python-cf17-03-numpypandas.ipynb

{
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   "source": [
    "Data Science In Python\n",
    "=======================\n",
    "Numpy and Pandas\n",
    "---------------\n",
    "**Cambridge, MA, January 9th 2017**\n",
    "<br>\n",
    "\n",
    "<center>\n",
    "<img src=http://ijstokes-public.s3.amazonaws.com/dspyr/img/AnacondaCIO_Logo width=400 />\n",
    "</center>\n",
    "\n",
    "**Copyrighted Continuum Analytics**\n",
    "\n",
    "<br>\n",
    "GitHub: https://github.com/Harvard-IACS/computefest2017-pythonml\n",
    "\n",
    "Anaconda Cloud: https://anaconda.org/ijstokes/python-cf17-03-numpypandas/notebook\n",
    "<br>\n",
    "\n",
    "Taught by:\n",
    "\n",
    "* Ian Stokes-Rees [ijstokes@continuum.io](mailto:ijstokes@continuum.io)\n",
    "    * Twitter: [@ijstokes](http://twitter.com/ijstokes)\n",
    "    * About.Me: [http://about.me/ijstokes](http://about.me/ijstokes)\n",
    "    * LinkedIn: [http://linkedin.com/in/ijstokes](http://linkedin.com/in/ijstokes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore the NumPy and Matplotlib packages that provide vectors, matrices (well, sort of), and Matlab-like plotting capabilities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "References\n",
    "----------\n",
    "\n",
    "* <a href=\"http://docs.python.org/2/tutorial/\" target=\"_parent\">Python Tutorial</a> - a good next step to learning Python (about a 2-3 hour commitment)\n",
    "\n",
    "* <a href=\"http://docs.python.org/2/reference/lexical_analysis.html#keywords\" target=\"_parent\">Python Reserved Words</a> - about 40 terms that form the base grammar of the language.  NOTE: Thes are not functions.\n",
    "\n",
    "* <a href=\"http://docs.python.org/2/library/functions.html#built-in-functions\" target=\"_parent\">Python builtin module</a> functions (60) and classes (20)\n",
    "\n",
    "* <a href=\"http://docs.python.org/2/library/\" target=\"_parent\">Python Standard Library</a>\n",
    "\n",
    "* <a href=\"https://pypi.python.org/pypi\" target=\"_parent\">Python Package Index</a> community contributed Python packages\n",
    "\n",
    "* <a href=\"http://python.net/~goodger/projects/pycon/2007/idiomatic/handout.html\" target=\"_parent\">Idiomatic Python</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy\n",
    "====="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "s1 = np.array([1, 4, 9, 16, 25])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s2 = np.array([[1,2,3,4,5],\n",
    "               [1,4,9,16,25],\n",
    "               [1,8,27,64,125]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 16, 25])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   2,   3,   4,   5],\n",
       "       [  1,   4,   9,  16,  25],\n",
       "       [  1,   8,  27,  64, 125]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v1 = s1[1:4] # different from Python list slices (which copy references)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 16, 25])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  9, 16])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s1[3] = 99"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  4,  9, 99, 25])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  9, 99])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v1[0] = 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([200,   9,  99])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 200,   9,  99,  25])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int64')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1,   8,  27,  64, 125])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   4,   9,  16,  25],\n",
       "       [  1,   8,  27,  64, 125]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[1,3] # fancy indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   2,   3,   4,   5],\n",
       "       [  1,   4,   9,  16,  25],\n",
       "       [  1,   8,  27,  64, 125]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img width=600 src=numpy.png>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 9, 16],\n",
       "       [27, 64]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[1:, 2:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[2][3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 200,   9,  99,  25])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   2,   3,   4,   5],\n",
       "       [  1,   4,   9,  16,  25],\n",
       "       [  1,   8,  27,  64, 125]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2, 202,  12, 103,  30],\n",
       "       [  2, 204,  18, 115,  50],\n",
       "       [  2, 208,  36, 163, 150]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 + s2 # s1 will be broadcast and added to each \"row\" in s2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy Exercise\n",
    "--------------\n",
    "\n",
    "Broadcasting, element-wise operations, slices, and ranges:\n",
    "\n",
    "1. Add `s1` and `s2` to observe broadcasting.\n",
    "\n",
    "2. Get the second value from `s1`.\n",
    "\n",
    "3. Get the third row from `s2`.\n",
    "\n",
    "4. Get the second column from `s2`.\n",
    "\n",
    "5. Generate a range of values from 1 to 20 in 0.5 step increments.\n",
    "\n",
    "6. Generate a range of values from 5 to 30 with a total of 50 entries.\n",
    "\n",
    "7. Use the `np.log10()` function to get the log values of these two ranges (from 5 and 6)., then plot them on the same graph. HINT: Use the lecture note example as a template.\n",
    "\n",
    "8. Use `np.sin()` to create an `ndarray` of 2 periods and 1000 data points.\n",
    "\n",
    "9. Use `numpy.random.randn()` to generate an `ndarray` of noise with 1000 data points (normally distributed). The normal distribution of the noise should have a median of `A0` (your choice, keep it single digits), and a standard deviation $10%$ of the sine wave amplitude. Add these together into a new `ndarray`. Calculate the mean value of this new `ndarray`. BONUS: Plot all three arrays overlayed on the same graph, using different colors and lines, and include a legend."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False, False, False, False],\n",
