 0.98828125,\n",
              " 0.98828125,\n",
              " 0.98828125,\n",
              " 0.98828125]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "lst1 = list(x_train[0])\n",
        "vals = lst1[200:210]\n",
        "vals"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "vals[1]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-RxIUHyhKw3f",
        "outputId": "45812a9f-a90b-4c17-c301-81129c160d51"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def chunks1(x,sz):\n",
        "  f=[]\n",
        "  for i in range(0,len(x),sz):\n",
        "    f.append(x[i:i+sz])\n",
        "  return f\n",
        "def chunks(x,sz):\n",
        "  for i in range(0,len(x),sz):yield x[i:i+sz]"
      ],
      "metadata": {
        "id": "heqLsqNRKZSa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(chunks(vals,3))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Cfykh3KULgsh",
        "outputId": "3e8e6f76-6fc8-4e12-e844-89824ad89b7a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<generator object chunks at 0x78bfa3530e40>\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e6GMf4diHWug"
      },
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "source": [
        "%%timeit\n",
        "list(chunks(lst1,5))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dTr6P-zrNQfz",
        "outputId": "b828db09-a301-40b0-ae3a-96fa3c42f7b9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The slowest run took 5.41 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "85.7 µs ± 47.2 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vhZ2KaKJHWuh",
        "outputId": "88cb3b5a-aa53-47b6-ff99-0cdcbfe01ad9"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "51.7 µs ± 1.3 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit\n",
        "list(chunks1(lst1, 3))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "akVdqpQtHWuh",
        "outputId": "89ec380b-e3ea-4a2d-b27f-d15800df64e0"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "mpl.rcParams['image.cmap'] = 'gray'\n",
        "plt.imshow(list(chunks(lst1, 28)));"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hsU3GHkbHWuh"
      },
      "source": [
        "[islice](https://docs.python.org/3/library/itertools.html#itertools.islice)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from itertools import islice"
      ],
      "metadata": {
        "id": "6JrD-WiJPSa2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "it=iter(vals)"
      ],
      "metadata": {
        "id": "L2rTChzFPkvv"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "list(islice(it,6))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8jhky3DqPXd5",
        "outputId": "5dc4f0c0-a4a5-4c7b-e756-eb654e6e172a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 0.0, 0.0, 0.19140625, 0.9296875, 0.98828125]"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "it=iter(lst1)\n",
        "img=list(iter(lambda:list(islice(it,28)),[]))"
      ],
      "metadata": {
        "id": "p8quXDgcPSGU"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.imshow(img)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "ppM8j6PtPR9M",
        "outputId": "558c7595-43ee-4e41-e56f-9413b6246b8d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x78bfa01cf640>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "SWganDRpPR0r"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "LaACppJ7PRpH"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "v1s12fEjPRXZ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "18T691IbPQ_G"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "HVRY1ffyPQY5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4mifrhPZHWui"
      },
      "outputs": [],
      "source": [
        "from itertools import islice"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LeXXuFG8HWui",
        "outputId": "087b45cd-4b2b-44c9-8961-6ae691a4aa42",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<itertools.islice at 0x78bf65a819e0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "it = iter(vals)\n",
        "islice(it, 5)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "99pr6r9eHWuj",
        "outputId": "41ccbc15-ff68-4ee0-cee2-ec9f3464c052",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 0.0, 0.0, 0.19140625, 0.9296875]"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "list(islice(it, 5))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_Cf0ymdgHWuj",
        "outputId": "aeaeb85b-88b2-4325-cedb-f8568b61dc96",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.98828125, 0.98828125, 0.98828125, 0.98828125, 0.98828125]"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "list(islice(it, 5))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qVud0QX1HWuj",
        "outputId": "e95d72bb-0c5b-4d39-e076-9ec4857d80fe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[]"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "list(islice(it, 5))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-5Yu6rrFHWuk"
      },
      "outputs": [],
      "source": [
        "it = iter(lst1)\n",
        "img = list(iter(lambda: list(islice(it, 28)), []))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vX3hjigrHWuk",
        "outputId": "49ba6ec6-32d6-4d28-e329-478036407ab9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.imshow(img);"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vHdVWsJiHWuk"
      },
      "source": [
        "## Matrix and tensor"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "M0Yw9uv-HWul",
        "outputId": "2f971752-a4e7-4caa-f7c9-b107aee66f8d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.98828125"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ],
      "source": [
        "img[20][15]"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "class Matrix:\n",
        "  def __init__(self,m): self.m=m\n",
        "  def __getitem__(self,i): return self.m[i[0]][i[1]]"
      ],
      "metadata": {
        "id": "8kEV8GmCSU06"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OSL8NiL5HWul"
      },
      "outputs": [],
      "source": [
        "#class Matrix:\n",
        " #   def __init__(self, xs): self.xs = xs\n",
        "  #  def __getitem__(self, idxs): return self.xs[idxs[0]][idxs[1]]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-csETge6HWul",
        "outputId": "5529885e-2004-42f6-ff5d-77152ac0801e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.98828125"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ],
      "source": [
        "m = Matrix(img)\n",
        "m[20,15]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gs32SyllHWum"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "from torch import tensor"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7wsK9afiHWun",
        "outputId": "3aed315b-7a1d-4d59-db13-dd4b7e8059fd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[   1,    2,    3],\n",
              "        [2323,  124,    2]])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ],
      "source": [
        "tensor([[1,2,3],[2323,124,2]])\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "K8V29HbMHWun",
        "outputId": "271b0b84-beee-4747-de55-d234240fa09e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([50000, 784])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ],
      "source": [
        "x_train,y_train,x_valid,y_valid = map(tensor,(x_train,y_train,x_valid,y_valid))\n",
        "x_train.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "id": "slDYvRAvHWun",
