.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/swissmetro/plot_b25triangular_mixture.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_swissmetro_plot_b25triangular_mixture.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_swissmetro_plot_b25triangular_mixture.py:


Triangular mixture of logit
===========================

 Example of a mixture of logit models, using Monte-Carlo integration.
 The mixing distribution is specified by the user. Here, a triangular
 distribution.

:author: Michel Bierlaire, EPFL
:date: Wed Apr 12 18:24:18 2023

.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: default


    import numpy as np
    import biogeme.biogeme_logging as blog
    import biogeme.biogeme as bio
    from biogeme import models
    from biogeme.expressions import Beta, bioDraws, log, MonteCarlo








.. GENERATED FROM PYTHON SOURCE LINES 23-24

See the data processing script: :ref:`swissmetro_data`.

.. GENERATED FROM PYTHON SOURCE LINES 24-41

.. code-block:: default

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

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Example b25triangular_mixture.py')





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

 .. code-block:: none

    Example b25triangular_mixture.py 




.. GENERATED FROM PYTHON SOURCE LINES 42-43

Parameters to be estimated.

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: default

    ASC_CAR = Beta('ASC_CAR', 0, None, None, 0)
    ASC_TRAIN = Beta('ASC_TRAIN', 0, None, None, 0)
    ASC_SM = Beta('ASC_SM', 0, None, None, 1)
    B_COST = Beta('B_COST', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 49-53

Define a random parameter with a triangular distribution, designed
to be used for Monte-Carlo simulation. The triangular distribution
is not directly available from Biogeme. The draws have to be
generated by a function provided by the user.

.. GENERATED FROM PYTHON SOURCE LINES 55-56

Mean of the distribution.

.. GENERATED FROM PYTHON SOURCE LINES 56-58

.. code-block:: default

    B_TIME = Beta('B_TIME', 0, None, None, 0)








.. GENERATED FROM PYTHON SOURCE LINES 59-61

Scale of the distribution.
It is advised not to use 0 as starting value for the following parameter.

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: default

    B_TIME_S = Beta('B_TIME_S', 1, None, None, 0)









.. GENERATED FROM PYTHON SOURCE LINES 65-66

Function generating the draws.

.. GENERATED FROM PYTHON SOURCE LINES 66-74

.. code-block:: default

    def the_triangular_generator(sample_size: int, number_of_draws: int) -> np.ndarray:
        """
        User-defined random number generator to the database.
        See the numpy.random documentation to obtain a list of other distributions.
        """
        return np.random.triangular(-1, 0, 1, (sample_size, number_of_draws))









.. GENERATED FROM PYTHON SOURCE LINES 75-76

Associate the function with a name.

.. GENERATED FROM PYTHON SOURCE LINES 76-83

.. code-block:: default

    myRandomNumberGenerators = {
        'TRIANGULAR': (
            the_triangular_generator,
            'Draws from a triangular distribution',
        )
    }








.. GENERATED FROM PYTHON SOURCE LINES 84-85

Submit the generator to the database.

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: default

    database.setRandomNumberGenerators(myRandomNumberGenerators)








.. GENERATED FROM PYTHON SOURCE LINES 88-90

Define a random parameter with a triangular distribution, designed to be used
for Monte-Carlo simulation.

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: default

    B_TIME_RND = B_TIME + B_TIME_S * bioDraws('B_TIME_RND', 'TRIANGULAR')








.. GENERATED FROM PYTHON SOURCE LINES 93-94

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 94-98

.. code-block:: default

    V1 = ASC_TRAIN + B_TIME_RND * TRAIN_TT_SCALED + B_COST * TRAIN_COST_SCALED
    V2 = ASC_SM + B_TIME_RND * SM_TT_SCALED + B_COST * SM_COST_SCALED
    V3 = ASC_CAR + B_TIME_RND * CAR_TT_SCALED + B_COST * CAR_CO_SCALED








.. GENERATED FROM PYTHON SOURCE LINES 99-100

Associate utility functions with the numbering of alternatives

.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. code-block:: default

    V = {1: V1, 2: V2, 3: V3}








.. GENERATED FROM PYTHON SOURCE LINES 103-104

Associate the availability conditions with the alternatives

.. GENERATED FROM PYTHON SOURCE LINES 104-106

.. code-block:: default

    av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}








.. GENERATED FROM PYTHON SOURCE LINES 107-108

Conditional to B_TIME_RND, we have a logit model (called the kernel)

