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

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

.. _sphx_glr_auto_examples_programmers_plot_results.py:


biogeme.results_processing
==========================

Examples of use of several functions.

This is designed for programmers who need examples of use of the
functions of the module. The examples are designed to illustrate the
syntax. They do not correspond to any meaningful model.

Michel Bierlaire
Mon Oct 7 18:46:39 2024

.. GENERATED FROM PYTHON SOURCE LINES 15-35

.. code-block:: Python


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

    from biogeme.biogeme import BIOGEME
    from biogeme.database import Database
    from biogeme.expressions import Beta, Variable, exp
    from biogeme.results_processing import (
        EstimateVarianceCovariance,
        EstimationResults,
        calc_p_value,
        compile_estimation_results,
        get_f12,
        get_html_estimated_parameters,
        get_latex_estimated_parameters,
        get_pandas_correlation_results,
        get_pandas_estimated_parameters,
    )
    from biogeme.version import get_text








.. GENERATED FROM PYTHON SOURCE LINES 36-37

Version of Biogeme.

.. GENERATED FROM PYTHON SOURCE LINES 37-39

.. code-block:: Python

    print(get_text())





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

 .. code-block:: none

    biogeme 3.3.1 [2025-09-03]
    Home page: http://biogeme.epfl.ch
    Submit questions to https://groups.google.com/d/forum/biogeme
    Michel Bierlaire, Transport and Mobility Laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL)





.. GENERATED FROM PYTHON SOURCE LINES 40-41

Definition of a database

.. GENERATED FROM PYTHON SOURCE LINES 41-55

.. code-block:: Python

    df = pd.DataFrame(
        {
            'Person': [1, 1, 1, 2, 2],
            'Exclude': [0, 0, 1, 0, 1],
            'Variable1': [1, 2, 3, 4, 5],
            'Variable2': [10, 20, 30, 40, 50],
            'Choice': [1, 2, 3, 1, 2],
            'Av1': [0, 1, 1, 1, 1],
            'Av2': [1, 1, 1, 1, 1],
            'Av3': [0, 1, 1, 1, 1],
        }
    )
    display(df)





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

 .. code-block:: none

       Person  Exclude  Variable1  Variable2  Choice  Av1  Av2  Av3
    0       1        0          1         10       1    0    1    0
    1       1        0          2         20       2    1    1    1
    2       1        1          3         30       3    1    1    1
    3       2        0          4         40       1    1    1    1
    4       2        1          5         50       2    1    1    1




.. GENERATED FROM PYTHON SOURCE LINES 56-58

.. code-block:: Python

    my_data = Database('test', df)








.. GENERATED FROM PYTHON SOURCE LINES 59-60

Definition of various expressions

.. GENERATED FROM PYTHON SOURCE LINES 60-68

.. code-block:: Python

    Variable1 = Variable('Variable1')
    Variable2 = Variable('Variable2')
    beta1 = Beta('beta1', -1.0, -3, 3, 0)
    beta2 = Beta('beta2', 2.0, -3, 10, 0)
    likelihood = -(beta1**2) * Variable1 - exp(beta2 * beta1) * Variable2 - beta2**4
    simul = beta1 / Variable1 + beta2 / Variable2
    dict_of_expressions = {'log_like': likelihood, 'beta1': beta1, 'simul': simul}








.. GENERATED FROM PYTHON SOURCE LINES 69-70

Creation of the BIOGEME object

.. GENERATED FROM PYTHON SOURCE LINES 70-75

.. code-block:: Python

    my_biogeme = BIOGEME(my_data, dict_of_expressions, bootstrap_samples=100)
    my_biogeme.model_name = 'simple_example'
    results = my_biogeme.estimate(run_bootstrap=True)
    print(results)





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

 .. code-block:: none


    Bootstraps:   0%|          | 0/100 [00:00<?, ?it/s]

      0%|          | 0/100 [00:00<?, ?it/s]

      1%|          | 1/100 [00:00<00:11,  8.54it/s]

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     76%|███████▌  | 76/100 [00:04<00:01, 17.36it/s]/Users/bierlair/python_envs/venv313/lib/python3.13/site-packages/joblib/externals/loky/process_executor.py:782: UserWarning: A worker stopped while some jobs were given to the executor. This can be caused by a too short worker timeout or by a memory leak.
      warnings.warn(