        "outputId": "fd35c754-20fb-4f6b-ee85-07e3ac288d93"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'torch.FloatTensor'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 33
        }
      ],
      "source": [
        "x_train.type()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jkZXHbjQHWun"
      },
      "source": [
        "[Tensor](https://pytorch.org/docs/stable/tensors.html)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PgSZdxdyHWuo",
        "outputId": "7b02fcca-8378-4801-efc4-077b9207974c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([50000, 28, 28])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ],
      "source": [
        "imgs = x_train.reshape(-1,28,28)\n",
        "imgs.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "ov7FkeHDHWuo",
        "outputId": "54512942-22c7-4346-a383-cb5ffb626c04"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.imshow(imgs[0]);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "H6d3A0_4HWuo",
        "outputId": "7787d4aa-eb02-4241-ae6c-5dd7e9d50972"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.9883)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ],
      "source": [
        "imgs[0,20,15]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z4z6sJteHWup",
        "outputId": "63aee857-2bff-4863-d10c-1557123d1ed8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([5, 0, 4,  ..., 8, 4, 8]), torch.Size([50000]))"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ],
      "source": [
        "n,c = x_train.shape\n",
        "y_train, y_train.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nSTIFrKyHWuq",
        "outputId": "83e88196-1a7e-403d-b381-e34a3311dbb9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0), tensor(9))"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ],
      "source": [
        "min(y_train),max(y_train)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IY9Qn0r2HWuq",
        "outputId": "16d7f0a8-da85-4464-9eb3-b958c7cf242b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(0), tensor(9))"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ],
      "source": [
        "y_train.min(), y_train.max()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KEcHV_7JHWuq"
      },
      "source": [
        "## Random numbers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ouow6kZqHWur"
      },
      "source": [
        "Based on the Wichmann Hill algorithm used before Python 2.3."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VyQSXy-jHWur"
      },
      "outputs": [],
      "source": [
        "rnd_state = None\n",
        "def seed(a):\n",
        "    global rnd_state\n",
        "    a, x = divmod(a, 30268)\n",
        "    a, y = divmod(a, 30306)\n",
        "    a, z = divmod(a, 30322)\n",
        "    rnd_state = int(x)+1, int(y)+1, int(z)+1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0I_ZCRLrHWur",
        "outputId": "cf401354-f695-4783-8687-ac7327f01425",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(4976, 20238, 499)"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "seed(457428938475)\n",
        "rnd_state"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ub83IaVBHWur"
      },
      "outputs": [],
      "source": [
        "def rand():\n",
        "    global rnd_state\n",
        "    x, y, z = rnd_state\n",
        "    x = (171 * x) % 30269\n",
        "    y = (172 * y) % 30307\n",
        "    z = (170 * z) % 30323\n",
        "    rnd_state = x,y,z\n",
        "    return (x/30269 + y/30307 + z/30323) % 1.0"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HE0IjOUxHWus",
        "outputId": "d4b74df8-14a3-4252-e1fe-30528edc57b8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.7645251082582081, 0.7920889799553945, 0.06912886811267205)"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "rand(),rand(),rand()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tngNlymhHWus",
        "outputId": "5d230c1b-671f-4b16-fdb8-42ffd9c454b1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "In parent: 0.9559050644103264\n",
            "In child: 0.9559050644103264\n"
          ]
        }
      ],
      "source": [
        "if os.fork(): print(f'In parent: {rand()}')\n",
        "else:\n",
        "    print(f'In child: {rand()}')\n",
        "    os._exit(os.EX_OK)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4Bp_6uy_HWus",
        "outputId": "5d07a2b9-81e3-4df7-a953-8b6adfa49142",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "In child: tensor([0.2634])In parent: tensor([0.2634])\n",
            "\n"
          ]
        }
      ],
      "source": [
        "if os.fork(): print(f'In parent: {torch.rand(1)}')\n",
        "else:\n",
        "    print(f'In child: {torch.rand(1)}')\n",
        "    os._exit(os.EX_OK)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lc_jE7_yHWut",
        "outputId": "a2e8e14c-eb0c-4f42-ba04-03b6d4d4b24f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.plot([rand() for _ in range(50)]);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EO2Lj6WmHWut",
        "outputId": "f31e2091-92f2-41a9-c52d-34fc425a2641",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        }
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "plt.hist([rand() for _ in range(10000)]);"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "z3Vl8Zf1HWut",
        "outputId": "31457950-4881-4d03-eabf-0535f8cf109d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.68 ms ± 575 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 10 list(chunks([rand() for _ in range(7840)], 10))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "A2HgUqlDHWuu",
        "outputId": "29c68fa4-8b12-4e7b-977a-ac830d630931",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The slowest run took 4.28 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
            "88.1 µs ± 68.2 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 10 torch.randn(784,10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rl_WD0uIHWuu"
      },
      "source": [
        "## Matrix multiplication"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DiDpWZK_HWuy"
      },
      "outputs": [],
      "source": [
        "torch.manual_seed(1)\n",
        "weights = torch.randn(784,10)\n",
        "bias = torch.zeros(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6ZOrFwqWHWuy"
      },
      "outputs": [],
      "source": [
        "m1 = x_valid[:5]\n",
        "m2 = weights"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Nrl2KY_MHWuz",
        "outputId": "3afcf4e6-13be-4c2e-819b-0ec09b7cf984",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([5, 784]), torch.Size([784, 10]))"
            ]
          },
          "metadata": {},
          "execution_count": 52
        }
      ],
      "source": [
        "m1.shape,m2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e-dxKnlpHWuz",
        "outputId": "4495e333-2c9b-4ad6-fa2d-68811acbbee2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((5, 784), (784, 10))"
            ]
          },
          "metadata": {},
          "execution_count": 53
        }
      ],
      "source": [
        "ar,ac = m1.shape # n_rows * n_cols\n",
        "br,bc = m2.shape\n",
        "(ar,ac),(br,bc)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iIxvsbcqHWu0",
        "outputId": "51e92aca-79ad-4be6-f33a-80acfea0b8c9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ],
      "source": [
        "t1 = torch.zeros(ar, bc)\n",
        "t1.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WWRn18Z7HWu0"
      },
      "outputs": [],
