.. 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.

Michel Bierlaire, EPFL
Sat Jun 28 2025, 21:09:19

.. GENERATED FROM PYTHON SOURCE LINES 12-22

.. code-block:: Python


    import numpy as np
    import pandas as pd
    from IPython.core.display_functions import display

    from biogeme.biogeme import BIOGEME
    from biogeme.database import Database
    from biogeme.draws import RandomNumberGeneratorTuple, get_halton_draws
    from biogeme.expressions import Draws, MonteCarlo, exp








.. GENERATED FROM PYTHON SOURCE LINES 23-25

.. code-block:: Python

    R = 2_000_000








.. GENERATED FROM PYTHON SOURCE LINES 26-28

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

.. GENERATED FROM PYTHON SOURCE LINES 28-33

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 34-47

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









.. GENERATED FROM PYTHON SOURCE LINES 48-54

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: Python

    U = Draws('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 = Draws('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 = Draws('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 93-98

.. code-block:: Python

    biosim = BIOGEME(
        database, simulate, random_number_generators=my_draws, number_of_draws=R
    )
    biosim.model_name = 'b03antithetic_explicit'








.. GENERATED FROM PYTHON SOURCE LINES 99-102

.. code-block:: Python

    results = biosim.simulate(the_beta_values={})
    display(results)





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

 .. code-block:: none

       Analytical Integral  ...  Error (MLHS)             
    0             1.718282  ...              -4.418821e-11

    [1 rows x 7 columns]




.. GENERATED FROM PYTHON SOURCE LINES 103-117

.. 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               1.71826         1.71828         1.71828
    Error              -1.74385e-05     5.57648e-08    -4.41882e-11





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

   **Total running time of the script:** (0 minutes 0.423 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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