.. 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 antithetic draws, explicitly generated.

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

.. GENERATED FROM PYTHON SOURCE LINES 12-21

.. code-block:: Python


    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
    from biogeme.native_draws import RandomNumberGeneratorTuple








.. GENERATED FROM PYTHON SOURCE LINES 22-24

.. code-block:: Python

    R = 10000








.. GENERATED FROM PYTHON SOURCE LINES 25-27

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

.. GENERATED FROM PYTHON SOURCE LINES 27-32

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 33-46

.. code-block:: Python

    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.get_halton_draws(sample_size, number_of_draws, base=13, skip=10)









.. GENERATED FROM PYTHON SOURCE LINES 47-54

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: Python

    U_halton13 = bioDraws('U_halton13', 'HALTON13')
    integrand_halton13 = exp(U_halton13) + exp(1 - U_halton13)
    simulated_integral_halton13 = MonteCarlo(integrand_halton13) / 2.0








.. GENERATED FROM PYTHON SOURCE LINES 65-69

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    true_integral = exp(1.0) - 1.0








.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: Python

    error = simulated_integral - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: Python

    error_halton13 = simulated_integral_halton13 - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: Python

    error_mlhs = simulated_integral_mlhs - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 82-92

.. code-block:: Python

    simulate = {
        'Analytical Integral': true_integral,
        'Simulated Integral': simulated_integral,
        'Error             ': error,
        'Simulated Integral (Halton13)': simulated_integral_halton13,
        'Error (Halton13)             ': error_halton13,
        'Simulated Integral (MLHS)': simulated_integral_mlhs,
        'Error (MLHS)             ': error_mlhs,
    }








.. GENERATED FROM PYTHON SOURCE LINES 93-96

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 97-100

.. code-block:: Python

    results = biosim.simulate(the_beta_values={})
    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>1.725178</td>
          <td>0.006897</td>
          <td>1.718669</td>
          <td>0.000387</td>
          <td>1.71837</td>
          <td>0.000088</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 101-115

.. code-block:: Python

    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               1.72518         1.71867         1.71837
    Error                0.00689653     0.000387301      8.7832e-05





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

   **Total running time of the script:** (0 minutes 0.012 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-jupyter

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

    .. 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-zip

      :download:`Download zipped: plot_b03antithetic_explicit.zip <plot_b03antithetic_explicit.zip>`


.. only:: html

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

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