.. only:: html

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

        Click :ref:`here <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
==========================================

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

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


.. code-block:: default

    import openturns as ot
    import openturns.viewer as otv
    import pylab as pl
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








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


.. code-block:: default

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









.. code-block:: default

    sampleSize = 10
    sample = distribution.getSample(sampleSize)









.. code-block:: default

    fig = otv.PlotDesign(sample, bounds);




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





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

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


.. code-block:: default

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









.. code-block:: default

    sampleSize = 10
    sample = distribution.getSample(sampleSize)









.. code-block:: default

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




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





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


.. code-block:: default

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








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


.. code-block:: default

    bounds = distribution.getRange()









.. code-block:: default

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




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





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

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


.. code-block:: default

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









.. code-block:: default

    bounds = distribution.getRange()









.. code-block:: default

    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, temperatureProfile, space_filling)
    # optimal design
    sample = algo.generate()









.. code-block:: default

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




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





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

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


.. code-block:: default

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









.. code-block:: default

    sequence = ot.SobolSequence(dim)









.. code-block:: default

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









.. code-block:: default

    samplesize





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

 Out:

 .. code-block:: none


    32




.. code-block:: default

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




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





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). 

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


.. code-block:: default

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









.. code-block:: default

    sequence = ot.HaltonSequence(dim)









.. code-block:: default

    samplesize = 2**2 * 3**2 # Halton sequence uses prime numbers 2 and 3 in two dimensions.
    experiment = ot.LowDiscrepancyExperiment(sequence, distribution, samplesize, False)
    sample = experiment.generate()









.. code-block:: default

    samplesize





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

 Out:

 .. code-block:: none


    36




.. code-block:: default

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




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





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). 


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

   **Total running time of the script:** ( 0 minutes  1.288 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_design_of_experiments.py:


.. only :: html

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



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

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



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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

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