.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/montecarlo/plot_b05normal_mixture_monte_carlo.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_montecarlo_plot_b05normal_mixture_monte_carlo.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_montecarlo_plot_b05normal_mixture_monte_carlo.py:


Monte-Carlo integration
=======================

Calculation of a mixtures of logit models where the integral is
calculated using numerical integration and Monte-Carlo integration
with various types of draws.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 20:58:50 2023

.. GENERATED FROM PYTHON SOURCE LINES 13-40

.. code-block:: default



    import biogeme.biogeme as bio
    from biogeme import models
    import biogeme.distributions as dist
    from biogeme.expressions import (
        Expression,
        Integrate,
        RandomVariable,
        MonteCarlo,
        bioDraws,
    )

    from swissmetro_one import (
        database,
        TRAIN_TT_SCALED,
        TRAIN_COST_SCALED,
        SM_TT_SCALED,
        SM_COST_SCALED,
        CAR_TT_SCALED,
        CAR_CO_SCALED,
        TRAIN_AV_SP,
        SM_AV,
        CAR_AV_SP,
        CHOICE,
    )








.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: default

    R = 10000








.. GENERATED FROM PYTHON SOURCE LINES 44-45

Parameters

.. GENERATED FROM PYTHON SOURCE LINES 45-52

.. code-block:: default

    ASC_CAR = 0.137
    ASC_TRAIN = -0.402
    ASC_SM = 0
    B_TIME = -2.26
    B_TIME_S = 1.66
    B_COST = -1.29








.. GENERATED FROM PYTHON SOURCE LINES 53-54

Generate several versions of the error component.

.. GENERATED FROM PYTHON SOURCE LINES 54-64

.. code-block:: default

    omega = RandomVariable('omega')
    density = dist.normalpdf(omega)
    B_TIME_RND = B_TIME + B_TIME_S * omega
    B_TIME_RND_normal = B_TIME + B_TIME_S * bioDraws('B_NORMAL', 'NORMAL')
    B_TIME_RND_anti = B_TIME + B_TIME_S * bioDraws('B_ANTI', 'NORMAL_ANTI')
    B_TIME_RND_halton = B_TIME + B_TIME_S * bioDraws('B_HALTON', 'NORMAL_HALTON2')
    B_TIME_RND_mlhs = B_TIME + B_TIME_S * bioDraws('B_MLHS', 'NORMAL_MLHS')
    B_TIME_RND_antimlhs = B_TIME + B_TIME_S * bioDraws('B_ANTIMLHS', 'NORMAL_MLHS_ANTI')









.. GENERATED FROM PYTHON SOURCE LINES 65-88

.. code-block:: default

    def logit(the_b_time_rnd: Expression) -> Expression:
        """
        Calculate the conditional logit model for a given random parameter.

        :param the_b_time_rnd: expression for the random parameter.

        :return: logit model to be integrated.
        """
        v_1 = ASC_TRAIN + the_b_time_rnd * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
        v_2 = ASC_SM + the_b_time_rnd * SM_TT_SCALED + B_COST * SM_COST_SCALED
        v_3 = ASC_CAR + the_b_time_rnd * CAR_TT_SCALED + B_COST * CAR_CO_SCALED

        # Associate utility functions with the numbering of alternatives
        v = {1: v_1, 2: v_2, 3: v_3}

        # Associate the availability conditions with the alternatives
        av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

        # The choice model is a logit, with availability conditions
        integrand = models.logit(v, av, CHOICE)
        return integrand









.. GENERATED FROM PYTHON SOURCE LINES 89-90

Generate each integral.

.. GENERATED FROM PYTHON SOURCE LINES 90-97

.. code-block:: default

    numericalI = Integrate(logit(B_TIME_RND) * density, 'omega')
    normal = MonteCarlo(logit(B_TIME_RND_normal))
    anti = MonteCarlo(logit(B_TIME_RND_anti))
    halton = MonteCarlo(logit(B_TIME_RND_halton))
    mlhs = MonteCarlo(logit(B_TIME_RND_mlhs))
    antimlhs = MonteCarlo(logit(B_TIME_RND_antimlhs))








.. GENERATED FROM PYTHON SOURCE LINES 98-107

.. code-block:: default

    simulate = {
        'Numerical': numericalI,
        'MonteCarlo': normal,
        'Antithetic': anti,
        'Halton': halton,
        'MLHS': mlhs,
        'Antithetic MLHS': antimlhs,
    }








.. GENERATED FROM PYTHON SOURCE LINES 108-111

.. code-block:: default

    biosim = bio.BIOGEME(database, simulate)
    biosim.number_of_draws = R








.. GENERATED FROM PYTHON SOURCE LINES 112-115

.. code-block:: default

    results = biosim.simulate(theBetaValues={})
    results






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <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>Numerical</th>
          <th>MonteCarlo</th>
          <th>Antithetic</th>
          <th>Halton</th>
          <th>MLHS</th>
          <th>Antithetic MLHS</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.63785</td>
          <td>0.637861</td>
          <td>0.63787</td>
          <td>0.637839</td>
          <td>0.637839</td>
          <td>0.637861</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 116-119

.. code-block:: default

    print(f'Number of draws: {R}')
    for c in results.columns:
        print(f'{c}:\t{results.loc[0,c]}')




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Number of draws: 10000
    Numerical:      0.6378498355784457
    MonteCarlo:     0.6378606134588761
    Antithetic:     0.6378697548073272
    Halton: 0.6378394335915274
    MLHS:   0.6378393019627554
    Antithetic MLHS:        0.6378608572485519





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (2 minutes 33.898 seconds)


.. _sphx_glr_download_auto_examples_montecarlo_plot_b05normal_mixture_monte_carlo.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example




    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_b05normal_mixture_monte_carlo.py <plot_b05normal_mixture_monte_carlo.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_b05normal_mixture_monte_carlo.ipynb <plot_b05normal_mixture_monte_carlo.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_