     80%|████████  | 80/100 [00:04<00:01, 12.98it/s]

     82%|████████▏ | 82/100 [00:06<00:03,  5.33it/s]

     84%|████████▍ | 84/100 [00:06<00:02,  5.71it/s]

     88%|████████▊ | 88/100 [00:06<00:01,  7.63it/s]

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    100%|██████████| 100/100 [00:07<00:00, 13.30it/s]
    Results for model simple_example
    Nbr of parameters:              2
    Sample size:                    5
    Excluded data:                  0
    Final log likelihood:           -67.06549
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499





.. GENERATED FROM PYTHON SOURCE LINES 76-77

Dump results on a file

.. GENERATED FROM PYTHON SOURCE LINES 77-81

.. code-block:: Python

    the_yaml_file = my_biogeme.yaml_filename
    results.dump_yaml_file(filename=the_yaml_file)
    print(the_yaml_file)





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

 .. code-block:: none

    simple_example~02.yaml




.. GENERATED FROM PYTHON SOURCE LINES 82-83

Results can be imported from a file previously generated

.. GENERATED FROM PYTHON SOURCE LINES 83-86

.. code-block:: Python

    read_results = EstimationResults.from_yaml_file(filename=the_yaml_file)
    print(read_results)





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

 .. code-block:: none

    Results for model simple_example
    Nbr of parameters:              2
    Sample size:                    5
    Excluded data:                  0
    Final log likelihood:           -67.06549
    Akaike Information Criterion:   138.131
    Bayesian Information Criterion: 137.3499





.. GENERATED FROM PYTHON SOURCE LINES 87-88

Results can be formatted in LaTeX

.. GENERATED FROM PYTHON SOURCE LINES 88-90

.. code-block:: Python

    print(get_latex_estimated_parameters(estimation_results=read_results))





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

 .. code-block:: none


    \begin{tabular}{rlr@{.}lr@{.}lr@{.}lr@{.}l}
              &              &   \multicolumn{2}{l}{}         & \multicolumn{2}{l}{Bootstrap}  &  \multicolumn{4}{l}{}  \\
    Parameter &              &   \multicolumn{2}{l}{Coeff.}   & \multicolumn{2}{l}{Asympt.}       & \multicolumn{4}{l}{}   \\
    number    &  Description &   \multicolumn{2}{l}{estimate} & \multicolumn{2}{l}{std. error}    & \multicolumn{2}{l}{$t$-stat}  &  \multicolumn{2}{l}{$p$-value} \\
    \hline
    0 & beta1 & -1&27 & 0&014 & -91&2 & 0&0 \\ 
    1 & beta2 & 1&25 & 0&0609 & 20&5 & 0&0 \\ 

    \end{tabular}





.. GENERATED FROM PYTHON SOURCE LINES 91-92

Results can be formatted in HTML

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    print(get_html_estimated_parameters(estimation_results=read_results))





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

 .. code-block:: none

    <table border="1">
    <tr class=biostyle><th>Id</th><th>Name</th><th>Value</th><th>Bootstrap std err.</th><th>Bootstrap t-stat.</th><th>Bootstrap p-value</th></tr>
    <tr class=biostyle><td>0</td><td>beta1</td><td>-1.27</td><td>0.014</td><td>-91.2</td><td>0</td></tr>
    <tr class=biostyle><td>1</td><td>beta2</td><td>1.25</td><td>0.0609</td><td>20.5</td><td>0</td></tr>
    </table>




.. GENERATED FROM PYTHON SOURCE LINES 95-96

General statistics, including a suggested format.

