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

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

.. _sphx_glr_examples_post_process_algorithms_plot_som.py:


Self-Organizing Map
===================

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

.. GENERATED FROM PYTHON SOURCE LINES 28-36

.. code-block:: Python


    from __future__ import annotations

    from gemseo import configure_logger
    from gemseo import create_discipline
    from gemseo import create_scenario
    from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace








.. GENERATED FROM PYTHON SOURCE LINES 37-41

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

.. GENERATED FROM PYTHON SOURCE LINES 41-44

.. code-block:: Python


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 45-69

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

The :class:`.SOM` post-processing performs a Self Organizing Map
clustering on the optimization history.
A :class:`.SOM` is a 2D representation of a design of experiments
which requires dimensionality reduction since it may be in a very high dimension.

A :term:`SOM` is built by using an unsupervised artificial neural network
:cite:`Kohonen:2001`.
A map of size ``n_x.n_y`` is generated, where
``n_x`` is the number of neurons in the :math:`x` direction and ``n_y``
is the number of neurons in the :math:`y` direction. The design space
(whatever the dimension) is reduced to a 2D representation based on
``n_x.n_y`` neurons. Samples are clustered to a neuron when their design
variables are close in terms of their L2 norm. A neuron is always located at the
same place on a map. Each neuron is colored according to the average value for
a given criterion. This helps to qualitatively analyze whether parts of the design
space are good according to some criteria and not for others, and where
compromises should be made. A white neuron has no sample associated with
it: not enough evaluations were provided to train the SOM.

SOM's provide a qualitative view of the :term:`objective function`, the
:term:`constraints`, and of their relative behaviors.

.. GENERATED FROM PYTHON SOURCE LINES 71-75

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

.. GENERATED FROM PYTHON SOURCE LINES 75-82

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 83-86

Create design space
-------------------
We also create the :class:`.SobieskiDesignSpace`.

.. GENERATED FROM PYTHON SOURCE LINES 86-88

.. code-block:: Python

    design_space = SobieskiDesignSpace()








.. GENERATED FROM PYTHON SOURCE LINES 89-95

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 Monte Carlo DOE algorithm and 30 samples.

.. GENERATED FROM PYTHON SOURCE LINES 95-107

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "y_4",
        design_space,
        formulation_name="MDF",
        maximize_objective=True,
        scenario_type="DOE",
    )
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, constraint_type="ineq")
    scenario.execute(algo_name="OT_MONTE_CARLO", n_samples=30)