       "       [False, False, False,  True,  True],\n",
       "       [False, False,  True,  True,  True]], dtype=bool)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2 > 10 # boolean selection array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([200,  99,  25])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1[s1>10] # fancy indexing using boolean selection array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False,  True, False,  True,  True], dtype=bool)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1 > 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1,   2,   3,   4,   5],\n",
       "       [  1,   4,   9,  16,  25],\n",
       "       [  1,   8,  27,  64, 125]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1,   1,   9,  25,   1,  27, 125])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s2[s2 >= s1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2,  5, -2,  5,  5])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(s1 > 10, 5, -2) # vectorized conditional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  1, 200,   9,  99,  25])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['small', 'big', 'small', 'big', 'big'], \n",
       "      dtype='|S5')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(s1 > 10, 'big', 'small')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([['odd', 'even', 'odd', 'even', 'odd'],\n",
       "       ['odd', 'even', 'odd', 'even', 'odd'],\n",
       "       ['odd', 'even', 'odd', 'even', 'odd']], \n",
       "      dtype='|S4')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(s2 % 2 == 0, 'even', 'odd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5],\n",
       "       [ 1,  4,  9, 10, 10],\n",
       "       [ 1,  8, 10, 10, 10]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(s2 > 10, 10, s2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pandas\n",
    "======\n",
    "Adapted from Jeff Reback's PyData New York (Nov 2015) tutorial: https://github.com/jreback/PyDataNYC2015\n",
    "\n",
    "Pandas is enormously popular because:\n",
    "* Amazing data input/output capabilities\n",
    "* Powerful API on top of NumPy `ndarray` data structure\n",
    "  * lots of great methods that auto-magically do the right thing\n",
    "* Analog to R DataFrame\n",
    "* Looks like a matrix when you need it to\n",
    "* Looks like a database table when you need it to"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supported data formats:\n",
    "- CSV\n",
    "- Excel\n",
    "- SQL\n",
    "- JSON\n",
    "- HDF5\n",
    "- pickle\n",
    "- msgpack\n",
    "- Stata\n",
    "- BigQuery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "u'0.18.1'"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "pd.options.display.max_rows = 20\n",
    "pd.options.display.max_columns = 15\n",
    "pd.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "['',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python27.zip',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/plat-darwin',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/plat-mac',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/plat-mac/lib-scriptpackages',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/lib-tk',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/lib-old',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/lib-dynload',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages/Sphinx-1.4.6-py2.7.egg',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages/aeosa',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages/setuptools-27.2.0-py2.7.egg',\n",
       " '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages/IPython/extensions',\n",
       " '/Users/ijstokes/.ipython']"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sitepkgs = '/Users/ijstokes/anaconda/envs/ana42py27/lib/python2.7/site-packages'\n",
    "testfile = '/pandas/io/tests/parser/data/utf16_ex.txt'\n",
    "altfile  = '/pandas/io/tests/data/utf16_ex.txt'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv(sitepkgs + testfile,\n",
    "                   sep='\\t', encoding='utf-16', parse_dates=['Date'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>State/City</th>\n",
       "      <th>Title</th>\n",
       "      <th>Date</th>\n",
       "      <th>Catalogue</th>\n",
       "      <th>Wikipedia Election Page</th>\n",
       "      <th>Wikipedia Individual Page</th>\n",
       "      <th>Electoral Institution in Country</th>\n",
       "      <th>Twitter</th>\n",
       "      <th>CANDIDATE NAME 1</th>\n",
       "      <th>CANDIDATE NAME 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Hugo Rafael Chavez Frias</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez Frías</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Venezuela</td>\n",
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       "      <td>Henrique Capriles Radonski</td>\n",
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       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles R.</td>\n",
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       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Maria Josefina Bolivar</td>\n",
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       "      <td>Maria Bolivar</td>\n",
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       "      <td>Maria Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
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       "      <td>Venezuela</td>\n",
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       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Orlando Chirino</td>\n",
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       "      <td>2012-10-07</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes Castillo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-28</td>\n",
