.. only:: html

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

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

    .. _sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.py:


Validate a polynomial chaos
===========================

In this example, we show how to perform the draw validation of a polynomial chaos for the :ref:`Ishigami function <use-case-ishigami>`.


.. code-block:: default

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    from math import pi
    ot.Log.Show(ot.Log.NONE)








Model description
-----------------

We load the Ishigami test function from the usecases module :


.. code-block:: default

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








The `IshigamiModel` data class contains the input distribution :math:`X=(X_1, X_2, X_3)` in `im.distributionX` and the Ishigami function in `im.model`.
We also have access to the input variable names with


.. code-block:: default

    input_names = im.distributionX.getDescription()









.. code-block:: default

    N = 100 
    inputTrain = im.distributionX.getSample(N)
    outputTrain = im.model(inputTrain)








Create the chaos
----------------

We could use only the input and output training samples: in this case, the distribution of the input sample is computed by selecting the best distribution that fits the data. 


.. code-block:: default

    chaosalgo = ot.FunctionalChaosAlgorithm(inputTrain, outputTrain)








Since the input distribution is known in our particular case, we instead create the multivariate basis from the distribution, that is three independent variables X1, X2 and X3.


.. code-block:: default

    multivariateBasis = ot.OrthogonalProductPolynomialFactory([im.X1, im.X2, im.X3])
    totalDegree = 8
    enumfunc = multivariateBasis.getEnumerateFunction()
    P = enumfunc.getStrataCumulatedCardinal(totalDegree)
    adaptiveStrategy = ot.FixedStrategy(multivariateBasis, P)









.. code-block:: default

    selectionAlgorithm = ot.LeastSquaresMetaModelSelectionFactory()
    projectionStrategy = ot.LeastSquaresStrategy(inputTrain, outputTrain, selectionAlgorithm)









.. code-block:: default

    chaosalgo = ot.FunctionalChaosAlgorithm(inputTrain, outputTrain, im.distributionX, adaptiveStrategy, projectionStrategy)









.. code-block:: default

    chaosalgo.run()
    result = chaosalgo.getResult()
    metamodel = result.getMetaModel()








Validation of the metamodel
---------------------------

In order to validate the metamodel, we generate a test sample.


.. code-block:: default

    n_valid = 1000
    inputTest = im.distributionX.getSample(n_valid)
    outputTest = im.model(inputTest)
    val = ot.MetaModelValidation(inputTest, outputTest, metamodel)
    Q2 = val.computePredictivityFactor()[0]
    Q2





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

 Out:

 .. code-block:: none


    0.9972078325177286



The Q2 is very close to 1: the metamodel is excellent.


.. code-block:: default

    graph = val.drawValidation()
    graph.setTitle("Q2=%.2f%%" % (Q2*100))
    view = viewer.View(graph)
    plt.show()




.. image:: /auto_meta_modeling/polynomial_chaos_metamodel/images/sphx_glr_plot_chaos_draw_validation_001.png
    :alt: Q2=99.72%
    :class: sphx-glr-single-img





The metamodel has a good predictivity, since the points are almost on the first diagonal.


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

   **Total running time of the script:** ( 0 minutes  0.192 seconds)


.. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_draw_validation.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_chaos_draw_validation.py <plot_chaos_draw_validation.py>`



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

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


.. only:: html

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

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