.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/sensitivity/chatterjee/chatterjee_ishigami.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_chatterjee_chatterjee_ishigami.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_chatterjee_chatterjee_ishigami.py:


Ishigami function
==============================================

The ishigami function is a non-linear, non-monotonic function that is commonly used to 
benchmark uncertainty and sensitivity analysis methods.

.. math::
    f(x_1, x_2, x_3) = sin(x_1) + a \cdot sin^2(x_2) + b \cdot x_3^4 sin(x_1)

.. math::
    x_1, x_2, x_3 \sim \mathcal{U}(-\pi, \pi), \quad a, b\in \mathbb{R}

.. GENERATED FROM PYTHON SOURCE LINES 18-29

.. code-block:: default

    import numpy as np

    from UQpy.run_model.RunModel import RunModel
    from UQpy.run_model.model_execution.PythonModel import PythonModel
    from UQpy.distributions import Uniform
    from UQpy.distributions.collection.JointIndependent import JointIndependent
    from UQpy.sensitivity.ChatterjeeSensitivity import ChatterjeeSensitivity
    from UQpy.sensitivity.PostProcess import *

    np.random.seed(123)


.. GENERATED FROM PYTHON SOURCE LINES 30-31

**Define the model and input distributions**

.. GENERATED FROM PYTHON SOURCE LINES 31-46

.. code-block:: default


    # Create Model object
    model = PythonModel(
        model_script="local_ishigami.py",
        model_object_name="evaluate",
        var_names=[r"$X_1$", "$X_2$", "$X_3$"],
        delete_files=True,
        params=[7, 0.1],
    )

    runmodel_obj = RunModel(model=model)

    # Define distribution object
    dist_object = JointIndependent([Uniform(-np.pi, 2 * np.pi)] * 3)


.. GENERATED FROM PYTHON SOURCE LINES 47-48

**Compute Chatterjee indices**

.. GENERATED FROM PYTHON SOURCE LINES 50-59

.. code-block:: default

    SA = ChatterjeeSensitivity(runmodel_obj, dist_object)

    SA.run(
        n_samples=100_000,
        estimate_sobol_indices=True,
        n_bootstrap_samples=100,
        confidence_level=0.95,
    )


.. GENERATED FROM PYTHON SOURCE LINES 60-61

**Chattererjee indices**

.. GENERATED FROM PYTHON SOURCE LINES 63-65

.. code-block:: default

    SA.first_order_chatterjee_indices


.. GENERATED FROM PYTHON SOURCE LINES 66-67

**Confidence intervals for the Chatterjee indices**

.. GENERATED FROM PYTHON SOURCE LINES 69-79

.. code-block:: default

    SA.confidence_interval_chatterjee

    # **Plot the Chatterjee indices**
    fig1, ax1 = plot_sensitivity_index(
        SA.first_order_chatterjee_indices[:, 0],
        SA.confidence_interval_chatterjee,
        plot_title="Chatterjee indices",
        color="C2",
    )


.. GENERATED FROM PYTHON SOURCE LINES 80-89

**Estimated Sobol indices**

Expected first order Sobol indices:

:math:`S_1`: 0.3139

:math:`S_2`: 0.4424

:math:`S_3`: 0.0

.. GENERATED FROM PYTHON SOURCE LINES 91-99

.. code-block:: default

    SA.first_order_sobol_indices

    # **Plot the first order Sobol indices**
    fig2, ax2 = plot_sensitivity_index(
        SA.first_order_sobol_indices[:, 0],
        plot_title="First order Sobol indices",
        color="C0",
    )


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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_sensitivity_chatterjee_chatterjee_ishigami.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/chatterjee/chatterjee_ishigami.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


.. only:: html

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

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