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  {
   "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": [
    "# 4.2. Profiling your code easily with cProfile and IPython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standard imports."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function generates an array with random, uniformly distributed +1 and -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def step(*shape):\n",
    "    # Create a random n-vector with +1 or -1 values.\n",
    "    return 2 * (np.random.random_sample(shape) < .5) - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We simulate $n$ random walks, and look at the histogram of the walks over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%prun -s cumulative -q -l 10 -T prun0\n",
    "# We profile the cell, sort the report by \"cumulative time\",\n",
    "# limit it to 10 lines, and save it to a file \"prun0\".\n",
    "n = 10000\n",
    "iterations = 50\n",
    "x = np.cumsum(step(iterations, n), axis=0)\n",
    "bins = np.arange(-30, 30, 1)\n",
    "y = np.vstack([np.histogram(x[i,:], bins)[0] for i in range(iterations)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(open('prun0', 'r').read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most expensive functions are respectively `histogram` (37 ms), `rand` (19 ms), and `cumsum` (5 ms)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the array `y`, representing the distribution of the particles over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(6,6));\n",
    "plt.imshow(y, cmap='hot');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now run the same code with 10 times more iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%%prun -s cumulative -q -l 10 -T prun1\n",
    "n = 10000\n",
    "iterations = 500\n",
    "x = np.cumsum(step(iterations, n), axis=0)\n",
    "bins = np.arange(-30, 30, 1)\n",
    "y = np.vstack([np.histogram(x[i,:], bins)[0] for i in range(iterations)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print(open('prun1', 'r').read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most expensive functions are this time respectively `histogram` (566 ms), `cumsum` (388 ms) and `rand` (241 ms). `cumsum`'s execution time was negligible in the first case, whereas it is not in this case (due to the higher number of iterations)."
   ]
  },
  {
   "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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