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

.. only:: html

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

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

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

.. _sphx_glr_examples_doe_plot_seed.py:


Change the seed of a DOE
========================

`Latin hypercube sampling <https://en.wikipedia.org/wiki/Latin_hypercube_sampling>`__
is an example of stochastic DOE algorithm:
given an input dimension and a number of samples,
running the algorithm twice will give two different DOEs.

For the sake of reproducibility,
|g| uses a `random seed <https://en.wikipedia.org/wiki/Random_seed>`__:
given an input dimension, a number of samples and a random seed,
running the algorithm twice will give the same DOE.

In this example,
we will see how |g| uses the random seed
and how the user can change its value.

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.. code-block:: Python


    from __future__ import annotations

    from gemseo import create_design_space
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo import execute_algo
    from gemseo.algos.doe.lib_openturns import OpenTURNS
    from gemseo.algos.opt_problem import OptimizationProblem
    from gemseo.core.mdofunctions.mdo_function import MDOFunction








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At the scenario level
---------------------
First,
we illustrate the use of the random seed at the :class:`.DOEScenario` level
which is the appropriate level for most users.
Then,
we will illustrate this use at the :class:`.OptimizationProblem` level
which can be useful for developers.

Let us consider an :class:`.MDODiscipline` representing the function :math:`y=x^2`:

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.. code-block:: Python

    discipline = create_discipline("AnalyticDiscipline", expressions={"y": "x**2"})








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This function is defined over the interval :math:`[-1,1]`:

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.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x", l_b=-1, u_b=1)








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We want to sample this discipline over this design space.
For that,
we express the sampling problem as a :class:`.DOEScenario`:

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.. code-block:: Python

    scenario = create_scenario(
        [discipline], "DisciplinaryOpt", "y", design_space, scenario_type="DOE"
    )








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and solve it:

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.. code-block:: Python

    scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2})
    scenario.formulation.opt_problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([-0.89534931]), array([0.73475608])]



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You can get the value of the random seed that has been used:

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.. code-block:: Python

    scenario._lib.seed





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

 .. code-block:: none


    1



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When using the same DOE algorithm,
a new call to :meth:`.DOEScenario.execute` increments the :attr:`.DOELibrary.seed`.
Then,
solving again this problem with the same configuration leads to a new result:

.. GENERATED FROM PYTHON SOURCE LINES 89-92

.. code-block:: Python

    scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2})
    scenario.formulation.opt_problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([0.04982439]), array([-0.48653892])]



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and we can check that the value of the seed was incremented:

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.. code-block:: Python

    scenario._lib.seed





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

 .. code-block:: none


    2



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You can also pass a custom ``"seed"`` to the DOE algorithm
with the key ``"algo_options"`` of the ``input_data``
passed to :meth:`.DOEScenario.execute`:

.. GENERATED FROM PYTHON SOURCE LINES 100-103

.. code-block:: Python

    scenario.execute({"algo": "OT_OPT_LHS", "n_samples": 2, "algo_options": {"seed": 123}})
    scenario.formulation.opt_problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([-0.09505332]), array([0.98400738])]



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You can verify that :attr:`.DOELibrary.seed` has not been replaced by the custom value
but incremented:

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.. code-block:: Python

    scenario._lib.seed





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

 .. code-block:: none


    3



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At the problem level
--------------------
Basic
~~~~~
Let us consider an :class:`.MDOFunction` representing the function :math:`y=x^2`:

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.. code-block:: Python

    function = MDOFunction(lambda x: x**2, "f", input_names=["x"], output_names=["y"])








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and defined over the unit interval :math:`x\in[0,1]`:

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.. code-block:: Python

    design_space = create_design_space()
    design_space.add_variable("x", l_b=-1, u_b=1)








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We want to sample this function over this design space.
For that,
we express the sampling problem as an :class:`.OptimizationProblem`:

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.. code-block:: Python

    problem = OptimizationProblem(design_space)
    problem.objective = function








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and solve it:

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.. code-block:: Python

    execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2)
    problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([-0.89534931]), array([0.73475608])]



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Note:
    We use the function :func:`.execute_algo`
    as the :class:`.OptimizationProblem` does not have a method :func:`execute`
    unlike the :class:`.Scenario`.

Solving again this problem with the same configuration leads to the same result:

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.. code-block:: Python

    execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2)
    problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([-0.89534931]), array([0.73475608])]



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and the result is still the same if we take 1 as random seed,
as 1 is the default value of this seed:

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.. code-block:: Python

    execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2, seed=1)
    problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([-0.89534931]), array([0.73475608])]



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If you want to use a different random seed,
you only have to change the value of ``seed``:

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.. code-block:: Python

    execute_algo(problem, "OT_OPT_LHS", algo_type="doe", n_samples=2, seed=3)
    problem.database.get_last_n_x_vect(2)





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

 .. code-block:: none


    [array([0.93088508]), array([-0.81399054])]



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Advanced
~~~~~~~~
You can also solve your problem with a lower level API
by directly instantiating the :class:`.DOELibrary` of interest.
A :class:`.DOELibrary` has a default seed generated by a :class:`.Seeder`
that is incremented at the beginning of each execution:

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.. code-block:: Python

    library = OpenTURNS()
    library.algo_name = "OT_OPT_LHS"
    library.execute(problem, n_samples=2)
    problem.database.get_last_n_x_vect(2)




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

 .. code-block:: none


    [array([0.93088508]), array([-0.81399054])]



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Solving again the problem will give different samples:

.. GENERATED FROM PYTHON SOURCE LINES 168-170

.. code-block:: Python

    library.execute(problem, n_samples=2)
    problem.database.get_last_n_x_vect(2)




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

 .. code-block:: none


    [array([0.04982439]), array([-0.48653892])]



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You can also use a specific seed instead of the default one:

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.. code-block:: Python

    library.execute(problem, n_samples=2, seed=123)
    problem.database.get_last_n_x_vect(2)




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

 .. code-block:: none


    [array([-0.09505332]), array([0.98400738])]




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

   **Total running time of the script:** (0 minutes 0.141 seconds)


.. _sphx_glr_download_examples_doe_plot_seed.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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