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

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

.. _sphx_glr_auto_examples_programmers_plot_cnl.py:


biogeme.cnl
===========

Example of usage of the cnl module.  This is for programmers who need
examples of use of the functions of the class. The examples are
designed to illustrate the syntax.

:author: Michel Bierlaire
:date: Fri Nov 17 08:27:24 2023

.. GENERATED FROM PYTHON SOURCE LINES 14-25

.. code-block:: default


    import numpy as np
    import pandas as pd
    import biogeme.cnl as cnl
    import biogeme.tools as tools
    import biogeme.biogeme_logging as blog
    from biogeme.nests import OneNestForCrossNestedLogit, NestsForCrossNestedLogit

    logger = blog.get_screen_logger(level=blog.INFO)
    logger.info('Logging on')





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

 .. code-block:: none

    Logging on 




.. GENERATED FROM PYTHON SOURCE LINES 26-27

Definition of the nests.

.. GENERATED FROM PYTHON SOURCE LINES 27-40

.. code-block:: default

    choice_set = ['i', 'j', 'k', 'ell']
    mu_nest_1 = 1.4
    alphas_1 = {'i': 1, 'j': 0.5, 'k': 0.2}
    nest_1 = OneNestForCrossNestedLogit(
        nest_param=mu_nest_1, dict_of_alpha=alphas_1, name='Nest 1'
    )
    mu_nest_2 = 1.2
    alphas_2 = {'j': 0.5, 'k': 0.8, 'ell': 1}
    nest_2 = OneNestForCrossNestedLogit(
        nest_param=mu_nest_2, dict_of_alpha=alphas_2, name='Nest 2'
    )
    nests = NestsForCrossNestedLogit(choice_set=choice_set, tuple_of_nests=(nest_1, nest_2))








.. GENERATED FROM PYTHON SOURCE LINES 41-43

We retrieve the G function of the cross-nested logit, and verify
numerically the implementation of the derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 45-47

.. code-block:: default

    G = cnl.cnl_G(choice_set, nests)








.. GENERATED FROM PYTHON SOURCE LINES 48-49

Draw a random point where to evaluate the function.

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: default

    y = np.random.uniform(low=0.01, high=2, size=4)
    y





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

 .. code-block:: none


    array([1.85473919, 0.51318999, 0.5561585 , 1.36406925])



.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: default

    f, g, h, gdiff, hdiff = tools.checkDerivatives(G, y, names=None, logg=True)
    f





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

 .. code-block:: none

    x               Gradient        FinDiff         Difference 
    x[0]            +9.776899E-01   +9.776899E-01   -5.542010E-10 
    x[1]            +5.602327E-01   +5.602327E-01   -1.488811E-08 
    x[2]            +6.683210E-01   +6.683210E-01   -1.352010E-08 
    x[3]            +9.459859E-01   +9.459859E-01   -2.156753E-09 
    Row             Col             Hessian FinDiff         Difference 
    x[0]            x[0]            +1.601040E-02   +1.601040E-02   +2.188207E-09 
    x[0]            x[1]            -4.416095E-02   -4.416095E-02   +1.228835E-09 
    x[0]            x[2]            -1.264418E-02   -1.264418E-02   +8.741659E-10 
    x[0]            x[3]            +0.000000E+00   +0.000000E+00   +0.000000E+00 
    x[1]            x[0]            -4.416095E-02   -4.416095E-02   -2.127112E-09 
    x[1]            x[1]            +2.819459E-01   +2.819459E-01   +2.296991E-08 
    x[1]            x[2]            -2.561778E-02   -2.561778E-02   +1.098153E-09 
    x[1]            x[3]            -3.558268E-02   -3.558268E-02   -1.176896E-09 
    x[2]            x[0]            -1.264418E-02   -1.264418E-02   -6.444130E-10 
    x[2]            x[1]            -2.561778E-02   -2.561778E-02   -1.207005E-11 
    x[2]            x[2]            +2.216909E-01   +2.216909E-01   +2.104954E-08 
    x[2]            x[3]            -6.355749E-02   -6.355749E-02   -2.485184E-09 
    x[3]            x[0]            +0.000000E+00   +0.000000E+00   +0.000000E+00 
    x[3]            x[1]            -3.558268E-02   -3.558268E-02   +8.337737E-10 
    x[3]            x[2]            -6.355749E-02   -6.355749E-02   +5.604779E-10 
    x[3]            x[3]            +3.930058E-02   +3.930058E-02   +3.785419E-09 

    3.7629483742533636



.. GENERATED FROM PYTHON SOURCE LINES 57-59

.. code-block:: default

    pd.DataFrame(g)