       "      <td>Carolina Montserrat Toha Morales</td>\n",
       "      <td>Carolina Tohá Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-29</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
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       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-30</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>None.</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
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       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
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       "      <td>Mauricio Rodas</td>\n",
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       "      <td>NaN</td>\n",
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       "      <th>42</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>None.</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
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       "      <th>44</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
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       "      <th>45</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>50 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Country State/City      Title       Date  \\\n",
       "0   Venezuela        NaN  President 2012-10-07   \n",
       "1   Venezuela        NaN  President 2012-10-07   \n",
       "2   Venezuela        NaN  President 2012-10-07   \n",
       "3   Venezuela        NaN  President 2012-10-07   \n",
       "4   Venezuela        NaN  President 2012-10-07   \n",
       "5   Venezuela        NaN  President 2012-10-07   \n",
       "6       Chile   Santiago      Mayor 2012-10-28   \n",
       "7       Chile   Santiago      Mayor 2012-10-29   \n",
       "8       Chile   Santiago      Mayor 2012-10-30   \n",
       "9       Chile   Santiago      Mayor 2012-10-31   \n",
       "..        ...        ...        ...        ...   \n",
       "40    Ecuador        NaN  President 2013-02-07   \n",
       "41    Ecuador        NaN  President 2013-02-07   \n",
       "42    Ecuador        NaN  President 2013-02-07   \n",
       "43        NaN        NaN        NaN        NaT   \n",
       "44        NaN        NaN        NaN        NaT   \n",
       "45        NaN        NaN        NaN        NaT   \n",
       "46        NaN        NaN        NaN        NaT   \n",
       "47        NaN        NaN        NaN        NaT   \n",
       "48        NaN        NaN        NaN        NaT   \n",
       "49        NaN        NaN        NaN        NaT   \n",
       "\n",
       "                           Catalogue     Wikipedia Election Page  \\\n",
       "0           Hugo Rafael Chavez Frias                 Hugo Chávez   \n",
       "1         Henrique Capriles Radonski  Henrique Capriles Radonski   \n",
       "2             Maria Josefina Bolivar               María Bolívar   \n",
       "3                    Orlando Chirino            Orlando Chirinos   \n",
       "4                         Luis Reyes         Luis Reyes Castillo   \n",
       "5                      Reina Sequera               Reina Sequera   \n",
       "6   Carolina Montserrat Toha Morales       Carolina Tohá Morales   \n",
       "7               Pablo Zalaquett Said        Pablo Zalaquett Said   \n",
       "8                   Waldo Mora Longa            Waldo Mora Longa   \n",
       "9                      Mario Aguilar       Mario Aguilar Arevalo   \n",
       "..                               ...                         ...   \n",
       "40           Alberto Acosta Espinosa     Alberto Acosta Espinosa   \n",
       "41            Mauricio Rodas Espinel              Mauricio Rodas   \n",
       "42                       Norman Wray                 Norman Wray   \n",
       "43                               NaN                         NaN   \n",
       "44                               NaN                         NaN   \n",
       "45                               NaN                         NaN   \n",
       "46                               NaN                         NaN   \n",
       "47                               NaN                         NaN   \n",
       "48                               NaN                         NaN   \n",
       "49                               NaN                         NaN   \n",
       "\n",
       "     Wikipedia Individual Page Electoral Institution in Country  \\\n",
       "0                  Hugo Chávez                      Hugo Chavez   \n",
       "1   Henrique Capriles Radonski       Henrique Capriles Radonski   \n",
       "2                María Bolívar                    Maria Bolivar   \n",
       "3                        None.                  Orlando Chirino   \n",
       "4                        None.                       Luis Reyes   \n",
       "5                Reina Sequera                    Reina Sequera   \n",
       "6                Carolina Tohá            Carolina Toha Morales   \n",
       "7              Pablo Zalaquett             Pablo Zalaquett Said   \n",
       "8                        None.                 Waldo Mora Longa   \n",
       "9                        None.            Mario Aguilar Arevalo   \n",
       "..                         ...                              ...   \n",
       "40     Alberto Acosta Espinosa                   Alberto Acosta   \n",
       "41              Mauricio Rodas                   Mauricio Rodas   \n",
       "42                       None.                      Norman Wray   \n",
       "43                         NaN                              NaN   \n",
       "44                         NaN                              NaN   \n",
       "45                         NaN                              NaN   \n",
       "46                         NaN                              NaN   \n",
       "47                         NaN                              NaN   \n",
