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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_sampling_plot_random.py>`
        to download the full example code

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

.. _sphx_glr_auto_sampling_plot_random.py:


Standard Random sampling
========================

To calculate the coefficients of the gPC matrix, a number of model evaluations need to be
performed to sample the probability space :math:`\Theta` and enable the estimation of the
polynomials. As for the computation of the coefficients, the input parameters :math:`\mathbf{\xi}`
can be sampled in a number of different ways. In **pygpc** the grid :math:`\mathcal{G}` for this
application is constructed in `pygpc/Grid.py <../../../../pygpc/Grid.py>`_.

Example
-------
In order to create a grid of sampling points, we have to define the random parameters first.

.. GENERATED FROM PYTHON SOURCE LINES 15-65



.. image-sg:: /auto_sampling/images/sphx_glr_plot_random_001.png
   :alt: plot random
   :srcset: /auto_sampling/images/sphx_glr_plot_random_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Ellipsis





|

.. code-block:: default


    import pygpc
    import numpy as np
    import matplotlib.pyplot as plt
    from collections import OrderedDict

    # define random parameters
    parameters = OrderedDict()
    parameters["x1"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[-np.pi, np.pi])
    parameters["x2"] = pygpc.Beta(pdf_shape=[1, 1], pdf_limits=[-np.pi, np.pi])

    # In the case of random sampling the samples will be randomly drawn according to the probability density function (PDF)
    # :math:`f(\xi)` of the input parameters.
    #
    # A simple random grid containing 200 sampling points can be generated by:

    grid = pygpc.Random(parameters_random=parameters,
                        n_grid=200,
                        options={"seed": None})

    # The following options are available for Random grids:
    #
    # - seed: set a seed to reproduce the grid
    #
    # The grid points are distributed as follows (in the normalized space between [-1, 1]):

    fig = plt.figure(figsize=(4, 3.5))
    plt.scatter(grid.coords_norm[:, 0], grid.coords_norm[:, 1], c="k")
    plt.xlabel("$x_1$", fontsize=12)
    plt.ylabel("$x_2$", fontsize=12)
    plt.xlim([-1, 1])
    plt.ylim([-1, 1])
    plt.xticks(np.linspace(-1, 1, 5))
    plt.yticks(np.linspace(-1, 1, 5))
    plt.grid()
    plt.tight_layout()

    # For each gPC algorithm, the sampling method can be selected accordingly by setting the following options
    # when setting up the algorithm:
    options = dict()
    ...
    options["grid"] = pygpc.Random
    options["grid_options"] = {"seed": None}
    ...

    # When using Windows you need to encapsulate the code in a main function and insert an
    # if __name__ == '__main__': guard in the main module to avoid creating subprocesses recursively:
    #
    # if __name__ == '__main__':
    #     main()


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

   **Total running time of the script:** ( 0 minutes  0.113 seconds)


.. _sphx_glr_download_auto_sampling_plot_random.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_random.py <plot_random.py>`

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

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


.. only:: html

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

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