notes-aaron-full-2017-03-03.ipynb

{
 "cells": [
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   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Jupyter-magics\" data-toc-modified-id=\"Jupyter-magics-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Jupyter magics</a></div><div class=\"lev2 toc-item\"><a href=\"#Available-magics\" data-toc-modified-id=\"Available-magics-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Available magics</a></div><div class=\"lev2 toc-item\"><a href=\"#Using-%timeit\" data-toc-modified-id=\"Using-%timeit-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Using <code>%timeit</code></a></div><div class=\"lev2 toc-item\"><a href=\"#Getting-help\" data-toc-modified-id=\"Getting-help-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Getting help</a></div><div class=\"lev1 toc-item\"><a href=\"#Shortcuts-and-conveniences\" data-toc-modified-id=\"Shortcuts-and-conveniences-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Shortcuts and conveniences</a></div><div class=\"lev2 toc-item\"><a href=\"#Using-shell-commands\" data-toc-modified-id=\"Using-shell-commands-21\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Using shell commands</a></div><div class=\"lev2 toc-item\"><a href=\"#Running-bash-in-a-sub-process\" data-toc-modified-id=\"Running-bash-in-a-sub-process-22\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Running bash in a sub-process</a></div><div class=\"lev2 toc-item\"><a href=\"#Running-R-as-a-sub-process\" data-toc-modified-id=\"Running-R-as-a-sub-process-23\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>Running R as a sub-process</a></div><div class=\"lev2 toc-item\"><a href=\"#Interactive-dashboards\" data-toc-modified-id=\"Interactive-dashboards-24\"><span class=\"toc-item-num\">2.4&nbsp;&nbsp;</span>Interactive dashboards</a></div><div class=\"lev1 toc-item\"><a href=\"#Pythonic-programming\" data-toc-modified-id=\"Pythonic-programming-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Pythonic programming</a></div><div class=\"lev2 toc-item\"><a href=\"#Generators\" data-toc-modified-id=\"Generators-31\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>Generators</a></div><div class=\"lev2 toc-item\"><a href=\"#map,-reduce,-filter,-zip\" data-toc-modified-id=\"map,-reduce,-filter,-zip-32\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span><code>map</code>, <code>reduce</code>, <code>filter</code>, <code>zip</code></a></div><div class=\"lev2 toc-item\"><a href=\"#Classes\" data-toc-modified-id=\"Classes-33\"><span class=\"toc-item-num\">3.3&nbsp;&nbsp;</span>Classes</a></div><div class=\"lev2 toc-item\"><a href=\"#The-imperative-approach\" data-toc-modified-id=\"The-imperative-approach-34\"><span class=\"toc-item-num\">3.4&nbsp;&nbsp;</span>The imperative approach</a></div><div class=\"lev2 toc-item\"><a href=\"#The-functional-approach\" data-toc-modified-id=\"The-functional-approach-35\"><span class=\"toc-item-num\">3.5&nbsp;&nbsp;</span>The functional approach</a></div><div class=\"lev1 toc-item\"><a href=\"#Fast-computations\" data-toc-modified-id=\"Fast-computations-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Fast computations</a></div><div class=\"lev2 toc-item\"><a href=\"#Memoization\" data-toc-modified-id=\"Memoization-41\"><span class=\"toc-item-num\">4.1&nbsp;&nbsp;</span>Memoization</a></div><div class=\"lev3 toc-item\"><a href=\"#First-Example:-factorial-computations\" data-toc-modified-id=\"First-Example:-factorial-computations-411\"><span class=\"toc-item-num\">4.1.1&nbsp;&nbsp;</span>First Example: factorial computations</a></div><div class=\"lev3 toc-item\"><a href=\"#Second-example:-Fibonacci-numbers\" data-toc-modified-id=\"Second-example:-Fibonacci-numbers-412\"><span class=\"toc-item-num\">4.1.2&nbsp;&nbsp;</span>Second example: Fibonacci numbers</a></div><div class=\"lev2 toc-item\"><a href=\"#Writing-good-code\" data-toc-modified-id=\"Writing-good-code-42\"><span class=\"toc-item-num\">4.2&nbsp;&nbsp;</span>Writing good code</a></div><div class=\"lev3 toc-item\"><a href=\"#Memory-allocation,-implicit-array-copying\" data-toc-modified-id=\"Memory-allocation,-implicit-array-copying-421\"><span class=\"toc-item-num\">4.2.1&nbsp;&nbsp;</span>Memory allocation, implicit array copying</a></div><div class=\"lev2 toc-item\"><a href=\"#Numba\" data-toc-modified-id=\"Numba-43\"><span class=\"toc-item-num\">4.3&nbsp;&nbsp;</span>Numba</a></div><div class=\"lev3 toc-item\"><a href=\"#Pure-python-version\" data-toc-modified-id=\"Pure-python-version-431\"><span class=\"toc-item-num\">4.3.1&nbsp;&nbsp;</span>Pure python version</a></div><div class=\"lev3 toc-item\"><a href=\"#Numba-version\" data-toc-modified-id=\"Numba-version-432\"><span class=\"toc-item-num\">4.3.2&nbsp;&nbsp;</span>Numba version</a></div><div class=\"lev2 toc-item\"><a href=\"#Numexpr\" data-toc-modified-id=\"Numexpr-44\"><span class=\"toc-item-num\">4.4&nbsp;&nbsp;</span>Numexpr</a></div><div class=\"lev2 toc-item\"><a href=\"#Cython\" data-toc-modified-id=\"Cython-45\"><span class=\"toc-item-num\">4.5&nbsp;&nbsp;</span>Cython</a></div><div class=\"lev2 toc-item\"><a href=\"#Ray-tracing-example\" data-toc-modified-id=\"Ray-tracing-example-46\"><span class=\"toc-item-num\">4.6&nbsp;&nbsp;</span>Ray tracing example</a></div><div class=\"lev3 toc-item\"><a href=\"#Pure-Python\" data-toc-modified-id=\"Pure-Python-461\"><span class=\"toc-item-num\">4.6.1&nbsp;&nbsp;</span>Pure Python</a></div><div class=\"lev3 toc-item\"><a href=\"#Naive-Cython\" data-toc-modified-id=\"Naive-Cython-462\"><span class=\"toc-item-num\">4.6.2&nbsp;&nbsp;</span>Naive Cython</a></div><div class=\"lev3 toc-item\"><a href=\"#Cython-array-buffers\" data-toc-modified-id=\"Cython-array-buffers-463\"><span class=\"toc-item-num\">4.6.3&nbsp;&nbsp;</span>Cython array buffers</a></div><div class=\"lev4 toc-item\"><a href=\"#Take-1\" data-toc-modified-id=\"Take-1-4631\"><span class=\"toc-item-num\">4.6.3.1&nbsp;&nbsp;</span>Take 1</a></div><div class=\"lev4 toc-item\"><a href=\"#Take-2\" data-toc-modified-id=\"Take-2-4632\"><span class=\"toc-item-num\">4.6.3.2&nbsp;&nbsp;</span>Take 2</a></div><div class=\"lev3 toc-item\"><a href=\"#Cython-with-structs\" data-toc-modified-id=\"Cython-with-structs-464\"><span class=\"toc-item-num\">4.6.4&nbsp;&nbsp;</span>Cython with structs</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jupyter magics\n",
    "\n",
    "Jupyter has a collection of built-in magics that make certain python tasks much easier (and much cleaner looking). Use them like decorators."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Available magics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "cell": {
        "!": "OSMagics",
        "HTML": "Other",
        "SVG": "Other",
        "bash": "Other",
        "capture": "ExecutionMagics",
        "debug": "ExecutionMagics",
        "file": "Other",
        "html": "DisplayMagics",
        "javascript": "DisplayMagics",
        "latex": "DisplayMagics",
        "perl": "Other",
        "prun": "ExecutionMagics",
        "pypy": "Other",
        "python": "Other",
        "python2": "Other",
        "python3": "Other",
        "ruby": "Other",
        "script": "ScriptMagics",
        "sh": "Other",
        "svg": "DisplayMagics",
        "sx": "OSMagics",
        "system": "OSMagics",
        "time": "ExecutionMagics",
        "timeit": "ExecutionMagics",
        "writefile": "OSMagics"
       },
       "line": {
        "alias": "OSMagics",
        "alias_magic": "BasicMagics",
        "autocall": "AutoMagics",
        "automagic": "AutoMagics",
        "autosave": "KernelMagics",
        "bookmark": "OSMagics",
        "cat": "Other",
        "cd": "OSMagics",
        "clear": "KernelMagics",
        "colors": "BasicMagics",
        "config": "ConfigMagics",
        "connect_info": "KernelMagics",
        "cp": "Other",
        "debug": "ExecutionMagics",
        "dhist": "OSMagics",
        "dirs": "OSMagics",
        "doctest_mode": "BasicMagics",
        "ed": "Other",
        "edit": "KernelMagics",
        "env": "OSMagics",
        "gui": "BasicMagics",
        "hist": "Other",
        "history": "HistoryMagics",
        "install_default_config": "DeprecatedMagics",
        "install_ext": "ExtensionMagics",
        "install_profiles": "DeprecatedMagics",
        "killbgscripts": "ScriptMagics",
        "ldir": "Other",
        "less": "KernelMagics",
        "lf": "Other",
        "lk": "Other",
        "ll": "Other",
        "load": "CodeMagics",
        "load_ext": "ExtensionMagics",
        "loadpy": "CodeMagics",
        "logoff": "LoggingMagics",
        "logon": "LoggingMagics",
        "logstart": "LoggingMagics",
        "logstate": "LoggingMagics",
        "logstop": "LoggingMagics",
        "ls": "Other",
        "lsmagic": "BasicMagics",
        "lx": "Other",
        "macro": "ExecutionMagics",
        "magic": "BasicMagics",
        "man": "KernelMagics",
        "matplotlib": "PylabMagics",
        "mkdir": "Other",
        "more": "KernelMagics",
        "mv": "Other",
        "notebook": "BasicMagics",
        "page": "BasicMagics",
        "pastebin": "CodeMagics",
        "pdb": "ExecutionMagics",
        "pdef": "NamespaceMagics",
        "pdoc": "NamespaceMagics",
        "pfile": "NamespaceMagics",
        "pinfo": "NamespaceMagics",
        "pinfo2": "NamespaceMagics",
        "popd": "OSMagics",
        "pprint": "BasicMagics",
        "precision": "BasicMagics",
        "profile": "BasicMagics",
        "prun": "ExecutionMagics",
        "psearch": "NamespaceMagics",
        "psource": "NamespaceMagics",
        "pushd": "OSMagics",
        "pwd": "OSMagics",
        "pycat": "OSMagics",
        "pylab": "PylabMagics",
        "qtconsole": "KernelMagics",
        "quickref": "BasicMagics",
        "recall": "HistoryMagics",
        "rehashx": "OSMagics",
        "reload_ext": "ExtensionMagics",
        "rep": "Other",
        "rerun": "HistoryMagics",
        "reset": "NamespaceMagics",
        "reset_selective": "NamespaceMagics",
        "rm": "Other",
        "rmdir": "Other",
        "run": "ExecutionMagics",
        "save": "CodeMagics",
        "sc": "OSMagics",
        "set_env": "OSMagics",
        "store": "StoreMagics",
        "sx": "OSMagics",
        "system": "OSMagics",
        "tb": "ExecutionMagics",
        "time": "ExecutionMagics",
        "timeit": "ExecutionMagics",
        "unalias": "OSMagics",
        "unload_ext": "ExtensionMagics",
        "who": "NamespaceMagics",
        "who_ls": "NamespaceMagics",
        "whos": "NamespaceMagics",
        "xdel": "NamespaceMagics",
        "xmode": "BasicMagics"
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       "Available line magics:\n",
       "%alias  %alias_magic  %autocall  %automagic  %autosave  %bookmark  %cat  %cd  %clear  %colors  %config  %connect_info  %cp  %debug  %dhist  %dirs  %doctest_mode  %ed  %edit  %env  %gui  %hist  %history  %install_default_config  %install_ext  %install_profiles  %killbgscripts  %ldir  %less  %lf  %lk  %ll  %load  %load_ext  %loadpy  %logoff  %logon  %logstart  %logstate  %logstop  %ls  %lsmagic  %lx  %macro  %magic  %man  %matplotlib  %mkdir  %more  %mv  %notebook  %page  %pastebin  %pdb  %pdef  %pdoc  %pfile  %pinfo  %pinfo2  %popd  %pprint  %precision  %profile  %prun  %psearch  %psource  %pushd  %pwd  %pycat  %pylab  %qtconsole  %quickref  %recall  %rehashx  %reload_ext  %rep  %rerun  %reset  %reset_selective  %rm  %rmdir  %run  %save  %sc  %set_env  %store  %sx  %system  %tb  %time  %timeit  %unalias  %unload_ext  %who  %who_ls  %whos  %xdel  %xmode\n",
       "\n",
       "Available cell magics:\n",
       "%%!  %%HTML  %%SVG  %%bash  %%capture  %%debug  %%file  %%html  %%javascript  %%latex  %%perl  %%prun  %%pypy  %%python  %%python2  %%python3  %%ruby  %%script  %%sh  %%svg  %%sx  %%system  %%time  %%timeit  %%writefile\n",
       "\n",
       "Automagic is ON, % prefix IS NOT needed for line magics."