      "source": [
        "for i in range(ar):         # 5\n",
        "    for j in range(bc):     # 10\n",
        "        for k in range(ac): # 784\n",
        "            t1[i,j] += m1[i,k] * m2[k,j]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZoxXCKhHHWu0",
        "outputId": "aaee6364-896a-453c-b50f-4dd05d88359c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.9417,  -0.6844,  -7.0038,  -4.0066,  -2.0857,  -3.3588,   3.9127,\n",
              "          -3.4375, -11.4696,  -2.1153],\n",
              "        [ 14.5430,   5.9977,   2.8914,  -4.0777,   6.5914, -14.7383,  -9.2787,\n",
              "           2.1577, -15.2772,  -2.6758],\n",
              "        [  2.2204,  -3.2171,  -4.7988,  -6.0453,  14.1661,  -8.9824,  -4.7922,\n",
              "          -5.4446, -20.6758,  13.5657],\n",
              "        [ -6.7097,   8.8998,  -7.4611,  -7.8966,   2.6994,  -4.7260, -11.0278,\n",
              "         -12.9776,  -6.4443,   3.6376],\n",
              "        [ -2.4444,  -6.4034,  -2.3984,  -9.0371,  11.1772,  -5.7724,  -8.9214,\n",
              "          -3.7862,  -8.9827,   5.2797]])"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ],
      "source": [
        "t1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FIJKrDtLHWu0",
        "outputId": "d0dcec3f-fd38-401b-d881-d48b68ab09fa",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ],
      "source": [
        "t1.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4H0KfvjYHWu1",
        "outputId": "edaebaa1-274c-46d6-86cb-cee66ed312c1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
              "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
              "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
              "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
              "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ],
      "source": [
        "torch.set_printoptions(precision=2, linewidth=140, sci_mode=False)\n",
        "t1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "J5xCxKgvHWu1"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "np.set_printoptions(precision=2, linewidth=140)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mH_B4hLRHWu2"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b):\n",
        "    (ar,ac),(br,bc) = a.shape,b.shape\n",
        "    c = torch.zeros(ar, bc)\n",
        "    for i in range(ar):\n",
        "        for j in range(bc):\n",
        "            for k in range(ac): c[i,j] += a[i,k] * b[k,j]\n",
        "    return c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_tqEKvRwHWu2",
        "outputId": "037b458c-cccc-4a7c-bf0f-e2c9b1df2e79",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CPU times: user 1.34 s, sys: 0 ns, total: 1.34 s\n",
            "Wall time: 1.39 s\n"
          ]
        }
      ],
      "source": [
        "%time _=matmul(m1, m2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vvpLNEi5HWu2",
        "outputId": "a3c6d9a8-fb40-4e85-f0af-90eb7b3b3f53",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "39200"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ],
      "source": [
        "ar*bc*ac"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Expt-n1rHWu2"
      },
      "source": [
        "## Numba"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Wu0bKAA-HWu2"
      },
      "outputs": [],
      "source": [
        "from numba import njit"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3fJNWiAUHWu3"
      },
      "outputs": [],
      "source": [
        "@njit\n",
        "def dot(a,b):\n",
        "    res = 0.\n",
        "    for i in range(len(a)): res+=a[i]*b[i]\n",
        "    return res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9zUIbme0HWu3"
      },
      "outputs": [],
      "source": [
        "from numpy import array"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KPDPtul9HWu4",
        "outputId": "6ea205f2-fd33-4d0a-ef02-1c340000755d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CPU times: user 720 ms, sys: 123 ms, total: 844 ms\n",
            "Wall time: 890 ms\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20.0"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ],
      "source": [
        "%time dot(array([1.,2,3]),array([2.,3,4]))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7oHlqG02HWu4",
        "outputId": "aa10d100-5226-42e2-de35-fe6365141ff9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CPU times: user 41 µs, sys: 0 ns, total: 41 µs\n",
            "Wall time: 45.8 µs\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20.0"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ],
      "source": [
        "%time dot(array([1.,2,3]),array([2.,3,4]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UvzP7GoIHWu4"
      },
      "source": [
        "Now only two of our loops are running in Python, not three:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gOnzKMCfHWu4"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b):\n",
        "    (ar,ac),(br,bc) = a.shape,b.shape\n",
        "    c = torch.zeros(ar, bc)\n",
        "    for i in range(ar):\n",
        "        for j in range(bc): c[i,j] = dot(a[i,:], b[:,j])\n",
        "    return c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "50dHXsFXHWu5"
      },
      "outputs": [],
      "source": [
        "m1a,m2a = m1.numpy(),m2.numpy()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "egkr9Y4bHWu5"
      },
      "outputs": [],
      "source": [
        "from fastcore.test import *"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1zo7LQB4HWu5"
      },
      "outputs": [],
      "source": [
        "test_close(t1,matmul(m1a, m2a))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "idY7AwozHWu5",
        "outputId": "aebe1c21-1bdf-49f0-ebac-559d35b54ab9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "786 µs ± 37.2 µs per loop (mean ± std. dev. of 7 runs, 50 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 50 matmul(m1a,m2a)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gK4bgrG2HWu6"
      },
      "source": [
        "## Elementwise ops"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZJqplanuHWu6"
      },
      "source": [
        "[TryAPL](https://tryapl.org/)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CF7v9GZsHWu6",
        "outputId": "16fc8256-204d-4e3a-e016-70e8e6ffc53c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([10.,  6., -4.]), tensor([2., 8., 7.]))"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ],
      "source": [
        "a = tensor([10., 6, -4])\n",
        "b = tensor([2., 8, 7])\n",
        "a,b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-SKDeIHHHWu6",
        "outputId": "66a0d584-e25d-4f9b-f681-a4c37cc70967",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([12., 14.,  3.])"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ],
      "source": [
        "a + b"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lLMe6Ig5HWu7",
        "outputId": "3dbafabb-d8da-4b26-bb11-37827aa3f401",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.67)"
            ]
          },
          "metadata": {},
          "execution_count": 75
        }
      ],
      "source": [
        "(a < b).float().mean()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UdxrxaORHWu7",
        "outputId": "73430ea0-fe58-4758-b4d1-2fffbad44790",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3.],\n",
              "        [4., 5., 6.],\n",
              "        [7., 8., 9.]])"
