{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is a simple demonstration of how you may be able to predict the phase of the gait cycle from the states from a simple linear regression.\n",
    "\n",
    "**warning** This notebook doesn't seem to run with Pandas < 0.14.0. I get an error calling `results.rsquared`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports and Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../src')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from pandas import concat\n",
    "import statsmodels.formula.api as smf\n",
    "from gaitanalysis.gait import plot_gait_cycles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import utils\n",
    "from gait_landmark_settings import settings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.core.pylabtools import figsize\n",
    "figsize(14, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load First Data Set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the path to the directory with the experimental data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "trials_dir = utils.config_paths()['raw_data_dir']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the \"training\" data set. We simple collect all of the gait cycles from the perturbed portion of one trial from subject \"A\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading pre-cleaned data: /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/cleaned-data/068-longitudinal-perturbation.h5\n",
      "_write_event_data_frame_to_disk took 0.04 s to execute.\n",
      "Loading pre-computed inverse dynamics from /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/gait-data/068-longitudinal-perturbation.h5.\n",
      "_write_inverse_dynamics_to_disk took 0.08 s to execute.\n",
      "Loading pre-computed gait cycles from /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/gait-data/068-longitudinal-perturbation.h5.\n",
      "_section_into_gait_cycles took 0.45 s to execute.\n"
     ]
    }
   ],
   "source": [
    "trial_number = '068'\n",
    "trial = utils.Trial('068')\n",
    "trial.prep_data('Longitudinal Perturbation')\n",
    "gait_cycles = trial.gait_data_objs['Longitudinal Perturbation'].gait_cycles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now create a big data frame which has a column with the percent gait cycle `phi`. It also contains columns for all of the state values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dfs = []\n",
    "for i, df in gait_cycles.iteritems():\n",
    "    dfs.append(df)\n",
    "bigdf = concat(dfs)\n",
    "bigdf['phi'] = bigdf.index.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fit a model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now specify a patsy formula for the module. We simply want to predict `phi` using all of the states as the multivariate linear regressors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'phi ~ Q(\"Right.Ankle.PlantarFlexion.Angle\") + Q(\"Right.Ankle.PlantarFlexion.Rate\") + Q(\"Right.Knee.Flexion.Angle\") + Q(\"Right.Knee.Flexion.Rate\") + Q(\"Right.Hip.Flexion.Angle\") + Q(\"Right.Hip.Flexion.Rate\") + Q(\"Left.Ankle.PlantarFlexion.Angle\") + Q(\"Left.Ankle.PlantarFlexion.Rate\") + Q(\"Left.Knee.Flexion.Angle\") + Q(\"Left.Knee.Flexion.Rate\") + Q(\"Left.Hip.Flexion.Angle\") + Q(\"Left.Hip.Flexion.Rate\")'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sensors, controls = utils.load_sensors_and_controls()\n",
    "model = 'phi ~ Q(\"' + '\") + Q(\"'.join(sensors) + '\")' #+ ' + Q(\"FP1.ForY\") + Q(\"FP2.ForY\")'\n",
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "results = smf.ols(model, data=bigdf).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results show that we have a decent model with a high $R^2$ value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    phi   R-squared:                       0.904\n",
      "Model:                            OLS   Adj. R-squared:                  0.904\n",
      "Method:                 Least Squares   F-statistic:                     6753.\n",
      "Date:                Fri, 24 Apr 2015   Prob (F-statistic):               0.00\n",
      "Time:                        12:12:24   Log-Likelihood:                 8567.3\n",
      "No. Observations:                8580   AIC:                        -1.711e+04\n",
      "Df Residuals:                    8567   BIC:                        -1.702e+04\n",
      "Df Model:                          12                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=========================================================================================================\n",
