.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/uncertainty/sensitivity/plot_sensitivity_comparison.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_uncertainty_sensitivity_plot_sensitivity_comparison.py>`
        to download the full example code.

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

.. _sphx_glr_examples_uncertainty_sensitivity_plot_sensitivity_comparison.py:


Comparing sensitivity indices
=============================

.. GENERATED FROM PYTHON SOURCE LINES 25-36

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo.problems.uncertainty.ishigami.ishigami_discipline import IshigamiDiscipline
    from gemseo.problems.uncertainty.ishigami.ishigami_space import IshigamiSpace
    from gemseo.uncertainty.sensitivity.correlation_analysis import CorrelationAnalysis
    from gemseo.uncertainty.sensitivity.morris_analysis import MorrisAnalysis

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 37-49

In this example,
we consider the Ishigami function :cite:`ishigami1990`

.. math::

   f(x_1,x_2,x_3)=\sin(x_1)+7\sin(x_2)^2+0.1x_3^4\sin(x_1)

implemented as an :class:`.Discipline` by the :class:`.IshigamiDiscipline`.
It is commonly used
with the independent random variables :math:`X_1`, :math:`X_2` and :math:`X_3`
uniformly distributed between :math:`-\pi` and :math:`\pi`
and defined in the :class:`.IshigamiSpace`.

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: Python

    discipline = IshigamiDiscipline()
    uncertain_space = IshigamiSpace()








.. GENERATED FROM PYTHON SOURCE LINES 53-60

We would like to carry out two sensitivity analyses,
e.g. a first one based on correlation coefficients
and a second one based on the Morris methodology,
and compare the results,

Firstly,
we create a :class:`.CorrelationAnalysis` and compute the sensitivity indices:

.. GENERATED FROM PYTHON SOURCE LINES 60-64

.. code-block:: Python

    correlation = CorrelationAnalysis()
    correlation.compute_samples([discipline], uncertain_space, 10)
    correlation.compute_indices()





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

 .. code-block:: none

     WARNING - 16:11:07: No coupling in MDA, switching chain_linearize to True.
        INFO - 16:11:07:  
        INFO - 16:11:07: *** Start CorrelationAnalysisSamplingPhase execution ***
        INFO - 16:11:07: CorrelationAnalysisSamplingPhase
        INFO - 16:11:07:    Disciplines: IshigamiDiscipline
        INFO - 16:11:07:    MDO formulation: MDF
        INFO - 16:11:07: Running the algorithm OT_MONTE_CARLO:
        INFO - 16:11:07:     10%|█         | 1/10 [00:00<00:00, 350.08 it/sec]
        INFO - 16:11:07:     20%|██        | 2/10 [00:00<00:00, 575.51 it/sec]
        INFO - 16:11:07:     30%|███       | 3/10 [00:00<00:00, 728.85 it/sec]
        INFO - 16:11:07:     40%|████      | 4/10 [00:00<00:00, 852.67 it/sec]
        INFO - 16:11:07:     50%|█████     | 5/10 [00:00<00:00, 951.09 it/sec]
        INFO - 16:11:07:     60%|██████    | 6/10 [00:00<00:00, 1030.88 it/sec]
        INFO - 16:11:07:     70%|███████   | 7/10 [00:00<00:00, 1097.04 it/sec]
        INFO - 16:11:07:     80%|████████  | 8/10 [00:00<00:00, 1152.64 it/sec]
        INFO - 16:11:07:     90%|█████████ | 9/10 [00:00<00:00, 1199.82 it/sec]
        INFO - 16:11:07:    100%|██████████| 10/10 [00:00<00:00, 1232.13 it/sec]
        INFO - 16:11:07: *** End CorrelationAnalysisSamplingPhase execution (time: 0:00:00.013647) ***

    CorrelationAnalysis.SensitivityIndices(kendall={'y': [{'x1': array([0.55555556]), 'x2': array([0.02222222]), 'x3': array([-0.11111111])}]}, pcc={'y': [{'x1': array([0.84696461]), 'x2': array([0.68814608]), 'x3': array([-0.29846394])}]}, pearson={'y': [{'x1': array([0.685388]), 'x2': array([0.09681897]), 'x3': array([-0.23027298])}]}, prcc={'y': [{'x1': array([0.90374102]), 'x2': array([0.76539572]), 'x3': array([-0.02232206])}]}, spearman={'y': [{'x1': array([0.74545455]), 'x2': array([0.04242424]), 'x3': array([-0.09090909])}]}, src={'y': [{'x1': array([0.94001308]), 'x2': array([0.55748872]), 'x3': array([-0.16157012])}]}, srrc={'y': [{'x1': array([1.06252802]), 'x2': array([0.60167726]), 'x3': array([-0.00959941])}]}, ssrc={'y': [{'x1': array([0.88362459]), 'x2': array([0.31079367]), 'x3': array([0.0261049])}]})



