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   "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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "id = lambda x: x.__array_interface__['data'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.zeros(10); x.strides"
   ]
  },
  {
   "cell_type": "markdown",
   "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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.zeros((10, 10)); y.strides"
   ]
  },
  {
   "cell_type": "markdown",
   "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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 1000; a = np.arange(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b = np.lib.stride_tricks.as_strided(a, (n, n), (0, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b.size, b.shape, b.nbytes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%timeit b * b.T"
   ]
  },
  {
   "cell_type": "markdown",
   "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": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%timeit np.tile(a, (n, 1)) * np.tile(a[:, np.newaxis], (1, n))"
   ]
  },
  {
   "cell_type": "markdown",
   "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)."
   ]
  }
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