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

.. only:: html

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

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

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

.. _sphx_glr_examples_formulations_plot_sobieski_mdf_example.py:


MDF-based MDO on the Sobieski SSBJ test case
============================================

.. GENERATED FROM PYTHON SOURCE LINES 26-35

.. code-block:: default

    from __future__ import division, unicode_literals

    from matplotlib import pyplot as plt

    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 36-43

Instantiate the  disciplines
----------------------------
First, we instantiate the four disciplines of the use case:
:class:`~gemseo.problems.sobieski.wrappers.SobieskiPropulsion`,
:class:`~gemseo.problems.sobieski.wrappers.SobieskiAerodynamics`,
:class:`~gemseo.problems.sobieski.wrappers.SobieskiMission`
and :class:`~gemseo.problems.sobieski.wrappers.SobieskiStructure`.

.. GENERATED FROM PYTHON SOURCE LINES 43-52

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 53-64

Build, execute and post-process the scenario
--------------------------------------------
Then, we build the scenario which links the disciplines
with the formulation and the optimization algorithm. Here, we use the
:class:`.MDF` formulation. We tell the scenario to minimize -y_4 instead of
minimizing y_4 (range), which is the default option.

Instantiate the scenario
^^^^^^^^^^^^^^^^^^^^^^^^
During the instantiation of the scenario, we provide some options for the
MDF formulations:

.. GENERATED FROM PYTHON SOURCE LINES 64-71

.. code-block:: default

    formulation_options = {
        "tolerance": 1e-10,
        "max_mda_iter": 50,
        "warm_start": True,
        "use_lu_fact": True,
        "linear_solver_tolerance": 1e-15,
    }







.. GENERATED FROM PYTHON SOURCE LINES 72-81

- :code:`'warm_start`: warm starts MDA,
- :code:`'warm_start`: optimize the adjoints resolution by storing
  the Jacobian matrix LU factorization for the multiple RHS
  (objective + constraints). This saves CPU time if you can pay for
  the memory and have the full Jacobians available, not just matrix vector
  products.
- :code:`'linear_solver_tolerance'`: set the linear solver tolerance,
  idem we need full convergence


.. GENERATED FROM PYTHON SOURCE LINES 82-92

.. code-block:: default

    design_space = SobieskiProblem().read_design_space()
    scenario = create_scenario(
        disciplines,
        "MDF",
        objective_name="y_4",
        design_space=design_space,
        maximize_objective=True,
        **formulation_options
    )








.. GENERATED FROM PYTHON SOURCE LINES 93-95

Set the design constraints
^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 95-98

.. code-block:: default

    for c_name in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(c_name, "ineq")








.. GENERATED FROM PYTHON SOURCE LINES 99-105

XDSMIZE the scenario
^^^^^^^^^^^^^^^^^^^^
Generate the XDSM file on the fly, setting print_statuses=true
will print the status in the console
html_output (default True), will generate a self contained
html file, that can be automatically open using open_browser=True

.. GENERATED FROM PYTHON SOURCE LINES 105-107

.. code-block:: default

    scenario.xdsmize(html_output=True, print_statuses=False, open_browser=False)





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 .. code-block:: none

        INFO - 21:52:40: Generating HTML XDSM file in : xdsm.html




.. GENERATED FROM PYTHON SOURCE LINES 108-119

Define the algorithm inputs
^^^^^^^^^^^^^^^^^^^^^^^^^^^
We set the maximum number of iterations, the optimizer
and the optimizer options. Algorithm specific options are passed there.
Use :meth:`~gemseo.api.get_algorithm_options_schema` API function for more
information or read the documentation.

Here ftol_rel option is a stop criteria based on the relative difference
in the objective between two iterates ineq_tolerance the tolerance
determination of the optimum; this is specific to the |g| wrapping and not
in the solver.

