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.. "auto_examples/sampling/latin_hypercube/plot_latin_hypercube_user_criterion.py"
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.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_sampling_latin_hypercube_plot_latin_hypercube_user_criterion.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_latin_hypercube_plot_latin_hypercube_user_criterion.py:


User Design Criterion
==================================

This example illustrates use of user-defined latin hypercube design criteria. In particular:

.. GENERATED FROM PYTHON SOURCE LINES 10-14

- How to define the Monte Carlo sampling method supported by UQpy
- How to append new samples to the existing ones
- How to transform existing samples to the unit hypercube
- How to plot histograms for each one of the sampled parameters and 2D scatter of the produced samples

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Initially we have to import the necessary modules.

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.. code-block:: default


    from UQpy.sampling import LatinHypercubeSampling
    import matplotlib.pyplot as plt
    from UQpy.distributions import Uniform
    from UQpy.sampling.stratified_sampling.latin_hypercube_criteria import *
    from UQpy.sampling.stratified_sampling.latin_hypercube_criteria import Criterion









.. GENERATED FROM PYTHON SOURCE LINES 32-37

Create user-defined criterion
----------------------------------------------
In order to create a user defined criterion, a concrete implementation of the :class:`.Criterion` abstract class must
be created. The :code:`generate_samples` method must be implemented, which receives as input the :code:`random_state`,
the randomly generated latin hypercube samples.

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.. code-block:: default



    class UserCriterion(Criterion):
        def generate_samples(self, random_state):
            lhs_samples = np.zeros_like(self.samples)
            for j in range(self.samples.shape[1]):
                order = np.random.permutation(self.samples.shape[0])
                lhs_samples[:, j] = self.samples[order, j]
            return lhs_samples









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Define Latin Hypercube sampling
----------------------------------------------
In order to initialize the LatinHypercube sampling class, the user needs to define a list of distributions
for each one of the parameters that need to be sampled.

Apart from the distributions list, the number of samples  :code:`nsamples` to be drawn is required.
The :code:`random_state` parameter defines the seed of the random generator.

Finally, the design criterion can be defined by the user. The default case is the :class:`.Random`.
For more details on the various criteria you can refer to the documentation of the criteria
:class:`.Random`, :class:`.Centered`, :class:`.Maximin`, :class:`.MinCorrelation`

In the case of user-defined criteria an instantiation of the UserCriterion class is provided instead of the
built-in criteria.

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.. code-block:: default


    dist1 = Uniform(loc=0., scale=1.)
    dist2 = Uniform(loc=0., scale=1.)

    lhs_user_defined = LatinHypercubeSampling(distributions=[dist1, dist2], nsamples=5,
                                              criterion=UserCriterion())
    print(lhs_user_defined._samples)





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

 .. code-block:: none

    [[0.68090275 0.60549567]
     [0.14175822 0.5948103 ]
     [0.39720161 0.39503455]
     [0.88606061 0.18531564]
     [0.44924163 0.86012738]]




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Plot the samples
------------------------------------

The samples generated using the LatinHypercube sampling method can be retrieved using the *samples* attribute. This
attribute is a :any:`numpy.ndarray`.

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.. code-block:: default


    # plot the samples
    fig, ax = plt.subplots()
    plt.title('LHS sampling - User Criterion')
    plt.scatter(lhs_user_defined._samples[:, 0], lhs_user_defined._samples[:, 1], marker='o')
    ax.yaxis.grid(True)
    ax.xaxis.grid(True)
    plt.ylim(0, 1)
    plt.xlim(0, 1)
    plt.show()



.. image-sg:: /auto_examples/sampling/latin_hypercube/images/sphx_glr_plot_latin_hypercube_user_criterion_001.png
   :alt: LHS sampling - User Criterion
   :srcset: /auto_examples/sampling/latin_hypercube/images/sphx_glr_plot_latin_hypercube_user_criterion_001.png
   :class: sphx-glr-single-img






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


.. _sphx_glr_download_auto_examples_sampling_latin_hypercube_plot_latin_hypercube_user_criterion.py:

.. only:: html

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      .. image:: images/binder_badge_logo.svg
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        :alt: Launch binder
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