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   "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": [
      "# 5.4. Accelerating Python code with Cython"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "We use Cython to accelerate the generation of the Mandelbrot fractal."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "import numpy as np"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "We initialize the simulation and generate the grid\n", 
      "in the complex plane."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "size = 200\n", 
      "iterations = 100"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "## Pure Python"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "def mandelbrot_python(m, size, iterations):\n", 
      "    for i in range(size):\n", 
      "        for j in range(size):\n", 
      "            c = -2 + 3./size*j + 1j*(1.5-3./size*i)\n", 
      "            z = 0\n", 
      "            for n in range(iterations):\n", 
      "                if np.abs(z) <= 10:\n", 
      "                    z = z*z + c\n", 
      "                    m[i, j] = n\n", 
      "                else:\n", 
      "                    break"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%%timeit -n1 -r1 m = np.zeros((size, size))\n", 
      "mandelbrot_python(m, size, iterations)"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "## Cython versions"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "We first import Cython."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%load_ext cythonmagic"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "### Take 1"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "First, we just add the %%cython magic."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%%cython -a\n", 
      "import numpy as np\n", 
      "\n", 
      "def mandelbrot_cython(m, size, iterations):\n", 
      "    for i in range(size):\n", 
      "        for j in range(size):\n", 
      "            c = -2 + 3./size*j + 1j*(1.5-3./size*i)\n", 
      "            z = 0\n", 
      "            for n in range(iterations):\n", 
      "                if np.abs(z) <= 10:\n", 
      "                    z = z*z + c\n", 
      "                    m[i, j] = n\n", 
      "                else:\n", 
      "                    break"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)\n", 
      "mandelbrot_cython(m, size, iterations)"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "Virtually no speedup."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "### Take 2"
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "source": [
      "Now, we add type information, using memory views for NumPy arrays."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%%cython -a\n", 
      "import numpy as np\n", 
      "\n", 
      "def mandelbrot_cython(int[:,::1] m, \n", 
      "                      int size, \n", 
      "                      int iterations):\n", 
      "    cdef int i, j, n\n", 
      "    cdef complex z, c\n", 
      "    for i in range(size):\n", 
      "        for j in range(size):\n", 
      "            c = -2 + 3./size*j + 1j*(1.5-3./size*i)\n", 
      "            z = 0\n", 
      "            for n in range(iterations):\n", 
      "                if z.real**2 + z.imag**2 <= 100:\n", 
      "                    z = z*z + c\n", 
      "                    m[i, j] = n\n", 
      "                else:\n", 
      "                    break"
     ], 
     "metadata": {}
    }, 
    {
     "cell_type": "code", 
     "language": "python", 
     "outputs": [], 
     "collapsed": false, 
     "input": [
      "%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)\n", 
      "mandelbrot_cython(m, size, iterations)"
     ], 
     "metadata": {}
    }, 
    {
     "source": [
      "Interesting speedup!"
     ], 
     "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)."
     ], 
     "cell_type": "markdown", 
     "metadata": {}
    }
   ], 
   "metadata": {}
  }
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