      "                                            coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "---------------------------------------------------------------------------------------------------------\n",
      "Intercept                                 1.1771      0.036     32.944      0.000         1.107     1.247\n",
      "Q(\"Right.Ankle.PlantarFlexion.Angle\")     0.4949      0.014     34.506      0.000         0.467     0.523\n",
      "Q(\"Right.Ankle.PlantarFlexion.Rate\")      0.0037      0.001      4.858      0.000         0.002     0.005\n",
      "Q(\"Right.Knee.Flexion.Angle\")            -0.0861      0.011     -7.510      0.000        -0.109    -0.064\n",
      "Q(\"Right.Knee.Flexion.Rate\")             -0.1039      0.001   -110.601      0.000        -0.106    -0.102\n",
      "Q(\"Right.Hip.Flexion.Angle\")             -0.6223      0.027    -22.968      0.000        -0.675    -0.569\n",
      "Q(\"Right.Hip.Flexion.Rate\")               0.0712      0.004     16.062      0.000         0.063     0.080\n",
      "Q(\"Left.Ankle.PlantarFlexion.Angle\")      0.0477      0.014      3.423      0.001         0.020     0.075\n",
      "Q(\"Left.Ankle.PlantarFlexion.Rate\")       0.0123      0.001     16.125      0.000         0.011     0.014\n",
      "Q(\"Left.Knee.Flexion.Angle\")              0.0050      0.011      0.438      0.662        -0.017     0.027\n",
      "Q(\"Left.Knee.Flexion.Rate\")               0.0500      0.001     56.917      0.000         0.048     0.052\n",
      "Q(\"Left.Hip.Flexion.Angle\")               0.8544      0.027     31.859      0.000         0.802     0.907\n",
      "Q(\"Left.Hip.Flexion.Rate\")               -0.1215      0.004    -29.435      0.000        -0.130    -0.113\n",
      "==============================================================================\n",
      "Omnibus:                     1487.314   Durbin-Watson:                   2.342\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             5339.237\n",
      "Skew:                           0.849   Prob(JB):                         0.00\n",
      "Kurtosis:                       6.472   Cond. No.                         150.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load validation data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we load in data from the same subject but at a different speed to test the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading pre-cleaned data: /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/cleaned-data/068-longitudinal-perturbation.h5\n",
      "_write_event_data_frame_to_disk took 0.06 s to execute.\n",
      "Loading pre-computed inverse dynamics from /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/gait-data/068-longitudinal-perturbation.h5.\n",
      "_write_inverse_dynamics_to_disk took 0.38 s to execute.\n",
      "Loading pre-computed gait cycles from /home/moorepants/Manuscripts/gait-control-direct-id-paper/processed-data/gait-data/068-longitudinal-perturbation.h5.\n",
      "_section_into_gait_cycles took 0.15 s to execute.\n"
     ]
    }
   ],
   "source": [
    "trial_number = '069'\n",
    "trial = utils.Trial('068')\n",
    "trial.prep_data('Longitudinal Perturbation')\n",
    "gait_cycles = trial.gait_data_objs['Longitudinal Perturbation'].gait_cycles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "dfs = []\n",
    "for i, df in gait_cycles.iteritems():\n",
    "    dfs.append(df)\n",
    "bigdf = concat(dfs)\n",
    "bigdf['phi'] = bigdf.index.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Test the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows the actual percent gait cycle and that predicted by the linear model given the states from the new trial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7828374a50>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "GIOcJiGEEEIIIYQYg5wmIYQQQgghhBjD/w/nC7wFpdM2ywAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7829d36fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(results.predict(bigdf)[:400])\n",
    "plt.plot(bigdf['phi'].values[:400])\n",
    "plt.legend(['Prediction', 'Actual'])\n",
    "plt.ylabel('Percent Gait Cycle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Footer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6af0c229bb0a9edf78f8489d5f0efe02d5685a57\r\n"
     ]
    }
   ],
   "source": [
    "!git rev-parse HEAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9e80dfdcfe0a14b44e0ebcbadb6e9e827d215c3c\r\n"
     ]
    }
   ],
   "source": [