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%lsmagic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we'll be making use of the %timeit magic to measure algorithm run time. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using `%timeit`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100000000 loops, best of 3: 8.94 ns per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 5: 15.15 ns per loop\n"
     ]
    }
   ],
   "source": [
    "timeitResult = %timeit -n100 -r5 -p5 -o x = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 148 µs per loop\n"
     ]
    }
   ],
   "source": [
    "from functools import reduce\n",
    "%timeit reduce(lambda x,y: x+y, range(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000 loops, best of 3: 19.4 µs per loop\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "N = int(1e5)\n",
    "w = np.random.randn(N, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 9.96 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "1000 loops, best of 100: 8.78 µs per loop\n",
      "1000 loops, best of 100: 91 µs per loop\n"
     ]
    }
   ],
   "source": [
    "t_wdot = %timeit -r100 -n1000 -o np.dot(w.T, w)\n",
    "t_sumsq = %timeit -r100 -n1000 -o (w**2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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rc0oeckQAG1dVjwFbkKYCHzRvGbKcrOMO1GEG96ZZRr+WlTK7aLIoo9W2KGnHvWX57JO6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\n/x+lN0VOdoayewAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ba5e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.hold(True)\n",
    "plt.plot(t_wdot.all_runs, 'b.', MarkerSize=10)\n",
    "plt.plot(t_sumsq.all_runs, 'r.', MarkerSize=10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Getting help"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%timeit?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also, Shift + Tab while cursor is over text for which docs are desired. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shortcuts and conveniences\n",
    "\n",
    "## Using shell commands"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent (master).ipynb   UBCS3.4 (28 October 2016).ipynb\r\n",
      "Gradient Descent (skeleton).ipynb UBCS3_2.1_20170120.ipynb\r\n",
      "Python utilities.ipynb            UBCS3_2.2_20170127.ipynb\r\n",
      "README                            UBCS3_2.3_20170203.ipynb\r\n",
      "UBCS3.1 (7 October 2016).ipynb    \u001b[1m\u001b[34mdata\u001b[m\u001b[m\r\n",
      "UBCS3.2 (14 October 2016).ipynb   flaskapp.py\r\n",
      "UBCS3.3 (21 October 2016).ipynb   test_file.py\r\n"
     ]
    }
   ],
   "source": [
    "!ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Gradient Descent (master).ipynb', 'Gradient Descent (skeleton).ipynb', 'Python utilities.ipynb', 'README', 'UBCS3.1 (7 October 2016).ipynb', 'UBCS3.2 (14 October 2016).ipynb', 'UBCS3.3 (21 October 2016).ipynb', 'UBCS3.4 (28 October 2016).ipynb', 'UBCS3_2.1_20170120.ipynb', 'UBCS3_2.2_20170127.ipynb', 'UBCS3_2.3_20170203.ipynb', 'data', 'flaskapp.py', 'test_file.py']\n"
     ]
    }
   ],
   "source": [
    "dirlist = !ls\n",
    "print(dirlist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loading files using Jupyter magics (note `test_file.py` in `!ls` output above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load test_file.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running bash in a sub-process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a\n",
      "b\n",
      "c\n"
     ]
    }
   ],
   "source": [
    "%%bash\n",
    "for i in a b c;\n",
    "do\n",
    "echo $i\n",
    "done"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running R as a sub-process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sadly, no code completion, though..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext rpy2.ipython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7KWXCeMAA6S9/OXI+numZgBUBbHY1r169OuIIVqxYoYKCgojTeBIBBBBAIHkCxx0n9Tos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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "x <- 1:10\n",
    "y <- x^2\n",
    "plot(x, y, pch=20, col=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       " num [1:5] 1.92e-06 1.58e-06 1.53e-06 1.52e-06 1.52e-06\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = timeitResult.all_runs\n",
    "%Rpush X\n",
    "%R str(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HxH/WX697m64HICLOjIjPRsTD9ffW6xuu59X112ei/vxsn3yvvy8ivhMRD0TEpyLihU3X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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ef0af98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%Rpull y\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.plot(range(10), y, 'b.', MarkerSize=15);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Interactive dashboards\n",
    "\n",
    "This blog has a few articles that talk about some intriguing ways of using Jupyter. Including an article about [building interactive dashboards in Jupyter](https://blog.dominodatalab.com/interactive-dashboards-in-jupyter/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pythonic programming"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From Wikipedia\n",
    "\n",
    "> A common neologism in the Python community is pythonic, which can have a wide range of meanings related to program style. To say that code is pythonic is to say that it uses Python idioms well, that it is natural or shows fluency in the language. Likewise, to say of an interface or language feature that it is pythonic is to say that it works well with Python idioms, that its use meshes well with the rest of the language.\n",
    ">\n",
    "> In contrast, a mark of unpythonic code is that it attempts to write C++ (or Lisp, Perl, or Java) code in Python—that is, provides a rough transcription rather than an idiomatic translation of forms from another language. The concept of pythonicity is tightly bound to Python's minimalist philosophy of readability and avoiding the \"there's more than one way to do it\" approach. Unreadable code or incomprehensible idioms are unpythonic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As an example of idiomatic python, check out this 900 line [implementation of Minecraft](https://github.com/fogleman/Minecraft/blob/master/main.py) in python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "list_with_repeats = [1,2,4,7,4,6,5,4,3,2,2,2,1]\n",
    "first_4 = next(j for j, x in enumerate(list_with_repeats) if x == 4)\n",
    "print(first_4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`enumerate`, itself, returns a generator object. Note that this approach is *in line* with **functional programming** but is distinct from **lazy evaluation**/**lazy lists** in that generators are use-once objects. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enumerate?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "range(0, 10)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "range(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<generator object <genexpr> at 0x117f3d6d0>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x**2 for x in range(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `map`, `reduce`, `filter`, `zip`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]\n"
     ]
    }
   ],
   "source": [
    "sqmap = list(map(lambda x: x**2, range(10)))\n",
    "print(sqmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "285\n"
     ]
    }
   ],
   "source": [
    "sumsq = reduce(lambda x,y: x + y, sqmap)\n",
    "print(sumsq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256]\n"
     ]
    }
   ],
   "source": [
    "def filterfun(x, th):\n",
    "    sqrt_x = x**.5\n",
    "    return (x < th) and (x > 0) and ((x % sqrt_x) == 0)\n",
    "\n",
    "sqltsumsq = list(filter(lambda x: filterfun(x, sumsq), range(1000)))\n",
    "print(sqltsumsq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),\n",
       " (0, 1, 2, 3, 4, 5, 6, 7, 8, 9),\n",
       " (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def unzip(tuples):\n",
    "    return zip(*tuples)\n",
    "\n",
    "list(unzip([(j,j,j) for j in range(10)]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Python, like C, Java, *etc.* can make use of classes for the kind of modularity expected of object-oriented programming languages. Defining a class in Python is very easy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class myNewClass:\n",
    "    def __init__(self):\n",
    "        print('Hello')\n",
    "    def clsmth(self):\n",
    "        \"\"\"\n",
    "        call a class method and instance method\n",
    "        \"\"\"\n",
    "        myNewClass.helper1()\n",
    "        self.helper2()\n",
    "    def helper1():\n",
    "        print('World!')\n",
    "    def helper2(self):\n",
    "        print('World!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And instantiating an instance of that class is just as easy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello\n"
     ]
    }
   ],
   "source": [
    "myNewInstance = myNewClass()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "World!\n",
      "World!\n"
     ]
    }
   ],
   "source": [
    "myNewInstance.clsmth()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "World!\n"
     ]
    }
   ],
   "source": [
    "myNewClass.helper1()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "World!\n"
     ]
    }
   ],
   "source": [
    "myNewClass.helper2(myNewInstance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "World!\n"
     ]
    }
   ],
   "source": [
    "myNewInstance.helper2()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The imperative approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The functional approach\n",
    "\n",
    "* [Functional Programming HOWTO from Python](https://docs.python.org/3/howto/functional.html)\n",
    "* [FP in Python from IBM](http://www.ibm.com/developerworks/library/l-prog/)\n",