            ]
          },
          "metadata": {},
          "execution_count": 76
        }
      ],
      "source": [
        "m = tensor([[1., 2, 3], [4,5,6], [7,8,9]]); m"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sGoQNDCcHWu7"
      },
      "source": [
        "Frobenius norm:\n",
        "\n",
        "$$\\| A \\|_F = \\left( \\sum_{i,j=1}^n | a_{ij} |^2 \\right)^{1/2}$$\n",
        "\n",
        "*Hint*: you don't normally need to write equations in LaTeX yourself, instead, you can click 'edit' in Wikipedia and copy the LaTeX from there (which is what I did for the above equation). Or on arxiv.org, click \"Download: Other formats\" in the top right, then \"Download source\"; rename the downloaded file to end in `.tgz` if it doesn't already, and you should find the source there, including the equations to copy and paste. This is the source LaTeX that I pasted to render the equation above:\n",
        "\n",
        "```latex\n",
        "$$\\| A \\|_F = \\left( \\sum_{i,j=1}^n | a_{ij} |^2 \\right)^{1/2}$$\n",
        "```"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Sz7uRTTxHWu8",
        "outputId": "282b86eb-57a9-48c7-a87b-c9c722c3d32e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(285.)"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ],
      "source": [
        "sf = (m*m).sum()\n",
        "sf"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ouhv7WelHWu8",
        "outputId": "667deacd-90d8-4b51-b384-f1488cadec09",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(16.88)"
            ]
          },
          "metadata": {},
          "execution_count": 78
        }
      ],
      "source": [
        "sf.sqrt()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "077Qo6ryHWu9",
        "outputId": "6294a5ff-7660-42e8-e7c7-b73481ba5f49",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([7., 8., 9.]), tensor([3., 6., 9.]))"
            ]
          },
          "metadata": {},
          "execution_count": 79
        }
      ],
      "source": [
        "m[2,:],m[:,2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oD0Yn9gWHWu9",
        "outputId": "76641469-38f3-447e-da6c-32af7329854a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([7., 8., 9.])"
            ]
          },
          "metadata": {},
          "execution_count": 80
        }
      ],
      "source": [
        "m[2]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7t4U7PB6HWu9"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b):\n",
        "    (ar,ac),(br,bc) = a.shape,b.shape\n",
        "    c = torch.zeros(ar, bc)\n",
        "    for i in range(ar):\n",
        "        for j in range(bc): c[i,j] = (a[i,:] * b[:,j]).sum()\n",
        "    return c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "eVx_2g66HWu-"
      },
      "outputs": [],
      "source": [
        "test_close(t1,matmul(m1, m2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5BZUOWStHWu-",
        "outputId": "efecdaf4-1680-4e92-c5a4-b249bdc97fe1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "2.65 ms ± 342 µs per loop (mean ± std. dev. of 7 runs, 50 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 50 _=matmul(m1, m2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "yQ2btVauHWu-"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b):\n",
        "    (ar,ac),(br,bc) = a.shape,b.shape\n",
        "    c = torch.zeros(ar, bc)\n",
        "    for i in range(ar):\n",
        "        for j in range(bc): c[i,j] = torch.dot(a[i,:], b[:,j])\n",
        "    return c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "u-FfUAfbHWu_"
      },
      "outputs": [],
      "source": [
        "test_close(t1,matmul(m1, m2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zbXLfmCWHWu_",
        "outputId": "0a1f02dc-30b2-43b1-f560-810ac35d711c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.68 ms ± 359 µs per loop (mean ± std. dev. of 7 runs, 50 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 50 _=matmul(m1, m2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mgUQdtl_HWvA"
      },
      "source": [
        "## Broadcasting"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hhZEIZIZHWvA"
      },
      "source": [
        "The term **broadcasting** describes how arrays with different shapes are treated during arithmetic operations.\n",
        "\n",
        "From the [Numpy Documentation](https://docs.scipy.org/doc/numpy-1.10.0/user/basics.broadcasting.html):\n",
        "\n",
        "    The term broadcasting describes how numpy treats arrays with\n",
        "    different shapes during arithmetic operations. Subject to certain\n",
        "    constraints, the smaller array is “broadcast” across the larger\n",
        "    array so that they have compatible shapes. Broadcasting provides a\n",
        "    means of vectorizing array operations so that looping occurs in C\n",
        "    instead of Python. It does this without making needless copies of\n",
        "    data and usually leads to efficient algorithm implementations.\n",
        "    \n",
        "In addition to the efficiency of broadcasting, it allows developers to write less code, which typically leads to fewer errors.\n",
        "\n",
        "*This section was adapted from [Chapter 4](http://nbviewer.jupyter.org/github/fastai/numerical-linear-algebra/blob/master/nbs/4.%20Compressed%20Sensing%20of%20CT%20Scans%20with%20Robust%20Regression.ipynb#4.-Compressed-Sensing-of-CT-Scans-with-Robust-Regression) of the fast.ai [Computational Linear Algebra](https://github.com/fastai/numerical-linear-algebra) course.*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lhEsVxo0HWvA"
      },
      "source": [
        "### Broadcasting with a scalar"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AUn5yQMWHWvB",
        "outputId": "97276575-4129-4abb-d635-6f7571042bb9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([10.,  6., -4.])"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ],
      "source": [
        "a"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "a2fmPV6QHWvB",
        "outputId": "f08b0558-eb4a-4987-e02d-886548623d64",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ True,  True, False])"
            ]
          },
          "metadata": {},
          "execution_count": 88
        }
      ],
      "source": [
        "a > 0"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OktATgkCHWvB"
      },
      "source": [
        "How are we able to do `a > 0`?  0 is being **broadcast** to have the same dimensions as a.\n",
        "\n",
        "For instance you can normalize our dataset by subtracting the mean (a scalar) from the entire data set (a matrix) and dividing by the standard deviation (another scalar), using broadcasting.\n",
        "\n",
        "Other examples of broadcasting with a scalar:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "mxvHgRhBHWvC",
        "outputId": "463a0388-42f1-4b26-feb4-9f5a49034b0d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([11.,  7., -3.])"
            ]
          },
          "metadata": {},
          "execution_count": 89
        }
      ],
      "source": [
        "a + 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kQX3TlRrHWvD",
        "outputId": "0f2caa18-3c59-49c2-a398-b04a63a34fd9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3.],\n",
              "        [4., 5., 6.],\n",
              "        [7., 8., 9.]])"
            ]
          },
          "metadata": {},
          "execution_count": 90
        }
      ],
      "source": [
        "m"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "AlhACZmrHWvE",
        "outputId": "590ba397-5108-4145-e8ca-44e1dab79f1f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 2.,  4.,  6.],\n",
              "        [ 8., 10., 12.],\n",
              "        [14., 16., 18.]])"