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Then,
we create an :class:`.MorrisAnalysis` and compute the sensitivity indices:

.. GENERATED FROM PYTHON SOURCE LINES 67-71

.. code-block:: Python

    morris = MorrisAnalysis()
    morris.compute_samples([discipline], uncertain_space, 10)
    morris.compute_indices()





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

 .. code-block:: none

     WARNING - 16:11:07: No coupling in MDA, switching chain_linearize to True.
        INFO - 16:11:07:  
        INFO - 16:11:07: *** Start MorrisAnalysisSamplingPhase execution ***
        INFO - 16:11:07: MorrisAnalysisSamplingPhase
        INFO - 16:11:07:    Disciplines: IshigamiDiscipline
        INFO - 16:11:07:    MDO formulation: MDF
        INFO - 16:11:07: Running the algorithm MorrisDOE:
        INFO - 16:11:07:     12%|█▎        | 1/8 [00:00<00:00, 2041.02 it/sec]
        INFO - 16:11:07:     25%|██▌       | 2/8 [00:00<00:00, 1842.84 it/sec]
        INFO - 16:11:07:     38%|███▊      | 3/8 [00:00<00:00, 1787.09 it/sec]
        INFO - 16:11:07:     50%|█████     | 4/8 [00:00<00:00, 1749.08 it/sec]
        INFO - 16:11:07:     62%|██████▎   | 5/8 [00:00<00:00, 1752.45 it/sec]
        INFO - 16:11:07:     75%|███████▌  | 6/8 [00:00<00:00, 1756.29 it/sec]
        INFO - 16:11:07:     88%|████████▊ | 7/8 [00:00<00:00, 1728.08 it/sec]
        INFO - 16:11:07:    100%|██████████| 8/8 [00:00<00:00, 1711.87 it/sec]
        INFO - 16:11:07: *** End MorrisAnalysisSamplingPhase execution (time: 0:00:00.010400) ***

    MorrisAnalysis.SensitivityIndices(mu={'y': [{'x1': array([0.73532408]), 'x2': array([-0.05115399]), 'x3': array([-1.6024484])}]}, mu_star={'y': [{'x1': array([0.76770333]), 'x2': array([2.09435091]), 'x3': array([1.6024484])}]}, sigma={'y': [{'x1': array([0.76770333]), 'x2': array([2.09435091]), 'x3': array([1.58984353])}]}, relative_sigma={'y': [{'x1': array([1.]), 'x2': array([1.]), 'x3': array([0.99213399])}]}, min={'y': [{'x1': array([0.03237925]), 'x2': array([2.04319692]), 'x3': array([0.01260487])}]}, max={'y': [{'x1': array([1.50302741]), 'x2': array([2.14550491]), 'x3': array([3.19229192])}]})



.. GENERATED FROM PYTHON SOURCE LINES 72-76

Lastly,
we compare these analyses
with the graphical method :meth:`.BaseSensitivityAnalysis.plot_comparison`,
either using a bar chart:

.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: Python

    morris.plot_comparison(correlation, "y", use_bar_plot=True, save=False, show=True)




.. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_001.png
   :alt: plot sensitivity comparison
   :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.dataset.bars.BarPlot object at 0x7f65f5b8bd60>



.. GENERATED FROM PYTHON SOURCE LINES 79-80

or a radar plot:

.. GENERATED FROM PYTHON SOURCE LINES 80-81

.. code-block:: Python

    morris.plot_comparison(correlation, "y", use_bar_plot=False, save=False, show=True)



.. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_002.png
   :alt: plot sensitivity comparison
   :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_sensitivity_comparison_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.dataset.radar_chart.RadarChart object at 0x7f65f5deef70>




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

   **Total running time of the script:** (0 minutes 0.430 seconds)


.. _sphx_glr_download_examples_uncertainty_sensitivity_plot_sensitivity_comparison.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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