       "48                         NaN                              NaN   \n",
       "49                         NaN                              NaN   \n",
       "\n",
       "                 Twitter   CANDIDATE NAME 1 CANDIDATE NAME 2  \n",
       "0      Hugo Chávez Frías        Hugo Chavez      Hugo Chávez  \n",
       "1   Henrique Capriles R.  Henrique Capriles              NaN  \n",
       "2          Maria Bolivar      Maria Bolivar    María Bolívar  \n",
       "3        Orlando Chirino    Orlando Chirino              NaN  \n",
       "4             Luis Reyes         Luis Reyes              NaN  \n",
       "5          Reina Sequera      Reina Sequera              NaN  \n",
       "6          Carolina Tohá      Carolina Tohá    Carolina Toha  \n",
       "7   Pablo Zalaquett Said    Pablo Zalaquett              NaN  \n",
       "8          Waldo Mora L.         Waldo Mora              NaN  \n",
       "9          Mario Aguilar      Mario Aguilar              NaN  \n",
       "..                   ...                ...              ...  \n",
       "40        Alberto Acosta     Alberto Acosta              NaN  \n",
       "41        Mauricio Rodas     Mauricio Rodas              NaN  \n",
       "42           Norman Wray        Norman Wray              NaN  \n",
       "43                   NaN                NaN              NaN  \n",
       "44                   NaN                NaN              NaN  \n",
       "45                   NaN                NaN              NaN  \n",
       "46                   NaN                NaN              NaN  \n",
       "47                   NaN                NaN              NaN  \n",
       "48                   NaN                NaN              NaN  \n",
       "49                   NaN                NaN              NaN  \n",
       "\n",
       "[50 rows x 11 columns]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.dropna(subset=['Country', 'Date', 'Title'], inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>State/City</th>\n",
       "      <th>Title</th>\n",
       "      <th>Date</th>\n",
       "      <th>Catalogue</th>\n",
       "      <th>Wikipedia Election Page</th>\n",
       "      <th>Wikipedia Individual Page</th>\n",
       "      <th>Electoral Institution in Country</th>\n",
       "      <th>Twitter</th>\n",
       "      <th>CANDIDATE NAME 1</th>\n",
       "      <th>CANDIDATE NAME 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Hugo Rafael Chavez Frias</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez Frías</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles R.</td>\n",
       "      <td>Henrique Capriles</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Maria Josefina Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirinos</td>\n",
       "      <td>None.</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes Castillo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-28</td>\n",
       "      <td>Carolina Montserrat Toha Morales</td>\n",
       "      <td>Carolina Tohá Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-29</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-30</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>None.</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora L.</td>\n",
       "      <td>Waldo Mora</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-31</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>Zulia</td>\n",
       "      <td>Governor</td>\n",
       "      <td>2012-12-16</td>\n",
       "      <td>Iris Rincón</td>\n",
       "      <td>Iris Rincón</td>\n",
       "      <td>None.</td>\n",
       "      <td>Iris Rincon</td>\n",
       "      <td>None.</td>\n",
       "      <td>Iris Rincon</td>\n",
       "      <td>Iris Rincón</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>Zulia</td>\n",
       "      <td>Governor</td>\n",
       "      <td>2012-12-16</td>\n",
       "      <td>Maria Bolívar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>Zulia</td>\n",
       "      <td>Governor</td>\n",
       "      <td>2012-12-16</td>\n",
       "      <td>Pablo Pérez</td>\n",
       "      <td>Pablo Pérez Álvarez</td>\n",
       "      <td>Pablo Pérez Álvarez</td>\n",
       "      <td>Pablo Perez</td>\n",
       "      <td>Pablo Pérez Álvarez</td>\n",
       "      <td>Pablo Perez</td>\n",
       "      <td>Pablo Pérez</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Rafael Vicente Correa Delgado</td>\n",
       "      <td>Rafael Correa</td>\n",
       "      <td>Rafael Correa</td>\n",
       "      <td>Rafael Correa</td>\n",
       "      <td>Rafael Correa</td>\n",
       "      <td>Rafael Correa</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Guillermo Alberto Santiago Lasso Mendoza</td>\n",
       "      <td>Guillermo Lasso</td>\n",
       "      <td>Guillermo Lasso</td>\n",
       "      <td>Guillermo Lasso</td>\n",
       "      <td>Guillermo Lasso</td>\n",
       "      <td>Guillermo Lasso</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Lucio Edwin Gutiérrez Borbúa</td>\n",
       "      <td>Lucio Gutiérrez</td>\n",
       "      <td>Lucio Gutiérrez</td>\n",
       "      <td>Lucio Gutiérrez</td>\n",
       "      <td>Lucio Gutiérrez</td>\n",
       "      <td>Lucio Gutierrez</td>\n",
       "      <td>Lucio Gutiérrez</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Álvaro Fernando Noboa Pontón</td>\n",
       "      <td>Álvaro Noboa</td>\n",
       "      <td>Álvaro Noboa</td>\n",
       "      <td>Alvaro Noboa</td>\n",
       "      <td>Alvaro Noboa</td>\n",
       "      <td>Alvaro Noboa</td>\n",
       "      <td>Álvaro Noboa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Alberto Acosta Espinosa</td>\n",
       "      <td>Alberto Acosta Espinosa</td>\n",
       "      <td>Alberto Acosta Espinosa</td>\n",
       "      <td>Alberto Acosta</td>\n",
       "      <td>Alberto Acosta</td>\n",