.. GENERATED FROM PYTHON SOURCE LINES 108-110

.. code-block:: default

    prob = models.logit(V, av, CHOICE)








.. GENERATED FROM PYTHON SOURCE LINES 111-112

We integrate over B_TIME_RND using Monte-Carlo

.. GENERATED FROM PYTHON SOURCE LINES 112-114

.. code-block:: default

    logprob = log(MonteCarlo(prob))








.. GENERATED FROM PYTHON SOURCE LINES 115-119

Create the Biogeme object.  As the objective is to illustrate the
syntax, we calculate the Monte-Carlo approximation with a small
number of draws. To achieve that, we provide a parameter file
different from the default one.

.. GENERATED FROM PYTHON SOURCE LINES 119-122

.. code-block:: default

    the_biogeme = bio.BIOGEME(database, logprob, parameter_file='few_draws.toml')
    the_biogeme.modelName = 'b25triangular_mixture'





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

 .. code-block:: none

    File few_draws.toml has been parsed. 




.. GENERATED FROM PYTHON SOURCE LINES 123-124

Estimate the parameters

.. GENERATED FROM PYTHON SOURCE LINES 124-126

.. code-block:: default

    results = the_biogeme.estimate()





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

 .. code-block:: none

    *** Initial values of the parameters are obtained from the file __b25triangular_mixture.iter 
    Cannot read file __b25triangular_mixture.iter. Statement is ignored. 
    Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds] 
    ** Optimization: Newton with trust region for simple bounds 
    Iter.         ASC_CAR       ASC_TRAIN          B_COST          B_TIME        B_TIME_S     Function    Relgrad   Radius      Rho      
        0           -0.24           -0.64           -0.43              -1             0.9      5.4e+03      0.042       10        1   ++ 
        1           0.033            -0.5              -1            -1.7             3.1      5.2e+03      0.029    1e+02        1   ++ 
        2           0.095           -0.43            -1.2            -2.1             3.5      5.2e+03     0.0039    1e+03      1.1   ++ 
        3            0.13            -0.4            -1.3            -2.2             3.8      5.2e+03    0.00049    1e+04      1.1   ++ 
        4            0.13            -0.4            -1.3            -2.2             3.9      5.2e+03    6.4e-06    1e+05        1   ++ 
        5            0.13            -0.4            -1.3            -2.2             3.9      5.2e+03    1.1e-09    1e+05        1   ++ 
    Results saved in file b25triangular_mixture.html 
    Results saved in file b25triangular_mixture.pickle 




.. GENERATED FROM PYTHON SOURCE LINES 127-129

.. code-block:: default

    print(results.short_summary())





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

 .. code-block:: none

    Results for model b25triangular_mixture
    Nbr of parameters:              5
    Sample size:                    6768
    Excluded data:                  3960
    Final log likelihood:           -5215.848
    Akaike Information Criterion:   10441.7
    Bayesian Information Criterion: 10475.8





.. GENERATED FROM PYTHON SOURCE LINES 130-132

.. code-block:: default

    pandas_results = results.getEstimatedParameters()
    pandas_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>Value</th>
          <th>Rob. Std err</th>
          <th>Rob. t-test</th>
          <th>Rob. p-value</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>ASC_CAR</th>
          <td>0.131377</td>
          <td>0.052072</td>
          <td>2.522989</td>
          <td>1.163620e-02</td>
        </tr>
        <tr>
          <th>ASC_TRAIN</th>
          <td>-0.400569</td>
          <td>0.065834</td>
          <td>-6.084497</td>
          <td>1.168578e-09</td>
        </tr>
        <tr>
          <th>B_COST</th>
          <td>-1.277153</td>
          <td>0.085682</td>
          <td>-14.905718</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME</th>
          <td>-2.244201</td>
          <td>0.117954</td>
          <td>-19.026152</td>
          <td>0.000000e+00</td>
        </tr>
        <tr>
          <th>B_TIME_S</th>
          <td>3.893612</td>
          <td>0.292471</td>
          <td>13.312801</td>
          <td>0.000000e+00</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 8.600 seconds)


.. _sphx_glr_download_auto_examples_swissmetro_plot_b25triangular_mixture.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_b25triangular_mixture.py <plot_b25triangular_mixture.py>`

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

      :download:`Download Jupyter notebook: plot_b25triangular_mixture.ipynb <plot_b25triangular_mixture.ipynb>`


.. only:: html

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

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