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.. only:: html

    .. note::
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        :ref:`Go to the end <sphx_glr_download_auto_examples_ex_pce.py>`
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.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_ex_pce.py:


Polynomial Chaos Expansion Construction
========================================

This tutorial demonstrates how to create a Polynomial Chaos Expansion (PCE) surrogate model for scalar valued
functions. We will use the ``pytuq.surrogates.pce`` wrapper class to approximate the function :math:`\sin^4(x)`.

PyTUQ provides a number of utilities for your workflows, including modules for mapping, test functions, and metric comparisons --
these, along with others, can be found in the ``utils`` directory. You can also explore the ``func`` directory for additional sample functions to use.

This example below outlines how to:

- Define basic parameters for the surrogate model
- Use a sample function of :math:`\sin^4(x)` from the ``utils`` directory
- Set up a PCE surrogate model
- And evaluate the performance of your model

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.. code-block:: Python


    import numpy as np
    import pytuq.utils.funcbank as fcb


    from pytuq.surrogates.pce import PCE
    from pytuq.utils.maps import scale01ToDom
    from pytuq.lreg.anl import anl
    from pytuq.lreg.lreg import lsq
    from pytuq.utils.mindex import get_mi



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.. code-block:: Python


    N = 14                      # Number of data points to generate
    order = 4                   # Polynomial order
    true_model = fcb.sin4       # Function to approximate 
    dim = 3                     # Dimensionality of input data
    # dim = 1


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    np.random.seed(42) 

    # Domain: defining range of input variable
    domain = np.ones((dim, 2))*np.array([-1.,1.])

    # Generating x-y data
    x = scale01ToDom(np.random.rand(N,dim), domain)
    y = true_model(x)

    # Testing PCE class:

    # (1) Construct polynomial chaos expansion
    pce = PCE(dim, order, 'LU')
    # pce = PCE(dim, order, 'HG')
    # pce = PCE(dim, order, ['LU', 'HG']) # dim = 2
    # pce = PCE(dim, order, ['HG', 'LU', 'HG', 'LU']) # dim = 4

    pce.set_training_data(x, y)

    # (2) Pick method for linear regression object, defaulting to least squares regression
    # print(pce.build(regression = 'anl'))
    # print(pce.build(regression = 'anl', method = 'vi'))
    print(pce.build())
    # print(pce.build(regression = 'lsq'))
    # print(pce.build(regression = 'bcs'))

    # (3) Make predictions for data points and print results:
    results = pce.evaluate(x)

    # np.random.seed(45) # Generate a single random data point within the domain:
    # single_point = scale01ToDom(np.random.rand(1, dim), domain)
    # results = pce.evaluate(single_point)

    # Generate random input for evaluation:
    # x_eval = scale01ToDom(np.random.rand(10,dim), domain)
    # results = pce.evaluate(x_eval)

    print(results)

.. _sphx_glr_download_auto_examples_ex_pce.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: ex_pce.zip <ex_pce.zip>`


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

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