.. 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:`.MDODiscipline`
with respect to some inputs, based on its analytical derivatives.

.. GENERATED FROM PYTHON SOURCE LINES 29-36

.. code-block:: Python


    from __future__ import annotations

    from numpy import array

    from gemseo.disciplines.analytic import AnalyticDiscipline








.. GENERATED FROM PYTHON SOURCE LINES 37-39

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

.. GENERATED FROM PYTHON SOURCE LINES 39-41

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 42-43

We can execute it with its default input values:

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python

    discipline.execute()
    discipline.local_data





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

 .. code-block:: none


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



.. GENERATED FROM PYTHON SOURCE LINES 47-48

or with custom ones:

.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. 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.])}



.. GENERATED FROM PYTHON SOURCE LINES 52-54

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

.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: Python

    jacobian_data = discipline.linearize()
    jacobian_data





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

 .. code-block:: none


    {}



.. GENERATED FROM PYTHON SOURCE LINES 58-67

There is no Jacobian data
because we need to set the input variables
against which to compute the Jacobian of the output ones.
For that,
we use the method :meth:`~.MDODiscipline.add_differentiated_inputs`.
We also need to set these output variables:
with the method :meth:`~.MDODiscipline.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 0x7f1df7aa7ca0>, {'z': defaultdict(None, {'a': array([[0.]])})})



.. GENERATED FROM PYTHON SOURCE LINES 73-77

By default,
|g| uses :attr:`.MDODiscipline.default_inputs` 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 0x7f1df7aa7ca0>, {'z': defaultdict(None, {'a': array([[3.]])})})



.. GENERATED FROM PYTHON SOURCE LINES 81-83

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 0x7f1df7aa7ca0>, {'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 0.022 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>`


.. only:: html

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

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