       "      <td>Alberto Acosta</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Mauricio Rodas Espinel</td>\n",
       "      <td>Mauricio Rodas</td>\n",
       "      <td>Mauricio Rodas</td>\n",
       "      <td>Mauricio Rodas</td>\n",
       "      <td>Mauricio Rodas</td>\n",
       "      <td>Mauricio Rodas</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>Ecuador</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2013-02-07</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>None.</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>Norman Wray</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>43 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Country State/City      Title       Date  \\\n",
       "0   Venezuela        NaN  President 2012-10-07   \n",
       "1   Venezuela        NaN  President 2012-10-07   \n",
       "2   Venezuela        NaN  President 2012-10-07   \n",
       "3   Venezuela        NaN  President 2012-10-07   \n",
       "4   Venezuela        NaN  President 2012-10-07   \n",
       "5   Venezuela        NaN  President 2012-10-07   \n",
       "6       Chile   Santiago      Mayor 2012-10-28   \n",
       "7       Chile   Santiago      Mayor 2012-10-29   \n",
       "8       Chile   Santiago      Mayor 2012-10-30   \n",
       "9       Chile   Santiago      Mayor 2012-10-31   \n",
       "..        ...        ...        ...        ...   \n",
       "33  Venezuela      Zulia   Governor 2012-12-16   \n",
       "34  Venezuela      Zulia   Governor 2012-12-16   \n",
       "35  Venezuela      Zulia   Governor 2012-12-16   \n",
       "36    Ecuador        NaN  President 2013-02-07   \n",
       "37    Ecuador        NaN  President 2013-02-07   \n",
       "38    Ecuador        NaN  President 2013-02-07   \n",
       "39    Ecuador        NaN  President 2013-02-07   \n",
       "40    Ecuador        NaN  President 2013-02-07   \n",
       "41    Ecuador        NaN  President 2013-02-07   \n",
       "42    Ecuador        NaN  President 2013-02-07   \n",
       "\n",
       "                                   Catalogue     Wikipedia Election Page  \\\n",
       "0                   Hugo Rafael Chavez Frias                 Hugo Chávez   \n",
       "1                 Henrique Capriles Radonski  Henrique Capriles Radonski   \n",
       "2                     Maria Josefina Bolivar               María Bolívar   \n",
       "3                            Orlando Chirino            Orlando Chirinos   \n",
       "4                                 Luis Reyes         Luis Reyes Castillo   \n",
       "5                              Reina Sequera               Reina Sequera   \n",
       "6           Carolina Montserrat Toha Morales       Carolina Tohá Morales   \n",
       "7                       Pablo Zalaquett Said        Pablo Zalaquett Said   \n",
       "8                           Waldo Mora Longa            Waldo Mora Longa   \n",
       "9                              Mario Aguilar       Mario Aguilar Arevalo   \n",
       "..                                       ...                         ...   \n",
       "33                               Iris Rincón                 Iris Rincón   \n",
       "34                             Maria Bolívar               María Bolívar   \n",
       "35                               Pablo Pérez         Pablo Pérez Álvarez   \n",
       "36             Rafael Vicente Correa Delgado               Rafael Correa   \n",
       "37  Guillermo Alberto Santiago Lasso Mendoza             Guillermo Lasso   \n",
       "38              Lucio Edwin Gutiérrez Borbúa             Lucio Gutiérrez   \n",
       "39              Álvaro Fernando Noboa Pontón                Álvaro Noboa   \n",
       "40                   Alberto Acosta Espinosa     Alberto Acosta Espinosa   \n",
       "41                    Mauricio Rodas Espinel              Mauricio Rodas   \n",
       "42                               Norman Wray                 Norman Wray   \n",
       "\n",
       "     Wikipedia Individual Page Electoral Institution in Country  \\\n",
       "0                  Hugo Chávez                      Hugo Chavez   \n",
       "1   Henrique Capriles Radonski       Henrique Capriles Radonski   \n",
       "2                María Bolívar                    Maria Bolivar   \n",
       "3                        None.                  Orlando Chirino   \n",
       "4                        None.                       Luis Reyes   \n",
       "5                Reina Sequera                    Reina Sequera   \n",
       "6                Carolina Tohá            Carolina Toha Morales   \n",
       "7              Pablo Zalaquett             Pablo Zalaquett Said   \n",
       "8                        None.                 Waldo Mora Longa   \n",
       "9                        None.            Mario Aguilar Arevalo   \n",
       "..                         ...                              ...   \n",
       "33                       None.                      Iris Rincon   \n",
       "34               María Bolívar                    Maria Bolivar   \n",
       "35         Pablo Pérez Álvarez                      Pablo Perez   \n",
       "36               Rafael Correa                    Rafael Correa   \n",
       "37             Guillermo Lasso                  Guillermo Lasso   \n",
       "38             Lucio Gutiérrez                  Lucio Gutiérrez   \n",
       "39                Álvaro Noboa                     Alvaro Noboa   \n",
       "40     Alberto Acosta Espinosa                   Alberto Acosta   \n",
       "41              Mauricio Rodas                   Mauricio Rodas   \n",
       "42                       None.                      Norman Wray   \n",
       "\n",
       "                 Twitter   CANDIDATE NAME 1 CANDIDATE NAME 2  \n",
       "0      Hugo Chávez Frías        Hugo Chavez      Hugo Chávez  \n",
       "1   Henrique Capriles R.  Henrique Capriles              NaN  \n",
       "2          Maria Bolivar      Maria Bolivar    María Bolívar  \n",