.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. code-block:: Python

    statistics = read_results.get_general_statistics()
    display(statistics)





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

 .. code-block:: none

    {'Number of estimated parameters': '2', 'Sample size': '5', 'Excluded observations': '0', 'Init log likelihood': '-67.06549', 'Final log likelihood': '-67.06549', 'Likelihood ratio test for the init. model': '-0', 'Rho-square for the init. model': '0', 'Rho-square-bar for the init. model': '-0.0298', 'Akaike Information Criterion': '138.131', 'Bayesian Information Criterion': '137.3499', 'Final gradient norm': '1.1521E-07', 'Bootstrapping time': '0:00:07.518484'}




.. GENERATED FROM PYTHON SOURCE LINES 100-101

Estimated parameters as pandas dataframe

.. GENERATED FROM PYTHON SOURCE LINES 101-104

.. code-block:: Python

    pandas_parameters = get_pandas_estimated_parameters(estimation_results=read_results)
    display(pandas_parameters)





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

 .. code-block:: none

        Name     Value  Bootstrap std err.  Bootstrap t-stat.  Bootstrap p-value
    0  beta1 -1.273264            0.013957         -91.229031                0.0
    1  beta2  1.248769            0.060945          20.489987                0.0




.. GENERATED FROM PYTHON SOURCE LINES 105-106

Correlation results

.. GENERATED FROM PYTHON SOURCE LINES 106-109

.. code-block:: Python

    pandas_correlation = get_pandas_correlation_results(estimation_results=read_results)
    display(pandas_correlation)





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

 .. code-block:: none

      First parameter Second parameter  ...  Bootstrap t-stat.  Bootstrap p-value
    0           beta2            beta1  ...          53.669506                0.0

    [1 rows x 6 columns]




.. GENERATED FROM PYTHON SOURCE LINES 110-111

Obtain the values of the parameters

.. GENERATED FROM PYTHON SOURCE LINES 111-114

.. code-block:: Python

    beta_values = read_results.get_beta_values()
    display(beta_values)





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

 .. code-block:: none

    {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}




.. GENERATED FROM PYTHON SOURCE LINES 115-116

Obtain the value of one or several specific parameters

.. GENERATED FROM PYTHON SOURCE LINES 116-119

.. code-block:: Python

    some_beta_values = read_results.get_beta_values(my_betas=['beta2'])
    display(some_beta_values)





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

 .. code-block:: none

    {'beta2': 1.2487688099301162}




.. GENERATED FROM PYTHON SOURCE LINES 120-121

Variance-covariance matrix (Rao-Cramer)

.. GENERATED FROM PYTHON SOURCE LINES 121-125

.. code-block:: Python

    rao_cramer = read_results.get_variance_covariance_matrix(
        variance_covariance_type=EstimateVarianceCovariance.RAO_CRAMER
    )
    display(rao_cramer)




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

 .. code-block:: none

    [[0.01325818 0.00167146]
     [0.00167146 0.00719613]]




.. GENERATED FROM PYTHON SOURCE LINES 126-127

Variance-covariance matrix (robust)

.. GENERATED FROM PYTHON SOURCE LINES 127-132

.. code-block:: Python

    robust = read_results.get_variance_covariance_matrix(
        variance_covariance_type=EstimateVarianceCovariance.ROBUST
    )
    display(robust)





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

 .. code-block:: none

    [[0.00018835 0.00081089]
     [0.00081089 0.00349115]]




.. GENERATED FROM PYTHON SOURCE LINES 133-134

Variance-covariance matrix (bootstrap)

.. GENERATED FROM PYTHON SOURCE LINES 134-139

.. code-block:: Python

    bootstrap = read_results.get_variance_covariance_matrix(
        variance_covariance_type=EstimateVarianceCovariance.BOOTSTRAP
    )
    display(bootstrap)





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

 .. code-block:: none

    [[0.00019479 0.00085044]
     [0.00085044 0.00371433]]




.. GENERATED FROM PYTHON SOURCE LINES 140-143

Draws for sensitivity analysis are generated using
bootstrapping. Any indicator can be generated by the model for each
draw, and its empirical distribution can be investigated.

