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.. only:: html

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        Click :ref:`here <sphx_glr_download_examples_post_process_plot_gradient_sensitivity.py>`
        to download the full example code

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

.. _sphx_glr_examples_post_process_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 28-36

.. code-block:: default

    from __future__ import annotations

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.problems.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 37-41

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

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: default


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-50

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

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

.. GENERATED FROM PYTHON SOURCE LINES 52-56

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

.. GENERATED FROM PYTHON SOURCE LINES 56-65

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 66-69

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

.. GENERATED FROM PYTHON SOURCE LINES 69-71

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 72-79

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 79-86

.. 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 87-93

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 93-98

.. code-block:: default

    scenario.set_differentiation_method("user")
    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 - 14:43:29:  
        INFO - 14:43:29: *** Start MDOScenario execution ***
        INFO - 14:43:29: MDOScenario
        INFO - 14:43:29:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 14:43:29:    MDO formulation: MDF
        INFO - 14:43:30: Optimization problem:
        INFO - 14:43:30:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:43:30:    with respect to x_1, x_2, x_3, x_shared
        INFO - 14:43:30:    subject to constraints:
        INFO - 14:43:30:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:30:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:30:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:43:30:    over the design space:
        INFO - 14:43:30:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:30:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 14:43:30:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:30:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:43:30:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 14:43:30:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:43:30:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:43:30:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 14:43:30:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 14:43:30:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:43:30:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:30:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 14:43:30:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 14:43:30:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:43:30: Solving optimization problem with algorithm SLSQP:
        INFO - 14:43:30: ...   0%|          | 0/10 [00:00<?, ?it]
        INFO - 14:43:30: ...  20%|██        | 2/10 [00:00<00:00, 40.63 it/sec, obj=-2.12e+3]
     WARNING - 14:43:30: MDAJacobi has reached its maximum number of iterations but the normed residual 1.4486313079508508e-06 is still above the tolerance 1e-06.
        INFO - 14:43:30: ...  30%|███       | 3/10 [00:00<00:00, 23.56 it/sec, obj=-3.75e+3]
        INFO - 14:43:30: ...  40%|████      | 4/10 [00:00<00:00, 17.21 it/sec, obj=-4.01e+3]
     WARNING - 14:43:30: MDAJacobi has reached its maximum number of iterations but the normed residual 2.928004141058104e-06 is still above the tolerance 1e-06.
        INFO - 14:43:30: ...  50%|█████     | 5/10 [00:00<00:00, 13.11 it/sec, obj=-4.49e+3]
        INFO - 14:43:30: ...  60%|██████    | 6/10 [00:00<00:00, 11.11 it/sec, obj=-3.4e+3]
        INFO - 14:43:31: ...  80%|████████  | 8/10 [00:01<00:00,  9.46 it/sec, obj=-4.76e+3]
        INFO - 14:43:31: ... 100%|██████████| 10/10 [00:01<00:00,  8.23 it/sec, obj=-4.56e+3]
        INFO - 14:43:31: ... 100%|██████████| 10/10 [00:01<00:00,  8.21 it/sec, obj=-4.56e+3]
        INFO - 14:43:31: Optimization result:
        INFO - 14:43:31:    Optimizer info:
        INFO - 14:43:31:       Status: None
        INFO - 14:43:31:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 14:43:31:       Number of calls to the objective function by the optimizer: 12
        INFO - 14:43:31:    Solution:
        INFO - 14:43:31:       The solution is feasible.
        INFO - 14:43:31:       Objective: -3749.8868975554387
        INFO - 14:43:31:       Standardized constraints:
        INFO - 14:43:31:          g_1 = [-0.01671296 -0.03238836 -0.04350867 -0.05123129 -0.05681738 -0.13780658
        INFO - 14:43:31:  -0.10219342]
        INFO - 14:43:31:          g_2 = -0.0004062839430756249
        INFO - 14:43:31:          g_3 = [-0.66482546 -0.33517454 -0.11023156 -0.183255  ]
        INFO - 14:43:31:       Design space: 
        INFO - 14:43:31:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:31:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 14:43:31:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:31:       | x_shared[0] |     0.01    | 0.05989842901423112 |     0.09    | float |
        INFO - 14:43:31:       | x_shared[1] |    30000    |  59853.73840058666  |    60000    | float |
        INFO - 14:43:31:       | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 14:43:31:       | x_shared[3] |     2.5     |  2.527371250092273  |     8.5     | float |
        INFO - 14:43:31:       | x_shared[4] |      40     |  69.86825198198687  |      70     | float |
        INFO - 14:43:31:       | x_shared[5] |     500     |  1495.734648986894  |     1500    | float |
        INFO - 14:43:31:       | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 14:43:31:       | x_1[1]      |     0.75    |  0.7521124139939552 |     1.25    | float |
        INFO - 14:43:31:       | x_2         |     0.75    |  0.7520888531444992 |     1.25    | float |
        INFO - 14:43:31:       | x_3         |     0.1     |  0.1398000762238233 |      1      | float |
        INFO - 14:43:31:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:43:31: *** End MDOScenario execution (time: 0:00:01.233712) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 99-120

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 122-130

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API 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 130-135

.. code-block:: default

    scenario.post_process(
        "GradientSensitivity", save=False, show=False, compute_missing_gradients=True
    )
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. image-sg:: /examples/post_process/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/images/sphx_glr_plot_gradient_sensitivity_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

     WARNING - 14:43:31: 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/4.1.0/lib/python3.9/site-packages/gemseo/post/gradient_sensitivity.py:201: UserWarning: FixedFormatter should only be used together with FixedLocator
      axe.set_xticklabels(design_names, fontsize=font_size, rotation=rotation)





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   **Total running time of the script:** ( 0 minutes  2.362 seconds)


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