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ],
      "source": [
        "2*m"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uZM5w1hnHWvF"
      },
      "source": [
        "### Broadcasting a vector to a matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "40xkQJRFHWvF"
      },
      "source": [
        "Although broadcasting a scalar is an idea that dates back to APL, the more powerful idea of broadcasting across higher rank tensors [comes from](https://mail.python.org/pipermail/matrix-sig/1995-November/000143.html) a little known language called [Yorick](https://software.llnl.gov/yorick-doc/manual/yorick_50.html).\n",
        "\n",
        "We can also broadcast a vector to a matrix:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ToIx75HPHWvF",
        "outputId": "577f330b-b25d-4adf-80f6-c7182d216e94",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([10., 20., 30.])"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ],
      "source": [
        "c = tensor([10.,20,30]); c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2ooXmn2MHWvF",
        "outputId": "85e5bd95-6fb2-451c-f8e7-62bafde0887e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1., 2., 3.],\n",
              "        [4., 5., 6.],\n",
              "        [7., 8., 9.]])"
            ]
          },
          "metadata": {},
          "execution_count": 93
        }
      ],
      "source": [
        "m"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "p2wGxigKHWvG",
        "outputId": "20d9794f-1157-4cbc-e90a-595dcdc00381",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([3, 3]), torch.Size([3]))"
            ]
          },
          "metadata": {},
          "execution_count": 94
        }
      ],
      "source": [
        "m.shape,c.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "31wl9tyuHWvG",
        "outputId": "1ff35ad1-fd20-47f6-eb85-8f462615fe42",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11., 22., 33.],\n",
              "        [14., 25., 36.],\n",
              "        [17., 28., 39.]])"
            ]
          },
          "metadata": {},
          "execution_count": 95
        }
      ],
      "source": [
        "m + c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uPFd8hi_HWvG",
        "outputId": "ef8b700e-542f-4b2b-c71a-34f5880b25e0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11., 22., 33.],\n",
              "        [14., 25., 36.],\n",
              "        [17., 28., 39.]])"
            ]
          },
          "metadata": {},
          "execution_count": 96
        }
      ],
      "source": [
        "c + m"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qoAQHd0oHWvG"
      },
      "outputs": [],
      "source": [
        "t = c.expand_as(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6bWkWw_THWvH",
        "outputId": "527a2726-03ee-4f0c-f7e2-cac0e72e6985",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[10., 20., 30.],\n",
              "        [10., 20., 30.],\n",
              "        [10., 20., 30.]])"
            ]
          },
          "metadata": {},
          "execution_count": 98
        }
      ],
      "source": [
        "t"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kFN5wKTnHWvH",
        "outputId": "06e797a4-5d41-4c02-ebae-65a78933b660",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11., 22., 33.],\n",
              "        [14., 25., 36.],\n",
              "        [17., 28., 39.]])"
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ],
      "source": [
        "m + t"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "28UMSdmpHWvH"
      },
      "source": [
        "We don't really copy the rows, but it looks as if we did. In fact, the rows are given a *stride* of 0."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "EHWMy7H3HWvH",
        "outputId": "66177ce0-3135-44c6-ad75-9be610efbe05",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-100-9fabd8d8a8f0>:1: UserWarning: TypedStorage is deprecated. It will be removed in the future and UntypedStorage will be the only storage class. This should only matter to you if you are using storages directly.  To access UntypedStorage directly, use tensor.untyped_storage() instead of tensor.storage()\n",
            "  t.storage()\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              " 10.0\n",
              " 20.0\n",
              " 30.0\n",
              "[torch.storage.TypedStorage(dtype=torch.float32, device=cpu) of size 3]"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ],
      "source": [
        "t.storage()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3Cgsq9J_HWvH",
        "outputId": "af3ae802-d655-443f-e691-197538c2b8ae",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((0, 1), torch.Size([3, 3]))"
            ]
          },
          "metadata": {},
          "execution_count": 101
        }
      ],
      "source": [
        "t.stride(), t.shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "90GQexXmHWvH"
      },
      "source": [
        "You can index with the special value [None] or use `unsqueeze()` to convert a 1-dimensional array into a 2-dimensional array (although one of those dimensions has value 1)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8reYYMgUHWvH",
        "outputId": "161e34d1-24b0-4fac-9919-003bad839bb4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[10., 20., 30.]]), tensor([[10., 20., 30.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 102
        }
      ],
      "source": [
        "c.unsqueeze(0), c[None, :]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qFcCc9H9HWvH",
        "outputId": "f1c8a81f-8a67-49fb-9119-58ae2ecbdc88",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([3]), torch.Size([1, 3]))"
            ]
          },
          "metadata": {},
          "execution_count": 103
        }
      ],
      "source": [
        "c.shape, c.unsqueeze(0).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "SjFcdtw3HWvI",
        "outputId": "299ef330-bb54-41ee-b100-ec19fe55735b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor([[10.],\n",
              "         [20.],\n",
              "         [30.]]),\n",
              " tensor([[10.],\n",
              "         [20.],\n",
              "         [30.]]))"
            ]
          },
          "metadata": {},
          "execution_count": 104
        }
      ],
      "source": [
        "c.unsqueeze(1), c[:, None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BbKmGnd_HWvI",
        "outputId": "90bd6d30-49e6-48ba-da87-0bf8e93948d5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([3]), torch.Size([3, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 105
        }
      ],
      "source": [
        "c.shape, c.unsqueeze(1).shape"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0GtcWAjpHWvI"
      },
      "source": [
        "You can always skip trailling ':'s. And '...' means '*all preceding dimensions*'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0V1oqUJHHWvI",
        "outputId": "d1682f03-072c-4cc0-f79e-1f7787decd78",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([1, 3]), torch.Size([3, 1]))"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ],
      "source": [
        "c[None].shape,c[...,None].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8JzohSYtHWvI",
        "outputId": "10726edd-4292-4db5-8f45-484580e30443",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[10., 10., 10.],\n",
              "        [20., 20., 20.],\n",
              "        [30., 30., 30.]])"
            ]
          },
          "metadata": {},
          "execution_count": 107
        }
      ],
      "source": [
        "c[:,None].expand_as(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fCwFM1kdHWvK",
        "outputId": "41e4f954-1aed-456e-db95-081ba8870928",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11., 12., 13.],\n",
              "        [24., 25., 26.],\n",
              "        [37., 38., 39.]])"