.. GENERATED FROM PYTHON SOURCE LINES 119-126

.. code-block:: default

    algo_options = {
        "ftol_rel": 1e-10,
        "ineq_tolerance": 2e-3,
        "normalize_design_space": True,
    }
    scn_inputs = {"max_iter": 10, "algo": "SLSQP", "algo_options": algo_options}








.. GENERATED FROM PYTHON SOURCE LINES 127-141

.. seealso::

   We can also generates a backup file for the optimization,
   as well as plots on the fly of the optimization history if option
   :code:`generate_opt_plot` is :code:`True`.
   This slows down a lot the process, here since SSBJ is very light

   .. code::

    scenario.set_optimization_history_backup(file_path="mdf_backup.h5",
                                             each_new_iter=True,
                                             each_store=False, erase=True,
                                             pre_load=False,
                                             generate_opt_plot=True)

.. GENERATED FROM PYTHON SOURCE LINES 143-145

Execute the scenario
^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 145-147

.. code-block:: default

    scenario.execute(scn_inputs)





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 .. code-block:: none

        INFO - 21:52:40:  
        INFO - 21:52:40: *** Start MDO Scenario execution ***
        INFO - 21:52:40: MDOScenario
        INFO - 21:52:40:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiMission SobieskiStructure
        INFO - 21:52:40:    MDOFormulation: MDF
        INFO - 21:52:40:    Algorithm: SLSQP
        INFO - 21:52:40: Optimization problem:
        INFO - 21:52:40:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
        INFO - 21:52:40:    With respect to: x_shared, x_1, x_2, x_3
        INFO - 21:52:40:    Subject to constraints:
        INFO - 21:52:40:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 21:52:40:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 21:52:40:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 21:52:40: Design space:
        INFO - 21:52:40: +----------+-------------+-------+-------------+-------+
        INFO - 21:52:40: | name     | lower_bound | value | upper_bound | type  |
        INFO - 21:52:40: +----------+-------------+-------+-------------+-------+
        INFO - 21:52:40: | x_shared |     0.01    |  0.05 |     0.09    | float |
        INFO - 21:52:40: | x_shared |    30000    | 45000 |    60000    | float |
        INFO - 21:52:40: | x_shared |     1.4     |  1.6  |     1.8     | float |
        INFO - 21:52:40: | x_shared |     2.5     |  5.5  |     8.5     | float |
        INFO - 21:52:40: | x_shared |      40     |   55  |      70     | float |
        INFO - 21:52:40: | x_shared |     500     |  1000 |     1500    | float |
        INFO - 21:52:40: | x_1      |     0.1     |  0.25 |     0.4     | float |
        INFO - 21:52:40: | x_1      |     0.75    |   1   |     1.25    | float |
        INFO - 21:52:40: | x_2      |     0.75    |   1   |     1.25    | float |
        INFO - 21:52:40: | x_3      |     0.1     |  0.5  |      1      | float |
        INFO - 21:52:40: +----------+-------------+-------+-------------+-------+
        INFO - 21:52:40: Optimization:   0%|          | 0/10 [00:00<?, ?it]
        INFO - 21:52:40: Optimization:  20%|██        | 2/10 [00:00<00:00, 64.08 it/sec, obj=2.12e+3]
        INFO - 21:52:40: Optimization:  40%|████      | 4/10 [00:00<00:00, 24.08 it/sec, obj=3.96e+3]
        INFO - 21:52:40: Optimization:  50%|█████     | 5/10 [00:00<00:00, 19.93 it/sec, obj=3.96e+3]
        INFO - 21:52:40: Optimization result:
        INFO - 21:52:40: Objective value = 3963.2972517816925
        INFO - 21:52:40: The result is feasible.
        INFO - 21:52:40: Status: 8
        INFO - 21:52:40: Optimizer message: Positive directional derivative for linesearch
        INFO - 21:52:40: Number of calls to the objective function by the optimizer: 6
        INFO - 21:52:40: Constraints values:
        INFO - 21:52:40:    g_1 = [-0.01804842 -0.03333726 -0.04424232 -0.05182875 -0.05732112 -0.13720955
        INFO - 21:52:40:  -0.10279045]
        INFO - 21:52:40:    g_2 = -6.362250333236119e-07
        INFO - 21:52:40:    g_3 = [-7.67181886e-01 -2.32818114e-01 -5.10664140e-06 -1.83254917e-01]
        INFO - 21:52:40: Design space:
        INFO - 21:52:40: +----------+-------------+---------------------+-------------+-------+
        INFO - 21:52:40: | name     | lower_bound |        value        | upper_bound | type  |
        INFO - 21:52:40: +----------+-------------+---------------------+-------------+-------+
        INFO - 21:52:40: | x_shared |     0.01    | 0.05999984094374165 |     0.09    | float |
        INFO - 21:52:40: | x_shared |    30000    |   59999.8385151636  |    60000    | float |
        INFO - 21:52:40: | x_shared |     1.4     |  1.400000637306172  |     1.8     | float |
        INFO - 21:52:40: | x_shared |     2.5     |  2.500019521788078  |     8.5     | float |
        INFO - 21:52:40: | x_shared |      40     |  69.99993932894773  |      70     | float |
        INFO - 21:52:40: | x_shared |     500     |  1499.998738377382  |     1500    | float |
        INFO - 21:52:40: | x_1      |     0.1     |         0.4         |     0.4     | float |
        INFO - 21:52:40: | x_1      |     0.75    |  0.7500004933147627 |     1.25    | float |
        INFO - 21:52:40: | x_2      |     0.75    |  0.750000101062501  |     1.25    | float |
        INFO - 21:52:40: | x_3      |     0.1     |  0.1562449912486662 |      1      | float |
        INFO - 21:52:40: +----------+-------------+---------------------+-------------+-------+
        INFO - 21:52:40: *** MDO Scenario run terminated in 0:00:00.511425 ***

