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 "metadata": {
  "name": "",
  "signature": "sha256:ab859015961b19530bb3c16fe1edf4e7f9baca715bdf8187c724e8c0c4cfc8ad"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Sebastian Raschka](http://sebastianraschka.com)  \n",
      "last updated: 05/06/2014\n",
      "\n",
      "- [Link to this IPython Notebook on GitHub](https://github.com/rasbt/python_reference/blob/master/benchmarks/palindrome_timeit.ipynb)  \n",
      "- [Link to the GitHub repository](https://github.com/rasbt/python_reference)  \n",
      "\n",
      "<br>\n",
      "<br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Timing different Implementations of palindrome functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import re\n",
      "import timeit\n",
      "import string\n",
      "\n",
      "# All functions return True if an input string is a palindrome. Else returns False.\n",
      "\n",
      "#############################################################\n",
      "#### case-insensitive ignoring punctuation characters\n",
      "############################################################\n",
      "\n",
      "def palindrome_short(my_str):\n",
      "    stripped_str = \"\".join(l.lower() for l in my_str if l.isalpha())\n",
      "    return stripped_str == stripped_str[::-1]\n",
      "\n",
      "def palindrome_regex(my_str):\n",
      "    return re.sub('\\W', '', my_str.lower()) == re.sub('\\W', '', my_str[::-1].lower())\n",
      "\n",
      "def palindrome_stringlib(my_str):\n",
      "    LOWERS = set(string.ascii_lowercase)\n",
      "    letters = [c for c in my_str.lower() if c in LOWERS]\n",
      "    return letters == letters[::-1]\n",
      "\n",
      "LOWERS = set(string.ascii_lowercase)\n",
      "def palindrome_stringlib2(my_str):\n",
      "    letters = [c for c in my_str.lower() if c in LOWERS]\n",
      "    return letters == letters[::-1]\n",
      "\n",
      "def palindrome_isalpha(my_str):\n",
      "    stripped_str = [l for l in my_str.lower() if l.isalpha()]\n",
      "    return stripped_str == stripped_str[::-1]\n",
      "\n",
      "\n",
      "\n",
      "############################################################\n",
      "#### functions considering all characters (case-sensitive)\n",
      "############################################################\n",
      "\n",
      "def palindrome_reverse1(my_str):\n",
      "    return my_str == my_str[::-1]\n",
      "\n",
      "def palindrome_reverse2(my_str):\n",
      "    return my_str == ''.join(reversed(my_str))\n",
      "\n",
      "def palindrome_recurs(my_str):\n",
      "    if len(my_str) < 2:\n",
      "        return True\n",
      "    if my_str[0] != my_str[-1]:\n",
      "        return False\n",
      "    return palindrome(my_str[1:-1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test_str = \"Go hang a salami. I'm a lasagna hog.\"\n",
      "\n",
      "print('case-insensitive functions ignoring punctuation characters')\n",
      "%timeit palindrome_short(test_str)\n",
      "%timeit palindrome_regex(test_str)\n",
      "%timeit palindrome_stringlib(test_str)\n",
      "%timeit palindrome_stringlib2(test_str)\n",
      "%timeit palindrome_isalpha(test_str)\n",
      "\n",
      "print('\\n\\nfunctions considering all characters (case-sensitive)')\n",
      "%timeit palindrome_reverse1(test_str)\n",
      "%timeit palindrome_reverse2(test_str)\n",
      "%timeit palindrome_recurs(test_str)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "case-insensitive functions ignoring punctuation characters\n",
        "10000 loops, best of 3: 15.5 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "10000 loops, best of 3: 19.5 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "100000 loops, best of 3: 11.7 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "100000 loops, best of 3: 8.24 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "100000 loops, best of 3: 9.38 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "\n",
        "functions considering all characters (case-sensitive)\n",
        "1000000 loops, best of 3: 507 ns per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "100000 loops, best of 3: 3.08 \u00b5s per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "1000000 loops, best of 3: 581 ns per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import timeit\n",
      "\n",
      "funcs_s = ['palindrome_short', 'palindrome_regex', 'palindrome_stringlib', \n",
      "         'palindrome_stringlib2', 'palindrome_isalpha'] \n",
      "\n",
      "funcs_ins = ['palindrome_reverse1', 'palindrome_reverse2', 'palindrome_recurs']\n",
      "\n",
      "times_s, times_ins = [], []\n",
      "\n",
      "for f in funcs_s:\n",
      "    times_s.append(min(timeit.Timer('%s(test_str)' %f, \n",
      "                      'from __main__ import %s, test_str' %f)\n",
      "                              .repeat(repeat=3, number=1000)))\n",
      "    \n",
      "for f in funcs_ins:\n",
      "    times_ins.append(min(timeit.Timer('%s(test_str)' %f, \n",
      "                      'from __main__ import %s, test_str' %f)\n",
      "                              .repeat(repeat=3, number=1000)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "labels = [('cy_lstsqr', 'Cython implementation'), \n",
      "          ('lin_lstsqr_mat', 'numpy matrix equation'),\n",
      "          ('numpy_lstsqr', 'numpy.linalg.lstsq()'), \n",
      "          ('scipy_lstsqr', 'scipy.stats.linregress()')] \n",
      "\n",
      "matplotlib.rcParams.update({'font.size': 12})\n",
      "\n",
      "fig = plt.figure(figsize=(10,8))\n",
      "for f in funcs_s:\n",
      "    plt.plot(orders_n, times_n[lb[0]], alpha=0.5, label=lb[1], marker='o', lw=3)\n",
      "plt.xlabel('sample size n')\n",
      "plt.ylabel('time per computation in milliseconds [ms]')\n",
      "plt.xlim([1,max(orders_n) + max(orders_n) * 10])\n",
      "plt.legend(loc=2)\n",
      "plt.grid()\n",
      "plt.xscale('log')\n",
      "plt.yscale('log')\n",
      "plt.title('Performance of least square fit implementations for different sample sizes')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "\n",
      "x_pos = np.arange(len(times_s))\n",
      "plt.bar(x_pos, times_s, align='center', alpha=0.5, color=\"green\")\n",
      "plt.xticks(x_pos, funcs_s, rotation=90)\n",
      "plt.ylabel('time per computation in ms')\n",
      "plt.title('Performance of different case-sensitive palindrome functions')\n",
      "plt.grid()\n",
      "plt.show()\n",
      "\n",
      "x_pos = np.arange(len(times_ins))\n",
      "plt.bar(x_pos, times_ins, align='center', alpha=0.5, color=\"blue\")\n",
      "plt.xticks(x_pos, funcs_ins, rotation=90)\n",
      "plt.ylabel('time per computation in ms')\n",
      "plt.title('Performance of different case-insensitive palindrome functions')\n",
      "plt.grid()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ORFpamnC9XC5HcHCwymy03Nxc2NvbAwBWrlyJ06dPY+vWrVUTawAf6oyNi0Ve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\nDzH9gT2pJYOrAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x105618160>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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hDHrO6ffff4erqytsbW1x/fp1XLt2DZ07d26O+IyOzzm1HHzOyfT4nFPLYXEz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\nIdyW99835TmWq/xkKzvAlOUnV9kB1l1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DB5TljIwMZeyCLB/Lj6h+bDlJjvN7yY3lR1Q/\nJifJ5ebmNvq+Wq1uljioaVh+RPVjciIiIovDMSciIrI4TE5ERGRxmJyIiMjiMDkREZHFYXIiIiKL\n8/8AVRvie0rr9RMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1056baba8>"
       ]
      }
     ],
     "prompt_number": 29
    }
   ],
   "metadata": {}
  }
 ]
}