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.. _sphx_glr_examples_post_process_algorithms_plot_variable_influence.py:


Variables influence
===================

In this example, we illustrate the use of the :class:`.VariableInfluence` 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.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 45-55

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

The **VariableInfluence** post-processing performs first-order variable
influence analysis.

The method computes :math:`\frac{d f}{d x_i} \cdot \left(x_{i_*} -
x_{initial_design}\right)`,
where :math:`x_{initial_design}` is the initial value of the variable
and :math:`x_{i_*}` is the optimal value of the variable.

.. GENERATED FROM PYTHON SOURCE LINES 57-61

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

.. GENERATED FROM PYTHON SOURCE LINES 61-68

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 69-72

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

.. GENERATED FROM PYTHON SOURCE LINES 72-74

.. code-block:: Python

    design_space = SobieskiDesignSpace()








.. GENERATED FROM PYTHON SOURCE LINES 75-82

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 82-94

.. code-block:: Python

    scenario = create_scenario(
        disciplines,
        "MDF",
        "y_4",
        design_space,
        maximize_objective=True,
    )
    scenario.set_differentiation_method()
    for constraint in ["g_1", "g_2", "g_3"]:
        scenario.add_constraint(constraint, constraint_type="ineq")
    scenario.execute({"algo": "SLSQP", "max_iter": 10})





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

 .. code-block:: none

        INFO - 13:57:40:  
        INFO - 13:57:40: *** Start MDOScenario execution ***
        INFO - 13:57:40: MDOScenario
        INFO - 13:57:40:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
        INFO - 13:57:40:    MDO formulation: MDF
        INFO - 13:57:40: Optimization problem:
        INFO - 13:57:40:    minimize -y_4(x_shared, x_1, x_2, x_3)
        INFO - 13:57:40:    with respect to x_1, x_2, x_3, x_shared
        INFO - 13:57:40:    subject to constraints:
        INFO - 13:57:40:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:40:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:40:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
        INFO - 13:57:40:    over the design space:
        INFO - 13:57:40:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:40:       | Name        | Lower bound | Value | Upper bound | Type  |
        INFO - 13:57:40:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:40:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
        INFO - 13:57:40:       | x_shared[1] |    30000    | 45000 |    60000    | float |
        INFO - 13:57:40:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
        INFO - 13:57:40:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
        INFO - 13:57:40:       | x_shared[4] |      40     |   55  |      70     | float |
        INFO - 13:57:40:       | x_shared[5] |     500     |  1000 |     1500    | float |
        INFO - 13:57:40:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
        INFO - 13:57:40:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
        INFO - 13:57:40:       | x_2         |     0.75    |   1   |     1.25    | float |
        INFO - 13:57:40:       | x_3         |     0.1     |  0.5  |      1      | float |
        INFO - 13:57:40:       +-------------+-------------+-------+-------------+-------+
        INFO - 13:57:40: Solving optimization problem with algorithm SLSQP:
        INFO - 13:57:40:     10%|█         | 1/10 [00:00<00:00, 10.54 it/sec, obj=-536]
        INFO - 13:57:40:     20%|██        | 2/10 [00:00<00:01,  7.44 it/sec, obj=-2.12e+3]
     WARNING - 13:57:41: MDAJacobi has reached its maximum number of iterations but the normed residual 1.7130677857005655e-05 is still above the tolerance 1e-06.
        INFO - 13:57:41:     30%|███       | 3/10 [00:00<00:01,  6.26 it/sec, obj=-3.75e+3]
        INFO - 13:57:41:     40%|████      | 4/10 [00:00<00:01,  5.97 it/sec, obj=-3.96e+3]
        INFO - 13:57:41:     50%|█████     | 5/10 [00:00<00:00,  5.81 it/sec, obj=-3.96e+3]
        INFO - 13:57:41: Optimization result:
        INFO - 13:57:41:    Optimizer info:
        INFO - 13:57:41:       Status: 8
        INFO - 13:57:41:       Message: Positive directional derivative for linesearch
        INFO - 13:57:41:       Number of calls to the objective function by the optimizer: 6
        INFO - 13:57:41:    Solution:
        INFO - 13:57:41:       The solution is feasible.
        INFO - 13:57:41:       Objective: -3963.408265187933
        INFO - 13:57:41:       Standardized constraints:
        INFO - 13:57:41:          g_1 = [-0.01806104 -0.03334642 -0.04424946 -0.0518346  -0.05732607 -0.13720865
        INFO - 13:57:41:  -0.10279135]
        INFO - 13:57:41:          g_2 = 3.333278582928756e-06
        INFO - 13:57:41:          g_3 = [-7.67181773e-01 -2.32818227e-01  8.30379541e-07 -1.83255000e-01]
        INFO - 13:57:41:       Design space:
        INFO - 13:57:41:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:41:          | Name        | Lower bound |        Value        | Upper bound | Type  |
        INFO - 13:57:41:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:41:          | x_shared[0] |     0.01    | 0.06000083331964572 |     0.09    | float |
        INFO - 13:57:41:          | x_shared[1] |    30000    |        60000        |    60000    | float |
        INFO - 13:57:41:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
        INFO - 13:57:41:          | x_shared[3] |     2.5     |         2.5         |     8.5     | float |
        INFO - 13:57:41:          | x_shared[4] |      40     |          70         |      70     | float |
        INFO - 13:57:41:          | x_shared[5] |     500     |         1500        |     1500    | float |
        INFO - 13:57:41:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
        INFO - 13:57:41:          | x_1[1]      |     0.75    |         0.75        |     1.25    | float |
        INFO - 13:57:41:          | x_2         |     0.75    |         0.75        |     1.25    | float |
        INFO - 13:57:41:          | x_3         |     0.1     |  0.1562448753887276 |      1      | float |
        INFO - 13:57:41:          +-------------+-------------+---------------------+-------------+-------+
        INFO - 13:57:41: *** End MDOScenario execution (time: 0:00:00.986196) ***

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



.. GENERATED FROM PYTHON SOURCE LINES 95-99

Post-process scenario
---------------------
Lastly, we post-process the scenario by means of the :class:`.VariableInfluence`
plot.

.. GENERATED FROM PYTHON SOURCE LINES 101-109

.. 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 109-111

.. code-block:: Python


    scenario.post_process("VariableInfluence", fig_size=(20, 20), save=False, show=True)



.. image-sg:: /examples/post_process/algorithms/images/sphx_glr_plot_variable_influence_001.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
   :srcset: /examples/post_process/algorithms/images/sphx_glr_plot_variable_influence_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        INFO - 13:57:41: Output name; most influential variables to explain 0.99% of the output variation 
        INFO - 13:57:41:    -y_4; x_1[1], x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[3], x_shared[4], x_shared[5]
        INFO - 13:57:41:    g_1[0]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 13:57:41:    g_1[1]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 13:57:41:    g_1[2]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 13:57:41:    g_1[3]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 13:57:41:    g_1[4]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
        INFO - 13:57:41:    g_1[5]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 13:57:42:    g_1[6]; x_1[0], x_1[1], x_shared[3], x_shared[5]
        INFO - 13:57:42:    g_2; x_shared[0]
        INFO - 13:57:42:    g_3[0]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 13:57:42:    g_3[1]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
        INFO - 13:57:42:    g_3[2]; x_3, x_shared[1], x_shared[2]
        INFO - 13:57:42:    g_3[3]; x_3, x_shared[1], x_shared[2]

    <gemseo.post.variable_influence.VariableInfluence object at 0x7f2d0c201e20>




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