    {'max_iter': 10, 'algo': 'SLSQP', 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.002, 'normalize_design_space': True}}



.. GENERATED FROM PYTHON SOURCE LINES 148-152

Save the optimization history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
We can save the whole optimization problem and its history for further post
processing:

.. GENERATED FROM PYTHON SOURCE LINES 152-153

.. code-block:: default

    scenario.save_optimization_history("mdf_history.h5", file_format="hdf5")




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

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 .. code-block:: none

        INFO - 21:52:40: Export optimization problem to file: mdf_history.h5




.. GENERATED FROM PYTHON SOURCE LINES 154-155

We can also save only calls to functions and design variables history:

.. GENERATED FROM PYTHON SOURCE LINES 155-157

.. code-block:: default

    scenario.save_optimization_history("mdf_history.xml", file_format="ggobi")





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

 Out:

 .. code-block:: none

        INFO - 21:52:40: Export to ggobi for functions: ['-y_4', 'Iter', 'g_1', 'g_2', 'g_3']
        INFO - 21:52:40: Export to ggobi file: mdf_history.xml




.. GENERATED FROM PYTHON SOURCE LINES 158-160

Print optimization metrics
^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 160-162

.. code-block:: default

    scenario.print_execution_metrics()





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

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 .. code-block:: none

        INFO - 21:52:40: * Scenario Executions statistics *
        INFO - 21:52:40: * Discipline: SobieskiPropulsion
        INFO - 21:52:40: Executions number: 87
        INFO - 21:52:40: Execution time:  0.09352406299967697 s
        INFO - 21:52:40: Linearizations number: 5
        INFO - 21:52:40: * Discipline: SobieskiAerodynamics
        INFO - 21:52:40: Executions number: 90
        INFO - 21:52:40: Execution time:  0.11011443200004578 s
        INFO - 21:52:40: Linearizations number: 5
        INFO - 21:52:40: * Discipline: SobieskiMission
        INFO - 21:52:40: Executions number: 5
        INFO - 21:52:40: Execution time:  0.00028568900052050594 s
        INFO - 21:52:40: Linearizations number: 5
        INFO - 21:52:40: * Discipline: SobieskiStructure
        INFO - 21:52:40: Executions number: 90
        INFO - 21:52:40: Execution time:  0.21148822200484574 s
        INFO - 21:52:40: Linearizations number: 5
        INFO - 21:52:40: Total number of executions calls 272
        INFO - 21:52:40: Total number of linearizations 20