    "!git --git-dir=/home/moorepants/src/GaitAnalysisToolKit/.git --work-tree=/home/moorepants/src/GaitAnalysisToolKit rev-parse HEAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Installed version_information.py. To use it, type:\n",
      "  %load_ext version_information\n"
     ]
    }
   ],
   "source": [
    "%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%load_ext version_information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]"
        },
        {
         "module": "IPython",
         "version": "3.0.0"
        },
        {
         "module": "OS",
         "version": "Linux 3.13.0 49 generic x86_64 with debian jessie sid"
        },
        {
         "module": "gaitanalysis",
         "version": "0.2.0dev"
        },
        {
         "module": "dtk",
         "version": "0.4.0"
        },
        {
         "module": "numpy",
         "version": "1.9.2"
        },
        {
         "module": "scipy",
         "version": "0.15.1"
        },
        {
         "module": "pandas",
         "version": "0.16.0"
        },
        {
         "module": "matplotlib",
         "version": "1.4.2"
        },
        {
         "module": "tables",
         "version": "3.1.1"
        },
        {
         "module": "statsmodels",
         "version": "0.6.1"
        },
        {
         "module": "oct2py",
         "version": "3.1.0"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]</td></tr><tr><td>IPython</td><td>3.0.0</td></tr><tr><td>OS</td><td>Linux 3.13.0 49 generic x86_64 with debian jessie sid</td></tr><tr><td>gaitanalysis</td><td>0.2.0dev</td></tr><tr><td>dtk</td><td>0.4.0</td></tr><tr><td>numpy</td><td>1.9.2</td></tr><tr><td>scipy</td><td>0.15.1</td></tr><tr><td>pandas</td><td>0.16.0</td></tr><tr><td>matplotlib</td><td>1.4.2</td></tr><tr><td>tables</td><td>3.1.1</td></tr><tr><td>statsmodels</td><td>0.6.1</td></tr><tr><td>oct2py</td><td>3.1.0</td></tr><tr><td colspan='2'>Fri Apr 24 12:12:26 2015 PDT</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)] \\\\ \\hline\n",
       "IPython & 3.0.0 \\\\ \\hline\n",
       "OS & Linux 3.13.0 49 generic x86\\_64 with debian jessie sid \\\\ \\hline\n",
       "gaitanalysis & 0.2.0dev \\\\ \\hline\n",
       "dtk & 0.4.0 \\\\ \\hline\n",
       "numpy & 1.9.2 \\\\ \\hline\n",
       "scipy & 0.15.1 \\\\ \\hline\n",
       "pandas & 0.16.0 \\\\ \\hline\n",
       "matplotlib & 1.4.2 \\\\ \\hline\n",
       "tables & 3.1.1 \\\\ \\hline\n",
       "statsmodels & 0.6.1 \\\\ \\hline\n",
       "oct2py & 3.1.0 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Fri Apr 24 12:12:26 2015 PDT} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 2.7.9 64bit [GCC 4.4.7 20120313 (Red Hat 4.4.7-1)]\n",
       "IPython 3.0.0\n",
       "OS Linux 3.13.0 49 generic x86_64 with debian jessie sid\n",
       "gaitanalysis 0.2.0dev\n",
       "dtk 0.4.0\n",
       "numpy 1.9.2\n",
       "scipy 0.15.1\n",
       "pandas 0.16.0\n",
       "matplotlib 1.4.2\n",
       "tables 3.1.1\n",
       "statsmodels 0.6.1\n",
       "oct2py 3.1.0\n",
       "Fri Apr 24 12:12:26 2015 PDT"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%version_information gaitanalysis, dtk, numpy, scipy, pandas, matplotlib, tables, statsmodels, oct2py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# packages in environment at /home/moorepants/anaconda/envs/gait-direct-id-paper:\n",
      "#\n",
      "backports.ssl-match-hostname 3.4.0.2                   <pip>\n",
      "cairo                     1.12.18                       0  \n",
      "dateutil                  2.4.1                    py27_0  \n",
      "dynamicisttoolkit         0.4.0                    py27_0  \n",
      "fastcache                 1.0.2                    py27_0  \n",
      "fontconfig                2.11.1                        2  \n",
      "freetype                  2.4.10                        0  \n",
      "gaitanalysistoolkit (/home/moorepants/src/GaitAnalysisToolKit) 0.2.0.dev0                <pip>\n",
      "hdf5                      1.8.14                        0  \n",
      "ipython                   3.0.0                    py27_0  \n",
      "ipython-notebook          3.0.0                    py27_1  \n",
      "jinja2                    2.7.3                    py27_1  \n",
      "jsonschema                2.4.0                    py27_0  \n",
      "libpng                    1.5.13                        1  \n",
      "libsodium                 0.4.5                         0  \n",
      "libxml2                   2.9.0                         0  \n",
