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

.. only:: html

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

        :ref:`Go to the end <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
==============================

.. GENERATED FROM PYTHON SOURCE LINES 6-10

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.

.. GENERATED FROM PYTHON SOURCE LINES 12-16

.. code-block:: Python

    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 17-19

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

.. GENERATED FROM PYTHON SOURCE LINES 19-27

.. code-block:: Python

    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 independent components
    distribution = ot.ComposedDistribution(
        [ot.Normal(), ot.Uniform(), ot.Gamma(2.75, 1.0), ot.Beta(2.5, 1.0, -1.0, 2.0)]
    )








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Prepare the input/output samples

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.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 35-36

build the orthogonal basis

.. GENERATED FROM PYTHON SOURCE LINES 36-43

.. code-block:: Python

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








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create the algorithm

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.. code-block:: Python

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








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get the metamodel function

.. GENERATED FROM PYTHON SOURCE LINES 57-60

.. code-block:: Python

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








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Print residuals

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.. code-block:: Python

    result.getResiduals()





.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    class=Point name=Unnamed dimension=1 values=[2.64115e-15]
    </div>
    <br />
    <br />


.. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_functional_chaos_database.py:

.. only:: html

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

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

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

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

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