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.. "auto_examples/sampling/true_stratified_sampling/true_stratified_voronoi.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_sampling_true_stratified_sampling_true_stratified_voronoi.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_sampling_true_stratified_sampling_true_stratified_voronoi.py:


Voronoi Stratified Sampling
==================================

In this example, the stratified sampling method is employed to generate samples from an exponential distribution using
Voronoi stratification.

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Import the necessary libraries. Here we import standard libraries such as numpy and matplotlib, but also need to
import the :class:`.TrueStratifiedSampling` class from :py:mod:`UQpy.sampling`.

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.. code-block:: default


    from UQpy.sampling.stratified_sampling.TrueStratifiedSampling import TrueStratifiedSampling
    from UQpy.sampling.stratified_sampling.strata import VoronoiStrata
    from UQpy.distributions import Exponential
    import matplotlib.pyplot as plt
    from scipy.spatial import voronoi_plot_2d


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Run :class:`.TrueStratifiedSampling` for 25 samples.

- 2 dimensions
- Five strata in each dimension
- Exponential distribution with location parameter = 1 and scale parameter = 1.

Create a distribution object.

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.. code-block:: default


    marginals = [Exponential(loc=1., scale=1.), Exponential(loc=1., scale=1.)]


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Equal number of samples in each stratum
----------------------------------------
Create strata object using :class:`.VoronoiStrata` class.

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.. code-block:: default


    strata_obj = VoronoiStrata(seeds_number=8, dimension=2)
    sts_vor_obj = TrueStratifiedSampling(distributions=marginals, strata_object=strata_obj,  random_state=3)


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Figure shows the stratification of domain using randomly generated seed points

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.. code-block:: default


    strata_obj

    voronoi_plot_2d(strata_obj.voronoi)
    plt.title('Stratified Sample - U(0,1)')
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.show()


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Run stratified sampling

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.. code-block:: default


    sts_vor_obj.run(nsamples_per_stratum=3)


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Plot the resulting stratified samples and the boundaries of the strata in the :math:`U(0,1)` space.

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.. code-block:: default


    voronoi_plot_2d(strata_obj.voronoi)
    plt.title('Stratified Sample - U(0,1)')
    plt.plot(sts_vor_obj.samplesU01[:, 0], sts_vor_obj.samplesU01[:, 1], 'dm')
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.show()

    sts_vor_obj.weights


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Proportional Sampling
---------------------
:class:`.TrueStratifiedSampling` class can generate samples proportional to volume of each stratum.

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.. code-block:: default


    sts_vor_obj1 = TrueStratifiedSampling(distributions=marginals, strata_object=strata_obj, random_state=1)
    sts_vor_obj1.run(nsamples=10)


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It can be noticed that new sample in each stratum is proportional to volume

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.. code-block:: default


    print('Volume: ', sts_vor_obj1.strata_object.volume)
    print('Number of samples in each stratum: ', sts_vor_obj1.nsamples_per_stratum)


    voronoi_plot_2d(strata_obj.voronoi)
    plt.title('Stratified Sample - U(0,1)')
    plt.plot(sts_vor_obj1.samplesU01[:, 0], sts_vor_obj1.samplesU01[:, 1], 'dm')
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.show()

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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_sampling_true_stratified_sampling_true_stratified_voronoi.py:

.. only:: html

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


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/sampling/true_stratified_sampling/true_stratified_voronoi.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


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