.. 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;
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        .dataframe tbody tr th {
            vertical-align: top;
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        .dataframe thead th {
            text-align: right;
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    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>0.977690</td>
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          <td>0.945986</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 60-62

.. code-block:: default

    pd.DataFrame(h)






.. 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;
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        .dataframe tbody tr th {
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          <td>-0.063557</td>
          <td>0.039301</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: default

    pd.DataFrame(gdiff)






.. 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 {
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        </tr>
        <tr>
          <th>2</th>
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        </tr>
        <tr>
          <th>3</th>
          <td>-2.156753e-09</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: default

    pd.DataFrame(hdiff)







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
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          <td>8.741659e-10</td>
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        </tr>
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          <td>-2.127112e-09</td>
          <td>2.296991e-08</td>
          <td>1.098153e-09</td>
          <td>-1.176896e-09</td>
        </tr>
        <tr>
          <th>2</th>
          <td>-6.444130e-10</td>
          <td>-1.207005e-11</td>
          <td>2.104954e-08</td>
          <td>-2.485184e-09</td>
        </tr>
        <tr>
          <th>3</th>
          <td>0.000000e+00</td>
          <td>8.337737e-10</td>
          <td>5.604779e-10</td>
          <td>3.785419e-09</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 70-71

We do the same for the CDF.

.. GENERATED FROM PYTHON SOURCE LINES 73-76

.. code-block:: default

    xi = np.random.uniform(low=-10, high=10, size=4)
    xi





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

 .. code-block:: none


    array([ 9.9789834 ,  1.02172755,  2.53060465, -6.92151866])



.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: default

    F = cnl.cnl_CDF(choice_set, nests)








.. GENERATED FROM PYTHON SOURCE LINES 80-83

.. code-block:: default

    f, g, h, gdiff, hdiff = tools.checkDerivatives(F, y, names=None, logg=True)
    f





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

 .. code-block:: none

    x               Gradient        FinDiff         Difference 
    x[0]            +2.901734E-02   +2.901734E-02   +3.696049E-09 
    x[1]            +1.394584E-01   +1.394584E-01   +5.265964E-09 
    x[2]            +1.315120E-01   +1.315120E-01   +4.664963E-09 
    x[3]            +5.588572E-02   +5.588572E-02   +3.847727E-09 
    Row             Col             Hessian FinDiff         Difference 
    x[0]            x[0]            -3.478215E-02   -3.478215E-02   -3.157892E-09 
    x[0]            x[1]            +2.153048E-02   +2.153048E-02   +2.995897E-10 
    x[0]            x[2]            +1.554827E-02   +1.554827E-02   +5.218916E-10 
    x[0]            x[3]            +5.833581E-03   +5.833581E-03   +4.022392E-10 
    x[1]            x[0]            +2.153048E-02   +2.153048E-02   +2.265892E-09 
    x[1]            x[1]            -9.062555E-02   -9.062555E-02   +2.166100E-09 
    x[1]            x[2]            +7.693634E-02   +7.693634E-02   +1.922201E-09 
    x[1]            x[3]            +3.123268E-02   +3.123268E-02   +1.911724E-09 
    x[2]            x[0]            +1.554827E-02   +1.554827E-02   +1.884139E-09 
    x[2]            x[1]            +7.693634E-02   +7.693634E-02   +2.199757E-09 
    x[2]            x[2]            -8.741174E-02   -8.741174E-02   +1.227572E-09 
    x[2]            x[3]            +3.177463E-02   +3.177462E-02   +1.951594E-09 
    x[3]            x[0]            +5.833581E-03   +5.833580E-03   +7.555838E-10 
    x[3]            x[1]            +3.123268E-02   +3.123268E-02   +8.846930E-10 
    x[3]            x[2]            +3.177463E-02   +3.177463E-02   +7.653369E-10 
    x[3]            x[3]            -5.318263E-02   -5.318262E-02   -2.425383E-09 

    0.27798626196217313



.. GENERATED FROM PYTHON SOURCE LINES 84-86

.. code-block:: default

    pd.DataFrame(g)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
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          <td>0.055886</td>
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      </tbody>
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    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 87-89

.. code-block:: default

    pd.DataFrame(h)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
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          <td>-0.053183</td>
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    </div>
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    <br />

.. GENERATED FROM PYTHON SOURCE LINES 90-92

.. code-block:: default

    pd.DataFrame(gdiff)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
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    </div>
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    <br />

.. GENERATED FROM PYTHON SOURCE LINES 93-94

.. code-block:: default

    pd.DataFrame(hdiff)





.. raw:: html

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    <br />


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

   **Total running time of the script:** (0 minutes 0.009 seconds)


.. _sphx_glr_download_auto_examples_programmers_plot_cnl.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_cnl.py <plot_cnl.py>`

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

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


.. only:: html

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

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