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

.. only:: html

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

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

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

.. _sphx_glr_examples_post_process_algorithms_plot_history_scatter_matrix.py:


Scatter plot matrix
===================

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

.. GENERATED FROM PYTHON SOURCE LINES 28-35

.. 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








.. GENERATED FROM PYTHON SOURCE LINES 36-40

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 40-43

.. code-block:: default


    configure_logger()





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

 .. code-block:: none


    <RootLogger root (INFO)>



.. GENERATED FROM PYTHON SOURCE LINES 44-52

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

The **ScatterPlotMatrix** post-processing builds the scatter plot matrix among
design variables and outputs functions.
Each non-diagonal block represents the samples
according to the x- and y- coordinates names while the diagonal ones approximate
the probability distributions of the variables, using a kernel-density estimator.

.. GENERATED FROM PYTHON SOURCE LINES 54-58

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

.. GENERATED FROM PYTHON SOURCE LINES 58-67

.. code-block:: default

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








.. GENERATED FROM PYTHON SOURCE LINES 68-71

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

.. GENERATED FROM PYTHON SOURCE LINES 71-73

.. code-block:: default

    design_space = SobieskiProblem().design_space








.. GENERATED FROM PYTHON SOURCE LINES 74-80

Create and execute scenario
---------------------------
The next step is to build a DOE 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 80-93

.. code-block:: default

    scenario = create_scenario(
        disciplines,
        formulation="MDF",
        objective_name="y_4",
        maximize_objective=True,
        design_space=design_space,
        scenario_type="DOE",
    )
    scenario.set_differentiation_method()
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, "ineq")
    scenario.execute({"algo": "OT_MONTE_CARLO", "n_samples": 30})





