.. 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 25-34

.. code-block:: Python


    from __future__ import annotations

    import pprint

    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








.. GENERATED FROM PYTHON SOURCE LINES 35-47

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 47-51

.. code-block:: Python


    discipline = IshigamiDiscipline()
    uncertain_space = IshigamiSpace()








.. GENERATED FROM PYTHON SOURCE LINES 52-54

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

.. GENERATED FROM PYTHON SOURCE LINES 54-58

.. code-block:: Python

    sensitivity_analysis = MorrisAnalysis()
    sensitivity_analysis.compute_samples([discipline], uncertain_space, n_samples=0)
    sensitivity_analysis.compute_indices()





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

 .. code-block:: none

        INFO - 16:22:32: *** Start MorrisAnalysisSamplingPhase execution ***
        INFO - 16:22:32: MorrisAnalysisSamplingPhase
        INFO - 16:22:32:    Disciplines: IshigamiDiscipline
        INFO - 16:22:32:    MDO formulation: MDF
        INFO - 16:22:32: Running the algorithm MorrisDOE:
        INFO - 16:22:32:      5%|▌         | 1/20 [00:00<00:00, 489.02 it/sec]
        INFO - 16:22:32:     10%|█         | 2/20 [00:00<00:00, 822.82 it/sec]
        INFO - 16:22:32:     15%|█▌        | 3/20 [00:00<00:00, 1097.79 it/sec]
        INFO - 16:22:32:     20%|██        | 4/20 [00:00<00:00, 1320.21 it/sec]
        INFO - 16:22:32:     25%|██▌       | 5/20 [00:00<00:00, 1511.35 it/sec]
        INFO - 16:22:32:     30%|███       | 6/20 [00:00<00:00, 1685.25 it/sec]
        INFO - 16:22:32:     35%|███▌      | 7/20 [00:00<00:00, 1829.18 it/sec]
        INFO - 16:22:32:     40%|████      | 8/20 [00:00<00:00, 1951.52 it/sec]
        INFO - 16:22:32:     45%|████▌     | 9/20 [00:00<00:00, 2064.35 it/sec]
        INFO - 16:22:32:     50%|█████     | 10/20 [00:00<00:00, 2170.63 it/sec]
        INFO - 16:22:32:     55%|█████▌    | 11/20 [00:00<00:00, 2217.82 it/sec]
        INFO - 16:22:32:     60%|██████    | 12/20 [00:00<00:00, 2282.51 it/sec]
        INFO - 16:22:32:     65%|██████▌   | 13/20 [00:00<00:00, 2359.31 it/sec]
        INFO - 16:22:32:     70%|███████   | 14/20 [00:00<00:00, 2435.92 it/sec]
        INFO - 16:22:32:     75%|███████▌  | 15/20 [00:00<00:00, 2499.29 it/sec]
        INFO - 16:22:32:     80%|████████  | 16/20 [00:00<00:00, 2545.18 it/sec]
        INFO - 16:22:32:     85%|████████▌ | 17/20 [00:00<00:00, 2607.25 it/sec]
        INFO - 16:22:32:     90%|█████████ | 18/20 [00:00<00:00, 2665.78 it/sec]
        INFO - 16:22:32:     95%|█████████▌| 19/20 [00:00<00:00, 2711.07 it/sec]
        INFO - 16:22:32:    100%|██████████| 20/20 [00:00<00:00, 2706.44 it/sec]
        INFO - 16:22:32: *** End MorrisAnalysisSamplingPhase execution ***

    MorrisAnalysis.SensitivityIndices(mu={'y': [{'x1': array([-0.60047199]), 'x2': array([0.51230435]), 'x3': array([-0.89800793])}]}, mu_star={'y': [{'x1': array([0.69887482]), 'x2': array([0.65136343]), 'x3': array([0.89805157])}]}, sigma={'y': [{'x1': array([0.96395158]), 'x2': array([0.6549141]), 'x3': array([0.79878356])}]}, relative_sigma={'y': [{'x1': array([1.37929075]), 'x2': array([1.00545113]), 'x3': array([0.88946291])}]}, min={'y': [{'x1': array([0.0338188]), 'x2': array([0.11821721]), 'x3': array([8.72820113e-05])}]}, max={'y': [{'x1': array([2.2360336]), 'x2': array([1.25769934]), 'x3': array([2.12052546])}]})



.. GENERATED FROM PYTHON SOURCE LINES 59-61

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 61-63

.. code-block:: Python

    sensitivity_analysis.indices





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

 .. code-block:: none


    MorrisAnalysis.SensitivityIndices(mu={'y': [{'x1': array([-0.60047199]), 'x2': array([0.51230435]), 'x3': array([-0.89800793])}]}, mu_star={'y': [{'x1': array([0.69887482]), 'x2': array([0.65136343]), 'x3': array([0.89805157])}]}, sigma={'y': [{'x1': array([0.96395158]), 'x2': array([0.6549141]), 'x3': array([0.79878356])}]}, relative_sigma={'y': [{'x1': array([1.37929075]), 'x2': array([1.00545113]), 'x3': array([0.88946291])}]}, min={'y': [{'x1': array([0.0338188]), 'x2': array([0.11821721]), 'x3': array([8.72820113e-05])}]}, max={'y': [{'x1': array([2.2360336]), 'x2': array([1.25769934]), 'x3': array([2.12052546])}]})



.. GENERATED FROM PYTHON SOURCE LINES 64-66

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

.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: Python

    pprint.pprint(sensitivity_analysis.main_indices)





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

 .. code-block:: none

    {'y': [{'x1': array([0.69887482]),
            'x2': array([0.65136343]),
            'x3': array([0.89805157])}]}




.. GENERATED FROM PYTHON SOURCE LINES 69-70

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

.. GENERATED FROM PYTHON SOURCE LINES 70-72

.. code-block:: Python

    pprint.pprint(sensitivity_analysis.outputs_bounds)





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

 .. code-block:: none

    {'y': (array([-1.42959705]), array([14.89344259]))}




.. GENERATED FROM PYTHON SOURCE LINES 73-74

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

.. GENERATED FROM PYTHON SOURCE LINES 74-76

.. code-block:: Python

    sensitivity_analysis.sort_input_variables("y")





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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 77-79

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

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. 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: PYDOE_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 82-84

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

.. GENERATED FROM PYTHON SOURCE LINES 84-85

.. 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>-0.600472</td>
          <td>0.698875</td>
          <td>0.963952</td>
          <td>1.379291</td>
          <td>0.033819</td>
          <td>2.236034</td>
        </tr>
        <tr>
          <th>x2</th>
          <td>0.512304</td>
          <td>0.651363</td>
          <td>0.654914</td>
          <td>1.005451</td>
          <td>0.118217</td>
          <td>1.257699</td>
        </tr>
        <tr>
          <th>x3</th>
          <td>-0.898008</td>
          <td>0.898052</td>
          <td>0.798784</td>
          <td>0.889463</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 0.087 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>`

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

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


.. only:: html

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

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