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


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

The ishigami function is a non-linear, non-monotonic function that is commonly used to 
benchmark uncertainty and senstivity 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 18-31

.. 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.CramerVonMisesSensitivity import CramerVonMisesSensitivity as cvm
    from UQpy.sensitivity.SobolSensitivity import SobolSensitivity
    from UQpy.sensitivity.PostProcess import *

    np.random.seed(123)


.. GENERATED FROM PYTHON SOURCE LINES 32-33

**Define the model and input distributions**

.. GENERATED FROM PYTHON SOURCE LINES 35-36

Create Model object

.. GENERATED FROM PYTHON SOURCE LINES 36-49

.. code-block:: default

    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 50-51

**Compute Sobol indices**

.. GENERATED FROM PYTHON SOURCE LINES 53-57

.. code-block:: default

    SA_sobol = SobolSensitivity(runmodel_obj, dist_object)

    SA_sobol.run(n_samples=100_000)


.. GENERATED FROM PYTHON SOURCE LINES 58-67

**First order 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 69-71

.. code-block:: default

    SA_sobol.first_order_indices


.. GENERATED FROM PYTHON SOURCE LINES 72-81

**Total order Sobol indices**

Expected total order Sobol indices:

:math:`S_{T_1}` = 0.55758886

:math:`S_{T_2}` = 0.44241114

:math:`S_{T_3}` =  0.24368366

.. GENERATED FROM PYTHON SOURCE LINES 83-85

.. code-block:: default

    SA_sobol.total_order_indices


.. GENERATED FROM PYTHON SOURCE LINES 86-87

**Compute Chatterjee indices**

.. GENERATED FROM PYTHON SOURCE LINES 89-93

.. code-block:: default

    SA_chatterjee = ChatterjeeSensitivity(runmodel_obj, dist_object)

    SA_chatterjee.run(n_samples=50_000)


.. GENERATED FROM PYTHON SOURCE LINES 94-96

.. code-block:: default

    SA_chatterjee.first_order_chatterjee_indices


.. GENERATED FROM PYTHON SOURCE LINES 97-98

**Compute Cramér-von Mises indices**

.. GENERATED FROM PYTHON SOURCE LINES 98-103

.. code-block:: default

    SA_cvm = cvm(runmodel_obj, dist_object)

    # Compute CVM indices using the pick and freeze algorithm
    SA_cvm.run(n_samples=20_000, estimate_sobol_indices=True)


.. GENERATED FROM PYTHON SOURCE LINES 104-106

.. code-block:: default

    SA_cvm.first_order_CramerVonMises_indices


.. GENERATED FROM PYTHON SOURCE LINES 107-108

**Plot all indices**

.. GENERATED FROM PYTHON SOURCE LINES 108-166

.. code-block:: default


    num_vars = 3
    _idx = np.arange(num_vars)
    variable_names = [r"$X_{}$".format(i + 1) for i in range(num_vars)]

    # round to 2 decimal places
    indices_1 = np.around(SA_sobol.first_order_indices[:, 0], decimals=2)
    indices_2 = np.around(SA_chatterjee.first_order_chatterjee_indices[:, 0], decimals=2)
    indices_3 = np.around(SA_cvm.first_order_CramerVonMises_indices[:, 0], decimals=2)

    fig, ax = plt.subplots()
    width = 0.3
    ax.spines["top"].set_visible(False)
    ax.spines["right"].set_visible(False)

    bar_indices_1 = ax.bar(
        _idx - width,  # x-axis
        indices_1,  # y-axis
        width=width,  # bar width
        color="C0",  # bar color
        # alpha=0.5,  # bar transparency
        label="Sobol",  # bar label
        ecolor="k",  # error bar color
        capsize=5,  # error bar cap size in pt
    )

    bar_indices_2 = ax.bar(
        _idx,  # x-axis
        indices_2,  # y-axis
        width=width,  # bar width
        color="C2",  # bar color
        # alpha=0.5,  # bar transparency
        label="Chatterjee",  # bar label
        ecolor="k",  # error bar color
        capsize=5,  # error bar cap size in pt
    )

    bar_indices_3 = ax.bar(
        _idx + width,  # x-axis
        indices_3,  # y-axis
        width=width,  # bar width
        color="C3",  # bar color
        # alpha=0.5,  # bar transparency
        label="Cramér-von Mises",  # bar label
        ecolor="k",  # error bar color
        capsize=5,  # error bar cap size in pt
    )

    ax.bar_label(bar_indices_1, label_type="edge", fontsize=10)
    ax.bar_label(bar_indices_2, label_type="edge", fontsize=10)
    ax.bar_label(bar_indices_3, label_type="edge", fontsize=10)
    ax.set_xticks(_idx, variable_names)
    ax.set_xlabel("Model inputs")
    ax.set_title("Comparison of sensitivity indices")
    ax.set_ylim(top=1)  # set only upper limit of y to 1
    ax.legend()

    plt.show()


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

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


.. _sphx_glr_download_auto_examples_sensitivity_comparison_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/comparison/ishigami.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


.. only:: html

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

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