{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# numpy: Broadcasting"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(3, 3)\n",
            "[[0 1 2]\n",
            " [3 4 5]\n",
            " [6 7 8]]\n",
            "(3, 3)\n",
            "[[ 4  5  6]\n",
            " [ 7  8  9]\n",
            " [10 11 12]]\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(9).reshape(3, 3)\n",
        "print(a.shape)\n",
        "print(a)\n",
        "b = np.arange(4, 4+9).reshape(3, 3)\n",
        "print(b.shape)\n",
        "print(b)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 4,  6,  8],\n",
              "       [10, 12, 14],\n",
              "       [16, 18, 20]])"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a+b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "So this is easy and one-to-one.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "---\n",
        "\n",
        "What if the shapes do not match?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "(3, 3)\n",
            "[[0 1 2]\n",
            " [3 4 5]\n",
            " [6 7 8]]\n",
            "(3,)\n",
            "[0 1 2]\n"
          ]
        }
      ],
      "source": [
        "a = np.arange(9).reshape(3, 3)\n",
        "print(a.shape)\n",
        "print(a)\n",
        "b = np.arange(3)\n",
        "print(b.shape)\n",
        "print(b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "What will this do?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  2,  4],\n",
              "       [ 3,  5,  7],\n",
              "       [ 6,  8, 10]])"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a+b"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "It has *broadcast* along the last axis!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "---\n",
        "\n",
        "Can we broadcast along the *first* axis?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2],\n",
              "       [ 4,  5,  6],\n",
              "       [ 8,  9, 10]])"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "a+b.reshape(3, 1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Rules:\n",
        "\n",
        "* Shapes are matched axis-by-axis from last to first.\n",
        "* A length-1 axis can be *broadcast* if necessary."
      ]
    }
  ],
  "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 0
}