       "3        Orlando Chirino    Orlando Chirino              NaN  \n",
       "4             Luis Reyes         Luis Reyes              NaN  \n",
       "5          Reina Sequera      Reina Sequera              NaN  \n",
       "6          Carolina Tohá      Carolina Tohá    Carolina Toha  \n",
       "7   Pablo Zalaquett Said    Pablo Zalaquett              NaN  \n",
       "8          Waldo Mora L.         Waldo Mora              NaN  \n",
       "9          Mario Aguilar      Mario Aguilar              NaN  \n",
       "..                   ...                ...              ...  \n",
       "33                 None.        Iris Rincon      Iris Rincón  \n",
       "34         Maria Bolivar      Maria Bolivar    María Bolívar  \n",
       "35   Pablo Pérez Álvarez        Pablo Perez      Pablo Pérez  \n",
       "36         Rafael Correa      Rafael Correa              NaN  \n",
       "37       Guillermo Lasso    Guillermo Lasso              NaN  \n",
       "38       Lucio Gutiérrez    Lucio Gutierrez  Lucio Gutiérrez  \n",
       "39          Alvaro Noboa       Alvaro Noboa     Álvaro Noboa  \n",
       "40        Alberto Acosta     Alberto Acosta              NaN  \n",
       "41        Mauricio Rodas     Mauricio Rodas              NaN  \n",
       "42           Norman Wray        Norman Wray              NaN  \n",
       "\n",
       "[43 rows x 11 columns]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data.to_excel('people.xls')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>State/City</th>\n",
       "      <th>Title</th>\n",
       "      <th>Date</th>\n",
       "      <th>Catalogue</th>\n",
       "      <th>Wikipedia Election Page</th>\n",
       "      <th>Wikipedia Individual Page</th>\n",
       "      <th>Electoral Institution in Country</th>\n",
       "      <th>Twitter</th>\n",
       "      <th>CANDIDATE NAME 1</th>\n",
       "      <th>CANDIDATE NAME 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-28</td>\n",
       "      <td>Carolina Montserrat Toha Morales</td>\n",
       "      <td>Carolina Tohá Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-29</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-30</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>None.</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora L.</td>\n",
       "      <td>Waldo Mora</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-31</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-11-01</td>\n",
       "      <td>Ivan Carrasco</td>\n",
       "      <td>Iván Carrasco Mora</td>\n",
       "      <td>None.</td>\n",
       "      <td>Ivan Carrasco Mora</td>\n",
       "      <td>None.</td>\n",
       "      <td>Iván Carrasco Mora</td>\n",
       "      <td>Ivan Carrasco Mora</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Country State/City  Title       Date                         Catalogue  \\\n",
       "6    Chile   Santiago  Mayor 2012-10-28  Carolina Montserrat Toha Morales   \n",
       "7    Chile   Santiago  Mayor 2012-10-29              Pablo Zalaquett Said   \n",
       "8    Chile   Santiago  Mayor 2012-10-30                  Waldo Mora Longa   \n",
       "9    Chile   Santiago  Mayor 2012-10-31                     Mario Aguilar   \n",
       "10   Chile   Santiago  Mayor 2012-11-01                     Ivan Carrasco   \n",
       "\n",
       "   Wikipedia Election Page Wikipedia Individual Page  \\\n",
       "6    Carolina Tohá Morales             Carolina Tohá   \n",
       "7     Pablo Zalaquett Said           Pablo Zalaquett   \n",
       "8         Waldo Mora Longa                     None.   \n",
       "9    Mario Aguilar Arevalo                     None.   \n",
       "10      Iván Carrasco Mora                     None.   \n",
       "\n",
       "   Electoral Institution in Country               Twitter    CANDIDATE NAME 1  \\\n",
       "6             Carolina Toha Morales         Carolina Tohá       Carolina Tohá   \n",
       "7              Pablo Zalaquett Said  Pablo Zalaquett Said     Pablo Zalaquett   \n",
       "8                  Waldo Mora Longa         Waldo Mora L.          Waldo Mora   \n",
       "9             Mario Aguilar Arevalo         Mario Aguilar       Mario Aguilar   \n",
       "10               Ivan Carrasco Mora                 None.  Iván Carrasco Mora   \n",
       "\n",
       "      CANDIDATE NAME 2  \n",
       "6        Carolina Toha  \n",
       "7                  NaN  \n",
       "8                  NaN  \n",
       "9                  NaN  \n",
       "10  Ivan Carrasco Mora  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data.Country == 'Chile']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Country</th>\n",
       "      <th>State/City</th>\n",
       "      <th>Title</th>\n",
       "      <th>Date</th>\n",
       "      <th>Catalogue</th>\n",
       "      <th>Wikipedia Election Page</th>\n",
       "      <th>Wikipedia Individual Page</th>\n",
       "      <th>Electoral Institution in Country</th>\n",
       "      <th>Twitter</th>\n",
       "      <th>CANDIDATE NAME 1</th>\n",
       "      <th>CANDIDATE NAME 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Hugo Rafael Chavez Frias</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez Frías</td>\n",
       "      <td>Hugo Chavez</td>\n",
       "      <td>Hugo Chávez</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles Radonski</td>\n",
       "      <td>Henrique Capriles R.</td>\n",
       "      <td>Henrique Capriles</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Maria Josefina Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>María Bolívar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>Maria Bolivar</td>\n",
       "      <td>María Bolívar</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirinos</td>\n",
       "      <td>None.</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>Orlando Chirino</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes Castillo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>Luis Reyes</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Venezuela</td>\n",