    "* [FP in Python from Mary Rose Cook](https://maryrosecook.com/blog/post/a-practical-introduction-to-functional-programming)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fast computations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
     ]
    }
   ],
   "source": [
    "%reset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Memoization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First Example: factorial computations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def factorial(k):\n",
    "    if k == 1:\n",
    "        return 1\n",
    "    return k * factorial(k-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "maximum recursion depth exceeded in comparison\n",
      "Whoops! We're asking too much from Python right now!\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    factorial(3000)\n",
    "except RecursionError as RE:\n",
    "    print(RE)\n",
    "    print('Whoops! We\\'re asking too much from Python right now!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "factorial_memo = {}\n",
    "def factorial2(k):\n",
    "    if k == 1:\n",
    "        return 1\n",
    "    if k not in factorial_memo:\n",
    "        factorial_memo[k] = k*factorial2(k-1)\n",
    "    return factorial_memo[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We can now get the answer we want:\n",
      "4149359603437854085556867093086612170951119194931809917689467657697558565123531950086000765217800342007518463538361711849575087111404590779455340216106833961162103790419917752206266339017968280516471969749596884245772876609710300372611109534024112711883315773881532843892973761302110631293037440148537872544607961029042949104979388812076251162513291700464166896211759020357517548898065357786891528509378246999467469919083209351106836382428706352226854433921377515048858810403681880909929291249714190050893899440471535147315453158744150996017426787508746036797411707236874727714398892068369161850360819845971809378445352395850537761108651116236314592088610855745087451394530543621371189815084719209442637420327502999633378494401477567141468082420749991471487835966972063895467058996017856948026338876711287106800495082740071712481947638640136919354435412031278660143479254995914353012065310340662550323102073835150219510314867361233873939509655146215934901578994994407231100442692483814014145548787273804585602356158320431794595305583069335124689072124615146848530872403126796708911354898273347537575689936517639642478173346251087901574343739892049226709831703393210717634398335244457604047656540041441469947998435455459779938670283942851341318891316569531084851352509400614777404700733140654179442800443669190368546927085727170164801151205745244860796877378480366065300910981563909129411063371562154090380013505867162426233390243416662871652122859027456883350489792686936979287837689484143657386643695507547396488225622218338001460076119685921760323480846745521633041173800433114422592624369055878291490797388575878458573982869539030238383726588242765430643751775789721504507136180173005162842447629422748575562782876349876719528136891358391882449928474159168313033403219994675208291488576434586383231354520507595591206206727329695138612299465860752731788445244986534816416923884488906149585093437344288981488442732181713127253389153450658114382338120587537980860508088976175388289625293363375045454916860026722959122552885458448268665532431301135375481240956123768607800770070793954184890714946737785440752830787298810391294512192986479370345125743644558145975714082270598632516535290658457112358527021193345298110556839880988409498034618507802527303873678404216942723798046430425004503080663703276001634192144280570880243085056789210864697745513953911983863616719030027814638013693248233277159518059619306950423783608262057088720929792979742940457687733831987744468554429480032174105668942371054502887041961191507273900003164201447421332329387161802955561400460286740042288538985465032802842851512229602879574180162182323609832097144104701253306731489615323678873498455394960439705035234776621139591451927042212223142699869208746352098068622435481337619439513194286811348653156222817321497648170538184615532659618753029647860116087226364044392225760192649461091688515101314394557439830319255715416215144246912237051914909786184943615096310993363959456179659339685195860533863117632414706684225719239474253172647955974999328324727980789647075305401419409020060971267475318636552540321275775785393069753005659520820745749947189814445377224820788844333511854560156885370818289289521830013965437694728641877666576281538973734015941054368143543734613424469206707008278242364555745088255667015724275281031714164063141068138433092402728131896088481304066522616955282563718386246494429568885939384672672369419947557132054601826342573102911535353272880818277302159678708843729341211708451158062996769726660166363527695996902150212210495425956727859318551626844710037443462042200353539120373839309542069502148620739065319091082134433425149789628423619857167477384812609744305503625086635472073097129808469719653772277989316020056072505800751240749444816339221439811849274828197865517847854774919871413848504229038395409057084203813727713566770356504108178052069503213623352169274053101534092176183407881773567464674907161660065323043890263978606550900530987243544568931560132994240711229501545377152105194244551279536497121487222219372928915983300174239797759253050131883788349488423222250731881639943893562781710287543258879455885774278039071716638125790379814914844552688587162993101451073321555477326457603591618429870832323756883791713507300602673829229468708103075194602037643813867710733377931258225735643553457716280403048092578590974723341393290407223986000544826929611039364012753953989939742002192526892862256495927913636954698324731449409429749421320871696366281296384619137811460921070103301211993426494166644913031089849353536640183128268311250657838642590653719701090727642933053475129733671692941504787094924177812153497949944973235844513021002972035999357650773056369695053999089125200481012009056963314436817919424796356338910248625077336724939980172345162704885014943834373582644005348147495742132887364847958955384383637827560143337779881612685446240649413441611910895265332676162766022113087921166592437949653483803023606429498198554101431156660173951853942600867319856458668463544273018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     ]
    }
   ],
   "source": [
    "factorial2(750)\n",
    "factorial2(1500)\n",
    "factorial2(2250)\n",
    "print('We can now get the answer we want:\\n{}'.format(factorial2(3000)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Second example: Fibonacci numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fibo(n):\n",
    "    if n == 1 or n == 2:\n",
    "        return 1\n",
    "    return fibo(n-1) + fibo(n-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 121 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "for k in range(1,5):\n",
    "    fibo(7*k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Memoize:\n",
    "    def __init__(self, f):\n",
    "        self.f = f\n",
    "        self.memo = {}\n",
    "    def __call__(self, *args):\n",
    "        if not args in self.memo:\n",
    "            self.memo[args] = self.f(*args)\n",
    "        return self.memo[args]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fibo = Memoize(fibo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The slowest run took 18.04 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
      "100000 loops, best of 3: 2.75 µs per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit\n",
    "for k in range(1,5):\n",
    "    fibo(7*k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Writing good code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Memory allocation, implicit array copying"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def nmz1(x):\n",
    "    return x / np.linalg.norm(x)\n",
    "\n",
    "def nmz2(x):\n",
    "    x /= np.linalg.norm(x)\n",
    "    return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 38.3 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit x = np.random.rand(3000,3000)\n",
    "nmz1(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 14.7 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit x = np.random.rand(3000,3000)\n",
    "nmz2(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section we provide an example of how to use Numba's `@jit` decorator to make fast computations happen *via* so-called \"just in time\" compiling. This tutorial can be found in its original format on the [IPython Cookbook](http://nbviewer.jupyter.org/github/ipython-books/cookbook-code/blob/master/notebooks/chapter05_hpc/01_numba.ipynb) website."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "size = 200\n",
    "iterations = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure python version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m = np.zeros((size, size))\n",
    "mandelbrot_python(m, size, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DtOtKGch2oZfMxNUxt9pnJ4q9h50KGrbZTXHqsiYtzKa0rUTXZNGoBdYhNsxKI6xaSJdQ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\nWKO1WHKGNVqLJWdYo7VYcsb/Ad4aWuMclhapAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e26ad68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.imshow(np.log(m), cmap=plt.cm.hot,);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 2.47 s per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit m = np.zeros((size, size))\n",
    "mandelbrot_python(m, size, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numba version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import Numba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numba\n",
    "from numba import jit, complex128"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add the @jit (just-in-time) decorator to the very same function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@jit(locals=dict(c=complex128, z=complex128))\n",