.. GENERATED FROM PYTHON SOURCE LINES 163-168

Post-process the results
------------------------

Plot the optimization history view
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 168-170

.. code-block:: default

    scenario.post_process("OptHistoryView", save=False, show=False)




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_001.png
          :alt: Evolution of the optimization variables
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_002.png
          :alt: Evolution of the objective value
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_003.png
          :alt: Distance to the optimum
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_004.png
          :alt: Hessian diagonal approximation
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_005.png
          :alt: Evolution of the inequality constraints
          :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f618ed23e80>



.. GENERATED FROM PYTHON SOURCE LINES 171-173

Plot the basic history view
^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 173-175

.. code-block:: default

    scenario.post_process("BasicHistory", data_list=["x_shared"], save=False, show=False)




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_006.png
    :alt: History plot
    :class: sphx-glr-single-img


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

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 .. code-block:: none


    <gemseo.post.basic_history.BasicHistory object at 0x7f618e011b80>



.. GENERATED FROM PYTHON SOURCE LINES 176-178

Plot the constraints and objective history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 178-180

.. code-block:: default

    scenario.post_process("ObjConstrHist", save=False, show=False)




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_007.png
    :alt: Evolution of the objective value and maximal constraint 
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    <gemseo.post.obj_constr_hist.ObjConstrHist object at 0x7f618e011400>



.. GENERATED FROM PYTHON SOURCE LINES 181-183

Plot the constraints history
^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 183-187

.. code-block:: default

    scenario.post_process(
        "ConstraintsHistory", save=False, show=False, constraints_list=["g_1", "g_2", "g_3"]
    )




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_008.png
    :alt: Evolution of the constraints w.r.t. iterations, g_1_1, g_1_2, g_1_3, g_1_4, g_1_5, g_1_6, g_1_7, g_2, g_3_1, g_3_2, g_3_3, g_3_4
    :class: sphx-glr-single-img


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

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 .. code-block:: none


    <gemseo.post.constraints_history.ConstraintsHistory object at 0x7f618dd20d30>



.. GENERATED FROM PYTHON SOURCE LINES 188-190

Plot the constraints history using a radar chart
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 190-194

.. code-block:: default

    scenario.post_process(
        "RadarChart", save=False, show=False, constraints_list=["g_1", "g_2", "g_3"]
    )




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_009.png
    :alt: Constraints at last iteration
    :class: sphx-glr-single-img


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

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    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.0/lib/python3.8/site-packages/gemseo/post/dataset/dataset_plot.py:383: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
      sub_figure.tight_layout()

    <gemseo.post.radar_chart.RadarChart object at 0x7f618dcbffd0>



.. GENERATED FROM PYTHON SOURCE LINES 195-197

Plot the quadratic approximation of the objective
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 197-199

.. code-block:: default

    scenario.post_process("QuadApprox", function="-y_4", save=False, show=False)




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_010.png
          :alt: Hessian matrix SR1 approximation of -y_4
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_011.png
          :alt: plot sobieski mdf example
          :class: sphx-glr-multi-img


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

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 .. code-block:: none


    <gemseo.post.quad_approx.QuadApprox object at 0x7f618c29d5e0>



.. GENERATED FROM PYTHON SOURCE LINES 200-202

Plot the functions using a SOM
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 202-204

.. code-block:: default

    scenario.post_process("SOM", save=False, show=False)




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_012.png
    :alt: Self Organizing Maps of the design space, -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
    :class: sphx-glr-single-img


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

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        INFO - 21:52:44: Building Self Organizing Map from optimization history:
        INFO - 21:52:44:     Number of neurons in x direction = 4
        INFO - 21:52:44:     Number of neurons in y direction = 4

    <gemseo.post.som.SOM object at 0x7f618c4ad0d0>



.. GENERATED FROM PYTHON SOURCE LINES 205-207

Plot the scatter matrix of variables of interest
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 207-215

.. code-block:: default

    scenario.post_process(
        "ScatterPlotMatrix",
        save=False,
        show=False,
        variables_list=["-y_4", "g_1"],
        fig_size=(14, 14),
    )




