.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/formulations/plot_doe_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_doe_sobieski_mdf_example.py>`
        to download the full example code

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

.. _sphx_glr_examples_formulations_plot_doe_sobieski_mdf_example.py:


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

.. GENERATED FROM PYTHON SOURCE LINES 24-37

.. code-block:: default

    from __future__ import annotations

    from os import name as os_name

    from gemseo.api import configure_logger
    from gemseo.api import create_discipline
    from gemseo.api import create_scenario
    from gemseo.api import generate_n2_plot
    from gemseo.problems.sobieski.core.problem import SobieskiProblem
    from matplotlib import pyplot as plt

    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 38-45

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

.. GENERATED FROM PYTHON SOURCE LINES 45-54

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 55-58

We can quickly access the most relevant information of any discipline (name, inputs,
and outputs) with Python's ``print()`` function. Moreover, we can get the default
input values of a discipline with the attribute :attr:`.MDODiscipline.default_inputs`

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: default

    for discipline in disciplines:
        print(discipline)
        print(f"Default inputs: {discipline.default_inputs}")





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

 .. code-block:: none

    SobieskiPropulsion
    Default inputs: {'y_23': array([12562.01206488]), 'x_3': array([0.5]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'c_3': array([4360.])}
    SobieskiAerodynamics
    Default inputs: {'x_2': array([1.]), 'y_32': array([0.50279625]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_12': array([5.06069742e+04, 9.50000000e-01]), 'c_4': array([0.01375])}
    SobieskiMission
    Default inputs: {'y_14': array([50606.9741711 ,  7306.20262124]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_24': array([4.15006276]), 'y_34': array([1.10754577])}
    SobieskiStructure
    Default inputs: {'y_21': array([50606.9741711]), 'y_31': array([6354.32430691]), 'x_1': array([0.25, 1.  ]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'c_0': array([2000.]), 'c_1': array([25000.]), 'c_2': array([6.])}




.. GENERATED FROM PYTHON SOURCE LINES 63-67

You may also be interested in plotting the couplings of your disciplines.
A quick way of getting this information is the API function
:func:`.generate_n2_plot`. A much more detailed explanation of coupling
visualization is available :ref:`here <coupling_visualization>`.

.. GENERATED FROM PYTHON SOURCE LINES 67-69

.. code-block:: default

    generate_n2_plot(disciplines, save=False, show=True)




.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
   :alt: plot doe sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 70-78

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:`.BiLevel` formulation. We tell the scenario to minimize -y_4
instead of minimizing y_4 (range), which is the default option.

We need to define the design space.

.. GENERATED FROM PYTHON SOURCE LINES 78-81

.. code-block:: default

    design_space = SobieskiProblem().design_space
    print(design_space)





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

 .. code-block:: none

    Design space: 
    +-------------+-------------+--------------------+-------------+-------+
    | name        | lower_bound |       value        | upper_bound | type  |
    +-------------+-------------+--------------------+-------------+-------+
    | x_shared[0] |     0.01    |        0.05        |     0.09    | float |
    | x_shared[1] |    30000    |       45000        |    60000    | float |
    | x_shared[2] |     1.4     |        1.6         |     1.8     | float |
    | x_shared[3] |     2.5     |        5.5         |     8.5     | float |
    | x_shared[4] |      40     |         55         |      70     | float |
    | x_shared[5] |     500     |        1000        |     1500    | float |
    | x_1[0]      |     0.1     |        0.25        |     0.4     | float |
    | x_1[1]      |     0.75    |         1          |     1.25    | float |
    | x_2         |     0.75    |         1          |     1.25    | float |
    | x_3         |     0.1     |        0.5         |      1      | float |
    | y_14[0]     |    24850    |   50606.9741711    |    77100    | float |
    | y_14[1]     |    -7700    |   7306.20262124    |    45000    | float |
    | y_32        |    0.235    | 0.5027962499999999 |    0.795    | float |
    | y_31        |     2960    |   6354.32430691    |    10185    | float |
    | y_24        |     0.44    |     4.15006276     |    11.13    | float |
    | y_34        |     0.44    |     1.10754577     |     1.98    | float |
    | y_23        |     3365    |   12194.2671934    |    26400    | float |
    | y_21        |    24850    |   50606.9741711    |    77250    | float |
    | y_12[0]     |    24850    |     50606.9742     |    77250    | float |
    | y_12[1]     |     0.45    |        0.95        |     1.5     | float |
    +-------------+-------------+--------------------+-------------+-------+