    "def mandelbrot_numba(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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m = np.zeros((size, size))\n",
    "mandelbrot_numba(m, size, iterations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 5.84 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit m = np.zeros((size, size))\n",
    "mandelbrot_numba(m, size, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Numexpr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's import NumPy and Numexpr."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numexpr as ne"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate three large vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x, y, z = np.random.rand(3, 1000000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we evaluate the time taken by NumPy to calculate a complex algebraic expression involving our vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 loops, best of 3: 20.3 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit x + (y**2 + (z*x + 1)*3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now, the same calculation performed by Numexpr. We need to give the formula as a string as Numexpr will parse it and compile it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 3.69 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit ne.evaluate('x + (y**2 + (z*x + 1)*3)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numexpr also makes use of multicore processors. Here, we have 4 physical cores and 8 virtual threads with hyperthreading. We can specify how many cores we want numexpr to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ne.ncores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 6.4 ms per loop\n",
      "100 loops, best of 3: 4.15 ms per loop\n",
      "100 loops, best of 3: 3.53 ms per loop\n",
      "100 loops, best of 3: 3.4 ms per loop\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 5):\n",
    "    ne.set_num_threads(i)\n",
    "    %timeit ne.evaluate('x + (y**2 + (z*x + 1)*3)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "<div class=\"cython\"><pre class=\"cython line score-19\" onclick='toggleDiv(this)'>+<span class=\"\">01</span>: <span class=\"k\">import</span> <span class=\"nn\">numpy</span> <span class=\"k\">as</span> <span class=\"nn\">np</span></pre>\n",
       "<pre class='cython code score-19 '>  __pyx_t_1 = <span class='pyx_c_api'>__Pyx_Import</span>(__pyx_n_s_numpy, 0, -1);<span class='error_goto'> if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
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       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "/* … */\n",
       "  __pyx_t_1 = <span class='py_c_api'>PyDict_New</span>();<span class='error_goto'> if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 1; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
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       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">02</span>: </pre>\n",
       "<pre class=\"cython line score-61\" onclick='toggleDiv(this)'>+<span class=\"\">03</span>: <span class=\"k\">def</span> <span class=\"nf\">mandelbrot_cython</span><span class=\"p\">(</span><span class=\"nb\">int</span><span class=\"p\">[:,::</span><span class=\"mf\">1</span><span class=\"p\">]</span> <span class=\"n\">m</span><span class=\"p\">,</span></pre>\n",
       "<pre class='cython code score-61 '>/* Python wrapper */\n",
       "static PyObject *__pyx_pw_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/\n",
       "static PyMethodDef __pyx_mdef_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_1mandelbrot_cython = {\"mandelbrot_cython\", (PyCFunction)__pyx_pw_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_1mandelbrot_cython, METH_VARARGS|METH_KEYWORDS, 0};\n",
       "static PyObject *__pyx_pw_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_1mandelbrot_cython(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {\n",
       "  __Pyx_memviewslice __pyx_v_m = { 0, 0, { 0 }, { 0 }, { 0 } };\n",
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       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
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       "      kw_args = <span class='py_c_api'>PyDict_Size</span>(__pyx_kwds);\n",
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       "      values[0] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 0);\n",
       "      values[1] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 1);\n",
       "      values[2] = <span class='py_macro_api'>PyTuple_GET_ITEM</span>(__pyx_args, 2);\n",
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       "    __pyx_v_m = <span class='pyx_c_api'>__Pyx_PyObject_to_MemoryviewSlice_d_dc_int</span>(values[0]);<span class='error_goto'> if (unlikely(!__pyx_v_m.memview)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "    __pyx_v_size = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(values[1]);<span class='error_goto'> if (unlikely((__pyx_v_size == (int)-1) &amp;&amp; PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 4; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "    __pyx_v_iterations = <span class='pyx_c_api'>__Pyx_PyInt_As_int</span>(values[2]);<span class='error_goto'> if (unlikely((__pyx_v_iterations == (int)-1) &amp;&amp; PyErr_Occurred())) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 5; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
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       "  goto __pyx_L4_argument_unpacking_done;\n",
       "  __pyx_L5_argtuple_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_RaiseArgtupleInvalid</span>(\"mandelbrot_cython\", 1, 3, 3, <span class='py_macro_api'>PyTuple_GET_SIZE</span>(__pyx_args)); <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L3_error;}</span>\n",
       "  __pyx_L3_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_cc0c3c710e01dec074c1bcec46022dd6.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
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       "  __pyx_L4_argument_unpacking_done:;\n",
       "  __pyx_r = __pyx_pf_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_mandelbrot_cython(__pyx_self, __pyx_v_m, __pyx_v_size, __pyx_v_iterations);\n",
       "  int __pyx_lineno = 0;\n",
       "  const char *__pyx_filename = NULL;\n",
       "  int __pyx_clineno = 0;\n",
       "\n",
       "  /* function exit code */\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "\n",
       "static PyObject *__pyx_pf_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_mandelbrot_cython(CYTHON_UNUSED PyObject *__pyx_self, __Pyx_memviewslice __pyx_v_m, int __pyx_v_size, int __pyx_v_iterations) {\n",
       "  int __pyx_v_i;\n",
       "  int __pyx_v_j;\n",
       "  int __pyx_v_n;\n",
       "  __pyx_t_double_complex __pyx_v_z;\n",
       "  __pyx_t_double_complex __pyx_v_c;\n",
       "  PyObject *__pyx_r = NULL;\n",
       "  <span class='refnanny'>__Pyx_RefNannyDeclarations</span>\n",
       "  <span class='refnanny'>__Pyx_RefNannySetupContext</span>(\"mandelbrot_cython\", 0);\n",
       "/* … */\n",
       "  /* function exit code */\n",
       "  __pyx_r = Py_None; <span class='pyx_macro_api'>__Pyx_INCREF</span>(Py_None);\n",
       "  goto __pyx_L0;\n",
       "  __pyx_L1_error:;\n",
       "  <span class='pyx_c_api'>__Pyx_AddTraceback</span>(\"_cython_magic_cc0c3c710e01dec074c1bcec46022dd6.mandelbrot_cython\", __pyx_clineno, __pyx_lineno, __pyx_filename);\n",
       "  __pyx_r = NULL;\n",
       "  __pyx_L0:;\n",
       "  __PYX_XDEC_MEMVIEW(&amp;__pyx_v_m, 1);\n",
       "  <span class='refnanny'>__Pyx_XGIVEREF</span>(__pyx_r);\n",
       "  <span class='refnanny'>__Pyx_RefNannyFinishContext</span>();\n",
       "  return __pyx_r;\n",
       "}\n",
       "/* … */\n",
       "  __pyx_tuple__14 = <span class='py_c_api'>PyTuple_Pack</span>(8, __pyx_n_s_m, __pyx_n_s_size, __pyx_n_s_iterations, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_n, __pyx_n_s_z, __pyx_n_s_c);<span class='error_goto'> if (unlikely(!__pyx_tuple__14)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_tuple__14);\n",
       "  <span class='refnanny'>__Pyx_GIVEREF</span>(__pyx_tuple__14);\n",
       "/* … */\n",
       "  __pyx_t_1 = PyCFunction_NewEx(&amp;__pyx_mdef_46_cython_magic_cc0c3c710e01dec074c1bcec46022dd6_1mandelbrot_cython, NULL, __pyx_n_s_cython_magic_cc0c3c710e01dec074);<span class='error_goto'> if (unlikely(!__pyx_t_1)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='refnanny'>__Pyx_GOTREF</span>(__pyx_t_1);\n",
       "  if (<span class='py_c_api'>PyDict_SetItem</span>(__pyx_d, __pyx_n_s_mandelbrot_cython, __pyx_t_1) &lt; 0) <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "  <span class='pyx_macro_api'>__Pyx_DECREF</span>(__pyx_t_1); __pyx_t_1 = 0;\n",
       "  __pyx_codeobj__15 = (PyObject*)<span class='pyx_c_api'>__Pyx_PyCode_New</span>(3, 0, 8, 0, 0, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__14, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_Users_berkas_ipython_cython__cy, __pyx_n_s_mandelbrot_cython, 3, __pyx_empty_bytes);<span class='error_goto'> if (unlikely(!__pyx_codeobj__15)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 3; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">04</span>:                       <span class=\"nb\">int</span> <span class=\"n\">size</span><span class=\"p\">,</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">05</span>:                       <span class=\"nb\">int</span> <span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">06</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">int</span> <span class=\"nf\">i</span><span class=\"p\">,</span> <span class=\"nf\">j</span><span class=\"p\">,</span> <span class=\"nf\">n</span></pre>\n",