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_013.png
    :alt: plot sobieski mdf example
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f618c48ac70>



.. GENERATED FROM PYTHON SOURCE LINES 216-218

Plot the variables using the parallel coordinates
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 218-220

.. code-block:: default

    scenario.post_process("ParallelCoordinates", save=False, show=False)




.. rst-class:: sphx-glr-horizontal


    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_014.png
          :alt: Design variables history colored by '-y_4'  value
          :class: sphx-glr-multi-img

    *

      .. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_015.png
          :alt: Objective function and constraints history colored by '-y_4' value
          :class: sphx-glr-multi-img


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

 Out:

 .. code-block:: none


    <gemseo.post.para_coord.ParallelCoordinates object at 0x7f6182c061c0>



.. GENERATED FROM PYTHON SOURCE LINES 221-223

Plot the robustness of the solution
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 223-225

.. code-block:: default

    scenario.post_process("Robustness", save=False, show=False)




.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_016.png
    :alt: Box plot of the optimization functions with normalized stddev 0.01
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none


    <gemseo.post.robustness.Robustness object at 0x7f6182ab97f0>



.. GENERATED FROM PYTHON SOURCE LINES 226-228

Plot the influence of the design variables
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 228-231

.. code-block:: default

    scenario.post_process("VariableInfluence", save=False, show=False, fig_size=(14, 14))
    # Workaround for HTML rendering, instead of ``show=True``
    plt.show()



.. image:: /examples/formulations/images/sphx_glr_plot_sobieski_mdf_example_017.png
    :alt: Partial variation of the functions wrt design variables, 9 variables required to explain 99% of -y_4 variations, 5 variables required to explain 99% of g_1_0 variations, 5 variables required to explain 99% of g_1_1 variations, 5 variables required to explain 99% of g_1_2 variations, 5 variables required to explain 99% of g_1_3 variations, 5 variables required to explain 99% of g_1_4 variations, 4 variables required to explain 99% of g_1_5 variations, 4 variables required to explain 99% of g_1_6 variations, 1 variables required to explain 99% of g_2 variations, 7 variables required to explain 99% of g_3_0 variations, 7 variables required to explain 99% of g_3_1 variations, 3 variables required to explain 99% of g_3_2 variations, 3 variables required to explain 99% of g_3_3 variations
    :class: sphx-glr-single-img


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

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 .. code-block:: none

        INFO - 21:52:49: VariableInfluence for function -y_4
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [1 4 3 2 5 9 7 8 0]
    /home/docs/checkouts/readthedocs.org/user_builds/gemseo/conda/3.2.0/lib/python3.8/site-packages/gemseo/post/variable_influence.py:223: UserWarning: FixedFormatter should only be used together with FixedLocator
      axe.set_xticklabels(x_labels, fontsize=12, rotation=90)
        INFO - 21:52:49: VariableInfluence for function g_1_0
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [0 7 3 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_1
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [7 0 3 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_2
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [7 0 3 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_3
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [7 0 3 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_4
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [7 0 3 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_5
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [3 7 5 6]
        INFO - 21:52:49: VariableInfluence for function g_1_6
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [3 7 5 6]
        INFO - 21:52:49: VariableInfluence for function g_2
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [0]
        INFO - 21:52:49: VariableInfluence for function g_3_0
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [1 9 5 2 4 0 8]
        INFO - 21:52:49: VariableInfluence for function g_3_1
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [1 9 5 2 4 0 8]
        INFO - 21:52:49: VariableInfluence for function g_3_2
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [1 9 2]
        INFO - 21:52:49: VariableInfluence for function g_3_3
        INFO - 21:52:49: Most influent variables indices to explain % of the function variation : 99
        INFO - 21:52:49: [9 1 2]





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

   **Total running time of the script:** ( 0 minutes  9.962 seconds)


.. _sphx_glr_download_examples_formulations_plot_sobieski_mdf_example.py:


.. only :: html

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



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

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



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

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


.. only:: html

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

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