            ]
          },
          "metadata": {},
          "execution_count": 108
        }
      ],
      "source": [
        "m + c[:,None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oupc-kGIHWvK",
        "outputId": "b0e23afd-c9f4-4032-e650-e0e2e9b57c33",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11., 22., 33.],\n",
              "        [14., 25., 36.],\n",
              "        [17., 28., 39.]])"
            ]
          },
          "metadata": {},
          "execution_count": 109
        }
      ],
      "source": [
        "m + c[None,:]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1b8rOVBxHWvK"
      },
      "source": [
        "### Broadcasting Rules"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Oe0PlKXvHWvK",
        "outputId": "99f06e81-b071-4165-eea2-6497428882e7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[10., 20., 30.]])"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ],
      "source": [
        "c[None,:]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "47vYRiUlHWvL",
        "outputId": "f63b49c5-65bc-42d7-a26b-6a6fa75adb1e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([1, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 111
        }
      ],
      "source": [
        "c[None,:].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "11JnqUpZHWvL",
        "outputId": "81c28247-e643-4e2d-e158-505dc6e16c9a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[10.],\n",
              "        [20.],\n",
              "        [30.]])"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ],
      "source": [
        "c[:,None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "n16zPHv4HWvL",
        "outputId": "3b64a496-3958-49fe-c95f-8d7782c8d0c5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([3, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 113
        }
      ],
      "source": [
        "c[:,None].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Kdp-McelHWvL",
        "outputId": "0195f8e9-7dd2-40e9-c54f-bb09459a03cb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[100., 200., 300.],\n",
              "        [200., 400., 600.],\n",
              "        [300., 600., 900.]])"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ],
      "source": [
        "c[None,:] * c[:,None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sNBJR_G9HWvL",
        "outputId": "55555080-601e-46f7-ccf8-3da40820a391",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[False,  True,  True],\n",
              "        [False, False,  True],\n",
              "        [False, False, False]])"
            ]
          },
          "metadata": {},
          "execution_count": 115
        }
      ],
      "source": [
        "c[None] > c[:,None]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IvyayTubHWvL",
        "outputId": "9ffabdaa-20d3-4345-b566-fa1fbd46bd1c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.,  4.,  9.],\n",
              "        [16., 25., 36.],\n",
              "        [49., 64., 81.]])"
            ]
          },
          "metadata": {},
          "execution_count": 116
        }
      ],
      "source": [
        "m*m"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V43K8dXSHWvL"
      },
      "source": [
        "When operating on two arrays/tensors, Numpy/PyTorch compares their shapes element-wise. It starts with the **trailing dimensions**, and works its way forward. Two dimensions are **compatible** when\n",
        "\n",
        "- they are equal, or\n",
        "- one of them is 1, in which case that dimension is broadcasted to make it the same size\n",
        "\n",
        "Arrays do not need to have the same number of dimensions. For example, if you have a `256*256*3` array of RGB values, and you want to scale each color in the image by a different value, you can multiply the image by a one-dimensional array with 3 values. Lining up the sizes of the trailing axes of these arrays according to the broadcast rules, shows that they are compatible:\n",
        "\n",
        "    Image  (3d array): 256 x 256 x 3\n",
        "    Scale  (1d array):             3\n",
        "    Result (3d array): 256 x 256 x 3\n",
        "\n",
        "The [numpy documentation](https://docs.scipy.org/doc/numpy-1.13.0/user/basics.broadcasting.html#general-broadcasting-rules) includes several examples of what dimensions can and can not be broadcast together."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s_6acu8oHWvL"
      },
      "source": [
        "## Matmul with broadcasting"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VE-8VWNiHWvN",
        "outputId": "0ed45f15-2d06-4499-db86-2c74bdfba35a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([784]), torch.Size([784, 10]))"
            ]
          },
          "metadata": {},
          "execution_count": 117
        }
      ],
      "source": [
        "digit = m1[0]\n",
        "digit.shape,m2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DkZrxESnHWvN",
        "outputId": "3f628cbc-66a1-42f0-99a7-eb0b867ba49b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([784, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 118
        }
      ],
      "source": [
        "digit[:,None].shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6v8sqbOzHWvN",
        "outputId": "f46d0d1f-c69b-43c2-f1e5-b9568e08a539",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([784, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ],
      "source": [
        "digit[:,None].expand_as(m2).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iZnPRwsaHWvN",
        "outputId": "f01c8958-2a33-492d-8d0d-aff94e0dc4d5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([784, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 120
        }
      ],
      "source": [
        "(digit[:,None]*m2).shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "74gtuD0dHWvN"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b):\n",
        "    (ar,ac),(br,bc) = a.shape,b.shape\n",
        "    c = torch.zeros(ar, bc)\n",
        "    for i in range(ar):\n",
        "#       c[i,j] = (a[i,:] * b[:,j]).sum()      # previous version\n",
        "        c[i]   = (a[i,:,None] * b).sum(dim=0) # broadcast version\n",
        "    return c"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tqIuLuDiHWvN"
      },
      "outputs": [],
      "source": [
        "test_close(t1,matmul(m1, m2))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Z_U3CmwyHWvN",
        "outputId": "8628d16e-f2ae-4d08-d81d-477aaf6ee52b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "259 µs ± 54.4 µs per loop (mean ± std. dev. of 7 runs, 50 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 50 _=matmul(m1, m2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dAteseelHWvN"
      },
      "source": [
        "Our time has gone from ~500ms to <0.1ms, an over 5000x improvement! We can run on the whole dataset now."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1rkMqXCoHWvN",
        "outputId": "5c4d4b1c-0bc4-4b9c-d63e-38643c5b1072",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[  0.96,  -2.96,  -2.11,  ..., -15.09, -17.69,   0.60],\n",
              "        [  6.89,  -0.34,   0.79,  ..., -17.13, -25.36,  16.23],\n",
              "        [-10.18,   7.38,   4.13,  ...,  -6.73,  -6.79,  -1.58],\n",
              "        ...,\n",
              "        [  7.40,   7.64,  -3.50,  ...,  -1.02, -16.22,   2.07],\n",
              "        [  3.25,   9.52,  -9.37,  ...,   2.98, -19.58,  -1.96],\n",
              "        [ 15.70,   4.12,  -5.62,  ...,   8.08, -12.21,   0.42]])"
            ]
          },
          "metadata": {},
          "execution_count": 124
        }
      ],
      "source": [
        "tr = matmul(x_train, weights)\n",
        "tr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BcF7i1pLHWvN",
        "outputId": "ff3864db-e3fe-4ee8-cf5d-541e3c837f81",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([50000, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 125
        }
      ],
      "source": [
        "tr.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "swWiHSwgHWvP",
        "outputId": "5112ace4-2bf8-478b-f786-818bdd8bcde7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CPU times: user 2.08 s, sys: 5.4 ms, total: 2.09 s\n",