       "<pre class=\"cython line score-0\">&#xA0;<span class=\"\">07</span>:     <span class=\"k\">cdef</span> <span class=\"kt\">complex</span> <span class=\"nf\">z</span><span class=\"p\">,</span> <span class=\"nf\">c</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">08</span>:     <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>  __pyx_t_1 = __pyx_v_size;\n",
       "  for (__pyx_t_2 = 0; __pyx_t_2 &lt; __pyx_t_1; __pyx_t_2+=1) {\n",
       "    __pyx_v_i = __pyx_t_2;\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">09</span>:         <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>    __pyx_t_3 = __pyx_v_size;\n",
       "    for (__pyx_t_4 = 0; __pyx_t_4 &lt; __pyx_t_3; __pyx_t_4+=1) {\n",
       "      __pyx_v_j = __pyx_t_4;\n",
       "</pre><pre class=\"cython line score-10\" onclick='toggleDiv(this)'>+<span class=\"\">10</span>:             <span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"o\">-</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">j</span> <span class=\"o\">+</span> <span class=\"mf\">1</span><span class=\"n\">j</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"o\">-</span><span class=\"mf\">3.</span><span class=\"o\">/</span><span class=\"n\">size</span><span class=\"o\">*</span><span class=\"n\">i</span><span class=\"p\">)</span></pre>\n",
       "<pre class='cython code score-10 '>      if (unlikely(__pyx_v_size == 0)) {\n",
       "        <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "        <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "      }\n",
       "      if (unlikely(__pyx_v_size == 0)) {\n",
       "        <span class='py_c_api'>PyErr_SetString</span>(PyExc_ZeroDivisionError, \"float division\");\n",
       "        <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 10; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "      }\n",
       "      __pyx_v_c = __Pyx_c_sum(__pyx_t_double_complex_from_parts((-2.0 + ((3. / __pyx_v_size) * __pyx_v_j)), 0), __Pyx_c_prod(__pyx_t_double_complex_from_parts(0, 1.0), __pyx_t_double_complex_from_parts((1.5 - ((3. / __pyx_v_size) * __pyx_v_i)), 0)));\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">11</span>:             <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mf\">0</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_v_z = __pyx_t_double_complex_from_parts(0, 0);\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">12</span>:             <span class=\"k\">for</span> <span class=\"n\">n</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">iterations</span><span class=\"p\">):</span></pre>\n",
       "<pre class='cython code score-0 '>      __pyx_t_5 = __pyx_v_iterations;\n",
       "      for (__pyx_t_6 = 0; __pyx_t_6 &lt; __pyx_t_5; __pyx_t_6+=1) {\n",
       "        __pyx_v_n = __pyx_t_6;\n",
       "</pre><pre class=\"cython line score-2\" onclick='toggleDiv(this)'>+<span class=\"\">13</span>:                 <span class=\"k\">if</span> <span class=\"n\">z</span><span class=\"o\">.</span><span class=\"n\">real</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">+</span> <span class=\"n\">z</span><span class=\"o\">.</span><span class=\"n\">imag</span><span class=\"o\">**</span><span class=\"mf\">2</span> <span class=\"o\">&lt;=</span> <span class=\"mf\">100</span><span class=\"p\">:</span></pre>\n",
       "<pre class='cython code score-2 '>        __pyx_t_7 = (((pow(<span class='pyx_macro_api'>__Pyx_CREAL</span>(__pyx_v_z), 2.0) + pow(<span class='pyx_macro_api'>__Pyx_CIMAG</span>(__pyx_v_z), 2.0)) &lt;= 100.0) != 0);\n",
       "        if (__pyx_t_7) {\n",
       "/* … */\n",
       "          goto __pyx_L9;\n",
       "        }\n",
       "</pre><pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">14</span>:                     <span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"n\">z</span><span class=\"o\">*</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"n\">c</span></pre>\n",
       "<pre class='cython code score-0 '>          __pyx_v_z = __Pyx_c_sum(__Pyx_c_prod(__pyx_v_z, __pyx_v_z), __pyx_v_c);\n",
       "</pre><pre class=\"cython line score-2\" onclick='toggleDiv(this)'>+<span class=\"\">15</span>:                     <span class=\"n\">m</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">n</span></pre>\n",
       "<pre class='cython code score-2 '>          __pyx_t_8 = __pyx_v_i;\n",
       "          __pyx_t_9 = __pyx_v_j;\n",
       "          __pyx_t_10 = -1;\n",
       "          if (__pyx_t_8 &lt; 0) {\n",
       "            __pyx_t_8 += __pyx_v_m.shape[0];\n",
       "            if (unlikely(__pyx_t_8 &lt; 0)) __pyx_t_10 = 0;\n",
       "          } else if (unlikely(__pyx_t_8 &gt;= __pyx_v_m.shape[0])) __pyx_t_10 = 0;\n",
       "          if (__pyx_t_9 &lt; 0) {\n",
       "            __pyx_t_9 += __pyx_v_m.shape[1];\n",
       "            if (unlikely(__pyx_t_9 &lt; 0)) __pyx_t_10 = 1;\n",
       "          } else if (unlikely(__pyx_t_9 &gt;= __pyx_v_m.shape[1])) __pyx_t_10 = 1;\n",
       "          if (unlikely(__pyx_t_10 != -1)) {\n",
       "            <span class='pyx_c_api'>__Pyx_RaiseBufferIndexError</span>(__pyx_t_10);\n",
       "            <span class='error_goto'>{__pyx_filename = __pyx_f[0]; __pyx_lineno = 15; __pyx_clineno = __LINE__; goto __pyx_L1_error;}</span>\n",
       "          }\n",
       "          *((int *) ( /* dim=1 */ ((char *) (((int *) ( /* dim=0 */ (__pyx_v_m.data + __pyx_t_8 * __pyx_v_m.strides[0]) )) + __pyx_t_9)) )) = __pyx_v_n;\n",
       "</pre><pre class=\"cython line score-0\">&#xA0;<span class=\"\">16</span>:                 <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
       "<pre class=\"cython line score-0\" onclick='toggleDiv(this)'>+<span class=\"\">17</span>:                     <span class=\"k\">break</span></pre>\n",
       "<pre class='cython code score-0 '>        /*else*/ {\n",
       "          goto __pyx_L8_break;\n",
       "        }\n",
       "        __pyx_L9:;\n",
       "      }\n",
       "      __pyx_L8_break:;\n",
       "    }\n",
       "  }\n",
       "</pre></div></body></html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 8.56 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%%timeit -n1 -r1 m = np.zeros((size, size), dtype=np.int32)\n",
    "mandelbrot_cython(m, size, iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ray tracing example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This series of examples was also taken from the [IPython Cookbook](http://nbviewer.jupyter.org/github/ipython-books/cookbook-code/blob/master/notebooks/chapter05_hpc/05_ray_1.ipynb) (see Section 5). It was included here so that the output of the code could also be included (since the output is not rendered in the Cookbook). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pure Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will render a sphere with a diffuse and specular material. The principle is to model a scene with a light source and a camera, and use the physical properties of light propagation to calculate the light intensity and color of every pixel of the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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KnWAtmZQKV1PTKdC17bRyB+hw2/4+cwBrobMGGG93lXBxKOUjfVPrrlpofJ5S1ZAIbFH8\nCVTVZb/V4uKh9f4leH+FuwErl1F5CJq+TSqJNbX+2l+/g7m/rnQzvSdVHiYJFZ8/BcgxQO8X3OFv\n5f1r8P7tdz3AC62Lh7brTEFXSiqEyoW3gA6dLPNtpgzd9n1XTe1H+5zddOoF41Se8hpUKfkGRrmu\n3H5quHseuLnfAFhLvfayvx2A9ElMuRqU+bnwdwqY2jFzy3P7BkLoz5MQ0Vh75an22hjei0l77lW+\nD4oPsn/xlBuBpnGI5c1Tv/md9jb9wAvUChJRWvNOKszly6Y4ZEA/ccSlHUM28fTBG/Y5zn8eDm8I\nASG4ATzay9i0N1DUddd9kcZA3I6ad2jgPZ9SAKfAnevI6d8AokzTlw0scOHQen8F5zaYdiJTF8MY\n0Kn5KUDljUObn5vHgW0RQnsCtg9Kyk05pNTOytthm6brSEGgU48o6kSx3w/h5U5N41QIrgGrQ6zd\n+LQopn8unHsF3n8d2vYy/yLzoqHdbt+KoniM8Xps7s4t1xtz0NQ2ch0NyP5+Q+gnnSKcHbDdvAhu\n27oeNBJW2SFCPtVD21D/Yv7AwM0N8OwZcH3dB5i7r4RXPp4HTHHYVMQyFvV046J4J7bbn8b19feO\nHWyRumho9f6oGiSAfnHI6RRgULbRtk0df9xZ5TE6WOPQtu0JWjd4xSkHlsPKuyYSnLRMQrvfR2gJ\nXIL35mZayDwOrvab5n5fLRLiutx0zYVDO9bPOAdw7sKYEqqN9YhKQZruXEHOGsNix8BtEEI5qLfK\nOit1+pfPw/KeTvIpH9oXufOzZ8DTpx28PGSW4Kb+7wdAL1we/raynDoXqd/3suu1Fw6tPHmpuzlN\npwAEhhfQWPibgnQM9uF6XTjs4FwE1jnfc9mmaVAUHk1T9MAlEOU7jilbyzv/8wfcNWj3+wgqOa4M\nlzXHnZKcykcv2nnIDXy7y9QKoJXZ3RxUUwdM3McUkDFxXgcwOWzbtvA+jkNo0LYFmsajaVyvLksv\nYZM9n+SbKeTL3VKvm+HgyjqurNvmwU3dFKHMy91kUzfCy9SFQys15Q6urTe27lTANZBxO4+acLo2\nS5mMim4bHdb1wG2aBt438N7jeCxQFPozrdxhuctSFlm+I0quo4HLnVYmpWSdlgPbJdVyLnvu7325\nWgG0Ux1Wm3cfw5jbap8Rg+26i7tFfAdyC2ryadsGzjm0bYO2Jaf10J6yAToH5S6aehsjb/bhz84S\nuDSkwmPe/NPVaWUbM0SZ/yapc5g7d5etFUALnA/mOetr28h5WhuuFsbrx+dOG5NQDiF4NM0Rw399\nd73+vvKdTlSXpdCYg87X5W5LSS2ClwZalg6PqT2ZRw7yu2Jk3jnn47K0Amhzd+OHAliuO8dtW8Ss\ndze/C5HbkxPxENmhbVvEN+w7OHc8Qdr9obQEVv5rgHwWlncplH8LwntG8cwxd1oN2LbtgO06hHCX\n5eNUWf6G7cg5uExdOLQ5sOiEa+tBrOfFdL5ZZn4mGWwMBinQuREQgmfwEqwOQAyP47w4HI8HOFed\nAHS9+iSvp2oPr3NoeSgt3wGldW+k/fbbawnYGM6nIgo9NIay/lR4L1MrgrZFd3LlSZYAEwwe+oVw\nn24rnRVieZekooRUvPAjWREGd1uv5YrTGwasG4S7lHziLsvf3yRDZA4lgSvfxMhh7RJQLYNWfseU\nwwLD35KfI+1ctGy4TK0I2uGdfTp8BIljZUC/kLQ6agpk+TnBthuGyRQeUxstgFOI3Nw6IoXPBHAM\nQTcIwfcAJEgPh64um/qrSxlSyyHlsBQWx95a7W1ddhgWy7I8T9r5GjuHl6uVQJtyWA4H3Z1TDqtt\nB3QgezafwIPYxmF4XL4ObscRTvn55Odqb90TALx3p/baCE8ItK+AEEqEQO243YvEtf+mleExb7bh\nUEp4+4/ttad6LH+ooQ/sEFx+3mRZA7ZVBnl+Lk8rgFYCmzrJKTCnACwvLLpgisx6NE45q1wPpxCZ\n3BYAOsdt21i3vd2SAeF9lwSKPab6/0igvSaG9iHdVnselztr07SnsLi9dVnusPR9JLDjTT389x07\nZ63Yz2XpwqFN1V1z86AsH0s8pQDXkljSNaXjdtMRUpofx+TABCt/ORp/gJ2/H7lzvPLUgyqCG/9p\nD7f/AyRfOyN7MMn/6unGAW0bBrDG4/Y7UUxz1/53Ho61c6e57mVqBdA20E/uOe5KAHOQp0Kduvjk\nPD5uWcaYvk8HfdeDKjDHjfO8L0513C6BFXtPFWjbAs4VKIoC9F9AvF2XS0Ibx6EHa4SZOysHFgLc\noavqfZFleYqzSpgvUyuANlfn0UJmgoIST1pdde5Ad33aV64jBR9TmbtxBDnC2t5e8Dw5RY4b3TLA\n+7gP5wrE525beB97TzlXsDbd+J2pmQjQ3Dac9oGem8qxrMN2dVn+vTRgc7+H9rumXNacdqHKAauV\nc+6aA3YMaLlMC5OhTAO4DYmHYXR0YQ6u64XKMUQuTvuIjh2B9SdgPZxrWC8q7WXuvI23A5F6OPUh\n7aCmz83fqpF3P7lsDNyxXIVBu1A1bEjdjbUTnsogc4AlqDJkJmnZZdmUk3fWGApDDZP74Lpbd41h\nsb+tE3cvOo/AxpC477AALwMpt9UcVIbC3XbSYek7ply2Wz78XbTzkavXXqZWAi2dRJrWsrr8pHtl\nPMVhtaxxClh+YQ4hHSaowBJT/fU6cGkhbX9asyVo4zYxlI6u2kHLgdWhJfXhHbopXz8kyMyHxany\nVJel83yZunBoj6eBTuJYOKVlf7mryrK2jganhDQXIkOsC2VdJOeH0LKuixSm+hO0VBeOAEd4Y/ju\nXHP7vQje7ibgGIQQZf0VrvlQOKccrPLcpM4jgXuZunBoD+igpROZOtGa22puKV2Vd6TQ6rY8TOMO\nOOzt1L0eR8LalSOUElyCyrF6bfd2i7g/fxsyx3E8TnRfl3BZctouo0xlCW+3PLAy7aevfLZYztOA\nTYXDdI7pZn2Zumho9/sn2G5fRlHwMFmr32qhMXfUlNtyp+UhMJeEHYB6M4CYR9LBjeEsBut1SSsd\n5A5gd2oq6rurHh4PoY1lJMr8g0mIxySjjNxvp0PbNP8b+/3fm3KwReqioW3bBiHw8DiXkJKJKM1t\nNYi1um3KFYA+3LLMx3QjADRwY13W3dZHu2UU1sZ1IrCyGSuw/XMwU+BKUB0r9zXdXXOSgPKyhJaX\n4zkO4Qto24/POeCidNHQRlG4NCeLnHLbVF1XC5dTsE4BNgdrvzxsDgJbp6uX9uupEt4UqH3H5XVb\nPn84r09o33lT0uqyvMzrsbwsIygaX65WAO0RsW7LT6oGLyViNLeV8Dro4E4JjzVgZUg4BVzanz9B\n04oQV2aeu2U6wDlgJby0v9CbJ9VPSuXAlTacC5G1/IM8t5ebhAJWAe0BXUJKJqUKpJ2Xuy0w7Bml\ngau5bQrinNtiQlke252yxGDrafVxDdbuUT4Jbbcu0AcvNY9uEnLZlPhYOmwOWj007s735erioW3b\nGm1bw3tZt+Vttg2G4asGZCopBaSTUak2XqB/Q6B90jQtT5W5m95+W5FYkssBPSR2Ak5aD+AA98dB\nzAP64fMwTJ6mOfVZ6a4N2vYzaNvfOuO4y9HFQ1vXNZzbw3vutkfEr04n3bMyhzEVGucgHktEkfQn\ne4bTchmXVpc9rRloeSozTPvTvpt0Tw3aOO6aeCTI8rOmwuNcaMyXaWGxBPeIpvlF1PW/SBzrMnTx\n0EYdANQYhsdjITKHUQOYpgtWTqnfS6k/T+t/nAqJ+UMH2mfiEMf1umxyVBdC85tMqn5L+8HtMuqQ\noUMqgZX70JRLQmk3P0pAyUQU3ZgvWyuCdo8O2iMiaDw0puYPXpeVzitdFRhCDTZfTgN6VpmXgf4N\nIFWX5esNO1sMHTMVMeScV87jgI8ll+ZIJp6onIKWg9u5rEF7QarrGsANNpsaQAVgg2G9NuWyNNYA\n5mUuHl6PZY05jMDQKTmY6bps2m25uPPq4NIDBnrTEMS0rNdqLntOAorGKZfVssZHHA7vR13/+wnH\nW7ZWAW18hIyHyFSn5eCS23I4JaC8KUGuQ/O0+quUhFSC65AOkamcg3PMVdN12WEzjYwoUqHxucDy\n49E4l4CiMXfY6LJt+1mE8NkZx1ymVgFtVIMYIteITluiDy4PlVP12ilJG6kUyDlwU72jxurYND+I\naZIEUc5L1Wc1t+XfTX73ucDScWg8JWssm3mo+nP5Wg20bXvE8bhHWfIQmeq2dMemi1zLJo8BC+gX\nrlZ3hTJPA5X2k+raqIEpw/VUHVdKwpsDfKxeO6e+K+uzc4GNTns8fght+ysTj7lsrQbapmng3B5l\nuQewRRdW0b/Fe/Tdloe+KXhJWpishchj4Do2D8i7bS75lHPYsRuPTDxJ99XA5Z8diemUcrDSNE8+\naaFxjePxg2iaj0085rK1GmgBIIQjmuYaRXGFLkTmWWQCVo5l3TZV5yXlLtixpp9UJnksVObNQIDu\nsGPwSiBT5dc7ASWdtl+XbZpfQwifm3C8y9CqoG2aBnV9g91ujxgiHxCBpbothch08Tt0LsvdFpny\nFOXA1RxcQppaBqRvLlPgld8lKPM0UO/qsrw8ljFu0W+6O6Cu/yWa5qMTj7l8rQraqAYhXMO5LTq3\nPaALkXmbrXZBd/tJKxUec2ngao6dq8/mOldMCYm1dXIhMRJj6ar3ERrTvFxd9oAQvoS1JKBIq4O2\naRpcXz/Fo0c7DENkCS4Pk6XbpsLkOZLgciiBPhi8nEtGSUc+B14tJIZYN1enzSWicu7Ky7kEFHWk\nqHF9/ZNo299MHOsytTpoAZze/PAMXRZZAzYVNsq22ruKgxvY8XMZZP55eBfIc0JibR1A/+5UTjXz\nzNFY1rhlZdn1lJ7k2SOEZxiPai5Lq4X2+voZrq6u4Bx3Wg6vgx4m8+GuITJfl4+pTNOpOi2fP7U9\neW4ySn6WHKhzw2JeHqvL9rsshvAENzc/gxB+d+IxL0erhBYAmuYI4AbpEHns4pdKXdhjIneV23Eo\n+f45qLStE8vPrc9KSHOJKO17zoV2asaYnLZr4gGeoWn+76m8Lq0WWgCo62tUVXlyWwJ3LCGlXbQ5\nmHl9TRPfTmuzzYWr2jS/CcyFN7VvrYlHfnbt+0ilHJbGMiwe9i8GarTtZ3E4vB9rS0CRVg3t4XDA\nZhOft40/xRRg+QVL4fGc15vIC1d2gpCum4I2V5eV68+BV4MYYlmuqSd1g5oCbKqJp9+RAvgcDof/\nmDjO5WvV0AJA0xzg3M3pP2/mhMfn1N+AvgumgKX9S4glQKn+x1rYTMcYC4m1Mh+n5mnT/LvJ6anZ\n4n5YHMLnTmHxerV6aPf7PQCgLAuRlBoLje9bGgAcNvo8vMzXmwpuDli+LZTl2med85uMNfGkkk/U\nJvt5HI8fwn7/72Yc8/K0emgBAtdjs9GcVksS0fSUsFgLC/k0DV7MSzX9cCDHElFTwuIxx9XGspya\np31f/h15OdXEQy67x/H4y9jv/41y3HXJoL1Vi1hfIqfNhcM55+GSSSh5oWrPw1JnDr4OB1V2opDg\nEqhzk1FQ5qecN1VOQaqVc2Exgdv1L47t6jcwGbS32u/3CAGoKrrgp4SVXIWYDso86aapC1nrcOHY\ncvkZc/OmuqyEMxUaA2l4pXKRhQYtzxjznk/XqOsPoK7Xm3ziMmiZDofY5hfBTSWl7qKc81BYG8S0\nDINzoTEHdUr2OzU9pYln6m+RyxRrTiuB3aOufx6Hw39BdFuTQcsUQjiB61BV/KIHpkErQSxEmV+4\nmutq9VoNUvo8Grha6D42aOtCGefKUhqs8vtyWCkk7tdjI7C/hBC+kDnWumTQCoUQ0DT0Pqk5LhvQ\n/ZwyNJYXbOpPrSWsKXCl82ruem4SCpl5XFPD4qkOK122BvDl1T0rO0UGrSJy3M1mDrCy/iaXA8OL\nWdZtU64rgZ1aj6V95OrouTKgQzs14si5rNa80088HQ4fWWXf4jEZtIratkVd7+EcUBRg/3OT0ljC\npWBjbTltL+u1ElDNYXP1WG2duWGx5rBBma/9FjmXTTtsCNdomo+irj+AEL6YOM56ZdAmFELAzc0N\ndjsH7wFn9Zd4AAAFs0lEQVSdWwmdnKeBmwuPKfmlQevFPAmv9qBAql4+5rraGInp1O+S+y0IWv4P\nhgTsU7Ttr+Pm5n2Ib1g0SRm0I7q+vsZuBwXc3AWZA5e29dDhpYw1XdgSVj6Pw6m5ac5hc/XaHKjn\nOCww/iDAASE8Qdv+Jq6v/1XiGCbAoJ2kPrhaPZQrBSxfNsV1Zb1WOirBmwuRW2XemLveh8OmfodU\npjiGxG37cVxf/9sJx1m3DNqJur6+xtVVQFkCekJFlnMhcot+KMyfLOLr8PmyfsrncYB5WTouxPwp\nYfEUWEnaDYr/LtpDADHp1DQfw83Nz8841npl0M4Q9ZrabOSFmKu3aeNCjGWorIXIEl4JJ3db+e6o\nKeGxLAPzgAV0aGVPJxrTK2Oe4HD4KOr6w7BuitNk0M4QNQUdjwcURY2qogswBWoplkmnlYDK53lz\n8EpwU/VXguicJJQsJ38ZDGHVHJa/46lGXf93NM0nEMIXEMKXJxzHBBi0s9W2LRsHVJXmItozoSUr\n8ws5FyZrLstB1ZwX6Dus9rwtRspQyimlgJXhcP9/d+r6Izgc/o816Zwhg/ZMkes6R+EywbqFDi0H\nl1yXg0vwcYgJPgkwTzBxgDmgY/VYLRQ+B1gap4DlL2SLfzla1x/F4fA/EcKTCccwSRm0d1AI4fYh\nemCPsmzgnPy3+Q367kvg0iOA/ALnjssh5QBLSPk0hzHXJ3ksCSXLg2+ujPMJpxCe4Hj8dUSX/TCs\nDfZ8GbT3oA7c9gQuNWVs0YHLQ2cClgNMAHJYC2WeBm8O0imJKG2c07xwOIQv43j8OPb7X5ywb9OY\nDNp7FMFbFEc4V59cV8LboP/fuPK9ywSoVqeVgwamhJiey53b1KNpajgcHTaEJwjhS2iaT2K//8jI\nr2eaKhe6v/4eLow9CUxnaLPZoKp2AK7g3BXivxnQPxrwP7WW0PJ3VGmvdJXQak6bct1UXRaJecCw\nwwRJa86iF4nvEeuu/wuHwzr+M/YhFEJQ76AG7QOrKErsdo8APEJ0XA5vKQaP/vuXU/8xNBdanlUe\nyxjz6ak9nHh3xBrX1x9A0/wOOtc1nSOD9jnKOQ/nPHa7x3Buhw7eDfrOS/VcDd4UsDmAgSHAQNpt\neXkKsPxvOp7h+voDCOGIEJ5i3rugTZoM2hdARRGds6quUBQc3goRUvozMC1k5skp3hSUq8/mQuOx\nTHEu2dTB2jSfQ11/DECDpvks+rCb7iKD9gVSUcR3LJflFmW5xRBeXtcl55V1Xd6mqwFLITEHGEpZ\nSjqsrLPGjPDx+Gkcj58+Pfv6mfN/DFNSBu0LqKIo4H2E0/sNNpsr9EPnVKIqFzKn6rdAHlit7bVf\nXz0cPom2vUF01c+jbe29TQ+pFLTW5PMc1TQNmibW/eLbMehf/DYoii28l9nmKfBO6VwBVk71GW7Q\ntjdoms+DHLauP3HKDJuep8xpX1BVVcWgjcA6V6Iothg6sFbfHavL9h21aZ4ihAM6aI9o2yeo699+\n2C9qSsrC4wuQ9wW225eQ/k9d6baaw5L6rrrfU+hrelFk0JpMC1MKWq/NNJlML64MWpNpYTJoTaaF\nyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNp\nYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9Zk\nWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1\nmRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJoTaaFyaA1mRYmg9ZkWpgMWpNpYTJo\nTaaFyaA1mRYmF0J43p/BZDLNkDmtybQwGbQm08Jk0JpMC5NBazItTAatybQw/R5eqme1iT/3OAAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f2f2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w, h = 200, 200  # Size of the screen in pixels.\n",
    "\n",
    "def normalize(x):\n",
    "    # This function normalizes a vector.\n",
    "    x /= np.linalg.norm(x)\n",
    "    return x\n",
    "\n",
    "def intersect_sphere(O, D, S, R):\n",
    "    # Return the distance from O to the intersection \n",
    "    # of the ray (O, D) with the sphere (S, R), or \n",
    "    # +inf if there is no intersection.\n",
    "    # O and S are 3D points, D (direction) is a \n",
    "    # normalized vector, R is a scalar.\n",
    "    a = np.dot(D, D)\n",
    "    OS = O - S\n",
    "    b = 2 * np.dot(D, OS)\n",
    "    c = np.dot(OS, OS) - R*R\n",
    "    disc = b*b - 4*a*c\n",
    "    if disc > 0:\n",
    "        distSqrt = np.sqrt(disc)\n",
    "        q = (-b - distSqrt) / 2.0 if b < 0 \\\n",
    "            else (-b + distSqrt) / 2.0\n",
    "        t0 = q / a\n",
    "        t1 = c / q\n",
    "        t0, t1 = min(t0, t1), max(t0, t1)\n",
    "        if t1 >= 0:\n",
    "            return t1 if t0 < 0 else t0\n",
    "    return np.inf\n",
    "\n",
    "def trace_ray(O, D):\n",
    "    # Find first point of intersection with the scene.\n",
    "    t = intersect_sphere(O, D, position, radius)\n",
    "    # No intersection?\n",
    "    if t == np.inf:\n",
    "        return\n",
    "    # Find the point of intersection on the object.\n",
    "    M = O + D * t\n",
    "    N = normalize(M - position)\n",
    "    toL = normalize(L - M)\n",
    "    toO = normalize(O - M)\n",
    "    # Ambient light.\n",
    "    col = ambient\n",
    "    # Lambert shading (diffuse).\n",
    "    col += diffuse * max(np.dot(N, toL), 0) * color\n",
    "    # Blinn-Phong shading (specular).\n",
    "    col += specular_c * color_light * \\\n",
    "        max(np.dot(N, normalize(toL + toO)), 0) \\\n",
    "           ** specular_k\n",
    "    return col\n",
    "\n",
    "def run():\n",
    "    img = np.zeros((h, w, 3))\n",
    "    # Loop through all pixels.\n",
    "    for i, x in enumerate(np.linspace(-1., 1., w)):\n",
    "        for j, y in enumerate(np.linspace(-1., 1., h)):\n",
    "            # Position of the pixel.\n",
    "            Q[0], Q[1] = x, y\n",
    "            # Direction of the ray going through the optical center.\n",
    "            D = normalize(Q - O)\n",
    "            # Launch the ray and get the color of the pixel.\n",
    "            col = trace_ray(O, D)\n",
    "            if col is None:\n",
    "                continue\n",
    "            img[h - j - 1, i, :] = np.clip(col, 0, 1)\n",
    "    return img\n",
    "\n",
    "# Sphere properties.\n",
    "position = np.array([0., 0., 1.])\n",
    "radius = 1.\n",
    "color = np.array([0., 0., 1.])\n",
    "diffuse = 1.\n",
    "specular_c = 1.\n",
    "specular_k = 50\n",
    "\n",
    "# Light position and color.\n",
    "L = np.array([5., 5., -10.])\n",
    "color_light = np.ones(3)\n",
    "ambient = .05\n",
    "\n",
    "# Camera.\n",
    "O = np.array([0., 0., -1.])  # Position.\n",
    "Q = np.array([0., 0., 0.])  # Pointing to.\n",
    "\n",
    "img = run()\n",
    "plt.imshow(img);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.5 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will render a sphere with a diffuse and specular material. The principle is to model a scene with a light source and a camera, and use the physical properties of light propagation to calculate the light intensity and color of every pixel of the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "#%load_ext cythonmagic\n",
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "\n",
    "w, h = 200, 200  # Size of the screen in pixels.\n",
    "\n",
    "def normalize(x):\n",
    "    # This function normalizes a vector.\n",
    "    x /= np.linalg.norm(x)\n",
    "    return x\n",
    "\n",
    "def intersect_sphere(O, D, S, R):\n",
    "    # Return the distance from O to the intersection \n",
    "    # of the ray (O, D) with the sphere (S, R), or \n",
    "    # +inf if there is no intersection.\n",
    "    # O and S are 3D points, D (direction) is a \n",
    "    # normalized vector, R is a scalar.\n",
    "    a = np.dot(D, D)\n",
    "    OS = O - S\n",
    "    b = 2 * np.dot(D, OS)\n",
    "    c = np.dot(OS, OS) - R*R\n",
    "    disc = b*b - 4*a*c\n",
    "    if disc > 0:\n",
    "        distSqrt = np.sqrt(disc)\n",
    "        q = (-b - distSqrt) / 2.0 if b < 0 \\\n",
    "            else (-b + distSqrt) / 2.0\n",
    "        t0 = q / a\n",
    "        t1 = c / q\n",
    "        t0, t1 = min(t0, t1), max(t0, t1)\n",
