.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/timing/plot03_mixtures.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_timing_plot03_mixtures.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_timing_plot03_mixtures.py:


Timing of a logit model
=======================

Michel Bierlaire
Tue Jul 2 14:48:52 2024

.. GENERATED FROM PYTHON SOURCE LINES 9-12

.. code-block:: Python


    from tabulate import tabulate


.. GENERATED FROM PYTHON SOURCE LINES 13-14

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

.. GENERATED FROM PYTHON SOURCE LINES 14-31

.. code-block:: Python

    from biogeme.data.swissmetro import (
        CAR_AV_SP,
        CAR_CO_SCALED,
        CAR_TT_SCALED,
        CHOICE,
        SM_AV,
        SM_COST_SCALED,
        SM_TT_SCALED,
        TRAIN_AV_SP,
        TRAIN_COST_SCALED,
        TRAIN_TT_SCALED,
        read_data,
    )
    from biogeme.expressions import Beta, Draws, MonteCarlo, log
    from biogeme.models import logit
    from timing_expression import timing_expression


.. GENERATED FROM PYTHON SOURCE LINES 32-33

Parameters to be estimated

.. GENERATED FROM PYTHON SOURCE LINES 33-37

.. code-block:: Python

    asc_car = Beta('asc_car', 0, None, None, 0)
    asc_train = Beta('asc_train', 0, None, None, 0)
    b_cost = Beta('b_cost', 0, None, None, 0)


.. GENERATED FROM PYTHON SOURCE LINES 38-40

Define a random parameter, normally distributed, designed to be used
for Monte-Carlo simulation.

.. GENERATED FROM PYTHON SOURCE LINES 40-42

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 43-44

It is advised *not* to use 0 as starting value for the following parameter.

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python

    b_time_s = Beta('b_time_s', 1, None, None, 0)
    b_time_rnd = b_time + b_time_s * Draws('b_time_rnd', 'NORMAL')


.. GENERATED FROM PYTHON SOURCE LINES 48-49

Definition of the utility functions.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: Python

    v_train = asc_train + b_time_rnd * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
    v_swissmetro = b_time_rnd * SM_TT_SCALED + b_cost * SM_COST_SCALED
    v_car = asc_car + b_time_rnd * CAR_TT_SCALED + b_cost * CAR_CO_SCALED


.. GENERATED FROM PYTHON SOURCE LINES 54-55

Associate utility functions with the numbering of alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 55-57

.. code-block:: Python

    V = {1: v_train, 2: v_swissmetro, 3: v_car}


.. GENERATED FROM PYTHON SOURCE LINES 58-59

Associate the availability conditions with the alternatives.

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: Python

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


.. GENERATED FROM PYTHON SOURCE LINES 62-63

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

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: Python

    prob = logit(V, av, CHOICE)


.. GENERATED FROM PYTHON SOURCE LINES 66-67

We integrate over b_time_rnd using Monte-Carlo.

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: Python

    log_probability = log(MonteCarlo(prob))


.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    database = read_data()


.. GENERATED FROM PYTHON SOURCE LINES 73-74

Number of draws

.. GENERATED FROM PYTHON SOURCE LINES 74-77

.. code-block:: Python

    number_of_draws = 100



.. GENERATED FROM PYTHON SOURCE LINES 78-79

Timing

.. GENERATED FROM PYTHON SOURCE LINES 79-88

.. code-block:: Python

    timing_results = timing_expression(
        the_expression=log_probability,
        the_database=database,
        number_of_draws=number_of_draws,
    )
    results = [[k, f'{v:.3g}'] for k, v in timing_results.items()]
    print(f'With {number_of_draws} draws...')
    print(tabulate(results, headers=['', 'Time (in sec.)'], tablefmt='github'))


.. GENERATED FROM PYTHON SOURCE LINES 89-90

Number of draws

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: Python

    number_of_draws = 1000


.. GENERATED FROM PYTHON SOURCE LINES 93-94

Timing

.. GENERATED FROM PYTHON SOURCE LINES 94-102

.. code-block:: Python

    timing_results = timing_expression(
        the_expression=log_probability,
        the_database=database,
        number_of_draws=number_of_draws,
    )
    results = [[k, f'{v:.3g}'] for k, v in timing_results.items()]
    print(f'With {number_of_draws} draws...')
    print(tabulate(results, headers=['', 'Time (in sec.)'], tablefmt='github'))


.. _sphx_glr_download_auto_examples_timing_plot03_mixtures.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot03_mixtures.ipynb <plot03_mixtures.ipynb>`

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

      :download:`Download Python source code: plot03_mixtures.py <plot03_mixtures.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot03_mixtures.zip <plot03_mixtures.zip>`


.. only:: html

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

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