Latin Hyopercube Sampling
=========================

.. code:: ipython3

    %matplotlib inline
    import pysd
    import numpy as np
    import pandas as pd
    import pyDOE
    import scipy.stats.distributions as dist
    import multiprocessing

.. code:: ipython3

    model = pysd.read_vensim('../../models/Capability_Trap/Capability Trap.mdl')

.. code:: ipython3

    # define the sample space
    ranges = {'Fraction of Effort for Sales':(0,1),
              'Startup Subsidy':(0,2),
              'Startup Subsidy Length':(0,12)}
    
    # generate LHS samples within the unit square
    lhs = pyDOE.lhs(n=len(ranges), samples=2000)
    
    # transform samples into our sample space
    samples = pd.DataFrame(
        data=dist.uniform(loc=[x[0] for x in ranges.values()],
                          scale=[x[1] for x in ranges.values()]).ppf(lhs),
        columns=ranges.keys())
    
    samples.head()




.. raw:: html

    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }
    
        .dataframe tbody tr th {
            vertical-align: top;
        }
    
        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>Fraction of Effort for Sales</th>
          <th>Startup Subsidy</th>
          <th>Startup Subsidy Length</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.611800</td>
          <td>1.367751</td>
          <td>2.058684</td>
        </tr>
        <tr>
          <th>1</th>
          <td>0.851258</td>
          <td>0.305343</td>
          <td>2.631837</td>
        </tr>
        <tr>
          <th>2</th>
          <td>0.114397</td>
          <td>1.789170</td>
          <td>2.471216</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.126074</td>
          <td>1.541200</td>
          <td>2.653847</td>
        </tr>
        <tr>
          <th>4</th>
          <td>0.546046</td>
          <td>0.012404</td>
          <td>6.980225</td>
        </tr>
      </tbody>
    </table>
    </div>



.. code:: ipython3

    def runner(params):
        market = market_model.run(dict(params),return_columns=['Tenure'])
        motiv = motivation_model.run(dict(params),return_columns=['Tenure'])
        return pd.Series({'market':market['Tenure'].iloc[-1], 
                          'motivation':motiv['Tenure'].iloc[-1]})

.. code:: ipython3

    def _apply_df(args):
        df, func, kwargs = args
        return df.apply(func, **kwargs)
    
    def apply_by_multiprocessing(df, func, workers=multiprocessing.cpu_count(), **kwargs):
        pool = multiprocessing.Pool(processes=workers)
        result = pool.map(_apply_df, [(d, func, kwargs) for d in np.array_split(df, workers)])
        pool.close()
        return pd.concat(list(result))
    
    res = apply_by_multiprocessing(samples, runner, axis=1)

.. code:: ipython3

    # define the sample space
    ranges = {'Fraction of Effort for Sales':(0,1),
              'Startup Subsidy':(0,2),
              'Startup Subsidy Length':(0,12)}
    
    # generate LHS samples within the unit square
    lhs = pyDOE.lhs(n=len(ranges), samples=2000)
    
    # transform samples into our sample space
    samples = pd.DataFrame(
        data=dist.uniform(loc=[x[0] for x in ranges.values()],
                          scale=[x[1] for x in ranges.values()]).ppf(lhs),
        columns=ranges.keys())
    
    samples.head()