    "        if t1 >= 0:\n",
    "            return t1 if t0 < 0 else t0\n",
    "    return np.inf\n",
    "\n",
    "def trace_ray(O, D):\n",
    "    # Find first point of intersection with the scene.\n",
    "    t = intersect_sphere(O, D, position, radius)\n",
    "    # No intersection?\n",
    "    if t == np.inf:\n",
    "        return\n",
    "    # Find the point of intersection on the object.\n",
    "    M = O + D * t\n",
    "    N = normalize(M - position)\n",
    "    toL = normalize(L - M)\n",
    "    toO = normalize(O - M)\n",
    "    # Ambient light.\n",
    "    col = ambient\n",
    "    # Lambert shading (diffuse).\n",
    "    col += diffuse * max(np.dot(N, toL), 0) * color\n",
    "    # Blinn-Phong shading (specular).\n",
    "    col += specular_c * color_light * \\\n",
    "        max(np.dot(N, normalize(toL + toO)), 0) \\\n",
    "           ** specular_k\n",
    "    return col\n",
    "\n",
    "def run():\n",
    "    img = np.zeros((h, w, 3))\n",
    "    # Loop through all pixels.\n",
    "    for i, x in enumerate(np.linspace(-1., 1., w)):\n",
    "        for j, y in enumerate(np.linspace(-1., 1., h)):\n",
    "            # Position of the pixel.\n",
    "            Q[0], Q[1] = x, y\n",
    "            # Direction of the ray going through the optical center.\n",
    "            D = normalize(Q - O)\n",
    "            depth = 0\n",
    "            # Launch the ray and get the color of the pixel.\n",
    "            col = trace_ray(O, D)\n",
    "            if col is None:\n",
    "                continue\n",
    "            img[h - j - 1, i, :] = np.clip(col, 0, 1)\n",
    "    return img\n",
    "\n",
    "# Sphere properties.\n",
    "position = np.array([0., 0., 1.])\n",
    "radius = 1.\n",
    "color = np.array([0., 0., 1.])\n",
    "diffuse = 1.\n",
    "specular_c = 1.\n",
    "specular_k = 50\n",
    "\n",
    "# Light position and color.\n",
    "L = np.array([5., 5., -10.])\n",
    "color_light = np.ones(3)\n",
    "ambient = .05\n",
    "\n",
    "# Camera.\n",
    "O = np.array([0., 0., -1.])  # Position.\n",
    "Q = np.array([0., 0., 0.])  # Pointing to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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KnWAtmZQKV1PTKdC17bRyB+hw2/4+cwBrobMGGG93lXBxKOUjfVPrrlpofJ5S1ZAIbFH8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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120470898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = run()\n",
    "plt.imshow(img);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 1: 1.41 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit -n1 -r1 run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cython array buffers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will render a sphere with a diffuse and specular material. The principle is to model a scene with a light source and a camera, and use the physical properties of light propagation to calculate the light intensity and color of every pixel of the screen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "#%load_ext cythonmagic\n",
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Take 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "from numpy import dot\n",
    "from libc.math cimport sqrt\n",
    "\n",
    "DBL = np.double\n",
    "ctypedef np.double_t DBL_C\n",
    "INT = np.int\n",
    "ctypedef np.int_t INT_C\n",
    "cdef INT_C w, h\n",
    "\n",
    "w, h = 200, 200  # Size of the screen in pixels.\n",
    "\n",
    "def normalize(np.ndarray[DBL_C, ndim=1] x):\n",
    "    # This function normalizes a vector.\n",
    "    x /= np.linalg.norm(x)\n",
    "    return x\n",
    "\n",
    "def intersect_sphere(np.ndarray[DBL_C, ndim=1] O, np.ndarray[DBL_C, ndim=1] D, \n",
    "                     np.ndarray[DBL_C, ndim=1] S, DBL_C R):\n",
    "    # Return the distance from O to the intersection \n",
    "    # of the ray (O, D) with the sphere (S, R), or \n",
    "    # +inf if there is no intersection.\n",
    "    # O and S are 3D points, D (direction) is a \n",
    "    # normalized vector, R is a scalar.\n",
    "    \n",
    "    cdef DBL_C a, b, c, disc, distSqrt, q, t0, t1\n",
    "    cdef np.ndarray[DBL_C, ndim=1] OS\n",
    "    \n",
    "    a = dot(D, D)\n",
    "    OS = O - S\n",
    "    b = 2 * dot(D, OS)\n",
    "    c = dot(OS, OS) - R*R\n",
    "    disc = b*b - 4*a*c\n",
    "    if disc > 0:\n",
    "        distSqrt = np.sqrt(disc)\n",
    "        q = (-b - distSqrt) / 2.0 if b < 0 \\\n",
    "            else (-b + distSqrt) / 2.0\n",
    "        t0 = q / a\n",
    "        t1 = c / q\n",
    "        t0, t1 = min(t0, t1), max(t0, t1)\n",
    "        if t1 >= 0:\n",
    "            return t1 if t0 < 0 else t0\n",
    "    return np.inf\n",
    "\n",
    "def trace_ray(np.ndarray[DBL_C, ndim=1] O, np.ndarray[DBL_C, ndim=1] D,\n",
    "               np.ndarray[DBL_C, ndim=1] position,\n",
    "               np.ndarray[DBL_C, ndim=1] color,\n",
    "               np.ndarray[DBL_C, ndim=1] L,\n",
    "               np.ndarray[DBL_C, ndim=1] color_light):\n",
    "        \n",
    "    cdef DBL_C t\n",
    "    cdef np.ndarray[DBL_C, ndim=1] M, N, toL, toO, col\n",
    "    \n",
    "    # Find first point of intersection with the scene.\n",
    "    t = intersect_sphere(O, D, position, radius)\n",
    "    # No intersection?\n",
    "    if t == np.inf:\n",
    "        return\n",
    "    # Find the point of intersection on the object.\n",
    "    M = O + D * t\n",
    "    N = normalize(M - position)\n",
    "    toL = normalize(L - M)\n",
    "    toO = normalize(O - M)\n",
    "    # Ambient light.\n",
    "    col = ambient * np.ones(3)\n",
    "    # Lambert shading (diffuse).\n",
    "    col += diffuse * max(dot(N, toL), 0) * color\n",
    "    # Blinn-Phong shading (specular).\n",
    "    col += specular_c * color_light * \\\n",
    "        max(dot(N, normalize(toL + toO)), 0) \\\n",
    "           ** specular_k\n",
    "    return col\n",
    "\n",
    "def run():\n",
    "    cdef np.ndarray[DBL_C, ndim=3] img\n",
    "    img = np.zeros((h, w, 3))\n",
    "    cdef INT_C i, j\n",
    "    cdef DBL_C x, y\n",
    "    cdef np.ndarray[DBL_C, ndim=1] O, Q, D, col, position, color, L, color_light\n",
    "\n",
    "    # Sphere properties.\n",
    "    position = np.array([0., 0., 1.])\n",
    "    color = np.array([0., 0., 1.])\n",
    "    L = np.array([5., 5., -10.])\n",
    "    color_light = np.ones(3)\n",
    "        \n",
    "    # Camera.\n",
    "    O = np.array([0., 0., -1.])  # Position.\n",
    "    Q = np.array([0., 0., 0.])  # Pointing to.\n",
    "        \n",
    "    # Loop through all pixels.\n",
    "    for i, x in enumerate(np.linspace(-1., 1., w)):\n",
    "        for j, y in enumerate(np.linspace(-1., 1., h)):\n",
    "            # Position of the pixel.\n",
    "            Q[0], Q[1] = x, y\n",
    "            # Direction of the ray going through the optical center.\n",
    "            D = normalize(Q - O)\n",
    "            # Launch the ray and get the color of the pixel.\n",
    "            col = trace_ray(O, D, position, color, L, color_light)\n",
    "            if col is None:\n",
    "                continue\n",
    "            img[h - j - 1, i, :] = np.clip(col, 0, 1)\n",
    "    return img\n",
    "\n",
    "cdef DBL_C radius, ambient, diffuse, specular_k, specular_c\n",
    "\n",
    "# Sphere and light properties.\n",
    "radius = 1.\n",
    "diffuse = 1.\n",
    "specular_c = 1.\n",
    "specular_k = 50.\n",
    "ambient = .05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ytTpoAZze/PAMXRZZAzYVNsq22ruKgxvY8XMZZP55eBfIc0JibR1A/+5UTjXz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12054da90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = run()\n",
    "plt.imshow(img);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.97 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Take 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this version, we rewrite normalize in pure C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "from numpy import dot\n",
    "from libc.math cimport sqrt\n",
    "\n",
    "DBL = np.double\n",
    "ctypedef np.double_t DBL_C\n",
    "INT = np.int\n",
    "ctypedef np.int_t INT_C\n",
    "cdef INT_C w, h\n",
    "\n",
    "w, h = 200, 200  # Size of the screen in pixels.\n",
    "\n",
    "# normalize is now a pure C function that does not make\n",
    "# use NumPy for the computations\n",
    "cdef normalize(np.ndarray[DBL_C, ndim=1] x):\n",
    "    cdef DBL_C n\n",
    "    n = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2])\n",
    "    x[0] /= n\n",
    "    x[1] /= n\n",
    "    x[2] /= n\n",
    "    return x\n",
    "\n",
    "def intersect_sphere(np.ndarray[DBL_C, ndim=1] O, np.ndarray[DBL_C, ndim=1] D, \n",
    "                     np.ndarray[DBL_C, ndim=1] S, DBL_C R):\n",
    "    # Return the distance from O to the intersection \n",
    "    # of the ray (O, D) with the sphere (S, R), or \n",
    "    # +inf if there is no intersection.\n",
    "    # O and S are 3D points, D (direction) is a \n",
    "    # normalized vector, R is a scalar.\n",
    "    \n",
    "    cdef DBL_C a, b, c, disc, distSqrt, q, t0, t1\n",
    "    cdef np.ndarray[DBL_C, ndim=1] OS\n",
    "    \n",
    "    a = dot(D, D)\n",
    "    OS = O - S\n",
    "    b = 2 * dot(D, OS)\n",
    "    c = dot(OS, OS) - R*R\n",
    "    disc = b*b - 4*a*c\n",
    "    if disc > 0:\n",
    "        distSqrt = np.sqrt(disc)\n",
    "        q = (-b - distSqrt) / 2.0 if b < 0 \\\n",
    "            else (-b + distSqrt) / 2.0\n",
    "        t0 = q / a\n",
    "        t1 = c / q\n",
    "        t0, t1 = min(t0, t1), max(t0, t1)\n",
    "        if t1 >= 0:\n",
    "            return t1 if t0 < 0 else t0\n",
    "    return np.inf\n",
    "\n",
    "def trace_ray(np.ndarray[DBL_C, ndim=1] O, np.ndarray[DBL_C, ndim=1] D,\n",
