.. 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_chaos_build_distribution.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_chaos_build_distribution.py>`
        to download the full example code

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

.. _sphx_glr_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_build_distribution.py:


Fit a distribution from an input sample
=======================================

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In this example we show how to use the `BuildDistribution` function to fit a distribution to an input sample.
This function is used by the `FunctionalChaosAlgorithm` class when we want to create a polynomial chaos metamodel and we have a design of experiments which have been computed beforehand.
In this case, we have to identify the distributions which best fit to the input sample in order to define the input probabilistic model.
This is, in turn, used by in the polynomial chaos to create the orthogonal basis.


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.. code-block:: Python

    import openturns as ot

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








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We first create the function `model`.

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.. code-block:: Python

    ot.RandomGenerator.SetSeed(0)
    dimension = 2
    input_names = ["x1", "x2"]
    formulas = ["cos(x1 + x2)", "(x2 + 1) * exp(x1)"]
    model = ot.SymbolicFunction(input_names, formulas)








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Then we create a sample `x` and compute the corresponding output sample `y`.

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.. code-block:: Python

    distribution = ot.Normal(dimension)
    samplesize = 1000
    inputSample = distribution.getSample(samplesize)
    outputSample = model(inputSample)








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Create a functional chaos model.
First, we need to fit a distribution on the input sample. We can do this automatically with the Lilliefors test.

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.. code-block:: Python

    ot.ResourceMap.SetAsUnsignedInteger("FittingTest-LillieforsMaximumSamplingSize", 100)








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.. code-block:: Python

    distribution = ot.FunctionalChaosAlgorithm.BuildDistribution(inputSample)








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.. code-block:: Python

    for i in range(dimension):
        marginal = distribution.getMarginal(i)
        marginalname = marginal.getImplementation().getClassName()
        print("Marginal #", i, ":", marginalname)
    distribution.getCopula()





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

 .. code-block:: none

    Marginal # 0 : Normal
    Marginal # 1 : Normal


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>IndependentCopula(dimension = 2)</p>
    </div>
    <br />
    <br />

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The previous call to `BuildDistribution` is what is done internally by the following constructor of `FunctionalChaosAlgorithm`.

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.. code-block:: Python

    algo = ot.FunctionalChaosAlgorithm(inputSample, outputSample)








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Reset default settings

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.. code-block:: Python

    ot.ResourceMap.Reload()








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

   **Total running time of the script:** (0 minutes 2.266 seconds)


.. _sphx_glr_download_auto_meta_modeling_polynomial_chaos_metamodel_plot_chaos_build_distribution.py:

.. only:: html

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

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

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

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

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