.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/montecarlo/plot_b01simple_integral.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_b01simple_integral.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_montecarlo_plot_b01simple_integral.py:


Simple integral
===============

Calculation of a simple integral using Monte-Carlo integration.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 20:42:24 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-19

.. code-block:: default


    import pandas as pd
    import biogeme.database as db
    import biogeme.biogeme as bio
    from biogeme.expressions import exp, bioDraws, MonteCarlo
    from biogeme.tools import TemporaryFile








.. GENERATED FROM PYTHON SOURCE LINES 20-22

We create a fake database with one entry, as it is required
to store the draws

.. GENERATED FROM PYTHON SOURCE LINES 22-26

.. code-block:: default

    df = pd.DataFrame()
    df['FakeColumn'] = [1.0]
    database = db.Database('fakeDatabase', df)








.. GENERATED FROM PYTHON SOURCE LINES 27-30

.. code-block:: default

    integrand = exp(bioDraws('U', 'UNIFORM'))
    simulatedI = MonteCarlo(integrand)








.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: default

    trueI = exp(1.0) - 1.0








.. GENERATED FROM PYTHON SOURCE LINES 34-37

.. code-block:: default

    R = 200
    MULTIPLIER = 100000








.. GENERATED FROM PYTHON SOURCE LINES 38-39

Create a parameter file to set the number of draws.

.. GENERATED FROM PYTHON SOURCE LINES 39-64

.. code-block:: default

    with TemporaryFile() as filename:
        with open(filename, 'w', encoding='utf-8') as f:
            print('[MonteCarlo]', file=f)
            print(f'number_of_draws = {R}', file=f)

        sampleVariance = MonteCarlo(integrand * integrand) - simulatedI * simulatedI
        stderr = (sampleVariance / R) ** 0.5
        error = simulatedI - trueI

        simulate = {
            'Analytical Integral': trueI,
            'Simulated Integral': simulatedI,
            'Sample variance   ': sampleVariance,
            'Std Error         ': stderr,
            'Error             ': error,
        }

        biosim = bio.BIOGEME(database, simulate, parameter_file=filename)
        R = biosim.number_of_draws
        biosim.modelName = f'01simpleIntegral_{R}'
        results = biosim.simulate(theBetaValues={})
        print(f'Number of draws: {R}')
        for c in results.columns:
            print(f'{c}: {results.loc[0,c]}')





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

 .. code-block:: none

    Number of draws: 200
    Analytical Integral: 1.718281828459045
    Simulated Integral: 1.7343161785792407
    Sample variance   : 0.23925624415037472
    Std Error         : 0.0345872985466034
    Error             : 0.016034350120195606




.. GENERATED FROM PYTHON SOURCE LINES 65-66

Create a parameter file to set the number of draws.

.. GENERATED FROM PYTHON SOURCE LINES 66-77

.. code-block:: default

    with TemporaryFile() as filename:
        with open(filename, 'w', encoding='utf-8') as f:
            print('[MonteCarlo]', file=f)
            print(f'number_of_draws = {MULTIPLIER * R}', file=f)

        biogeme2 = bio.BIOGEME(database, simulate, parameter_file=filename)
        biogeme2.modelName = '01simpleIntegral_{multiplier*R}'
        results2 = biogeme2.simulate(theBetaValues={})
        print(f'Number of draws: {MULTIPLIER * R}')
        for c in results2.columns:
            print(f'{c}: {results2.loc[0, c]}')




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

 .. code-block:: none

    Number of draws: 20000000
    Analytical Integral: 1.718281828459045
    Simulated Integral: 1.7182868032455962
    Sample variance   : 0.2420428918652573
    Std Error         : 0.034788136761348495
    Error             : 4.974786551148469e-06





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

   **Total running time of the script:** (0 minutes 15.244 seconds)


.. _sphx_glr_download_auto_examples_montecarlo_plot_b01simple_integral.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_b01simple_integral.py <plot_b01simple_integral.py>`

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

      :download:`Download Jupyter notebook: plot_b01simple_integral.ipynb <plot_b01simple_integral.ipynb>`


.. only:: html

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

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