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

.. only:: html

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

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

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

.. _sphx_glr_examples_post_process_algorithms_plot_gradient_sensitivity.py:


Gradient Sensitivity
====================

In this example, we illustrate the use of the :class:`.GradientSensitivity`
plot on the Sobieski's SSBJ problem.

.. GENERATED FROM PYTHON SOURCE LINES 28-35

.. code-block:: default

    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem








.. GENERATED FROM PYTHON SOURCE LINES 36-40

Import
------
The first step is to import some high-level functions
and a method to get the design space.

.. GENERATED FROM PYTHON SOURCE LINES 40-43

.. code-block:: default


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 44-49

Description
-----------

The :class:`.GradientSensitivity` post-processor
builds histograms of derivatives of the objective and the constraints.

.. GENERATED FROM PYTHON SOURCE LINES 51-55

Create disciplines
------------------
At this point, we instantiate the disciplines of Sobieski's SSBJ problem:
Propulsion, Aerodynamics, Structure and Mission

.. GENERATED FROM PYTHON SOURCE LINES 55-64

.. code-block:: default

    disciplines = create_discipline(
        [
            "SobieskiPropulsion",
            "SobieskiAerodynamics",
            "SobieskiStructure",
            "SobieskiMission",
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 65-68

Create design space
-------------------
We also read the design space from the :class:`.SobieskiProblem`.

.. GENERATED FROM PYTHON SOURCE LINES 68-70

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 71-78

Create and execute scenario
---------------------------
The next step is to build an MDO scenario in order to maximize the range,
encoded ``"y_4"``, with respect to the design parameters, while satisfying the
inequality constraints ``"g_1"``, ``"g_2"`` and ``"g_3"``. We can use the MDF
formulation, the SLSQP optimization algorithm and a maximum number of iterations
equal to 100.

.. GENERATED FROM PYTHON SOURCE LINES 78-85

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        objective_name="y_4",
        maximize_objective=True,
        design_space=design_space,
    )







.. GENERATED FROM PYTHON SOURCE LINES 86-92

The differentiation method used by default is ``"user"``, which means that the
gradient will be evaluated from the Jacobian defined in each discipline. However, some
disciplines may not provide one, in that case, the gradient may be approximated
with the techniques ``"finite_differences"`` or ``"complex_step"`` with the method
:meth:`~.Scenario.set_differentiation_method`. The following line is shown as an
example, it has no effect because it does not change the default method.

.. GENERATED FROM PYTHON SOURCE LINES 92-97

.. code-block:: default

    scenario.set_differentiation_method()
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, "ineq")
    scenario.execute({"algo": "SLSQP", "max_iter": 10})





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

 .. code-block:: none

        INFO - 16:24:49:  
        INFO - 16:24:49: *** Start MDOScenario execution ***
        INFO - 16:24:49: MDOScenario
        INFO - 16:24:49:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:24:49:    MDO formulation: MDF
        INFO - 16:24:49: Optimization problem:
        INFO - 16:24:49:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 16:24:49:    with respect to x_1, x_2, x_3, x_shared
        INFO - 16:24:49:    subject to constraints:
        INFO - 16:24:49:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:49:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:49:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:24:49:    over the design space:
        INFO - 16:24:49:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:49:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:24:49:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:49:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:24:49:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:24:49:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:24:49:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:24:49:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:24:49:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:24:49:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 16:24:49:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 16:24:49:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 16:24:49:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 16:24:49:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:24:49: Solving optimization problem with algorithm SLSQP:
        INFO - 16:24:49: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 16:24:49: ...  10%|█         | 1/10 [00:00<00:00, 10.31 it/sec, obj=-536]
        INFO - 16:24:49: ...  20%|██        | 2/10 [00:00<00:01,  7.46 it/sec, obj=-2.12e+3]
     WARNING - 16:24:49: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 16:24:49: ...  30%|███       | 3/10 [00:00<00:01,  6.44 it/sec, obj=-3.75e+3]
        INFO - 16:24:50: ...  40%|████      | 4/10 [00:00<00:00,  6.23 it/sec, obj=-4.01e+3]
     WARNING - 16:24:50: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 16:24:50: ...  50%|█████     | 5/10 [00:00<00:00,  5.91 it/sec, obj=-4.49e+3]
        INFO - 16:24:50: ...  60%|██████    | 6/10 [00:01<00:00,  5.97 it/sec, obj=-3.4e+3]
        INFO - 16:24:50: ...  70%|███████   | 7/10 [00:01<00:00,  6.57 it/sec, obj=-4.93e+3]
        INFO - 16:24:50: ...  80%|████████  | 8/10 [00:01<00:00,  6.93 it/sec, obj=-4.76e+3]
        INFO - 16:24:50: ...  90%|█████████ | 9/10 [00:01<00:00,  7.29 it/sec, obj=-4.62e+3]
        INFO - 16:24:50: ... 100%|██████████| 10/10 [00:01<00:00,  7.66 it/sec, obj=-4.56e+3]
        INFO - 16:24:50: Optimization result:
        INFO - 16:24:50:    Optimizer info:
        INFO - 16:24:50:       Status: None
        INFO - 16:24:50:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 16:24:50:       Number of calls to the objective function by the optimizer: 12
        INFO - 16:24:50:    Solution:
        INFO - 16:24:50:       The solution is feasible.
        INFO - 16:24:50:       Objective: -3749.8868975554387
        INFO - 16:24:50:       Standardized constraints:
        INFO - 16:24:50:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 16:24:50:  -0.10219342]
        INFO - 16:24:50:          g_2 = -0.0004062839430756249
        INFO - 16:24:50:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 16:24:50:       Design space: 
        INFO - 16:24:50:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:50:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 16:24:50:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:50:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 16:24:50:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 16:24:50:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 16:24:50:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 16:24:50:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 16:24:50:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 16:24:50:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 16:24:50:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 16:24:50:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 16:24:50:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 16:24:50:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:24:50: *** End MDOScenario execution (time: 0:00:01.325807) ***

