.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/post_process/algorithms/plot_correlations.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_post_process_algorithms_plot_correlations.py>`
        to download the full example code.

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

.. _sphx_glr_examples_post_process_algorithms_plot_correlations.py:


Correlations
============

In this example, we illustrate the use of the :class:`.Correlations` post-processing
on the Sobieski's SSBJ problem.

A correlation coefficient indicates whether there is a linear relationship between two
quantities :math:`x` and :math:`y`. It is the normalized covariance between the two
quantities defined as:

.. math::

   R_{xy}=\frac {\sum \limits _{i=1}^n(x_i-{\bar{x}})(y_i-{\bar{y}})}{ns_{x}s_{y}}
   =\frac {\sum \limits _{i=1}^n(x_i-{\bar{x}})(y_i-{\bar{y}})}{\sqrt {\sum
   \limits _{i=1}^n(x_i-{\bar{x}})^{2}\sum \limits _{i=1}^n(y_i-{\bar{y}})^{2}}}

The :class:`.Correlations` post-processing provides scatter plots of correlated
variables among design variables, outputs functions, and constraints.

By default, only the variables with a correlation coefficient greater than 0.95 are
considered. The threshold value can be modified in the post-processing settings.

.. GENERATED FROM PYTHON SOURCE LINES 44-60



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_correlations_001.png
         :alt: R=-0.98093, R=0.98093, R=-0.96059, R=-0.96066, R=0.99723, R=0.96067, R=-0.99723, R=-1.00000, R=-0.96068, R=0.99723, R=1.00000, R=-1.00000, R=-0.96068, R=0.99723, R=1.00000, R=-1.00000, R=1.00000, R=-0.99817, R=0.96068, R=-0.99723, R=-1.00000, R=1.00000, R=-1.00000, R=0.96068, R=-0.99722
         :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_correlations_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_correlations_002.png
         :alt: R=-1.00000, R=1.00000, R=-1.00000, R=-1.00000, R=1.00000, R=-0.98196, R=-0.98224, R=0.98223, R=-0.98223, R=-0.98223, R=0.98223, R=0.98223
         :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_correlations_002.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none

        INFO - 16:25:43: Importing the optimization problem from the file sobieski_mdf_scenario.h5
        INFO - 16:25:43: Detected 37 correlations > 0.95

    <gemseo.post.correlations.Correlations object at 0x72a4d89b7e90>





|

.. code-block:: Python


    from __future__ import annotations

    from gemseo import execute_post
    from gemseo.settings.post import Correlations_Settings

    # Correlations of the constraint `g_3`.
    execute_post(
        "sobieski_mdf_scenario.h5",
        settings_model=Correlations_Settings(
            func_names=["g_3"],
            coeff_limit=0.95,  # Default value, here for illustration purpose.
            save=False,
            show=True,
        ),
    )


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

   **Total running time of the script:** (0 minutes 1.417 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_correlations.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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