    "               np.ndarray[DBL_C, ndim=1] position,\n",
    "               np.ndarray[DBL_C, ndim=1] color,\n",
    "               np.ndarray[DBL_C, ndim=1] L,\n",
    "               np.ndarray[DBL_C, ndim=1] color_light):\n",
    "        \n",
    "    cdef DBL_C t\n",
    "    cdef np.ndarray[DBL_C, ndim=1] M, N, toL, toO, col\n",
    "    \n",
    "    # Find first point of intersection with the scene.\n",
    "    t = intersect_sphere(O, D, position, radius)\n",
    "    # No intersection?\n",
    "    if t == np.inf:\n",
    "        return\n",
    "    # Find the point of intersection on the object.\n",
    "    M = O + D * t\n",
    "    N = normalize(M - position)\n",
    "    toL = normalize(L - M)\n",
    "    toO = normalize(O - M)\n",
    "    # Ambient light.\n",
    "    col = ambient * np.ones(3)\n",
    "    # Lambert shading (diffuse).\n",
    "    col += diffuse * max(dot(N, toL), 0) * color\n",
    "    # Blinn-Phong shading (specular).\n",
    "    col += specular_c * color_light * \\\n",
    "        max(dot(N, normalize(toL + toO)), 0) \\\n",
    "           ** specular_k\n",
    "    return col\n",
    "\n",
    "def run():\n",
    "    cdef np.ndarray[DBL_C, ndim=3] img\n",
    "    img = np.zeros((h, w, 3))\n",
    "    cdef INT_C i, j\n",
    "    cdef DBL_C x, y\n",
    "    cdef np.ndarray[DBL_C, ndim=1] O, Q, D, col, position, color, L, color_light\n",
    "\n",
    "    # Sphere properties.\n",
    "    position = np.array([0., 0., 1.])\n",
    "    color = np.array([0., 0., 1.])\n",
    "    L = np.array([5., 5., -10.])\n",
    "    color_light = np.ones(3)\n",
    "        \n",
    "    # Camera.\n",
    "    O = np.array([0., 0., -1.])  # Position.\n",
    "    Q = np.array([0., 0., 0.])  # Pointing to.\n",
    "        \n",
    "    # Loop through all pixels.\n",
    "    for i, x in enumerate(np.linspace(-1., 1., w)):\n",
    "        for j, y in enumerate(np.linspace(-1., 1., h)):\n",
    "            # Position of the pixel.\n",
    "            Q[0], Q[1] = x, y\n",
    "            # Direction of the ray going through the optical center.\n",
    "            D = normalize(Q - O)\n",
    "            # Launch the ray and get the color of the pixel.\n",
    "            col = trace_ray(O, D, position, color, L, color_light)\n",
    "            if col is None:\n",
    "                continue\n",
    "            img[h - j - 1, i, :] = np.clip(col, 0, 1)\n",
    "    return img\n",
    "\n",
    "cdef DBL_C radius, ambient, diffuse, specular_k, specular_c\n",
    "\n",
    "# Sphere and light properties.\n",
    "radius = 1.\n",
    "diffuse = 1.\n",
    "specular_c = 1.\n",
    "specular_k = 50.\n",
    "ambient = .05"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ytTpoAZze/PAMXRZZAzYVNsq22ruKgxvY8XMZZP55eBfIc0JibR1A/+5UTjXz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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1206e8748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = run()\n",
    "plt.imshow(img);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.07 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cython with structs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import cython"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Cython extension is already loaded. To reload it, use:\n",
      "  %reload_ext Cython\n"
     ]
    }
   ],
   "source": [
    "#%load_ext cythonmagic\n",
    "%load_ext Cython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now use a pure C structure to represent a 3D vector. We also implement all operations we need by hand in pure C."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%%cython\n",
    "cimport cython\n",
    "import numpy as np\n",
    "cimport numpy as np\n",
    "DBL = np.double\n",
    "ctypedef np.double_t DBL_C\n",
    "from libc.math cimport sqrt\n",
    "\n",
    "cdef int w, h\n",
    "\n",
    "cdef struct Vec3:\n",
    "    double x, y, z\n",
    "        \n",
    "cdef Vec3 vec3(double x, double y, double z):\n",
    "    cdef Vec3 v\n",
    "    v.x = x\n",
    "    v.y = y\n",
    "    v.z = z\n",
    "    return v\n",
    "\n",
    "cdef double dot(Vec3 x, Vec3 y):\n",
    "    return x.x * y.x + x.y * y.y + x.z * y.z\n",
    "\n",
    "cdef Vec3 normalize(Vec3 x):\n",
    "    cdef double n\n",
    "    n = sqrt(x.x * x.x + x.y * x.y + x.z * x.z)\n",
    "    return vec3(x.x / n, x.y / n, x.z / n)\n",
    "\n",
    "cdef double max(double x, double y):\n",
    "    return x if x > y else y\n",
    "\n",
    "cdef double min(double x, double y):\n",
    "    return x if x < y else y\n",
    "\n",
    "cdef double clip_(double x, double m, double M):\n",
    "    return min(max(x, m), M)\n",
    "\n",
    "cdef Vec3 clip(Vec3 x, double m, double M):\n",
    "    return vec3(clip_(x.x, m, M), clip_(x.y, m, M), clip_(x.z, m, M),)\n",
    "\n",
    "cdef Vec3 add(Vec3 x, Vec3 y):\n",
    "    return vec3(x.x + y.x, x.y + y.y, x.z + y.z)\n",
    "\n",
    "cdef Vec3 subtract(Vec3 x, Vec3 y):\n",
    "    return vec3(x.x - y.x, x.y - y.y, x.z - y.z)\n",
    "\n",
    "cdef Vec3 minus(Vec3 x):\n",
    "    return vec3(-x.x, -x.y, -x.z)\n",
    "\n",
    "cdef Vec3 multiply(Vec3 x, Vec3 y):\n",
    "    return vec3(x.x * y.x, x.y * y.y, x.z * y.z)\n",
    "    \n",
    "cdef Vec3 multiply_s(Vec3 x, double c):\n",
    "    return vec3(x.x * c, x.y * c, x.z * c)\n",
    "    \n",
    "cdef double intersect_sphere(Vec3 O, \n",
    "                      Vec3 D, \n",
    "                      Vec3 S, \n",
    "                      double R):\n",
    "    # Return the distance from O to the intersection of the ray (O, D) with the \n",
    "    # sphere (S, R), or +inf if there is no intersection.\n",
    "    # O and S are 3D points, D (direction) is a normalized vector, R is a scalar.\n",
    "    cdef double a, b, c, disc, distSqrt, q, t0, t1\n",
    "    cdef Vec3 OS\n",
    "    \n",
    "    a = dot(D, D)\n",
    "    OS = subtract(O, S)\n",
    "    b = 2 * dot(D, OS)\n",
    "    c = dot(OS, OS) - R * R\n",
    "    disc = b * b - 4 * a * c\n",
    "    if disc > 0:\n",
    "        distSqrt = sqrt(disc)\n",
    "        q = (-b - distSqrt) / 2.0 if b < 0 else (-b + distSqrt) / 2.0\n",
    "        t0 = q / a\n",
    "        t1 = c / q\n",
    "        t0, t1 = min(t0, t1), max(t0, t1)\n",
    "        if t1 >= 0:\n",
    "            return t1 if t0 < 0 else t0\n",
    "    return 1000000\n",
    "\n",
    "cdef Vec3 trace_ray(Vec3 O, Vec3 D,):\n",
    "    \n",
    "    cdef double t, radius, diffuse, specular_k, specular_c, DF, SP\n",
    "    cdef Vec3 M, N, L, toL, toO, col_ray, \\\n",
    "        position, color, color_light, ambient\n",
    "\n",
    "    # Sphere properties.\n",
    "    position = vec3(0., 0., 1.)\n",
    "    radius = 1.\n",
    "    color = vec3(0., 0., 1.)\n",
    "    diffuse = 1.\n",
    "    specular_c = 1.\n",
    "    specular_k = 50.\n",
    "    \n",
    "    # Light position and color.\n",
    "    L = vec3(5., 5., -10.)\n",
    "    color_light = vec3(1., 1., 1.)\n",
    "    ambient = vec3(.05, .05, .05)\n",
    "    \n",
    "    # Find first point of intersection with the scene.\n",
    "    t = intersect_sphere(O, D, position, radius)\n",
    "    # Return None if the ray does not intersect any object.\n",
    "    if t == 1000000:\n",
    "        col_ray.x = 1000000\n",
    "        return col_ray\n",
    "    # Find the point of intersection on the object.\n",
    "    M = vec3(O.x + D.x * t, O.y + D.y * t, O.z + D.z * t)\n",
    "    N = normalize(subtract(M, position))\n",
    "    toL = normalize(subtract(L, M))\n",
    "    toO = normalize(subtract(O, M))\n",
    "    DF = diffuse * max(dot(N, toL), 0)\n",
    "    SP = specular_c * max(dot(N, normalize(add(toL, toO))), 0) ** specular_k\n",
    "    \n",
    "    return add(ambient, add(multiply_s(color, DF), multiply_s(color_light, SP)))\n",
    "\n",
    "def run(int w, int h):\n",
    "    cdef DBL_C[:,:,:] img = np.zeros((h, w, 3))\n",
    "    cdef Vec3 img_\n",
    "    cdef int i, j\n",
    "    cdef double x, y\n",
    "    cdef Vec3 O, Q, D, col_ray\n",
    "    cdef double w_ = float(w)\n",
    "    cdef double h_ = float(h)\n",
    "    \n",
    "    col_ray = vec3(0., 0., 0.)\n",
    "    \n",
    "    # Camera.\n",
    "    O = vec3(0., 0., -1.)  # Position.\n",
    "        \n",
    "    # Loop through all pixels.\n",
    "    for i in range(w):\n",
    "        Q = vec3(0., 0., 0.)\n",
    "        for j in range(h):\n",
    "            x = -1. + 2*(i)/w_\n",
    "            y = -1. + 2*(j)/h_\n",
    "            Q.x = x\n",
    "            Q.y = y\n",
    "            col_ray = trace_ray(O, normalize(subtract(Q, O)))\n",
    "            if col_ray.x == 1000000:\n",
    "                continue\n",
    "            img_ = clip(col_ray, 0., 1.)\n",
    "            img[h - j - 1, i, 0] = img_.x\n",
    "            img[h - j - 1, i, 1] = img_.y\n",
    "            img[h - j - 1, i, 2] = img_.z\n",
    "    return img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "w, h = 200, 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12094a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = run(w, h)\n",
    "plt.imshow(img);\n",
    "plt.xticks([]); plt.yticks([]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100 loops, best of 3: 2.26 ms per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit run(w, h)"
   ]
  }
 ],
 "metadata": {
  "_draft": {
   "nbviewer_url": "https://gist.github.com/c374786d46403e82546f7e45646391e9"
  },
  "gist": {
   "data": {
    "description": "Python utilities.ipynb",
    "public": true
   },
   "id": "c374786d46403e82546f7e45646391e9"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  },
  "toc": {
   "nav_menu": {
    "height": "264px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": true,
   "threshold": 4,
   "toc_cell": true,
   "toc_section_display": "block",
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}