.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/disciplines/basics/plot_compute_jacobian.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_basics_plot_compute_jacobian.py>`
        to download the full example code.

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

.. _sphx_glr_examples_disciplines_basics_plot_compute_jacobian.py:


Compute the Jacobian of a discipline analytically
=================================================

In this example,
we will compute the Jacobians of some outputs of an :class:`.Discipline`
with respect to some inputs, based on its analytical derivatives.

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.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo.disciplines.analytic import AnalyticDiscipline








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First,
we create a discipline, e.g. an :class:`.AnalyticDiscipline`:

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.. code-block:: Python

    discipline = AnalyticDiscipline({"y": "a**2+b", "z": "a**3+b**2"})








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We can execute it with its default input values:

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.. code-block:: Python

    discipline.execute()
    discipline.local_data





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

 .. code-block:: none


    {'a': array([0.]), 'b': array([0.]), 'y': array([0.]), 'z': array([0.])}



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or with custom ones:

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.. code-block:: Python

    discipline.execute({"a": array([1.0])})
    discipline.local_data





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

 .. code-block:: none


    {'a': array([1.]), 'b': array([0.]), 'y': array([1.]), 'z': array([1.])}



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Then,
we use the method :meth:`.Discipline.linearize` to compute the derivatives:

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.. code-block:: Python

    jacobian_data = discipline.linearize()
    jacobian_data





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

 .. code-block:: none


    {}



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There is no Jacobian data
because we need to set the input variables
with respect to which to compute the Jacobian of the output ones.
For that,
we use the method :meth:`~.Discipline.add_differentiated_inputs`.
We also need to set these output variables:
with the method :meth:`~.Discipline.add_differentiated_outputs`.
For instance,
we may want to only compute the derivative of ``"z"`` with respect to ``"a"``:

.. GENERATED FROM PYTHON SOURCE LINES 67-72

.. code-block:: Python

    discipline.add_differentiated_inputs(["a"])
    discipline.add_differentiated_outputs(["z"])
    jacobian_data = discipline.linearize()
    jacobian_data





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

 .. code-block:: none


    defaultdict(<function _default_dict_factory at 0x72a513d149a0>, {'z': defaultdict(None, {'a': array([[0.]])})})



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By default,
|g| uses :attr:`.Discipline.default_input_data` as input data
for which to compute the Jacobian on.
We can change them with ``input_data``:

.. GENERATED FROM PYTHON SOURCE LINES 77-80

.. code-block:: Python

    jacobian_data = discipline.linearize({"a": array([1.0])})
    jacobian_data





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

 .. code-block:: none


    defaultdict(<function _default_dict_factory at 0x72a513d149a0>, {'z': defaultdict(None, {'a': array([[3.]])})})



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We can also force the discipline to compute
the derivatives of all the outputs with respect to all the inputs:

.. GENERATED FROM PYTHON SOURCE LINES 83-85

.. code-block:: Python

    jacobian_data = discipline.linearize(compute_all_jacobians=True)
    jacobian_data




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

 .. code-block:: none


    defaultdict(<function _default_dict_factory at 0x72a513d149a0>, {'y': defaultdict(None, {'a': array([[0.]]), 'b': array([[1.]])}), 'z': defaultdict(None, {'a': array([[0.]]), 'b': array([[0.]])})})




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

   **Total running time of the script:** (0 minutes 0.013 seconds)


.. _sphx_glr_download_examples_disciplines_basics_plot_compute_jacobian.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_compute_jacobian.zip <plot_compute_jacobian.zip>`


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