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

.. only:: html

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

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

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

.. _sphx_glr_examples_post_process_plot_robustness.py:


Robustness
==========

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

.. GENERATED FROM PYTHON SOURCE LINES 30-34

.. code-block:: default

    from __future__ import division, unicode_literals

    from matplotlib import pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 35-39

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 39-44

.. code-block:: default

    from gemseo.api import configure_logger, create_discipline, create_scenario
    from gemseo.problems.sobieski.core import SobieskiProblem

    configure_logger()





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

 Out:

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-60

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

In the :class:`~gemseo.post.robustness.Robustness` post-processing,
the robustness of the optimum is represented by a box plot. Using the
quadratic approximations of all the output functions, we
propagate analytically a normal distribution with 1% standard deviation
on all the design variables, assuming no cross-correlations of inputs,
to obtain the mean and standard deviation of the resulting normal
distribution. A series of samples are randomly generated from the resulting
distribution, whose quartiles are plotted, relatively to the values of
the function at the optimum. For each function (in abscissa), the plot
shows the extreme values encountered in the samples (top and bottom
bars). Then, 95% of the values are within the blue boxes. The average is
given by the red bar.

.. GENERATED FROM PYTHON SOURCE LINES 62-66

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

.. GENERATED FROM PYTHON SOURCE LINES 66-75

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 76-79

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

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: default

    design_space = SobieskiProblem().read_design_space()








.. GENERATED FROM PYTHON SOURCE LINES 82-89

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 89-101

.. code-block:: default

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

 Out:

 .. code-block:: none

        INFO - 14:42:28:  
        INFO - 14:42:28: *** Start MDO Scenario execution ***
        INFO - 14:42:28: MDOScenario
        INFO - 14:42:28:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
        INFO - 14:42:28:    MDOFormulation: MDF
        INFO - 14:42:28:    Algorithm: SLSQP
        INFO - 14:42:28: Optimization problem:
        INFO - 14:42:28:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:42:28:    With respect to: x_shared, x_1, x_2, x_3
        INFO - 14:42:28:    Subject to constraints:
        INFO - 14:42:28:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:42:28:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:42:28:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:42:28: Design space:
        INFO - 14:42:28: +----------+-------------+-------+-------------+-------+
        INFO - 14:42:28: | name     | lower_bound | value | upper_bound | type  |
        INFO - 14:42:28: +----------+-------------+-------+-------------+-------+
        INFO - 14:42:28: | x_shared |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:42:28: | x_shared |    30000    | 45000 |    60000    | float |
        INFO - 14:42:28: | x_shared |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:42:28: | x_shared |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:42:28: | x_shared |      40     |   55  |      70     | float |
        INFO - 14:42:28: | x_shared |     500     |  1000 |     1500    | float |
        INFO - 14:42:28: | x_1      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:42:28: | x_1      |     0.75    |   1   |     1.25    | float |
        INFO - 14:42:28: | x_2      |     0.75    |   1   |     1.25    | float |
        INFO - 14:42:28: | x_3      |     0.1     |  0.5  |      1      | float |
        INFO - 14:42:28: +----------+-------------+-------+-------------+-------+
        INFO - 14:42:28: Optimization:   0%|          | 0/10 [00:00<?, ?it]
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.2/lib/python3.8/site-packages/scipy/sparse/linalg/dsolve/linsolve.py:407: SparseEfficiencyWarning: splu requires CSC matrix format
      warn('splu requires CSC matrix format', SparseEfficiencyWarning)
        INFO - 14:42:29: Optimization:  20%|██        | 2/10 [00:00<00:00, 53.25 it/sec, obj=2.12e+3]
        INFO - 14:42:29: Optimization:  40%|████      | 4/10 [00:00<00:00, 21.33 it/sec, obj=3.97e+3]
        INFO - 14:42:29: Optimization:  50%|█████     | 5/10 [00:00<00:00, 16.64 it/sec, obj=3.96e+3]
        INFO - 14:42:29: Optimization:  60%|██████    | 6/10 [00:00<00:00, 13.63 it/sec, obj=3.96e+3]
        INFO - 14:42:29: Optimization:  70%|███████   | 7/10 [00:00<00:00, 11.55 it/sec, obj=3.96e+3]
        INFO - 14:42:29: Optimization:  90%|█████████ | 9/10 [00:01<00:00,  9.84 it/sec, obj=3.96e+3]
        INFO - 14:42:29: Optimization: 100%|██████████| 10/10 [00:01<00:00,  9.16 it/sec, obj=3.96e+3]
        INFO - 14:42:29: Optimization result:
        INFO - 14:42:29: Objective value = 3963.595455433326
        INFO - 14:42:29: The result is feasible.
        INFO - 14:42:29: Status: None
        INFO - 14:42:29: Optimizer message: Maximum number of iterations reached. GEMSEO Stopped the driver
        INFO - 14:42:29: Number of calls to the objective function by the optimizer: 12
        INFO - 14:42:29: Constraints values:
        INFO - 14:42:29:    g_1 = [-0.01814919 -0.03340982 -0.04429875 -0.05187486 -0.05736009 -0.13720854
        INFO - 14:42:29:  -0.10279146]
        INFO - 14:42:29:    g_2 = 3.236261671801799e-05
        INFO - 14:42:29:    g_3 = [-7.67067574e-01 -2.32932426e-01 -9.19662628e-05 -1.83255000e-01]
        INFO - 14:42:29: Design space:
        INFO - 14:42:29: +----------+-------------+--------------------+-------------+-------+
        INFO - 14:42:29: | name     | lower_bound |       value        | upper_bound | type  |
        INFO - 14:42:29: +----------+-------------+--------------------+-------------+-------+
        INFO - 14:42:29: | x_shared |     0.01    | 0.0600080906541795 |     0.09    | float |
        INFO - 14:42:29: | x_shared |    30000    |       60000        |    60000    | float |
        INFO - 14:42:29: | x_shared |     1.4     |        1.4         |     1.8     | float |
        INFO - 14:42:29: | x_shared |     2.5     |        2.5         |     8.5     | float |
        INFO - 14:42:29: | x_shared |      40     |         70         |      70     | float |
        INFO - 14:42:29: | x_shared |     500     |        1500        |     1500    | float |
        INFO - 14:42:29: | x_1      |     0.1     | 0.3999993439500847 |     0.4     | float |
        INFO - 14:42:29: | x_1      |     0.75    |        0.75        |     1.25    | float |
        INFO - 14:42:29: | x_2      |     0.75    |        0.75        |     1.25    | float |
        INFO - 14:42:29: | x_3      |     0.1     | 0.156230376400943  |      1      | float |
        INFO - 14:42:29: +----------+-------------+--------------------+-------------+-------+
        INFO - 14:42:29: *** MDO Scenario run terminated in 0:00:01.101634 ***

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



.. GENERATED FROM PYTHON SOURCE LINES 102-107

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.Robustness`
which plots any of the constraint or
objective functions w.r.t. the optimization iterations or sampling snapshots.

.. GENERATED FROM PYTHON SOURCE LINES 109-117

.. tip::

   Each post-processing method requires different inputs and offers a variety
   of customization options. Use the API function
   :meth:`~gemseo.api.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 117-121

.. code-block:: default


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



.. image:: /examples/post_process/images/sphx_glr_plot_robustness_001.png
    :alt: Box plot of the optimization functions with normalized stddev 0.01
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  1.305 seconds)


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