{
 "metadata": {
  "name": "",
  "signature": "sha256:2ec741daefdcbdc8c7f2b2a5e3a8523ae84dbc5c7556d678eb085df29ef4aff8"
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": [],
     "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": [
      "# 4.8. Making efficient selections in arrays with NumPy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "id = lambda x: x.__array_interface__['data'][0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We create a large array."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n, d = 100000, 100"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.random.random_sample((n, d)); aid = id(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Array views and fancy indexing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We take a selection using two different methods: with a view and with fancy indexing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b1 = a[::10]\n",
      "b2 = a[np.arange(0, n, 10)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.array_equal(b1, b2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The view refers to the original data buffer, whereas fancy indexing yields a copy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "id(b1) == aid, id(b2) == aid"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fancy indexing is several orders of magnitude slower as it involves copying a large array. Fancy indexing is more general as it allows to select any portion of an array (using any list of indices), not just a strided selection."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit a[::10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit a[np.arange(0, n, 10)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Alternatives to fancy indexing: list of indices"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given a list of indices, there are two ways of selecting the corresponding sub-array: fancy indexing, or the np.take function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = np.arange(0, n, 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b1 = a[i]\n",
      "b2 = np.take(a, i, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.array_equal(b1, b2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit a[i]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit np.take(a, i, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using np.take instead of fancy indexing is faster."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Note**: Performance of fancy indexing has been improved in recent versions of NumPy; this trick is especially useful on older versions of NumPy."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Alternatives to fancy indexing: mask of booleans"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's create a mask of booleans, where each value indicates whether the corresponding row needs to be selected in x."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = np.random.random_sample(n) < .5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The selection can be made using fancy indexing or the np.compress function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b1 = a[i]\n",
      "b2 = np.compress(i, a, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.array_equal(b1, b2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit a[i]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit np.compress(i, a, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Once again, the alternative method to fancy indexing is faster."
     ]
    },
    {
     "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)."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}