.. GENERATED FROM PYTHON SOURCE LINES 82-84

Instantiate the scenario
^^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 84-93

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 94-96

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

.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 100-103

Execute the scenario
^^^^^^^^^^^^^^^^^^^^
Use provided analytic derivatives

.. GENERATED FROM PYTHON SOURCE LINES 103-105

.. code-block:: default

    scenario.set_differentiation_method("user")








.. GENERATED FROM PYTHON SOURCE LINES 106-111

Multiprocessing
^^^^^^^^^^^^^^^
It is possible to run a DOE in parallel using multiprocessing, in order to do
this, we specify the number of processes to be used for the computation of
the samples.

.. GENERATED FROM PYTHON SOURCE LINES 113-123

.. warning::
   The multiprocessing option has some limitations on Windows.
   Due to problems with sphinx, we disable it in this example.
   For Python versions < 3.7 and Numpy < 1.20.0, subprocesses may get hung
   randomly during execution. It is strongly recommended to update your
   environment to avoid this problem.
   The features :class:`.MemoryFullCache` and :class:`.HDF5Cache` are not
   available for multiprocessing on Windows.
   As an alternative, we recommend the method
   :meth:`.DOEScenario.set_optimization_history_backup`.

.. GENERATED FROM PYTHON SOURCE LINES 125-127

We define the algorithm options. Here the criterion = center option of pyDOE
centers the points within the sampling intervals.

.. GENERATED FROM PYTHON SOURCE LINES 127-138

.. code-block:: default

    algo_options = {
        "criterion": "center",
        # Evaluate gradient of the MDA
        # with coupled adjoint
        "eval_jac": True,
        # Run in parallel on 1 or 4 processors
        "n_processes": 1 if os_name == "nt" else 4,
    }

    scenario.execute({"n_samples": 30, "algo": "lhs", "algo_options": algo_options})





