.. 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 25-37

.. code-block:: Python


    from __future__ import annotations

    import pprint

    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.morris.analysis import MorrisAnalysis

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 38-50

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 50-54

.. code-block:: Python


    discipline = IshigamiDiscipline()
    uncertain_space = IshigamiSpace()








.. GENERATED FROM PYTHON SOURCE LINES 55-57

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

.. GENERATED FROM PYTHON SOURCE LINES 57-60

.. code-block:: Python

    sensitivity_analysis = MorrisAnalysis([discipline], uncertain_space, n_samples=None)
    sensitivity_analysis.compute_indices()





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

 .. code-block:: none

     WARNING - 08:55:22: No coupling in MDA, switching chain_linearize to True.
     WARNING - 08:55:22: No coupling in MDA, switching chain_linearize to True.
        INFO - 08:55:22:  
        INFO - 08:55:22: *** Start MorrisAnalysisSamplingPhase execution ***
        INFO - 08:55:22: MorrisAnalysisSamplingPhase
        INFO - 08:55:22:    Disciplines: _OATSensitivity
        INFO - 08:55:22:    MDO formulation: MDF
        INFO - 08:55:22: Running the algorithm lhs:
        INFO - 08:55:22:     20%|██        | 1/5 [00:00<00:00, 55.75 it/sec]
        INFO - 08:55:22:     40%|████      | 2/5 [00:00<00:00, 90.19 it/sec]
        INFO - 08:55:22:     60%|██████    | 3/5 [00:00<00:00, 114.55 it/sec]
        INFO - 08:55:22:     80%|████████  | 4/5 [00:00<00:00, 132.27 it/sec]
        INFO - 08:55:22:    100%|██████████| 5/5 [00:00<00:00, 146.04 it/sec]
        INFO - 08:55:22: *** End MorrisAnalysisSamplingPhase execution (time: 0:00:00.046215) ***

    {'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])}]}}



.. GENERATED FROM PYTHON SOURCE LINES 61-63

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 63-65

.. code-block:: Python

    pprint.pprint(sensitivity_analysis.indices)





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

 .. code-block:: none

    {'MAX': {'y': [{'x1': array([2.2360336]),
                    'x2': array([1.83987522]),
                    'x3': array([2.12052546])}]},
     'MIN': {'y': [{'x1': array([0.0338188]),
                    'x2': array([0.11821721]),
                    'x3': array([8.72820113e-05])}]},
     '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])}]},
     'RELATIVE_SIGMA': {'y': [{'x1': array([1.45296254]),
                               'x2': array([0.88929976]),
                               'x3': array([1.11074761])}]},
     'SIGMA': {'y': [{'x1': array([0.98724949]),
                      'x2': array([0.79064599]),
                      'x3': array([0.8074493])}]}}




.. GENERATED FROM PYTHON SOURCE LINES 66-68

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

.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: Python

    pprint.pprint(sensitivity_analysis.main_indices)





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

 .. code-block:: none

    {'y': [{'x1': array([0.67947346]),
            'x2': array([0.88906579]),
            'x3': array([0.72694219])}]}




.. GENERATED FROM PYTHON SOURCE LINES 71-72

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

.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: Python

    pprint.pprint(sensitivity_analysis.outputs_bounds)





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

 .. code-block:: none

    {'y': [array([-1.00881748]), array([14.89344259])]}




.. GENERATED FROM PYTHON SOURCE LINES 75-76

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

.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: Python

    sensitivity_analysis.sort_parameters("y")





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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 79-81

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

.. GENERATED FROM PYTHON SOURCE LINES 81-83

.. code-block:: Python

    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=5) - Relative step: 0.05 - Output: y
   :srcset: /examples/uncertainty/sensitivity/images/sphx_glr_plot_morris_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <Figure size 640x480 with 1 Axes>



.. GENERATED FROM PYTHON SOURCE LINES 84-86

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

.. GENERATED FROM PYTHON SOURCE LINES 86-87

.. code-block:: Python

    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>-0.360004</td>
          <td>0.679473</td>
          <td>0.987249</td>
          <td>1.452963</td>
          <td>0.033819</td>
          <td>2.236034</td>
        </tr>
        <tr>
          <th>x2</th>
          <td>0.777819</td>
          <td>0.889066</td>
          <td>0.790646</td>
          <td>0.889300</td>
          <td>0.118217</td>
          <td>1.839875</td>
        </tr>
        <tr>
          <th>x3</th>
          <td>-0.709905</td>
          <td>0.726942</td>
          <td>0.807449</td>
          <td>1.110748</td>
          <td>0.000087</td>
          <td>2.120525</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />


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

   **Total running time of the script:** (0 minutes 0.462 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-jupyter

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

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

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


.. only:: html

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

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