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

 .. code-block:: none

        INFO - 16:55:39:  
        INFO - 16:55:39: *** Start DOEScenario execution ***
        INFO - 16:55:39: DOEScenario
        INFO - 16:55:39:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 16:55:39:    MDO formulation: MDF
        INFO - 16:55:39: Optimization problem:
        INFO - 16:55:39:    minimize -y_4(x_shared, x_1, x_2, x_3) = -y_4(x_shared, x_1, x_2, x_3)
        INFO - 16:55:39:    with respect to x_1, x_2, x_3, x_shared
        INFO - 16:55:39:    subject to constraints:
        INFO - 16:55:39:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:55:39:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:55:39:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 16:55:39:    over the design space:
        INFO - 16:55:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:55:39:    | name        | lower_bound | value | upper_bound | type  |
        INFO - 16:55:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:55:39:    | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 16:55:39:    | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 16:55:39:    | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 16:55:39:    | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 16:55:39:    | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 16:55:39:    | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 16:55:39:    | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 16:55:39:    | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 16:55:39:    | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 16:55:39:    | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 16:55:39:    +-------------+-------------+-------+-------------+-------+
        INFO - 16:55:39: Solving optimization problem with algorithm OT_MONTE_CARLO:
        INFO - 16:55:39: ...   0%|          | 0/30 [00:00<?, ?it]
        INFO - 16:55:39: ...   3%|▎         | 1/30 [00:00<00:02,  9.98 it/sec, obj=-166]
        INFO - 16:55:39: ...   7%|▋         | 2/30 [00:00<00:01, 14.38 it/sec, obj=-484]
        INFO - 16:55:39: ...  10%|█         | 3/30 [00:00<00:01, 16.95 it/sec, obj=-481]
        INFO - 16:55:39: ...  13%|█▎        | 4/30 [00:00<00:01, 18.70 it/sec, obj=-384]
        INFO - 16:55:39: ...  17%|█▋        | 5/30 [00:00<00:01, 19.90 it/sec, obj=-1.14e+3]
        INFO - 16:55:39: ...  20%|██        | 6/30 [00:00<00:01, 20.78 it/sec, obj=-290]
        INFO - 16:55:39: ...  23%|██▎       | 7/30 [00:00<00:01, 21.38 it/sec, obj=-630]
        INFO - 16:55:39: ...  27%|██▋       | 8/30 [00:00<00:01, 21.44 it/sec, obj=-346]
        INFO - 16:55:39: ...  30%|███       | 9/30 [00:00<00:00, 21.70 it/sec, obj=-626]
        INFO - 16:55:39: ...  33%|███▎      | 10/30 [00:00<00:00, 21.94 it/sec, obj=-621]
        INFO - 16:55:39: ...  37%|███▋      | 11/30 [00:00<00:00, 21.91 it/sec, obj=-280]
        INFO - 16:55:39: ...  40%|████      | 12/30 [00:00<00:00, 21.58 it/sec, obj=-288]
        INFO - 16:55:39: ...  43%|████▎     | 13/30 [00:00<00:00, 21.00 it/sec, obj=-257]
        INFO - 16:55:39: ...  47%|████▋     | 14/30 [00:00<00:00, 20.65 it/sec, obj=-367]
        INFO - 16:55:39: ...  50%|█████     | 15/30 [00:00<00:00, 20.61 it/sec, obj=-1.08e+3]
        INFO - 16:55:39: ...  53%|█████▎    | 16/30 [00:00<00:00, 20.81 it/sec, obj=-344]
        INFO - 16:55:39: ...  57%|█████▋    | 17/30 [00:00<00:00, 20.65 it/sec, obj=-368]
        INFO - 16:55:39: ...  60%|██████    | 18/30 [00:00<00:00, 20.62 it/sec, obj=-253]
        INFO - 16:55:40: ...  63%|██████▎   | 19/30 [00:00<00:00, 20.49 it/sec, obj=-129]
        INFO - 16:55:40: ...  67%|██████▋   | 20/30 [00:00<00:00, 20.57 it/sec, obj=-1.07e+3]
        INFO - 16:55:40: ...  70%|███████   | 21/30 [00:01<00:00, 20.80 it/sec, obj=-341]
        INFO - 16:55:40: ...  73%|███████▎  | 22/30 [00:01<00:00, 20.94 it/sec, obj=-1e+3]
        INFO - 16:55:40: ...  77%|███████▋  | 23/30 [00:01<00:00, 20.73 it/sec, obj=-586]
        INFO - 16:55:40: ...  80%|████████  | 24/30 [00:01<00:00, 20.85 it/sec, obj=-483]
        INFO - 16:55:40: ...  83%|████████▎ | 25/30 [00:01<00:00, 20.97 it/sec, obj=-392]
        INFO - 16:55:40: ...  87%|████████▋ | 26/30 [00:01<00:00, 21.15 it/sec, obj=-406]
        INFO - 16:55:40: ...  90%|█████████ | 27/30 [00:01<00:00, 21.03 it/sec, obj=-207]
        INFO - 16:55:40: ...  93%|█████████▎| 28/30 [00:01<00:00, 21.20 it/sec, obj=-702]
        INFO - 16:55:40: ...  97%|█████████▋| 29/30 [00:01<00:00, 21.42 it/sec, obj=-423]
        INFO - 16:55:40: ... 100%|██████████| 30/30 [00:01<00:00, 21.49 it/sec, obj=-664]
        INFO - 16:55:40: Optimization result:
        INFO - 16:55:40:    Optimizer info:
        INFO - 16:55:40:       Status: None
        INFO - 16:55:40:       Message: None
        INFO - 16:55:40:       Number of calls to the objective function by the optimizer: 30
        INFO - 16:55:40:    Solution:
        INFO - 16:55:40:       The solution is feasible.
        INFO - 16:55:40:       Objective: -367.45739115001027
        INFO - 16:55:40:       Standardized constraints:
        INFO - 16:55:40:          g_1 = [-0.02478574 -0.00310924 -0.00855146 -0.01702654 -0.02484732 -0.04764585
        INFO - 16:55:40:  -0.19235415]
        INFO - 16:55:40:          g_2 = -0.09000000000000008
        INFO - 16:55:40:          g_3 = [-0.98722984 -0.01277016 -0.60760341 -0.0557087 ]
        INFO - 16:55:40:       Design space: 
        INFO - 16:55:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:55:40:       | name        | lower_bound |        value        | upper_bound | type  |
        INFO - 16:55:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:55:40:       | x_shared[0] |     0.01    | 0.01230934749207792 |     0.09    | float |
        INFO - 16:55:40:       | x_shared[1] |    30000    |  43456.87364611478  |    60000    | float |
        INFO - 16:55:40:       | x_shared[2] |     1.4     |  1.731884935123487  |     1.8     | float |
        INFO - 16:55:40:       | x_shared[3] |     2.5     |  3.894765253193514  |     8.5     | float |
        INFO - 16:55:40:       | x_shared[4] |      40     |  57.92631048228255  |      70     | float |
        INFO - 16:55:40:       | x_shared[5] |     500     |  520.4048463450415  |     1500    | float |
        INFO - 16:55:40:       | x_1[0]      |     0.1     |  0.3994784918586811 |     0.4     | float |
        INFO - 16:55:40:       | x_1[1]      |     0.75    |  0.9500312867674923 |     1.25    | float |
        INFO - 16:55:40:       | x_2         |     0.75    |  1.205851870260564  |     1.25    | float |
        INFO - 16:55:40:       | x_3         |     0.1     |  0.2108042391973412 |      1      | float |
        INFO - 16:55:40:       +-------------+-------------+---------------------+-------------+-------+
        INFO - 16:55:40: *** End DOEScenario execution (time: 0:00:01.412002) ***

    {'eval_jac': False, 'algo': 'OT_MONTE_CARLO', 'n_samples': 30}



.. GENERATED FROM PYTHON SOURCE LINES 94-99

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.ScatterPlotMatrix`
plot which builds scatter plot matrix among design variables, objective
function and constraints.

.. GENERATED FROM PYTHON SOURCE LINES 101-109

.. 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 109-117

.. code-block:: default


    design_variables = ["x_shared", "x_1", "x_2", "x_3"]
    scenario.post_process(
        "ScatterPlotMatrix",
        variable_names=design_variables + ["-y_4"],
        save=False,
        show=True,
    )



.. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_history_scatter_matrix_001.png
   :alt: plot history scatter matrix
   :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_history_scatter_matrix_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    <gemseo.post.scatter_mat.ScatterPlotMatrix object at 0x7fbc55ac4a30>




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

   **Total running time of the script:** ( 0 minutes  5.710 seconds)


.. _sphx_glr_download_examples_post_process_algorithms_plot_history_scatter_matrix.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_history_scatter_matrix.py <plot_history_scatter_matrix.py>`

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

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


.. only:: html

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

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