.. only:: html

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

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

    .. _sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py:


Polynomial chaos over database
==============================

In this example we are going to create a global approximation of a model response using functional chaos over a design of experiment.

You will need to specify the distribution of the input parameters.
If not known, statistical inference can be used to select a possible candidate, and fitting tests can validate such an hypothesis.


.. 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)








Create a function R^n --> R^p
For example R^4 --> R


.. code-block:: default

    myModel = ot.SymbolicFunction(['x1', 'x2', 'x3', 'x4'], ['1+x1*x2 + 2*x3^2+x4^4'])

    # Create a distribution of dimension n
    # for example n=3 with indpendent components
    distribution = ot.ComposedDistribution(
        [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)])








Prepare the input/output samples


.. code-block:: default

    sampleSize = 250
    X = distribution.getSample(sampleSize)
    Y = myModel(X)
    dimension = X.getDimension()








build the orthogonal basis


.. code-block:: default

    coll = [ot.StandardDistributionPolynomialFactory(distribution.getMarginal(i)) for i in range(dimension)]
    enumerateFunction = ot.LinearEnumerateFunction(dimension)
    productBasis = ot.OrthogonalProductPolynomialFactory(coll, enumerateFunction)








create the algorithm


.. code-block:: default

    degree = 6
    adaptiveStrategy = ot.FixedStrategy(
        productBasis, enumerateFunction.getStrataCumulatedCardinal(degree))
    projectionStrategy = ot.LeastSquaresStrategy()
    algo = ot.FunctionalChaosAlgorithm(X, Y, distribution, adaptiveStrategy, projectionStrategy)
    algo.run()








get the metamodel function


.. code-block:: default

    result = algo.getResult()
    metamodel = result.getMetaModel()








Print residuals


.. code-block:: default

    result.getResiduals()





.. raw:: html

    <p>[1.5987e-12]</p>
    <br />
    <br />


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

   **Total running time of the script:** ( 0 minutes  0.020 seconds)


.. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.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_functional_chaos_database.py <plot_functional_chaos_database.py>`



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

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


.. only:: html

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

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