       "      <td>NaN</td>\n",
       "      <td>President</td>\n",
       "      <td>2012-10-07</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>Reina Sequera</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-28</td>\n",
       "      <td>Carolina Montserrat Toha Morales</td>\n",
       "      <td>Carolina Tohá Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha Morales</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Tohá</td>\n",
       "      <td>Carolina Toha</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-29</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett Said</td>\n",
       "      <td>Pablo Zalaquett</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-30</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>None.</td>\n",
       "      <td>Waldo Mora Longa</td>\n",
       "      <td>Waldo Mora L.</td>\n",
       "      <td>Waldo Mora</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Chile</td>\n",
       "      <td>Santiago</td>\n",
       "      <td>Mayor</td>\n",
       "      <td>2012-10-31</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>None.</td>\n",
       "      <td>Mario Aguilar Arevalo</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>Mario Aguilar</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Country State/City      Title       Date  \\\n",
       "0  Venezuela        NaN  President 2012-10-07   \n",
       "1  Venezuela        NaN  President 2012-10-07   \n",
       "2  Venezuela        NaN  President 2012-10-07   \n",
       "3  Venezuela        NaN  President 2012-10-07   \n",
       "4  Venezuela        NaN  President 2012-10-07   \n",
       "5  Venezuela        NaN  President 2012-10-07   \n",
       "6      Chile   Santiago      Mayor 2012-10-28   \n",
       "7      Chile   Santiago      Mayor 2012-10-29   \n",
       "8      Chile   Santiago      Mayor 2012-10-30   \n",
       "9      Chile   Santiago      Mayor 2012-10-31   \n",
       "\n",
       "                          Catalogue     Wikipedia Election Page  \\\n",
       "0          Hugo Rafael Chavez Frias                 Hugo Chávez   \n",
       "1        Henrique Capriles Radonski  Henrique Capriles Radonski   \n",
       "2            Maria Josefina Bolivar               María Bolívar   \n",
       "3                   Orlando Chirino            Orlando Chirinos   \n",
       "4                        Luis Reyes         Luis Reyes Castillo   \n",
       "5                     Reina Sequera               Reina Sequera   \n",
       "6  Carolina Montserrat Toha Morales       Carolina Tohá Morales   \n",
       "7              Pablo Zalaquett Said        Pablo Zalaquett Said   \n",
       "8                  Waldo Mora Longa            Waldo Mora Longa   \n",
       "9                     Mario Aguilar       Mario Aguilar Arevalo   \n",
       "\n",
       "    Wikipedia Individual Page Electoral Institution in Country  \\\n",
       "0                 Hugo Chávez                      Hugo Chavez   \n",
       "1  Henrique Capriles Radonski       Henrique Capriles Radonski   \n",
       "2               María Bolívar                    Maria Bolivar   \n",
       "3                       None.                  Orlando Chirino   \n",
       "4                       None.                       Luis Reyes   \n",
       "5               Reina Sequera                    Reina Sequera   \n",
       "6               Carolina Tohá            Carolina Toha Morales   \n",
       "7             Pablo Zalaquett             Pablo Zalaquett Said   \n",
       "8                       None.                 Waldo Mora Longa   \n",
       "9                       None.            Mario Aguilar Arevalo   \n",
       "\n",
       "                Twitter   CANDIDATE NAME 1 CANDIDATE NAME 2  \n",
       "0     Hugo Chávez Frías        Hugo Chavez      Hugo Chávez  \n",
       "1  Henrique Capriles R.  Henrique Capriles              NaN  \n",
       "2         Maria Bolivar      Maria Bolivar    María Bolívar  \n",
       "3       Orlando Chirino    Orlando Chirino              NaN  \n",
       "4            Luis Reyes         Luis Reyes              NaN  \n",
       "5         Reina Sequera      Reina Sequera              NaN  \n",
       "6         Carolina Tohá      Carolina Tohá    Carolina Toha  \n",
       "7  Pablo Zalaquett Said    Pablo Zalaquett              NaN  \n",
       "8         Waldo Mora L.         Waldo Mora              NaN  \n",
       "9         Mario Aguilar      Mario Aguilar              NaN  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[data.Date < '2012-11']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([u'Venezuela', u'Chile', u'Nicaragua', u'Ecuador'], dtype=object)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Country.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Venezuela    25\n",
       "Ecuador       7\n",
       "Nicaragua     6\n",
       "Chile         5\n",
       "Name: Country, dtype: int64"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.Country.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib\n",
    "=========="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from   pylab import *\n",
    "\n",
    "n     = 200\n",
    "x     = np.linspace(0,10,n)\n",
    "data  = np.sin(x)\n",
