{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# How are numpy arrays stored?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Numpy presents an n-dimensional abstraction that has to be fit into 1-dimensional computer memory.\n",
        "\n",
        "Even for 2 dimensions (matrices), this leads to confusion: row-major, column-major."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[[0 1 2]\n",
            " [3 4 5]\n",
            " [6 7 8]]\n"
          ]
        }
      ],
      "source": [
        "A = np.arange(9).reshape(3, 3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Strides and in-memory representation"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "How is this represented in memory?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(24, 8)"
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.strides"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "* `strides` stores for each axis by how many bytes one needs to jump to get from one entry to the next (in that axis)\n",
        "* So how is the array above stored?\n",
        "* This captures row-major (\"C\" order) and column-major (\"Fortran\" order), but is actually much more general."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "We can also ask for Fortran order:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[0, 3, 6],\n",
              "       [1, 4, 7],\n",
              "       [2, 5, 8]])"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A2 = np.arange(9).reshape(3, 3, order=\"F\")\n",
        "A2"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "`numpy` defaults to row-major order."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(8, 24)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A2.strides"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Strides and Contiguity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "How is the stride model more general than just saying \"row major\" or \"column major\"?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2,  3],\n",
              "       [ 4,  5,  6,  7],\n",
              "       [ 8,  9, 10, 11],\n",
              "       [12, 13, 14, 15]])"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A = np.arange(16).reshape(4, 4)\n",
        "A"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(32, 8)"
            ]
          },
          "execution_count": 18,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "A.strides"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[ 0,  1,  2],\n",
              "       [ 4,  5,  6],\n",
              "       [ 8,  9, 10]])"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Asub = A[:3, :3]\n",
        "Asub"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Recall that `Asub` constitutes a *view* of the original data in `A`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "(32, 8)"
            ]
          },
          "execution_count": 19,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Asub.strides"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now `Asub` is no longer a *contiguous* array!\n",
        "\n",
        "From the linear-memory representation (as show by the increasing numbers in `A`) 3, 7, 11 are missing.\n",
        "\n",
        "This is easy to check by a flag:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "  C_CONTIGUOUS : False\n",
              "  F_CONTIGUOUS : False\n",
              "  OWNDATA : False\n",
              "  WRITEABLE : True\n",
              "  ALIGNED : True\n",
              "  UPDATEIFCOPY : False"
            ]
          },
          "execution_count": 20,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "Asub.flags"
      ]
    }
  ],
  "metadata": {},
  "nbformat": 4,
  "nbformat_minor": 0
}