.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/montecarlo/plot_b03antithetic.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.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_montecarlo_plot_b03antithetic.py:


Antithetic draws
================

Calculation of a simple integral using Monte-Carlo integration. It
illustrates how to use antithetic draws.

:author: Michel Bierlaire, EPFL
:date: Thu Apr 13 20:48:02 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

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

.. GENERATED FROM PYTHON SOURCE LINES 24-29

.. code-block:: Python

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









.. GENERATED FROM PYTHON SOURCE LINES 30-48

.. code-block:: Python

    def halton13_anti(sample_size: int, number_of_draws: int) -> np.array:
        """The user can define new draws. For example, antithetic 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.

        """

        # We first generate half of the number of requested draws.
        the_draws = draws.get_halton_draws(
            sample_size, int(number_of_draws / 2.0), base=13, skip=10
        )
        # We complement them with their antithetic version.
        return np.concatenate((the_draws, 1 - the_draws), axis=1)









.. GENERATED FROM PYTHON SOURCE LINES 49-57

.. code-block:: Python

    mydraws = {
        'HALTON13_ANTI': RandomNumberGeneratorTuple(
            halton13_anti,
            'Antithetic Halton draws, base 13, skipping 10',
        )
    }
    database.set_random_number_generators(mydraws)








.. GENERATED FROM PYTHON SOURCE LINES 58-59

Integrate with antithetic pseudo-random number generator.

.. GENERATED FROM PYTHON SOURCE LINES 59-62

.. code-block:: Python

    integrand = exp(bioDraws('U', 'UNIFORM_ANTI'))
    simulated_integral = MonteCarlo(integrand)








.. GENERATED FROM PYTHON SOURCE LINES 63-64

Integrate with antithetic Halton draws, base 13.

.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. code-block:: Python

    integrand_halton13 = exp(bioDraws('U_halton13', 'HALTON13_ANTI'))
    simulated_integral_halton13 = MonteCarlo(integrand_halton13)








.. GENERATED FROM PYTHON SOURCE LINES 68-69

Integrate with antithetic MLHS.

.. GENERATED FROM PYTHON SOURCE LINES 69-72

.. code-block:: Python

    integrand_mlhs = exp(bioDraws('U_mlhs', 'UNIFORM_MLHS_ANTI'))
    simulated_integral_mlhs = MonteCarlo(integrand_mlhs)








.. GENERATED FROM PYTHON SOURCE LINES 73-74

True value

.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

    true_integral = exp(1.0) - 1.0








.. GENERATED FROM PYTHON SOURCE LINES 77-78

Number of draws.

.. GENERATED FROM PYTHON SOURCE LINES 78-80

.. code-block:: Python

    R = 20000








.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python

    error = simulated_integral - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: Python

    error_halton13 = simulated_integral_halton13 - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: Python

    error_mlhs = simulated_integral_mlhs - true_integral








.. GENERATED FROM PYTHON SOURCE LINES 90-101

.. 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 102-107

.. code-block:: Python

    biosim = bio.BIOGEME(database, simulate)
    biosim.modelName = 'b03antithetic'
    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>1.724525</td>
          <td>0.006243</td>
          <td>1.718331</td>
          <td>0.000049</td>
          <td>1.717795</td>
          <td>-0.000487</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 108-109

Reorganize the results.

.. GENERATED FROM PYTHON SOURCE LINES 109-123

.. 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               1.72453         1.71833         1.71779
    Error                0.00624328     4.91843e-05    -0.000487064





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

   **Total running time of the script:** (0 minutes 0.010 seconds)


.. _sphx_glr_download_auto_examples_montecarlo_plot_b03antithetic.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.ipynb <plot_b03antithetic.ipynb>`

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

      :download:`Download Python source code: plot_b03antithetic.py <plot_b03antithetic.py>`

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

      :download:`Download zipped: plot_b03antithetic.zip <plot_b03antithetic.zip>`


.. only:: html

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

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