            "Wall time: 2.1 s\n"
          ]
        }
      ],
      "source": [
        "%time _=matmul(x_train, weights)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u-RHoom1HWvP"
      },
      "source": [
        "## Einstein summation"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "m=torch.einsum(\"ik,kj->ikj\",m1,m2)\n",
        "m.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KwYdRrfcM3QF",
        "outputId": "92b689cb-60a8-4957-f343-fd9bfd9b450a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 784, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "m.sum(1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CFf8V_imNlN1",
        "outputId": "0e99db24-ae66-45dc-8b71-c99ab1063ba5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
              "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
              "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
              "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
              "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
            ]
          },
          "metadata": {},
          "execution_count": 130
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-S5ApV6qHWvP"
      },
      "source": [
        "[Einstein summation](https://ajcr.net/Basic-guide-to-einsum/) ([`einsum`](https://numpy.org/doc/stable/reference/generated/numpy.einsum.html)) is a compact representation for combining products and sums in a general way. The key rules are:\n",
        "\n",
        "- Repeating letters between input arrays means that values along those axes will be multiplied together.\n",
        "- Omitting a letter from the output means that values along that axis will be summed."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m38AdI8SHWvP",
        "outputId": "bb87fa91-6bf6-4c86-9f5e-9cd193ed7dd6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(torch.Size([5, 784]), torch.Size([784, 10]))"
            ]
          },
          "metadata": {},
          "execution_count": 131
        }
      ],
      "source": [
        "m1.shape,m2.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-RPpaKplHWvP",
        "outputId": "ce31ca49-2990-4ba5-caaf-eb8c96ba17c7",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([5, 784, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 132
        }
      ],
      "source": [
        "# c[i,j] += a[i,k] * b[k,j]\n",
        "# c[i,j] = (a[i,:] * b[:,j]).sum()\n",
        "mr = torch.einsum('ik,kj->ikj', m1, m2)\n",
        "mr.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sX-0-DXVHWvP",
        "outputId": "8dc7fb37-d007-4d28-a6d8-fc6df63a793b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
              "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
              "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
              "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
              "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
            ]
          },
          "metadata": {},
          "execution_count": 133
        }
      ],
      "source": [
        "mr.sum(1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "B0RW0-oNHWvP",
        "outputId": "e4a11257-5c18-4a8c-c31b-6ef6e81d7914",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
              "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
              "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
              "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
              "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
            ]
          },
          "metadata": {},
          "execution_count": 134
        }
      ],
      "source": [
        "torch.einsum('ik,kj->ij', m1, m2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "omfh4yDKHWvP"
      },
      "outputs": [],
      "source": [
        "def matmul(a,b): return torch.einsum('ik,kj->ij', a, b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BL7hNSjsHWvP"
      },
      "outputs": [],
      "source": [
        "test_close(tr, matmul(x_train, weights), eps=1e-3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bkZlfV17HWvP",
        "outputId": "a426b80a-1fdb-44f5-eb74-7d52bf2b2c5a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "43.1 ms ± 550 µs per loop (mean ± std. dev. of 7 runs, 5 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 5 _=matmul(x_train, weights)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oBPTmk19HWvQ"
      },
      "source": [
        "## pytorch op"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PLN_zJooHWvQ"
      },
      "source": [
        "We can use pytorch's function or operator directly for matrix multiplication."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WDf1ZI1-HWvQ"
      },
      "outputs": [],
      "source": [
        "test_close(tr, x_train@weights, eps=1e-3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aOcVtzXYHWvQ",
        "outputId": "4f110e00-3657-4e9a-bf85-22ba358876fe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "43.5 ms ± 1.16 ms per loop (mean ± std. dev. of 7 runs, 5 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 5 _=torch.matmul(x_train, weights)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wV9EN2PZHWvQ"
      },
      "source": [
        "## CUDA"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UD2VFCBrHWvS"
      },
      "outputs": [],
      "source": [
        "def matmul(grid, a,b,c):\n",
        "    i,j = grid\n",
        "    if i < c.shape[0] and j < c.shape[1]:\n",
        "        tmp = 0.\n",
        "        for k in range(a.shape[1]): tmp += a[i, k] * b[k, j]\n",
        "        c[i,j] = tmp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lLxE-z1YHWvS",
        "outputId": "23a36aac-995f-4a1e-cc31-1f580d22e1ce",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00],\n",
              "        [  0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00],\n",
              "        [  0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00],\n",
              "        [  0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00],\n",
              "        [  0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00,   0.00]])"
            ]
          },
          "metadata": {},
          "execution_count": 142
        }
      ],
      "source": [
        "res = torch.zeros(ar, bc)\n",
        "matmul((0,0), m1, m2, res)\n",
        "res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sfessDKyHWvS"
      },
      "outputs": [],
      "source": [
        "def launch_kernel(kernel, grid_x, grid_y, *args, **kwargs):\n",
        "    for i in range(grid_x):\n",
        "        for j in range(grid_y): kernel((i,j), *args, **kwargs)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "RgTB8E0PHWvS",
        "outputId": "89c0eb0a-187a-4077-ff51-359768ffe13d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-10.94,  -0.68,  -7.00,  -4.01,  -2.09,  -3.36,   3.91,  -3.44, -11.47,  -2.12],\n",
              "        [ 14.54,   6.00,   2.89,  -4.08,   6.59, -14.74,  -9.28,   2.16, -15.28,  -2.68],\n",
              "        [  2.22,  -3.22,  -4.80,  -6.05,  14.17,  -8.98,  -4.79,  -5.44, -20.68,  13.57],\n",
              "        [ -6.71,   8.90,  -7.46,  -7.90,   2.70,  -4.73, -11.03, -12.98,  -6.44,   3.64],\n",
              "        [ -2.44,  -6.40,  -2.40,  -9.04,  11.18,  -5.77,  -8.92,  -3.79,  -8.98,   5.28]])"
            ]
          },
          "metadata": {},
          "execution_count": 144
        }
      ],
      "source": [
        "res = torch.zeros(ar, bc)\n",
        "launch_kernel(matmul, ar, bc, m1, m2, res)\n",
        "res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CxTsIe3IHWvS"
      },
      "outputs": [],
      "source": [
        "from numba import cuda"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MPrf3f6ZHWvS"
      },
      "outputs": [],
      "source": [
        "def matmul(grid, a,b,c):\n",
        "    i,j = grid\n",
        "    if i < c.shape[0] and j < c.shape[1]:\n",
        "        tmp = 0.\n",
        "        for k in range(a.shape[1]): tmp += a[i, k] * b[k, j]\n",
        "        c[i,j] = tmp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nHAfuQTPHWvT"