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

 .. code-block:: none

        INFO - 14:46:41:  
        INFO - 14:46:41: *** Start DOEScenario execution ***
        INFO - 14:46:41: DOEScenario
        INFO - 14:46:41:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 14:46:41:    MDO formulation: MDF
        INFO - 14:46:41: Optimization problem:
        INFO - 14:46:41:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 14:46:41:    with respect to x_1, x_2, x_3, x_shared
        INFO - 14:46:41:    subject to constraints:
        INFO - 14:46:41:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:46:41:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:46:41:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 14:46:41:    over the design space:
        INFO - 14:46:41:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:46:41:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 14:46:41:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:46:41:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 14:46:41:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 14:46:41:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 14:46:41:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 14:46:41:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 14:46:41:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 14:46:41:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 14:46:41:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 14:46:41:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 14:46:41:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 14:46:41:    +-------------+-------------+-------+-------------+-------+
        INFO - 14:46:41: Solving optimization problem with algorithm lhs:
        INFO - 14:46:41: ...   0%|          | 0/30 [00:00<?, ?it]
        INFO - 14:46:41: Running DOE in parallel on n_processes = 4
        INFO - 14:46:41: ...   3%|▎         | 1/30 [00:00<00:00, 47.29 it/sec, obj=-222]
        INFO - 14:46:42: ...  10%|█         | 3/30 [00:00<00:00, 37.84 it/sec, obj=-567]
        INFO - 14:46:42: ...  17%|█▋        | 5/30 [00:01<00:00, 27.33 it/sec, obj=-429]
        INFO - 14:46:42: ...  23%|██▎       | 7/30 [00:01<00:01, 22.33 it/sec, obj=-519]
        INFO - 14:46:42: ...  30%|███       | 9/30 [00:01<00:01, 20.24 it/sec, obj=-419]
        INFO - 14:46:43: ...  37%|███▋      | 11/30 [00:01<00:01, 16.76 it/sec, obj=-538]
        INFO - 14:46:43: ...  43%|████▎     | 13/30 [00:01<00:01, 15.63 it/sec, obj=-556]
        INFO - 14:46:43: ...  50%|█████     | 15/30 [00:02<00:01, 13.81 it/sec, obj=-621]
        INFO - 14:46:43: ...  57%|█████▋    | 17/30 [00:02<00:01, 12.52 it/sec, obj=-481]
        INFO - 14:46:43: ...  60%|██████    | 18/30 [00:02<00:01, 11.99 it/sec, obj=-1.07e+3]
        INFO - 14:46:43: ...  63%|██████▎   | 19/30 [00:02<00:00, 11.41 it/sec, obj=-287]
        INFO - 14:46:44: ...  67%|██████▋   | 20/30 [00:02<00:00, 10.73 it/sec, obj=-602]
        INFO - 14:46:44: ...  73%|███████▎  | 22/30 [00:02<00:00, 10.03 it/sec, obj=-414]
        INFO - 14:46:44: ...  77%|███████▋  | 23/30 [00:03<00:00,  9.33 it/sec, obj=-1.18e+3]
        INFO - 14:46:44: ...  87%|████████▋ | 26/30 [00:03<00:00,  8.61 it/sec, obj=-383]
        INFO - 14:46:44: ...  93%|█████████▎| 28/30 [00:03<00:00,  8.29 it/sec, obj=-606]
        INFO - 14:46:44: ... 100%|██████████| 30/30 [00:03<00:00,  7.97 it/sec, obj=-405]
        INFO - 14:46:45: ... 100%|██████████| 30/30 [00:03<00:00,  7.88 it/sec, obj=-405]
        INFO - 14:46:45: Optimization result:
        INFO - 14:46:45:    Optimizer info:
        INFO - 14:46:45:       Status: None
        INFO - 14:46:45:       Message: None
        INFO - 14:46:45:       Number of calls to the objective function by the optimizer: 30
        INFO - 14:46:45:    Solution:
        INFO - 14:46:45:       The solution is feasible.
        INFO - 14:46:45:       Objective: -485.49220045924955
        INFO - 14:46:45:       Standardized constraints:
        INFO - 14:46:45:          g_1 = [-0.11350951 -0.10812292 -0.1045109  -0.10204971 -0.10028641 -0.01838903
        INFO - 14:46:45:  -0.22161097]
        INFO - 14:46:45:          g_2 = -0.02400000000000002
        INFO - 14:46:45:          g_3 = [-0.33063157 -0.66936843 -0.73821755 -0.07789536]
        INFO - 14:46:45:       Design space: 
        INFO - 14:46:45:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:46:45:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 14:46:45:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:46:45:       | x_shared[0] |     0.01    | 0.05400000000000001 |     0.09    | float |
        INFO - 14:46:45:       | x_shared[1] |    30000    |        46500        |    60000    | float |
        INFO - 14:46:45:       | x_shared[2] |     1.4     |  1.686666666666667  |     1.8     | float |
        INFO - 14:46:45:       | x_shared[3] |     2.5     |         5.2         |     8.5     | float |
        INFO - 14:46:45:       | x_shared[4] |      40     |         66.5        |      70     | float |
        INFO - 14:46:45:       | x_shared[5] |     500     |  583.3333333333334  |     1500    | float |
        INFO - 14:46:45:       | x_1[0]      |     0.1     |        0.185        |     0.4     | float |
        INFO - 14:46:45:       | x_1[1]      |     0.75    |  0.9416666666666667 |     1.25    | float |
        INFO - 14:46:45:       | x_2         |     0.75    |        0.775        |     1.25    | float |
        INFO - 14:46:45:       | x_3         |     0.1     |        0.115        |      1      | float |
        INFO - 14:46:45:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 14:46:45: *** End DOEScenario execution (time: 0:00:03.821692) ***

