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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_plot_sparse_grid_uq.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_plot_sparse_grid_uq.py:


Sparse Grid Interpolation
=========================

We will use the Genz benchmark to illustrate how to use a sparse grid
as a surrogate for uncertainty quantification and sensitivity analysis

First we must load the benchmark

.. GENERATED FROM PYTHON SOURCE LINES 10-24

.. code-block:: default

    import numpy as np
    from pyapprox.benchmarks import setup_benchmark
    from pyapprox import surrogates
    from pyapprox.analysis import visualize
    from pyapprox import util
    import matplotlib.pyplot as plt
    benchmark = setup_benchmark('genz', nvars=2, test_name="oscillatory")
    np.random.seed(1)

    #We can set a maximum number of samples using the options dictionary
    options = {"max_nsamples": 100, "verbose": 0}
    approx = surrogates.adaptive_approximate(
        benchmark.fun, benchmark.variable, "sparse_grid", options).approx








.. GENERATED FROM PYTHON SOURCE LINES 25-26

Plot the sparse grid samples with

.. GENERATED FROM PYTHON SOURCE LINES 26-30

.. code-block:: default

    sparse_grid_samples = approx.get_samples()
    util.plot_2d_samples(sparse_grid_samples, marker='o')
    plt.show()




.. image-sg:: /auto_examples/images/sphx_glr_plot_sparse_grid_uq_001.png
   :alt: plot sparse grid uq
   :srcset: /auto_examples/images/sphx_glr_plot_sparse_grid_uq_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 31-32

We can estimate the error in the surrogate using some validation samples.

.. GENERATED FROM PYTHON SOURCE LINES 32-39

.. code-block:: default

    validation_samples = benchmark.variable.rvs(100)
    validation_values = benchmark.fun(validation_samples)
    approx_values = approx(validation_samples)
    error = np.linalg.norm(validation_values-approx_values, axis=0)/np.sqrt(
        validation_values.shape[0])
    print(f"The RMSE error is {error}")





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

 .. code-block:: none

    The RMSE error is [4.6830029e-16]




.. GENERATED FROM PYTHON SOURCE LINES 40-42

and building a kernel density estimator. Lets first just plot the marginal
PDFs of the output

.. GENERATED FROM PYTHON SOURCE LINES 42-46

.. code-block:: default

    surrogate_samples = benchmark.variable.rvs(10000)
    approx_values = approx(surrogate_samples)
    visualize.plot_qoi_marginals(approx_values)
    plt.show()



.. image-sg:: /auto_examples/images/sphx_glr_plot_sparse_grid_uq_002.png
   :alt: plot sparse grid uq
   :srcset: /auto_examples/images/sphx_glr_plot_sparse_grid_uq_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.129 seconds)


.. _sphx_glr_download_auto_examples_plot_sparse_grid_uq.py:

.. only:: html

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




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

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

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

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


.. only:: html

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

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