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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py>`
        to download the full example code

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

.. _sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py:


Various design of experiments in OpenTURNS
==========================================

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The goal of this example is to present several design of experiments available in OpenTURNS.

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Distribution
------------

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.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv

    ot.Log.Show(ot.Log.NONE)








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Monte-Carlo sampling in 2D
--------------------------

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.. code-block:: Python

    dim = 2
    X = [ot.Uniform()] * dim
    distribution = ot.ComposedDistribution(X)
    bounds = distribution.getRange()








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.. code-block:: Python

    sampleSize = 10
    sample = distribution.getSample(sampleSize)








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.. code-block:: Python

    fig = otv.PlotDesign(sample, bounds)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_001.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_001.png
   :class: sphx-glr-single-img





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We see that there a empty zones in the input space.

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Monte-Carlo sampling in 3D
--------------------------

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.. code-block:: Python

    dim = 3
    X = [ot.Uniform()] * dim
    distribution = ot.ComposedDistribution(X)
    bounds = distribution.getRange()








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.. code-block:: Python

    sampleSize = 10
    sample = distribution.getSample(sampleSize)








.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: Python

    fig = otv.PlotDesign(sample, bounds)
    fig.set_size_inches(10, 10)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_002.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_002.png
   :class: sphx-glr-single-img





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Latin Hypercube Sampling
------------------------

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.. code-block:: Python

    distribution = ot.ComposedDistribution([ot.Uniform()] * 3)
    samplesize = 5
    experiment = ot.LHSExperiment(distribution, samplesize, False, False)
    sample = experiment.generate()








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In order to see the LHS property, we need to set the bounds.

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.. code-block:: Python

    bounds = distribution.getRange()








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.. code-block:: Python

    fig = otv.PlotDesign(sample, bounds)
    fig.set_size_inches(10, 10)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_003.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_003.png
   :class: sphx-glr-single-img





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We see that each column or row exactly contains one single point.
This shows that a LHS design of experiments has good 1D projection properties, and, hence, is a good candidate for a space filling design.

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Optimized LHS
-------------

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.. code-block:: Python

    distribution = ot.ComposedDistribution([ot.Uniform()] * 3)
    samplesize = 10








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.. code-block:: Python

    bounds = distribution.getRange()








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.. code-block:: Python

    lhs = ot.LHSExperiment(distribution, samplesize)
    lhs.setAlwaysShuffle(True)  # randomized
    space_filling = ot.SpaceFillingC2()
    temperatureProfile = ot.GeometricProfile(10.0, 0.95, 1000)
    algo = ot.SimulatedAnnealingLHS(lhs, space_filling, temperatureProfile)
    # optimal design
    sample = algo.generate()








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.. code-block:: Python

    fig = otv.PlotDesign(sample, bounds)
    fig.set_size_inches(10, 10)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_004.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_004.png
   :class: sphx-glr-single-img





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We see that this LHS is optimized in the sense that it fills the space more evenly than a non-optimized does in general.

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Sobol' low discrepancy sequence
-------------------------------

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.. code-block:: Python

    dim = 2
    distribution = ot.ComposedDistribution([ot.Uniform()] * dim)
    bounds = distribution.getRange()








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.. code-block:: Python

    sequence = ot.SobolSequence(dim)








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.. code-block:: Python

    samplesize = 2**5  # Sobol' sequences are in base 2
    experiment = ot.LowDiscrepancyExperiment(sequence, distribution, samplesize, False)
    sample = experiment.generate()








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.. code-block:: Python

    samplesize





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

 .. code-block:: none


    32



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.. code-block:: Python

    subdivisions = [2**2, 2**1]
    fig = otv.PlotDesign(sample, bounds, subdivisions)
    fig.set_size_inches(6, 6)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_005.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_005.png
   :class: sphx-glr-single-img





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We have elementary intervals in 2 dimensions, each having a volume equal to 1/8.
Since there are 32 points, the Sobol' sequence is so that each elementary interval contains exactly 32/8 = 4 points.
Notice that each elementary interval is closed on the left (or bottom) and open on the right (or top).

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Halton low discrepancy sequence
-------------------------------

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.. code-block:: Python

    dim = 2
    distribution = ot.ComposedDistribution([ot.Uniform()] * dim)
    bounds = distribution.getRange()








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.. code-block:: Python

    sequence = ot.HaltonSequence(dim)








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Halton sequence uses prime numbers 2 and 3 in two dimensions.

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.. code-block:: Python

    samplesize = 2**2 * 3**2
    experiment = ot.LowDiscrepancyExperiment(sequence, distribution, samplesize, False)
    sample = experiment.generate()








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.. code-block:: Python

    samplesize





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

 .. code-block:: none


    36



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.. code-block:: Python

    subdivisions = [2**2, 3]
    fig = otv.PlotDesign(sample, bounds, subdivisions)
    fig.set_size_inches(6, 6)




.. image-sg:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_006.png
   :alt: plot design of experiments
   :srcset: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_design_of_experiments_006.png
   :class: sphx-glr-single-img





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We have elementary intervals in 2 dimensions, each having a volume equal to 1/12.
Since there are 36 points, the Halton sequence is so that each elementary interval contains exactly 36/12 = 3 points.
Notice that each elementary interval is closed on the left (or bottom) and open on the right (or top).


.. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py:

.. only:: html

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

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

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

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

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