.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/montecarlo/plot_b03antithetic_explicit.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_b03antithetic_explicit.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_montecarlo_plot_b03antithetic_explicit.py:


Antithetic draws explicitly generated
=====================================

Calculation of a simple integral using Monte-Carlo integration. It
illustrates how to use antothetic draws, explicitly generared.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 20:49:50 2023

.. GENERATED FROM PYTHON SOURCE LINES 12-20

.. code-block:: default


    import numpy as np
    import pandas as pd
    import biogeme.database as db
    import biogeme.biogeme as bio
    from biogeme import draws
    from biogeme.expressions import exp, bioDraws, MonteCarlo








.. GENERATED FROM PYTHON SOURCE LINES 21-23

.. code-block:: default

    R = 10000








.. GENERATED FROM PYTHON SOURCE LINES 24-26

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

.. GENERATED FROM PYTHON SOURCE LINES 26-31

.. code-block:: default

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









.. GENERATED FROM PYTHON SOURCE LINES 32-45

.. code-block:: default

    def halton13(sample_size: int, number_of_draws: int) -> np.array:
        """
        The user can define new draws. For example, Halton draws
        with base 13, skipping the first 10 draws.

        :param sample_size: number of observations for which draws must be
                           generated.
        :param number_of_draws: number of draws to generate.

        """
        return draws.getHaltonDraws(sample_size, number_of_draws, base=13, skip=10)









.. GENERATED FROM PYTHON SOURCE LINES 46-49

.. code-block:: default

    my_draws = {'HALTON13': (halton13, 'Halton draws, base 13, skipping 10')}
    database.setRandomNumberGenerators(my_draws)








.. GENERATED FROM PYTHON SOURCE LINES 50-54

.. code-block:: default

    U = bioDraws('U', 'UNIFORM')
    integrand = exp(U) + exp(1 - U)
    simulatedI = MonteCarlo(integrand) / 2.0








.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: default

    U_halton13 = bioDraws('U_halton13', 'HALTON13')
    integrand_halton13 = exp(U_halton13) + exp(1 - U_halton13)
    simulatedI_halton13 = MonteCarlo(integrand_halton13) / 2.0








.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: default

    U_mlhs = bioDraws('U_mlhs', 'UNIFORM_MLHS')
    integrand_mlhs = exp(U_mlhs) + exp(1 - U_mlhs)
    simulatedI_mlhs = MonteCarlo(integrand_mlhs) / 2.0








.. GENERATED FROM PYTHON SOURCE LINES 65-67

.. code-block:: default

    trueI = exp(1.0) - 1.0








.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: default

    error = simulatedI - trueI








.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: default

    error_halton13 = simulatedI_halton13 - trueI








.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: default

    error_mlhs = simulatedI_mlhs - trueI








.. GENERATED FROM PYTHON SOURCE LINES 77-87

.. code-block:: default

    simulate = {
        'Analytical Integral': trueI,
        'Simulated Integral': simulatedI,
        'Error             ': error,
        'Simulated Integral (Halton13)': simulatedI_halton13,
        'Error (Halton13)             ': error_halton13,
        'Simulated Integral (MLHS)': simulatedI_mlhs,
        'Error (MLHS)             ': error_mlhs,
    }








.. GENERATED FROM PYTHON SOURCE LINES 88-91

.. code-block:: default

    biosim = bio.BIOGEME(database, simulate)
    biosim.modelName = 'b03antithetic_explicit'








.. GENERATED FROM PYTHON SOURCE LINES 92-95

.. 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>Analytical Integral</th>
          <th>Simulated Integral</th>
          <th>Error</th>
          <th>Simulated Integral (Halton13)</th>
          <th>Error (Halton13)</th>
          <th>Simulated Integral (MLHS)</th>
          <th>Error (MLHS)</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>1.718282</td>
          <td>1.718282</td>
          <td>3.982962e-07</td>
          <td>1.718282</td>
          <td>1.315155e-08</td>
          <td>1.718282</td>
          <td>4.733991e-13</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 96-110

.. code-block:: default

    print(f"Analytical integral: {results.iloc[0]['Analytical Integral']:.6f}")
    print(
        f"         \t{'Uniform (Anti)':>15}\t{'Halton13 (Anti)':>15}\t{'MLHS (Anti)':>15}"
    )
    print(
        f"Simulated\t{results.iloc[0]['Simulated Integral']:>15.6g}\t"
        f"{results.iloc[0]['Simulated Integral (Halton13)']:>15.6g}\t"
        f"{results.iloc[0]['Simulated Integral (MLHS)']:>15.6g}"
    )
    print(
        f"Error\t\t{results.iloc[0]['Error             ']:>15.6g}\t"
        f"{results.iloc[0]['Error (Halton13)             ']:>15.6g}\t"
        f"{results.iloc[0]['Error (MLHS)             ']:>15.6g}"
    )




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

 .. code-block:: none

    Analytical integral: 1.718282
                     Uniform (Anti) Halton13 (Anti)     MLHS (Anti)
    Simulated               1.71828         1.71828         1.71828
    Error               3.98296e-07     1.31515e-08     4.73399e-13





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

   **Total running time of the script:** (0 minutes 40.093 seconds)


.. _sphx_glr_download_auto_examples_montecarlo_plot_b03antithetic_explicit.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_b03antithetic_explicit.py <plot_b03antithetic_explicit.py>`

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

      :download:`Download Jupyter notebook: plot_b03antithetic_explicit.ipynb <plot_b03antithetic_explicit.ipynb>`


.. only:: html

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

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