    {'max_iter': 10, 'algo': 'SLSQP'}



.. GENERATED FROM PYTHON SOURCE LINES 98-119

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.GradientSensitivity`
post-processor which builds histograms of derivatives of objective and constraints.
The sensitivities shown in the plot are calculated with the gradient at the optimum
or the least-non feasible point when the result is not feasible. One may choose any
other iteration instead.

.. note::
   In some cases, the iteration that is being used to compute the sensitivities
   corresponds to a point for which the algorithm did not request the evaluation of
   the gradients, and a ``ValueError`` is raised. A way to avoid this issue is to set
   the option ``compute_missing_gradients`` of :class:`.GradientSensitivity` to
   ``True``, this way |g| will compute the gradients for the requested iteration if
   they are not available.

.. warning::
   Please note that this extra computation may be expensive depending on the
   :class:`.OptimizationProblem` defined by the user. Additionally, keep in mind that
   |g| cannot compute missing gradients for an :class:`.OptimizationProblem` that was
   imported from an HDF5 file.

.. GENERATED FROM PYTHON SOURCE LINES 121-129

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the high-level function
   :func:`.get_post_processing_options_schema` to print a table with
   the options for any post-processing algorithm.
   Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 129-135

.. code-block:: default

    scenario.post_process(
        "GradientSensitivity",
        compute_missing_gradients=True,
        save=False,
        show=True,
    )



.. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_gradient_sensitivity_001.png
   :alt: Derivatives of objective and constraints with respect to design variables, -y_4, g_1_0, g_1_1, g_1_2, g_1_3, g_1_4, g_1_5, g_1_6, g_2, g_3_0, g_3_1, g_3_2, g_3_3
   :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_gradient_sensitivity_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.0/lib/python3.9/site-packages/genson/schema/strategies/base.py:42: UserWarning: Schema incompatible. Keyword 'description' has conflicting values ('The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.' vs. 'The width and height of the figure in inches, e.g. `(w, h)`.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'). Using 'The width and height of the figure in inches, e.g. ``(w, h)``.\nIf ``None``, use the :attr:`.OptPostProcessor.DEFAULT_FIG_SIZE`\nof the post-processor.'
      warn(('Schema incompatible. Keyword {0!r} has conflicting '
     WARNING - 16:24:50: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/envs/5.0.0/lib/python3.9/site-packages/gemseo/post/gradient_sensitivity.py:209: UserWarning: FixedFormatter should only be used together with FixedLocator
      axe.set_xticklabels(design_names, fontsize=font_size, rotation=rotation)

    <gemseo.post.gradient_sensitivity.GradientSensitivity object at 0x7fea50b7c9d0>




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

   **Total running time of the script:** ( 0 minutes  2.602 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_gradient_sensitivity.py:

.. only:: html

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

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

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


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