.. GENERATED FROM PYTHON SOURCE LINES 143-145

.. code-block:: Python

    read_results.get_betas_for_sensitivity_analysis(['beta1', 'beta2'], size=10)





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

 .. code-block:: none


    [{'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.2611085813010015, 'beta2': 1.3007517002098443}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2611085813010015, 'beta2': 1.3007517002098443}, {'beta1': -1.2573978799513064, 'beta2': 1.3165120810083486}, {'beta1': -1.2981035069734936, 'beta2': 1.1393434553785933}, {'beta1': -1.243923633974187, 'beta2': 1.373502065868922}, {'beta1': -1.3170661906585204, 'beta2': 1.0497320768282947}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2611085813405174, 'beta2': 1.3007516144406395}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.287332492839996, 'beta2': 1.1875193084801916}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.269026040455536, 'beta2': 1.2669668836379888}, {'beta1': -1.2777126116342759, 'beta2': 1.2295568140731905}, {'beta1': -1.2873325027193596, 'beta2': 1.1875194143603178}, {'beta1': -1.2573978799513064, 'beta2': 1.3165120810083486}, {'beta1': -1.2873324919847893, 'beta2': 1.187519300827712}, {'beta1': -1.2573978799513064, 'beta2': 1.3165120810083486}, {'beta1': -1.2649797727418584, 'beta2': 1.284263172308228}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2504079893334659, 'beta2': 1.3461108405007625}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.269026040455536, 'beta2': 1.2669668836379888}, {'beta1': -1.2777126116342759, 'beta2': 1.2295568140731905}, {'beta1': -1.2873325027193596, 'beta2': 1.1875194143603178}, {'beta1': -1.298103506705179, 'beta2': 1.1393434542527645}, {'beta1': -1.282393821462994, 'beta2': 1.2091960928148573}, {'beta1': -1.3103131424440955, 'beta2': 1.0825801152308525}, {'beta1': -1.2732639874634077, 'beta2': 1.2487688091207687}, {'beta1': -1.298103506705179, 'beta2': 1.1393434542527645}, {'beta1': -1.2690260404854072, 'beta2': 1.2669668816538486}, {'beta1': -1.2573978799513064, 'beta2': 1.3165120810083486}, {'beta1': -1.2649797727418584, 'beta2': 1.284263172308228}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2504079893334659, 'beta2': 1.3461108405007625}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2777126116342759, 'beta2': 1.2295568140731905}, {'beta1': -1.292558011774817, 'beta2': 1.1643229811019848}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2925579238204843, 'beta2': 1.1643222008081031}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.298103506705179, 'beta2': 1.1393434542527645}, {'beta1': -1.2573978838405362, 'beta2': 1.3165118203767316}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2611085813405174, 'beta2': 1.3007516144406395}, {'beta1': -1.2925578214686664, 'beta2': 1.164322217510277}, {'beta1': -1.2823937457787886, 'beta2': 1.2091956298296247}, {'beta1': -1.298103506705179, 'beta2': 1.1393434542527645}, {'beta1': -1.2690260404854072, 'beta2': 1.2669668816538486}, {'beta1': -1.2538348107653448, 'beta2': 1.331612380127896}, {'beta1': -1.2732639365473521, 'beta2': 1.2487701544564327}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2777126116342759, 'beta2': 1.2295568140731905}, {'beta1': -1.273263987607468, 'beta2': 1.248768812102508}, {'beta1': -1.2611085813010015, 'beta2': 1.3007517002098443}, {'beta1': -1.26497977397441, 'beta2': 1.2842631509636993}, {'beta1': -1.2573978799513064, 'beta2': 1.3165120810083486}, {'beta1': -1.2873324919847893, 'beta2': 1.187519300827712}, {'beta1': -1.2538348107653448, 'beta2': 1.331612380127896}, {'beta1': -1.2732639365473521, 'beta2': 1.2487701544564327}, {'beta1': -1.2925578214686664, 'beta2': 1.164322217510277}, {'beta1': -1.2732640875536856, 'beta2': 1.248769699775698}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2538348107653448, 'beta2': 1.331612380127896}, {'beta1': -1.2732639365473521, 'beta2': 1.2487701544564327}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2823937666074936, 'beta2': 1.2091966201417774}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.287332533620085, 'beta2': 1.1875198317198776}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2573978830118717, 'beta2': 1.3165118359003405}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2925578214686664, 'beta2': 1.164322217510277}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2873324919775402, 'beta2': 1.1875193007862883}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2823937485848418, 'beta2': 1.2091958966297875}, {'beta1': -1.2690260405244644, 'beta2': 1.2669668838392423}, {'beta1': -1.2573978810083073, 'beta2': 1.3165119010872348}, {'beta1': -1.273263987213694, 'beta2': 1.2487688099301162}, {'beta1': -1.2649797742013058, 'beta2': 1.2842631765105266}, {'beta1': -1.2777126116342759, 'beta2': 1.2295568140731905}, {'beta1': -1.273263987607468, 'beta2': 1.248768812102508}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.2777126118096789, 'beta2': 1.229556814569854}, {'beta1': -1.282393736283639, 'beta2': 1.209195603860136}, {'beta1': -1.2777126118096789, 'beta2': 1.229556814569854}, {'beta1': -1.3103131424440955, 'beta2': 1.0825801152308525}, {'beta1': -1.257397883841623, 'beta2': 1.316511820405938}]