    {'eval_jac': False, 'algo': 'lhs', 'algo_options': {'criterion': 'center', 'eval_jac': True, 'n_processes': 4, 'seed': 1, 'n_samples': 30}, 'n_samples': 30}



.. GENERATED FROM PYTHON SOURCE LINES 139-145

.. warning::
   On Windows, the progress bar may show duplicated instances during the
   initialization of each subprocess. In some cases it may also print the
   conclusion of an iteration ahead of another one that was concluded first.
   This is a consequence of the pickling process and does not affect the
   computations of the scenario.

.. GENERATED FROM PYTHON SOURCE LINES 147-154

Exporting the problem data.
^^^^^^^^^^^^^^^^^^^^^^^^^^^
After the execution of the scenario, you may want to export your data to use it
elsewhere. The method :meth:`.Scenario.export_to_dataset` will allow you to export
your results to a :class:`.Dataset`, the basic |g| class to store data.
From a dataset, you can even obtain a Pandas dataframe with its method
:meth:`~.Dataset.export_to_dataframe`:

.. GENERATED FROM PYTHON SOURCE LINES 154-159

.. code-block:: default

    dataset = scenario.export_to_dataset("a_name_for_my_dataset")
    dataframe = dataset.export_to_dataframe(
        variable_names=["-y_4", "x_1", "x_2", "x_3", "x_shared"]
    )








.. GENERATED FROM PYTHON SOURCE LINES 160-162

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

.. GENERATED FROM PYTHON SOURCE LINES 162-164

.. code-block:: default

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




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


    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_002.png
         :alt: Evolution of the optimization variables
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_003.png
         :alt: Evolution of the objective value
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_004.png
         :alt: Distance to the optimum
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_005.png
         :alt: Hessian diagonal approximation
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_006.png
         :alt: Evolution of the inequality constraints
         :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_006.png
         :class: sphx-glr-multi-img


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

 .. code-block:: none


    <gemseo.post.opt_history_view.OptHistoryView object at 0x7f3c137915e0>



.. GENERATED FROM PYTHON SOURCE LINES 165-172

.. 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 attributes for any post-processing algo. Or refer to our dedicated page:
   :ref:`gen_post_algos`.

.. GENERATED FROM PYTHON SOURCE LINES 174-176

Plot the scatter matrix
^^^^^^^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 176-180

.. code-block:: default

    scenario.post_process(
        "ScatterPlotMatrix", show=False, save=False, variable_names=["y_4", "x_shared"]
    )




.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_007.png
   :alt: plot doe sobieski mdf example
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_007.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7f3bfbe49dc0>



.. GENERATED FROM PYTHON SOURCE LINES 181-183

Plot correlations
^^^^^^^^^^^^^^^^^

.. GENERATED FROM PYTHON SOURCE LINES 183-186

.. code-block:: default

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



.. image-sg:: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_008.png
   :alt: R=0.98987, R=0.97511, R=0.99671, R=0.96235, R=0.99119, R=0.99866, R=0.95205, R=0.98584, R=0.99618, R=0.99936
   :srcset: /examples/formulations/images/sphx_glr_plot_doe_sobieski_mdf_example_008.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 14:46:48: Detected 10 correlations > 0.95





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

   **Total running time of the script:** ( 0 minutes  8.094 seconds)


.. _sphx_glr_download_examples_formulations_plot_doe_sobieski_mdf_example.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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