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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/sampling/refined_stratified_sampling/refined_stratified_rectangular_random.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_refined_stratified_sampling_refined_stratified_rectangular_random.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_refined_stratified_sampling_refined_stratified_rectangular_random.py:


Rectangular Refined Stratified Sampling - Random Refinement
============================================================

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

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In this example, Stratified sampling is used to generate samples from Uniform probability distribution and sample are
added using adaptive approach Refined Stratified Sampling.

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

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.. code-block:: default


    from UQpy.sampling.stratified_sampling.strata import RectangularStrata
    from UQpy.sampling import TrueStratifiedSampling, RefinedStratifiedSampling, RandomRefinement
    from UQpy.distributions import Uniform
    import matplotlib.pyplot as plt
    import matplotlib.patches as patches
    import numpy as np


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Create a distribution object.

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.. code-block:: default


    marginals = [Uniform(loc=0., scale=1.), Uniform(loc=0., scale=1.)]


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Create a strata object

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.. code-block:: default


    strata = RectangularStrata(strata_number=[4, 4])


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Run stratified sampling.

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.. code-block:: default


    x = TrueStratifiedSampling(distributions=marginals, strata_object=strata, nsamples_per_stratum=1, random_state=1)


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Using UQpy :class:`.RefinedStratifiedSampling` class to expand samples generated by :class:`.TrueStratifiedSampling`
class. In this example, two new samples are generated using rectangular stratification .

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.. code-block:: default


    refinement = RandomRefinement(strata=strata)
    y = RefinedStratifiedSampling(stratified_sampling=x, refinement_algorithm=refinement,
                                  nsamples=18, samples_per_iteration=2, random_state=2)


.. GENERATED FROM PYTHON SOURCE LINES 63-66

In the first figure shown below, samples generated from :class:`.TrueStratifiedSampling` class are plotted. Second
figure, shows the new stratification corresponding to two generated samples using :class:`.RefinedStratifiedSampling`
class.

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.. code-block:: default


    fig1 = strata.plot_2d()
    plt.plot(x.samples[:16, 0], x.samples[:16, 1], 'ro')
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.show()

    fig2 = strata.plot_2d()
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.plot(y.samples[:16, 0], y.samples[:16, 1], 'ro')
    plt.plot(y.samples[16:, 0], y.samples[16:, 1], 'yo')
    plt.show()


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Further, :class:`.RefinedStratifiedSampling` class is used to adaptively increase the sample size. In this example,
samples are added in strata with maximum weights associated with it and strata's are cut randomly along the maximum
width.

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.. code-block:: default


    y.run(nsamples=100)


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In the figure shown below, all samples generated from :class:`.TrueStratifiedSampling` and
:class:`.RefinedStratifiedSampling` class are plotted.

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.. code-block:: default


    fig3 = strata.plot_2d()
    plt.xlim([0, 1])
    plt.ylim([0, 1])
    plt.plot(y.samplesU01[:16, 0], y.samplesU01[:16, 1], 'ro')
    plt.plot(y.samplesU01[16:, 0], y.samplesU01[16:, 1], 'go')
    plt.show()


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

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


.. _sphx_glr_download_auto_examples_sampling_refined_stratified_sampling_refined_stratified_rectangular_random.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/refined_stratified_sampling/refined_stratified_rectangular_random.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


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