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.. 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

        Click :ref:`here <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
=============================

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.. code-block:: default

    from __future__ import annotations

    from gemseo.uncertainty.sensitivity.correlation.analysis import CorrelationAnalysis
    from gemseo.uncertainty.sensitivity.morris.analysis import MorrisAnalysis
    from gemseo.uncertainty.use_cases.ishigami.ishigami_discipline import IshigamiDiscipline
    from gemseo.uncertainty.use_cases.ishigami.ishigami_space import IshigamiSpace








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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:`.MDODiscipline` 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`.

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.. code-block:: default

    discipline = IshigamiDiscipline()
    uncertain_space = IshigamiSpace()








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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:

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.. code-block:: default

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





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

 .. code-block:: none


    {'pearson': {'y': [{'x1': array([0.685388]), 'x2': array([0.09681897]), 'x3': array([-0.23027298])}]}, 'spearman': {'y': [{'x1': array([0.74545455]), 'x2': array([0.04242424]), 'x3': array([-0.09090909])}]}, 'pcc': {'y': [{'x1': array([0.84696461]), 'x2': array([0.68814608]), 'x3': array([-0.29846394])}]}, 'prcc': {'y': [{'x1': array([0.90374102]), 'x2': array([0.76539572]), 'x3': array([-0.02232206])}]}, '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])}]}, 'ssrrc': {'y': [{'x1': array([0.94001308]), 'x2': array([0.55748872]), 'x3': array([-0.16157012])}]}}



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

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.. code-block:: default

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





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

 .. code-block:: none


    {'mu': {'y': [{'x1': array([-0.36000398]), 'x2': array([0.77781853]), 'x3': array([-0.70990541])}]}, 'mu_star': {'y': [{'x1': array([0.67947346]), 'x2': array([0.88906579]), 'x3': array([0.72694219])}]}, 'sigma': {'y': [{'x1': array([0.98724949]), 'x2': array([0.79064599]), 'x3': array([0.8074493])}]}, 'relative_sigma': {'y': [{'x1': array([1.45296254]), 'x2': array([0.88929976]), 'x3': array([1.11074761])}]}, 'min': {'y': [{'x1': array([0.0338188]), 'x2': array([0.11821721]), 'x3': array([8.72820113e-05])}]}, 'max': {'y': [{'x1': array([2.2360336]), 'x2': array([1.83987522]), 'x3': array([2.12052546])}]}}



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

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.. code-block:: default

    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 0x7fbc555df280>



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or a radar plot:

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.. code-block:: default

    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 0x7fbc55f9f820>




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

   **Total running time of the script:** ( 0 minutes  0.502 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-python

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

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

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


.. only:: html

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

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