.. GENERATED FROM PYTHON SOURCE LINES 146-147

Results can be produced in the ALOGIT F12 format

.. GENERATED FROM PYTHON SOURCE LINES 147-149

.. code-block:: Python

    print(get_f12(estimation_results=read_results))





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

 .. code-block:: none

                                                                     simple_example
    From biogeme 3.3.1                                      2025-09-03 02:00:59  
    END
       0      beta1 F  -1.273263987214e+00 +1.395678510435e-02
       0      beta2 F  +1.248768809930e+00 +6.094531842799e-02
      -1
           5                  0                   0 -6.706549047946e+01
       0   0  2025-09-03 02:00:59
      99981





.. GENERATED FROM PYTHON SOURCE LINES 150-151

Miscellaneous functions

.. GENERATED FROM PYTHON SOURCE LINES 153-154

Likelihood ratio test. Let's first estimate a constrained model

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.. code-block:: Python

    beta2_constrained = Beta('beta2_constrained', 2.0, -3, 10, 1)
    likelihood_constrained = (
        -(beta1**2) * Variable1
        - exp(beta2_constrained * beta1) * Variable2
        - beta2_constrained**4
    )
    my_biogeme_constrained = BIOGEME(my_data, likelihood_constrained)
    my_biogeme_constrained.model_name = 'simple_example_constrained'
    results_constrained = my_biogeme_constrained.estimate()
    print(results_constrained.short_summary())





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

 .. code-block:: none


    Bootstraps:   0%|          | 0/100 [00:07<?, ?it/s]
    Results for model simple_example_constrained
    Nbr of parameters:              1
    Sample size:                    5
    Excluded data:                  0
    Final log likelihood:           -114.7702
    Akaike Information Criterion:   231.5403
    Bayesian Information Criterion: 231.1498





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We can now perform a likelihood ratio test.

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.. code-block:: Python

    test_results = results.likelihood_ratio_test(results_constrained, 0.95)
    print(test_results.message)
    print(f'Statistic: {test_results.statistic}')
    print(f'Threshold: {test_results.threshold}')





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

 .. code-block:: none

    H0 can be rejected at level 95.0%
    Statistic: 95.40936413216045
    Threshold: 0.003932140000019531




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Calculation of the :math:`p`-value

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.. code-block:: Python

    calc_p_value(1.96)





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

 .. code-block:: none


    np.float64(0.04999579029644097)



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Compilation of results

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.. code-block:: Python

    dict_of_results = {'Model A': read_results, 'Model B': the_yaml_file}








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.. code-block:: Python

    df = compile_estimation_results(dict_of_results)
    display(df)




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

 .. code-block:: none

    (                                       Model A         Model B
    Number of estimated parameters               2               2
    Sample size                                  5               5
    Final log likelihood                 -67.06549       -67.06549
    Akaike Information Criterion           138.131         138.131
    Bayesian Information Criterion        137.3499        137.3499
    beta1 (t-test)                  -1.27  (-92.8)  -1.27  (-92.8)
    beta2 (t-test)                    1.25  (21.1)    1.25  (21.1), {'Model A': 'Model A', 'Model B': 'Model B'})





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

   **Total running time of the script:** (0 minutes 7.982 seconds)


.. _sphx_glr_download_auto_examples_programmers_plot_results.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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

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

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


.. only:: html

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

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