.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/uncertainty/sensitivity/plot_morris.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_morris.py>`
        to download the full example code

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

.. _sphx_glr_examples_uncertainty_sensitivity_plot_morris.py:


Morris analysis
===============

.. GENERATED FROM PYTHON SOURCE LINES 25-33

.. code-block:: default

    from __future__ import annotations

    import pprint

    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








.. GENERATED FROM PYTHON SOURCE LINES 34-46

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`.

.. GENERATED FROM PYTHON SOURCE LINES 46-50

.. code-block:: default


    discipline = IshigamiDiscipline()
    uncertain_space = IshigamiSpace()








.. GENERATED FROM PYTHON SOURCE LINES 51-53

Then,
we run sensitivity analysis of type :class:`.MorrisAnalysis`:

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: default

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





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

 .. code-block:: none


    {'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 57-59

The resulting indices are the empirical means and the standard deviations
of the absolute output variations due to input changes.

.. GENERATED FROM PYTHON SOURCE LINES 59-61

.. code-block:: default

    pprint.pprint(sensitivity_analysis.indices)





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

 .. code-block:: none

    {'MAX': {'y': [{'x1': array([1.50302741]),
                    'x2': array([2.14550491]),
                    'x3': array([3.19229192])}]},
     'MIN': {'y': [{'x1': array([0.03237925]),
                    'x2': array([2.04319692]),
                    'x3': array([0.01260487])}]},
     '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])}]},
     'RELATIVE_SIGMA': {'y': [{'x1': array([1.]),
                               'x2': array([1.]),
                               'x3': array([0.99213399])}]},
     'SIGMA': {'y': [{'x1': array([0.76770333]),
                      'x2': array([2.09435091]),
                      'x3': array([1.58984353])}]}}




.. GENERATED FROM PYTHON SOURCE LINES 62-64

The main indices corresponds to these empirical means
(this main method can be changed with :attr:`.MorrisAnalysis.main_method`):

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.. code-block:: default

    pprint.pprint(sensitivity_analysis.main_indices)





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

 .. code-block:: none

    {'y': [{'x1': array([0.76770333]),
            'x2': array([2.09435091]),
            'x3': array([1.6024484])}]}




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and can be interpreted with respect to the empirical bounds of the outputs:

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.. code-block:: default

    pprint.pprint(sensitivity_analysis.outputs_bounds)





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

 .. code-block:: none

    {'y': [array([0.3861887]), array([14.38383568])]}




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We can also get the input parameters sorted by decreasing order of influence:

.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: default

    sensitivity_analysis.sort_parameters("y")





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

 .. code-block:: none


    ['x2', 'x3', 'x1']



.. GENERATED FROM PYTHON SOURCE LINES 75-77

We can use the method :meth:`.MorrisAnalysis.plot`
to visualize the different series of indices:

.. GENERATED FROM PYTHON SOURCE LINES 77-79

.. code-block:: default

    sensitivity_analysis.plot("y", save=False, show=True, lower_mu=0, lower_sigma=0)




.. image-sg:: /examples/uncertainty/sensitivity/images/sphx_glr_plot_morris_001.png
   :alt: Sampling: lhs(size=2) - Relative step: 0.05 - Output: y
   :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_morris_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 80-82

Lastly,
the sensitivity indices can be exported to a :class:`.Dataset`:

.. GENERATED FROM PYTHON SOURCE LINES 82-83

.. code-block:: default

    sensitivity_analysis.to_dataset()





.. 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 {
            vertical-align: top;
        }

        .dataframe thead tr th {
            text-align: left;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr>
          <th>GROUP</th>
          <th>MU</th>
          <th>MU_STAR</th>
          <th>SIGMA</th>
          <th>RELATIVE_SIGMA</th>
          <th>MIN</th>
          <th>MAX</th>
        </tr>
        <tr>
          <th>VARIABLE</th>
          <th>y</th>
          <th>y</th>
          <th>y</th>
          <th>y</th>
          <th>y</th>
          <th>y</th>
        </tr>
        <tr>
          <th>COMPONENT</th>
          <th>0</th>
          <th>0</th>
          <th>0</th>
          <th>0</th>
          <th>0</th>
          <th>0</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>x1</th>
          <td>0.735324</td>
          <td>0.767703</td>
          <td>0.767703</td>
          <td>1.000000</td>
          <td>0.032379</td>
          <td>1.503027</td>
        </tr>
        <tr>
          <th>x2</th>
          <td>-0.051154</td>
          <td>2.094351</td>
          <td>2.094351</td>
          <td>1.000000</td>
          <td>2.043197</td>
          <td>2.145505</td>
        </tr>
        <tr>
          <th>x3</th>
          <td>-1.602448</td>
          <td>1.602448</td>
          <td>1.589844</td>
          <td>0.992134</td>
          <td>0.012605</td>
          <td>3.192292</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.477 seconds)


.. _sphx_glr_download_examples_uncertainty_sensitivity_plot_morris.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_morris.py <plot_morris.py>`

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

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


.. only:: html

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