    "noise = np.random.randn(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x114ef75d0>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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u7bor7LxzvD+PElFUfPMNPP+8zvpIoiZNbCtXnN/EEj3ptPWm0Pqu5CnflbZm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\nAwtp2HUPJTmrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ba9e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118006810>]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pBbWhSv04+AjGuYXt1I9RiQawz7MIBw9vQDo2mHCw6HMO5v0cUBqfwTiny3Sl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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114e9fd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,noise, 'rx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JR6vqSa21e+ewP4AdY9p5NpaWlrJnz54ZVcNONvMA0Fq77ZS3f1pVn07yF0men+St59ru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\n/wOE6T69QphHhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11803b150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = hist(noise, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118346a50>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ODhyIfpfKgZnAdpGD5WXax/YztDFtWpwsggRk66QXFqJiVZo7KA7+HuvVydVb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\ncCBJkloMB5IkqcVwIEmSWgwHkiSp5X8oDEczrWSi/AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118205050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "obs = data + noise\n",
    "plot(x, obs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O0lLrPHMLqdTWch8jU3bdKo3W1QEXXgi8+CJwxhnun+UmOMrK2Ck+/3weC2bO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\nRVESRwWHoiiKoiiJ8/8AtaOQ6jnFj9EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11837ac90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "obs = data + noise\n",
    "figure()\n",
    "subplot(211)\n",
    "title('sin + $\\mathcal{N}$(0,1) noise')\n",
    "xlabel('time (s)')\n",
    "ylabel('reading (mV)')\n",
    "plot(x, obs, 'r')\n",
    "subplot(212)\n",
    "plot(x, data, 'r')\n",
    "plot(x, noise, 'x')\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matplotlib Exercise\n",
    "-------------------\n",
    "\n",
    "Create a figure showing the following functions on the range $-5\\pi$ to $+5\\pi$:\n",
    "\n",
    "```\n",
    "    f(x) = x\n",
    "    g(x) = -x\n",
    "    h(x) = sin(x)\n",
    "    k(x) = x*sin(x)\n",
    "```\n",
    "\n",
    "Each function should be a different color and use a difernet line style.\n",
    "\n",
    "The figure needs lablled x- and y-axes, a legend and a title.\n",
    "\n",
    "Use `pyplot.annotate()` to label the minima of `k(x)=x*sin(x)` in the region of interest. Use the `.min()` and `.argmin()` methods to locate the minima point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scipy\n",
    "====="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.optimize\n",
    "from numpy.random import rand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'optimize' in dir(sp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$signal = A\\times cos(2{\\pi}x-1.32) + 0.22x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "points = 200\n",
    "x      = np.linspace(0, 10, points)\n",
    "\n",
    "# func-> A*cos(2pi*x-B)+x*C+noise\n",
    "signal = 12.0 * np.cos(2*np.pi*x-1.32) + 0.22 * x\n",
    "noise  = 4 * ((0.5-rand(points)) * np.exp(2*rand(points)**2))\n",
    "combined = signal + noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dBeKDD/T7K1aoGzYoqEaObOkqszbQb4GwwVdcgb8FFxAA4Jy71zl3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\n3Qg6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119f230d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure()\n",
    "subplot(211)\n",
    "plot(x, noise)\n",
    "subplot(212)\n",
    "_ = hist(noise,20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x118173b10>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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od3IORKUEG7oLoykhfAaiMjh6Qnnargd9n2tR9nwEs5S1C0XLtL7kJcC73539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\niIiIqDIGEERERFQZAwgiIiKq7P8DsfNrNyVygIcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1184b8cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x, combined, 'x')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$model = p_0 \\times cos(2\\pi x - p_1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = lambda p, x:    p[0] * np.cos(2*np.pi*x-p[1])\n",
    "err   = lambda p, x, y: model(p, x) - y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "guess = [1., 0.8]\n",
    "fitted, success = sp.optimize.leastsq(err, guess, args=(x, combined))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "success"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1184df7d0>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1I1yio6ODmpqaQQVEbm4uHo8nbgXExIkTyQ3UaoGB4u4Fj4da4MLy8oQ7lTYU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\nNBpNyGgBodFoNBqNJmT+f9QVt587LK3hAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11856f990>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, combined,'r^')\n",
    "plt.plot(x, model(fitted,x), 'k-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11849fe90>]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h5oQJWTtSlkqUiY8alhCRWqDhBgmtGunv1I01NTwwCXgU+GfgtZYW/uSUU3DO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\nTzSceIpYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1182054d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data  = 3.23 * np.exp(-x*.23) + 0.02 * x\n",
    "noise = .2 * ( (0.5 - rand(points)) * np.exp(2*rand(points)**2))\n",
    "y     = data + noise\n",
    "plt.plot(x, y, 'r^')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_exp = lambda p, x:    p[0] * np.exp(-x*p[1])\n",
    "err_exp   = lambda p, x, y: model_exp(p, x) - y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11a491110>,\n",
       " <matplotlib.lines.Line2D at 0x11a491210>]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FCKXeAgYEPXdu6fOC79v+taNHM3Phwrh/y4610DHUstP+m/t330F2Nrz66oN0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\nREQkJQUJIiIikpKCBBEREUnp/wF3ulXUEpn0igAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1184df8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "guess = [5., -0.8]\n",
    "\n",
    "fitted_exp, success = sp.optimize.leastsq(err_exp, guess, args=(x, y))\n",
    "plt.plot(x, y, \"r^\", x, model_exp(fitted_exp, x), \"b-\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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