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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_sensitivity_morris_plot_morris_nonlinearities.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_sensitivity_morris_plot_morris_nonlinearities.py:


Function with nonlinearities / parameter dependencies
=================================================================

.. math:: Y = h(X) = 0.01 X_{1} + 1.0 X_{2} + 0.4 X_{3}^{2} + X_{4} X_{5}

ranking of input parameters:

- :math:`X_{1}` is non-influential
- :math:`X_{2}` is influential, linear/additive effect (expect large :math:`\mu^{\star}` and small :math:`\sigma`)
- :math:`X_{3}` is somewhat influential, nonlinear effect,
- :math:`X_{4}, X_{5}` are influential with dependence

.. GENERATED FROM PYTHON SOURCE LINES 18-19

Initially we have to import the necessary modules.

.. GENERATED FROM PYTHON SOURCE LINES 22-30

.. code-block:: default

    import shutil

    from UQpy.run_model.RunModel import RunModel
    from UQpy.run_model.model_execution.PythonModel import PythonModel
    from UQpy.distributions import Uniform
    from UQpy.sensitivity import MorrisSensitivity
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 31-32

Set-up problem with g-function.

.. GENERATED FROM PYTHON SOURCE LINES 35-59

.. code-block:: default



    model = PythonModel(model_script='local_pfn.py', model_object_name='fun2_sensitivity', delete_files=True,
                        var_names=['X{}'.format(i) for i in range(5)])
    runmodel_object = RunModel(model=model)

    dist_object = [Uniform(), ] * 5


    sens = MorrisSensitivity(runmodel_object=runmodel_object,
                             distributions=dist_object,
                             n_levels=20, maximize_dispersion=True)
    sens.run(n_trajectories=10)


    fig, ax = plt.subplots(figsize=(5, 3.5))
    ax.scatter(sens.mustar_indices, sens.sigma_indices, s=60)
    for i, (mu, sig) in enumerate(zip(sens.mustar_indices, sens.sigma_indices)):
        ax.text(x=mu + 0.01, y=sig + 0.01, s='X{}'.format(i + 1), fontsize=14)
    ax.set_xlabel(r'$\mu^{\star}$', fontsize=18)
    ax.set_ylabel(r'$\sigma$', fontsize=18)
    # ax.set_title('Morris sensitivity indices', fontsize=16)
    plt.show()




.. image-sg:: /auto_examples/sensitivity/morris/images/sphx_glr_plot_morris_nonlinearities_001.png
   :alt: plot morris nonlinearities
   :srcset: /auto_examples/sensitivity/morris/images/sphx_glr_plot_morris_nonlinearities_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.986 seconds)


.. _sphx_glr_download_auto_examples_sensitivity_morris_plot_morris_nonlinearities.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/sensitivity/morris/plot_morris_nonlinearities.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


.. only:: html

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

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