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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_sampling_simplex_plot_simplex.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_simplex_plot_simplex.py:


Simplex Sampling
==================================

This example shows the use of the Simplex sampling class. In particular:

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- How to define the Simplex sampling method supported by UQpy
- How to draw samples using Simplex sampling
- How to plot simplices as well as their corresponding samples.

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Initially we have to import the necessary modules.

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.. code-block:: default


    from UQpy.sampling import SimplexSampling
    import numpy as np
    import matplotlib.pyplot as plt








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Define Simplices
----------------------------------------------
Create an array of 3 points in 2-D, which will be the vertex coordinates of the simplex.

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.. code-block:: default


    vertex = np.array([[0, 0], [0.5, 1], [1, 0]])








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Add new samples to existing sampling object
----------------------------------------------
Use Simplex class to generate uniformly distributed samples. This class needs two input parameters,
i.e. :code:`nodes` and :code:`nsamples`. Nodes are the vertex coordinates of simplex and nsamples is the number of new
samples to be generated. In this example, we are generating ten new samples inside our simplex.

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.. code-block:: default


    x = SimplexSampling(nodes=vertex, nsamples=10, random_state=1)








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Plot the samples of the simplex
------------------------------------
A schematic illustration of the 2-D simplex and new samples generated using Simplex class are presented below.

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.. code-block:: default


    plt.plot(np.array([0, 0.5, 1, 0]), np.array([0, 1, 0, 0]), color='blue')
    plt.scatter(x.samples[:, 0], x.samples[:, 1], color='red')
    plt.show()




.. image-sg:: /auto_examples/sampling/simplex/images/sphx_glr_plot_simplex_001.png
   :alt: plot simplex
   :srcset: /auto_examples/sampling/simplex/images/sphx_glr_plot_simplex_001.png
   :class: sphx-glr-single-img





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User can also define a Simplex object using vertices and generate samples using :py:meth:`run` method.

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.. code-block:: default


    y = SimplexSampling(nodes=vertex)
    y.run(nsamples=5)








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

   **Total running time of the script:** ( 0 minutes  0.043 seconds)


.. _sphx_glr_download_auto_examples_sampling_simplex_plot_simplex.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/simplex/plot_simplex.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


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