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

.. only:: html

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

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

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

.. _sphx_glr_auto_numerical_methods_general_methods_plot_combinatorial_generator.py:


Combinatorial generators
========================

.. GENERATED FROM PYTHON SOURCE LINES 6-20

In this example we are going to expose the various design of experiments that allow one to generate all the integer collections satisfying a given combinatorial constraint:

- The Tuples generator, which allows one to generate all the elements of a Cartesian product :math:`E=\{0,\dots,n_0-1\}\times\dots\times\{0,\dots,n_{d-1}-1\}`.

  The total number of generated points is :math:`N=\prod_{k=0}^{d-1}n_k`.

- The K-permutations generator, which allows one to generate all the injective functions from :math:`\{0,\dots,k-1\}` into :math:`\{0,\dots,n-1\}`

  The total number of generated points is :math:`N=\dfrac{n!}{(n-k)!}`.

- The Combinations generator, which allows one to generate all the subsets of size :math:`k` of :math:`\{0,\dots,n-1\}`

  The total number of generated points is :math:`N=\dfrac{n!}{k!(n-k)!}`.


.. GENERATED FROM PYTHON SOURCE LINES 22-26

.. code-block:: Python

    import openturns as ot

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








.. GENERATED FROM PYTHON SOURCE LINES 27-29

Tuples
------

.. GENERATED FROM PYTHON SOURCE LINES 29-32

.. code-block:: Python

    experiment = ot.Tuples([2, 3, 5])
    print(experiment.generate())





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

 .. code-block:: none

    [[0,0,0],[1,0,0],[0,1,0],[1,1,0],[0,2,0],[1,2,0],[0,0,1],[1,0,1],[0,1,1],[1,1,1],[0,2,1],[1,2,1],[0,0,2],[1,0,2],[0,1,2],[1,1,2],[0,2,2],[1,2,2],[0,0,3],[1,0,3],[0,1,3],[1,1,3],[0,2,3],[1,2,3],[0,0,4],[1,0,4],[0,1,4],[1,1,4],[0,2,4],[1,2,4]]#30




.. GENERATED FROM PYTHON SOURCE LINES 33-35

K-permutations
--------------

.. GENERATED FROM PYTHON SOURCE LINES 35-38

.. code-block:: Python

    experiment = ot.KPermutations(3, 4)
    print(experiment.generate())





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

 .. code-block:: none

    [[0,1,2],[0,2,1],[1,0,2],[1,2,0],[2,0,1],[2,1,0],[0,1,3],[0,3,1],[1,0,3],[1,3,0],[3,0,1],[3,1,0],[0,2,3],[0,3,2],[2,0,3],[2,3,0],[3,0,2],[3,2,0],[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]#24




.. GENERATED FROM PYTHON SOURCE LINES 39-41

Combinations
------------

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    experiment = ot.Combinations(4, 6)
    print(experiment.generate())




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

 .. code-block:: none

    [[0,1,2,3],[0,1,2,4],[0,1,2,5],[0,1,3,4],[0,1,3,5],[0,1,4,5],[0,2,3,4],[0,2,3,5],[0,2,4,5],[0,3,4,5],[1,2,3,4],[1,2,3,5],[1,2,4,5],[1,3,4,5],[2,3,4,5]]#15





.. _sphx_glr_download_auto_numerical_methods_general_methods_plot_combinatorial_generator.py:

.. only:: html

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

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

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

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

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