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

 .. code-block:: none

     WARNING - 08:38:59: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
     WARNING - 08:38:59: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
        INFO - 08:38:59:  
        INFO - 08:38:59: *** Start DOEScenario execution ***
        INFO - 08:38:59: DOEScenario
        INFO - 08:38:59:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 08:38:59:    MDO formulation: MDF
        INFO - 08:38:59: Optimization problem:
        INFO - 08:38:59:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 08:38:59:    with respect to x_1, x_2, x_3, x_shared
        INFO - 08:38:59:    subject to constraints:
        INFO - 08:38:59:       g_1(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:38:59:       g_2(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:38:59:       g_3(x_shared, x_1, x_2, x_3) <= 0
        INFO - 08:38:59:    over the design space:
        INFO - 08:38:59:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:38:59:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 08:38:59:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:38:59:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 08:38:59:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 08:38:59:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 08:38:59:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 08:38:59:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 08:38:59:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 08:38:59:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 08:38:59:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 08:38:59:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 08:38:59:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 08:38:59:       +-------------+-------------+-------+-------------+-------+
        INFO - 08:38:59: Solving optimization problem with algorithm OT_MONTE_CARLO:
        INFO - 08:38:59:      3%|▎         | 1/30 [00:00<00:01, 14.92 it/sec, obj=-166]
        INFO - 08:38:59:      7%|▋         | 2/30 [00:00<00:01, 19.43 it/sec, obj=-484]
        INFO - 08:38:59:     10%|█         | 3/30 [00:00<00:01, 21.72 it/sec, obj=-481]
        INFO - 08:38:59:     13%|█▎        | 4/30 [00:00<00:01, 23.08 it/sec, obj=-384]
        INFO - 08:38:59:     17%|█▋        | 5/30 [00:00<00:01, 23.99 it/sec, obj=-1.14e+3]
        INFO - 08:38:59:     20%|██        | 6/30 [00:00<00:00, 24.64 it/sec, obj=-290]
        INFO - 08:38:59:     23%|██▎       | 7/30 [00:00<00:00, 24.74 it/sec, obj=-630]
        INFO - 08:38:59:     27%|██▋       | 8/30 [00:00<00:00, 24.52 it/sec, obj=-346]
        INFO - 08:38:59:     30%|███       | 9/30 [00:00<00:00, 24.63 it/sec, obj=-626]
        INFO - 08:38:59:     33%|███▎      | 10/30 [00:00<00:00, 24.70 it/sec, obj=-621]
        INFO - 08:38:59:     37%|███▋      | 11/30 [00:00<00:00, 24.76 it/sec, obj=-280]
        INFO - 08:38:59:     40%|████      | 12/30 [00:00<00:00, 24.17 it/sec, obj=-288]
        INFO - 08:38:59:     43%|████▎     | 13/30 [00:00<00:00, 23.71 it/sec, obj=-257]
        INFO - 08:38:59:     47%|████▋     | 14/30 [00:00<00:00, 23.32 it/sec, obj=-367]
        INFO - 08:38:59:     50%|█████     | 15/30 [00:00<00:00, 23.14 it/sec, obj=-1.08e+3]
        INFO - 08:38:59:     53%|█████▎    | 16/30 [00:00<00:00, 23.27 it/sec, obj=-344]
        INFO - 08:38:59:     57%|█████▋    | 17/30 [00:00<00:00, 23.12 it/sec, obj=-368]
        INFO - 08:38:59:     60%|██████    | 18/30 [00:00<00:00, 22.95 it/sec, obj=-253]
        INFO - 08:39:00:     63%|██████▎   | 19/30 [00:00<00:00, 22.72 it/sec, obj=-129]
        INFO - 08:39:00:     67%|██████▋   | 20/30 [00:00<00:00, 22.62 it/sec, obj=-1.07e+3]
        INFO - 08:39:00:     70%|███████   | 21/30 [00:00<00:00, 22.83 it/sec, obj=-341]
        INFO - 08:39:00:     73%|███████▎  | 22/30 [00:00<00:00, 22.91 it/sec, obj=-1e+3]
        INFO - 08:39:00:     77%|███████▋  | 23/30 [00:01<00:00, 22.53 it/sec, obj=-586]
        INFO - 08:39:00:     80%|████████  | 24/30 [00:01<00:00, 22.64 it/sec, obj=-483]
        INFO - 08:39:00:     83%|████████▎ | 25/30 [00:01<00:00, 22.83 it/sec, obj=-392]
        INFO - 08:39:00:     87%|████████▋ | 26/30 [00:01<00:00, 23.00 it/sec, obj=-406]
        INFO - 08:39:00:     90%|█████████ | 27/30 [00:01<00:00, 22.82 it/sec, obj=-207]
        INFO - 08:39:00:     93%|█████████▎| 28/30 [00:01<00:00, 22.97 it/sec, obj=-702]
        INFO - 08:39:00:     97%|█████████▋| 29/30 [00:01<00:00, 23.21 it/sec, obj=-423]
        INFO - 08:39:00:    100%|██████████| 30/30 [00:01<00:00, 23.28 it/sec, obj=-664]
        INFO - 08:39:00: Optimization result:
        INFO - 08:39:00:    Optimizer info:
        INFO - 08:39:00:       Status: None
        INFO - 08:39:00:       Message: None
        INFO - 08:39:00:       Number of calls to the objective function by the optimizer: 30
        INFO - 08:39:00:    Solution:
        INFO - 08:39:00:       The solution is feasible.
        INFO - 08:39:00:       Objective: -367.45728393799953
        INFO - 08:39:00:       Standardized constraints:
        INFO - 08:39:00:          g_1 = [-0.02478574 -0.00310924 -0.00855146 -0.01702654 -0.02484732 -0.04764585
        INFO - 08:39:00:  -0.19235415]
        INFO - 08:39:00:          g_2 = -0.09000000000000008
        INFO - 08:39:00:          g_3 = [-0.98722984 -0.01277016 -0.60760341 -0.0557087 ]
        INFO - 08:39:00:       Design space:
        INFO - 08:39:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:39:00:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 08:39:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:39:00:          | x_shared[0] |     0.01    | 0.01230934749207792 |     0.09    | float |
        INFO - 08:39:00:          | x_shared[1] |    30000    |  43456.87364611478  |    60000    | float |
        INFO - 08:39:00:          | x_shared[2] |     1.4     |  1.731884935123487  |     1.8     | float |
        INFO - 08:39:00:          | x_shared[3] |     2.5     |  3.894765253193514  |     8.5     | float |
        INFO - 08:39:00:          | x_shared[4] |      40     |  57.92631048228255  |      70     | float |
        INFO - 08:39:00:          | x_shared[5] |     500     |  520.4048463450415  |     1500    | float |
        INFO - 08:39:00:          | x_1[0]      |     0.1     |  0.3994784918586811 |     0.4     | float |
        INFO - 08:39:00:          | x_1[1]      |     0.75    |  0.9500312867674923 |     1.25    | float |
        INFO - 08:39:00:          | x_2         |     0.75    |  1.205851870260564  |     1.25    | float |
        INFO - 08:39:00:          | x_3         |     0.1     |  0.2108042391973412 |      1      | float |
        INFO - 08:39:00:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 08:39:00: *** End DOEScenario execution (time: 0:00:01.298635) ***




.. GENERATED FROM PYTHON SOURCE LINES 108-113

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the
:class:`.SOM` plot which performs a self organizing map
clustering on optimization history.

.. GENERATED FROM PYTHON SOURCE LINES 115-123

.. 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 123-126

.. code-block:: Python


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




.. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_som_001.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]
   :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_som_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 08:39:00: Building Self Organizing Map from optimization history:
        INFO - 08:39:00:     Number of neurons in x direction = 4
        INFO - 08:39:00:     Number of neurons in y direction = 4

    <gemseo.post.som.SOM object at 0x7f6dbfcf4250>



.. GENERATED FROM PYTHON SOURCE LINES 127-146

The following figure illustrates another :term:`SOM` on the Sobieski
use case. The optimization method is a (costly) derivative free algorithm
(``NLOPT_COBYLA``), indeed all the relevant information for the optimization
is obtained at the cost of numerous evaluations of the functions. For
more details, please read the paper by
:cite:`kumano2006multidisciplinary` on wing MDO post-processing
using SOM.

.. figure:: /tutorials/ssbj/figs/MDOScenario_SOM_v100.png

    SOM example on the Sobieski problem.

A DOE may also be a good way to produce SOM maps.
The following figure shows an example with 10000 points on
the same test case. This produces more relevant SOM plots.

.. figure:: /tutorials/ssbj/figs/som_fine.png

    SOM example on the Sobieski problem with a 10 000 samples DOE.


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

   **Total running time of the script:** (0 minutes 2.425 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_som.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_som.zip <plot_som.zip>`


.. only:: html

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

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