.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_sample_correlation.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_data_analysis_manage_data_and_samples_plot_sample_correlation.py:


Estimate correlation coefficients
=================================

In this example we are going to estimate the correlation between an output sample Y and the corresponding inputs using various estimators:

- Pearson coefficients
- Spearman coefficients
- PCC: Partial Correlation Coefficients
- PRCC: Partial Rank Correlation Coefficient
- SRC: Standard Regression Coefficients
- SRRC: Standard Rank Regression Coefficient


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








To illustrate the usage of the method mentionned above, we define a set of X/Y data using the :ref:`Ishigami model <use-case-ishigami>`. This classical model is defined in a data class :


.. code-block:: default

    from openturns.usecases import ishigami_function as ishigami_function
    im = ishigami_function.IshigamiModel()








Create X/Y data
We get the input variables description :


.. code-block:: default

    input_names = im.distributionX.getDescription()

    size = 100
    inputDesign = ot.SobolIndicesExperiment(im.distributionX, size, True).generate()
    outputDesign = im.model(inputDesign)








PCC coefficients
------------------
We compute here `PCC` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    pcc_indices = ot.CorrelationAnalysis.PCC(inputDesign, outputDesign)
    print(pcc_indices)





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

 Out:

 .. code-block:: none

    [0.48083,0.0118573,-0.0399335]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(pcc_indices, input_names, "PCC coefficients")
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_001.png
    :alt: PCC coefficients
    :class: sphx-glr-single-img





PRCC coefficients
--------------------
We compute here `PRCC` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    prcc_indices = ot.CorrelationAnalysis.PRCC(inputDesign, outputDesign)
    print(prcc_indices)





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

 Out:

 .. code-block:: none

    [0.48438,-0.00850357,-0.0310585]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(prcc_indices, input_names, "PRCC coefficients")
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_002.png
    :alt: PRCC coefficients
    :class: sphx-glr-single-img





SRC coefficients
-------------------
We compute here `SRC` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    src_indices = ot.CorrelationAnalysis.SRC(inputDesign, outputDesign)
    print(src_indices)





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

 Out:

 .. code-block:: none

    [0.231036,0.000107773,0.00122827]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(src_indices, input_names, 'SRC coefficients')
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_003.png
    :alt: SRC coefficients
    :class: sphx-glr-single-img





Case where coefficients sum to 1 : 


.. code-block:: default

    scale_src_indices = ot.CorrelationAnalysis.SRC(inputDesign, outputDesign, True)
    print(scale_src_indices)





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

 Out:

 .. code-block:: none

    [0.99425,0.000463796,0.00528582]




And its associated graph:


.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(scale_src_indices, input_names, 'Scaled SRC coefficients')
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_004.png
    :alt: Scaled SRC coefficients
    :class: sphx-glr-single-img





Finally, using signed src: we get the trend importance :


.. code-block:: default

    signed_src_indices = ot.CorrelationAnalysis.SignedSRC(inputDesign, outputDesign)
    print(signed_src_indices)





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

 Out:

 .. code-block:: none

    [0.480662,0.0103814,-0.0350468]




and its graph :


.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(signed_src_indices, input_names, 'Signed SRC coefficients')
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_005.png
    :alt: Signed SRC coefficients
    :class: sphx-glr-single-img





SRRC coefficients
--------------------
We compute here `SRRC` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    srrc_indices = ot.CorrelationAnalysis.SRRC(inputDesign, outputDesign)
    print(srrc_indices)





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

 Out:

 .. code-block:: none

    [0.234826,5.52475e-05,0.00074076]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(srrc_indices, input_names, 'SRRC coefficients')
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_006.png
    :alt: SRRC coefficients
    :class: sphx-glr-single-img





Pearson coefficients
-----------------------
We compute here the Pearson :math:`\rho` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    pearson_correlation = ot.CorrelationAnalysis.PearsonCorrelation(inputDesign, outputDesign)
    print(pearson_correlation)





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

 Out:

 .. code-block:: none

    [0.482871,0.0178456,-0.0638373]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(pearson_correlation,
                                                         input_names,
                                                         "Pearson correlation coefficients")
    view = viewer.View(graph)




.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_007.png
    :alt: Pearson correlation coefficients
    :class: sphx-glr-single-img





Spearman coefficients
-----------------------
We compute here the Pearson :math:`\rho_s` coefficients using the `CorrelationAnalysis`


.. code-block:: default

    spearman_correlation = ot.CorrelationAnalysis.SpearmanCorrelation(inputDesign, outputDesign)
    print(spearman_correlation)





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

 Out:

 .. code-block:: none

    [0.486298,-0.00194796,-0.0585667]





.. code-block:: default

    graph = ot.SobolIndicesAlgorithm.DrawCorrelationCoefficients(spearman_correlation, 
                                                         input_names, 
                                                         "Spearman correlation coefficients")
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_data_analysis/manage_data_and_samples/images/sphx_glr_plot_sample_correlation_008.png
    :alt: Spearman correlation coefficients
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.590 seconds)


.. _sphx_glr_download_auto_data_analysis_manage_data_and_samples_plot_sample_correlation.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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