      },
      "outputs": [],
      "source": [
        "@cuda.jit\n",
        "def matmul(a,b,c):\n",
        "    i, j = cuda.grid(2)\n",
        "    if i < c.shape[0] and j < c.shape[1]:\n",
        "        tmp = 0.\n",
        "        for k in range(a.shape[1]): tmp += a[i, k] * b[k, j]\n",
        "        c[i,j] = tmp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "91HbuUL2HWvT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 585
        },
        "outputId": "fc0dc195-47f2-424e-992b-040e94910ceb"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "CudaSupportError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mCudaSupportError\u001b[0m                          Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-148-fdfec1bcaf82>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mm1g\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mm2g\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcuda\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_device\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mx_train\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mweights\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numba/cuda/cudadrv/devices.py\u001b[0m in \u001b[0;36m_require_cuda_context\u001b[0;34m(*args, **kws)\u001b[0m\n\u001b[1;32m    229\u001b[0m     \u001b[0;34m@\u001b[0m\u001b[0mfunctools\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwraps\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    230\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_require_cuda_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkws\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 231\u001b[0;31m         \u001b[0;32mwith\u001b[0m \u001b[0m_runtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    232\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkws\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    233\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/lib/python3.10/contextlib.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    133\u001b[0m         \u001b[0;32mdel\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfunc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    134\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 135\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mnext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgen\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    136\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mStopIteration\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    137\u001b[0m             \u001b[0;32mraise\u001b[0m \u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"generator didn't yield\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numba/cuda/cudadrv/devices.py\u001b[0m in \u001b[0;36mensure_context\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    119\u001b[0m         \u001b[0many\u001b[0m \u001b[0mtop\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mlevel\u001b[0m \u001b[0mNumba\u001b[0m \u001b[0mCUDA\u001b[0m \u001b[0mAPI\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    120\u001b[0m         \"\"\"\n\u001b[0;32m--> 121\u001b[0;31m         \u001b[0;32mwith\u001b[0m \u001b[0mdriver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_active_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    122\u001b[0m             \u001b[0moldctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_attached_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    123\u001b[0m             \u001b[0mnewctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_or_create_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numba/cuda/cudadrv/driver.py\u001b[0m in \u001b[0;36m__enter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    486\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    487\u001b[0m                 \u001b[0mhctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdrvapi\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcu_context\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 488\u001b[0;31m                 \u001b[0mdriver\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcuCtxGetCurrent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbyref\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mhctx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    489\u001b[0m                 \u001b[0mhctx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mhctx\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mhctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalue\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    490\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numba/cuda/cudadrv/driver.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, fname)\u001b[0m\n\u001b[1;32m    286\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    287\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minitialization_error\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 288\u001b[0;31m             raise CudaSupportError(\"Error at driver init: \\n%s:\" %\n\u001b[0m\u001b[1;32m    289\u001b[0m                                    self.initialization_error)\n\u001b[1;32m    290\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mCudaSupportError\u001b[0m: Error at driver init: \n\nCUDA driver library cannot be found.\nIf you are sure that a CUDA driver is installed,\ntry setting environment variable NUMBA_CUDA_DRIVER\nwith the file path of the CUDA driver shared library.\n:",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ],
          "errorDetails": {
            "actions": [
              {
                "action": "open_url",
                "actionText": "Open Examples",
                "url": "/notebooks/snippets/importing_libraries.ipynb"
              }
            ]
          }
        }
      ],
      "source": [
        "r = np.zeros(tr.shape)\n",
        "m1g,m2g,rg = map(cuda.to_device, (x_train,weights,r))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Lsk7B43VHWvT",
        "outputId": "0de2d2da-8c64-4ef9-f302-5a878c8a10fc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 10)"
            ]
          },
          "metadata": {},
          "execution_count": 149
        }
      ],
      "source": [
        "r.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_ct5gMqMHWvT",
        "outputId": "9f3a5808-deb8-41f6-d652-06e7a29795b4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3125, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 150
        }
      ],
      "source": [
        "TPB = 16\n",
        "rr,rc = r.shape\n",
        "blockspergrid = (math.ceil(rr / TPB), math.ceil(rc / TPB))\n",
        "blockspergrid"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6gYIKhSGHWvT"
      },
      "outputs": [],
      "source": [
        "matmul[blockspergrid, (TPB,TPB)](m1g,m2g,rg)\n",
        "r = rg.copy_to_host()\n",
        "test_close(tr, r, eps=1e-3)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3q42zOFCHWvT",
        "outputId": "f6a2e5fd-c769-43de-a4e9-932b93cd70c5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "3.61 ms ± 708 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ],
      "source": [
        "%%timeit -n 10\n",
        "matmul[blockspergrid, (TPB,TPB)](m1g,m2g,rg)\n",
        "r = rg.copy_to_host()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "coibfng1HWvT"
      },
      "outputs": [],
      "source": [
        "m1c,m2c = x_train.cuda(),weights.cuda()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "IKWdzEYhHWvT"
      },
      "outputs": [],
      "source": [
        "r=(m1c@m2c).cpu()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OhULlKXxHWvT",
        "outputId": "b176cea6-26a5-4b0b-c9d9-899fdba811e7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "458 µs ± 93.1 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit -n 10 r=(m1c@m2c).cpu()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8t_9jf2mHWvV"
      },
      "source": [
        "Our broadcasting version was >500ms, and our CUDA version is around 0.5ms, which is another 1000x improvement compared to broadcasting. So our total speedup is around 5 million times!"
      ]
    },
    {
      "cell_type": "code",
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