.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.py:


Generate low discrepancy sequences
==================================

In this examples we are going to expose the available low discrepancy sequences in order to approximate some integrals.

The following low-discrepancy sequences are available:

- Sobol
- Faure
- Halton
- reverse Halton
- Haselgrove

To illustrate these sequences we generate their first 1024 points and compare with the sequence obtained from the pseudo random generator (Merse Twister) as the latter has a higher discrepancy.


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import math as m
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








1. Sobol sequence


.. code-block:: default

    dimension = 2
    size = 1024
    sequence = ot.SobolSequence(2)
    sample = sequence.generate(size)
    graph = ot.Graph("Sobol", "", "", True, "")
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    view = viewer.View(graph)




.. image:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_low_discrepancy_sequence_001.png
    :alt: Sobol
    :class: sphx-glr-single-img





2. Halton sequence


.. code-block:: default

    dimension = 2
    sequence = ot.HaltonSequence(2)
    sample = sequence.generate(size)
    graph = ot.Graph("Halton", "", "", True, "")
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    view = viewer.View(graph)




.. image:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_low_discrepancy_sequence_002.png
    :alt: Halton
    :class: sphx-glr-single-img





3. Reverse Halton sequence


.. code-block:: default

    sequence = ot.ReverseHaltonSequence(dimension)
    sample = sequence.generate(size)
    print('discrepancy=', ot.LowDiscrepancySequenceImplementation.ComputeStarDiscrepancy(sample))
    graph = ot.Graph("Reverse Halton", "", "", True, "")
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    view = viewer.View(graph)




.. image:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_low_discrepancy_sequence_003.png
    :alt: Reverse Halton
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    discrepancy= 0.0035074981424325635




4. Haselgrove sequence


.. code-block:: default

    sequence = ot.HaselgroveSequence(dimension)
    sample = sequence.generate(size)
    graph = ot.Graph("Haselgrove", "", "", True, "")
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    view = viewer.View(graph)




.. image:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_low_discrepancy_sequence_004.png
    :alt: Haselgrove
    :class: sphx-glr-single-img





Compare with uniform random sequence


.. code-block:: default

    distribution = ot.ComposedDistribution([ot.Uniform(0.0, 1.0)]*2)
    sample = distribution.getSample(size)
    print('discrepancy=', ot.LowDiscrepancySequenceImplementation.ComputeStarDiscrepancy(sample))
    graph = ot.Graph("Mersenne Twister", "", "", True, "")
    cloud = ot.Cloud(sample)
    graph.add(cloud)
    view = viewer.View(graph)
    plt.show()



.. image:: /auto_reliability_sensitivity/design_of_experiments/images/sphx_glr_plot_low_discrepancy_sequence_005.png
    :alt: Mersenne Twister
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    discrepancy= 0.030727095301450208





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

   **Total running time of the script:** ( 0 minutes  0.460 seconds)


.. _sphx_glr_download_auto_reliability_sensitivity_design_of_experiments_plot_low_discrepancy_sequence.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_low_discrepancy_sequence.py <plot_low_discrepancy_sequence.py>`



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

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


.. only:: html

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

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_