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

.. only:: html

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

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

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

.. _sphx_glr_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_rank_sobol.py:


Sobol' sensitivity indices using rank-based algorithm
=====================================================

.. GENERATED FROM PYTHON SOURCE LINES 5-11

.. code-block:: Python


    import openturns as ot
    import openturns.experimental as otexp
    import openturns.viewer as viewer
    from openturns.usecases import ishigami_function








.. GENERATED FROM PYTHON SOURCE LINES 12-15

In this example we are going to compute global sensitivity indices in a data driven framework.
For that purpose, we are using the rank-based algorithm which provides the first order Sobol' indices.
We present the method on the :ref:`Ishigami function<use-case-ishigami>`.

.. GENERATED FROM PYTHON SOURCE LINES 15-18

.. code-block:: Python


    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 19-23

Definition of the model
-----------------------

We load the model from the usecases module.

.. GENERATED FROM PYTHON SOURCE LINES 23-25

.. code-block:: Python

    im = ishigami_function.IshigamiModel()








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We generate an input sample of size 500 (and dimension 3).

.. GENERATED FROM PYTHON SOURCE LINES 27-31

.. code-block:: Python

    size = 500
    ot.RandomGenerator.SetSeed(10)
    X = im.distributionX.getSample(size)








.. GENERATED FROM PYTHON SOURCE LINES 32-33

We compute the output by applying the Ishigami model to the input sample.

.. GENERATED FROM PYTHON SOURCE LINES 33-35

.. code-block:: Python

    Y = im.model(X)








.. GENERATED FROM PYTHON SOURCE LINES 36-37

Estimate Sobol' first order indices via rank-based algorithm.

.. GENERATED FROM PYTHON SOURCE LINES 37-41

.. code-block:: Python

    mySobol = otexp.RankSobolSensitivityAlgorithm(X, Y)
    indices = mySobol.getFirstOrderIndices()
    print("First order indices:", indices)





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

 .. code-block:: none

    First order indices: [0.29008,0.421935,0.0856989]




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Draw Sobol' indices.

Options for confidence interval estimation can be defined.

.. GENERATED FROM PYTHON SOURCE LINES 45-50

.. code-block:: Python

    ot.ResourceMap.SetAsUnsignedInteger("SobolIndicesAlgorithm-DefaultBootstrapSize", 200)
    ot.ResourceMap.SetAsScalar(
        "RankSobolSensitivityAlgorithm-DefaultBootstrapSampleRatio", 0.85
    )








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if `SobolIndicesAlgorithm-DefaultBootstrapSize` > 1, the draw() method will call bootstrap method to compute the confidence intervals.

.. GENERATED FROM PYTHON SOURCE LINES 52-59

.. code-block:: Python


    graph = mySobol.draw()
    graph.setTitle("Sobol' indices")
    view = viewer.View(graph)

    print("confidence intervals:", mySobol.getFirstOrderIndicesInterval())




.. image-sg:: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_rank_sobol_001.png
   :alt: Sobol' indices
   :srcset: /auto_reliability_sensitivity/sensitivity_analysis/images/sphx_glr_plot_sensitivity_rank_sobol_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    confidence intervals: [0.238895, 0.337643]
    [0.381658, 0.485514]
    [-0.030505, 0.151549]




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It is possible that Sobol' indices estimates take negative values, that is inconsistent with the theory. Therefore, a larger number of samples is required to get consistent indices.


.. _sphx_glr_download_auto_reliability_sensitivity_sensitivity_analysis_plot_sensitivity_rank_sobol.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_rank_sobol.ipynb <plot_sensitivity_rank_sobol.ipynb>`

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

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