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

.. only:: html

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

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

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

.. _sphx_glr_examples_disciplines_types_plot_analytic_discipline.py:


Create a discipline from analytical expressions
===============================================

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.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo import configure_logger
    from gemseo import create_discipline








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Import
------

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.. code-block:: Python


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



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Introduction
------------
A simple :class:`.MDODiscipline` can be created
using analytic formulas, e.g. :math:`y_1=2x^2` and :math:`y_2=5+3x^2z^3`,
thanks to the :class:`.AnalyticDiscipline` class
which is a quick alternative to model a simple analytic MDO problem.

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Create the dictionary of analytic outputs
-----------------------------------------
First of all, we have to define the output expressions in a dictionary
where keys are output names and values are formula with ``string``
format:

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.. code-block:: Python

    expressions = {"y_1": "2*x**2", "y_2": "5+3*x**2+z**3"}








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Create the discipline
---------------------
Then, we create and instantiate the corresponding
:class:`.AnalyticDiscipline`,
which is a particular :class:`.MDODiscipline`.
For that, we use the API function :func:`.create_discipline` with:

- ``discipline_name="AnalyticDiscipline"``,
- ``name="analytic"``,
- ``expressions=expr_dict``.

In practice, we write:

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.. code-block:: Python

    disc = create_discipline("AnalyticDiscipline", expressions=expressions)








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.. note::

   |g| takes care of the grammars and
   :meth:`!MDODiscipline._run` method generation
   from the ``expressions`` argument.
   In the background, |g| considers that ``x`` is a monodimensional
   float input parameter and ``y_1`` and ``y_2`` are
   monodimensional float output parameters.

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Execute the discipline
----------------------
Lastly, we can execute this discipline any other:

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.. code-block:: Python

    input_data = {"x": array([2.0]), "z": array([3.0])}
    disc.execute(input_data)





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

 .. code-block:: none


    {'x': array([2.]), 'z': array([3.]), 'y_2': array([44.]), 'y_1': array([8.])}



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About the analytic jacobian
---------------------------
The discipline will provide analytic derivatives (Jacobian) automatically
using the `sympy library <https://www.sympy.org/fr/>`_.

This can be checked easily using
:meth:`.MDODiscipline.check_jacobian`:

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.. code-block:: Python

    disc.check_jacobian(
        input_data,
        derr_approx=disc.ApproximationMode.FINITE_DIFFERENCES,
        step=1e-5,
        threshold=1e-3,
    )




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

 .. code-block:: none

        INFO - 09:00:36: Jacobian: dp y_1/dp x succeeded.
        INFO - 09:00:36: Jacobian: dp y_1/dp z succeeded.
        INFO - 09:00:36: Jacobian: dp y_2/dp x succeeded.
        INFO - 09:00:36: Jacobian: dp y_2/dp z succeeded.
        INFO - 09:00:36: Linearization of MDODiscipline: AnalyticDiscipline is correct.

    True




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

   **Total running time of the script:** (0 minutes 0.020 seconds)


.. _sphx_glr_download_examples_disciplines_types_plot_analytic_discipline.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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