      "markupsafe                0.23                     py27_0  \n",
      "matplotlib                1.4.2                np19py27_0  \n",
      "mistune                   0.5.1                    py27_0  \n",
      "nose                      1.3.4                    py27_1  \n",
      "numexpr                   2.3.1                np19py27_0  \n",
      "numpy                     1.9.2                    py27_0  \n",
      "oct2py                    3.1.0                    py27_0  \n",
      "openssl                   1.0.1k                        1  \n",
      "pandas                    0.16.0               np19py27_1  \n",
      "patsy                     0.3.0                np19py27_0  \n",
      "pip                       6.1.1                    py27_0  \n",
      "pixman                    0.26.2                        0  \n",
      "ptyprocess                0.4                      py27_0  \n",
      "py2cairo                  1.10.0                   py27_2  \n",
      "pygments                  2.0.2                    py27_0  \n",
      "pyparsing                 2.0.1                    py27_0  \n",
      "pyqt                      4.10.4                   py27_0  \n",
      "pyside                    1.2.1                    py27_1  \n",
      "pytables                  3.1.1                np19py27_2  \n",
      "python                    2.7.9                         2  \n",
      "python-dateutil           2.4.2                    py27_0  \n",
      "pytz                      2015.2                   py27_0  \n",
      "pyyaml                    3.11                     py27_0  \n",
      "pyzmq                     14.5.0                   py27_0  \n",
      "qt                        4.8.5                         0  \n",
      "readline                  6.2                           2  \n",
      "scipy                     0.15.1               np19py27_0  \n",
      "seaborn                   0.5.1                np19py27_0  \n",
      "setuptools                15.1                     py27_1  \n",
      "shiboken                  1.2.1                    py27_0  \n",
      "sip                       4.15.5                   py27_0  \n",
      "six                       1.9.0                    py27_0  \n",
      "snakeviz                  0.3.1                     <pip>\n",
      "sqlite                    3.8.4.1                       1  \n",
      "ssl_match_hostname        3.4.0.2                  py27_0  \n",
      "statsmodels               0.6.1                np19py27_0  \n",
      "sympy                     0.7.6                    py27_0  \n",
      "system                    5.8                           2  \n",
      "tables                    3.1.1                     <pip>\n",
      "terminado                 0.5                      py27_0  \n",
      "tk                        8.5.18                        0  \n",
      "tornado                   4.1                      py27_0  \n",
      "yaml                      0.1.4                         0  \n",
      "zeromq                    4.0.4                         0  \n",
      "zlib                      1.2.8                         0  \n"
     ]
    }
   ],
   "source": [
    "!conda list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "backports.ssl-match-hostname==3.4.0.2\r\n",
      "DynamicistToolKit==0.4.0\r\n",
      "fastcache==1.0.2\r\n",
      "-e git+git@github.com:csu-hmc/GaitAnalysisToolKit.git@9e80dfdcfe0a14b44e0ebcbadb6e9e827d215c3c#egg=GaitAnalysisToolKit-origin_speedup-inverse-dynamics\r\n",
      "ipython==3.0.0\r\n",
      "Jinja2==2.7.3\r\n",
      "jsonschema==2.4.0\r\n",
      "MarkupSafe==0.23\r\n",
      "matplotlib==1.4.2\r\n",
      "mistune==0.5.1\r\n",
      "nose==1.3.4\r\n",
      "numexpr==2.3.1\r\n",
      "numpy==1.9.2\r\n",
      "oct2py==3.1.0\r\n",
      "pandas==0.16.0\r\n",
      "patsy==0.3.0\r\n",
      "ptyprocess==0.4\r\n",
      "Pygments==2.0.2\r\n",
      "pyparsing==2.0.1\r\n",
      "PySide==1.2.1\r\n",
      "python-dateutil==2.4.2\r\n",
      "pytz==2015.2\r\n",
      "PyYAML==3.11\r\n",
      "pyzmq==14.5.0\r\n",
      "scipy==0.15.1\r\n",
      "seaborn==0.5.1\r\n",
      "six==1.9.0\r\n",
      "snakeviz==0.3.1\r\n",
      "statsmodels==0.6.1\r\n",
      "sympy==0.7.6\r\n",
      "tables==3.1.1\r\n",
      "terminado==0.5\r\n",
      "tornado==4.1\r\n"
     ]
    }
   ],
   "source": [
    "!pip freeze"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
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 },
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