{
 "nbformat": 3, 
 "nbformat_minor": 0, 
 "worksheets": [
  {
   "cells": [
    {
     "source": [
      "> This is one of the 100 recipes of the [IPython Cookbook](http://ipython-books.github.io/), the definitive guide to high-performance scientific computing and data science in Python.\n"
     ], 
     "cell_type": "markdown", 
     "metadata": []
    }, 
    {
     "source": [
      "# 4.6. Using stride tricks with NumPy"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "Every array has a number of dimensions, a shape, a data type, and strides. Strides are integer numbers describing, for each dimension, the byte step in the contiguous block of memory. The address of an item in the array is a linear combination of its indices: the coefficients are the strides."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "import numpy as np"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "id = lambda x: x.__array_interface__['data'][0]"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "x = np.zeros(10); x.strides"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "This vector contains float64 (8 bytes) items: one needs to go 8 bytes forward to go from one item to the next."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "y = np.zeros((10, 10)); y.strides"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "In the first dimension (vertical), one needs to go 80 bytes (10 float64 items) forward to go from one item to the next, because the items are internally stored in row-major order. In the second dimension (horizontal), one needs to go 8 bytes forward to go from one item to the next."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "### Broadcasting revisited"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "We create a new array pointing to the same memory block as `a`, but with a different shape. The strides are such that this array looks like it is a vertically tiled version of `a`. NumPy is *tricked*: it thinks `b` is a 2D `n * n` array with `n^2` elements, whereas the data buffer really contains only `n` elements."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "n = 1000; a = np.arange(n)"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "b = np.lib.stride_tricks.as_strided(a, (n, n), (0, 4))"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "b"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "b.size, b.shape, b.nbytes"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%timeit b * b.T"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "This first version does not involve any copy, as `b` and `b.T` are arrays pointing to the same data buffer in memory, but with different strides."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%timeit np.tile(a, (n, 1)) * np.tile(a[:, np.newaxis], (1, n))"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "> You'll find all the explanations, figures, references, and much more in the book (to be released later this summer).\n\n> [IPython Cookbook](http://ipython-books.github.io/), by [Cyrille Rossant](http://cyrille.rossant.net), Packt Publishing, 2014 (500 pages)."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }
   ], 
   "metadata": {}
  }
 ], 
 "metadata": {
  "name": "", 
  "signature": "sha256:b24dc9fc21de16e5b73784c0a8696b89f36dfff0b3cd8e0e1b61bb7de8a62251"
 }
}