.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/post_process/plot_correlations.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:here  to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_post_process_plot_correlations.py: Correlations ============ In this example, we illustrate the use of the :class:.Correlations plot on the Sobieski's SSBJ problem. .. GENERATED FROM PYTHON SOURCE LINES 28-34 .. code-block:: default 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 from matplotlib import pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 35-39 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 39-42 .. code-block:: default configure_logger() .. rst-class:: sphx-glr-script-out Out: .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 43-62 Description ----------- A correlation coefficient indicates whether there is a linear relationship between 2 quantities :math:x and :math:y, in which case it equals 1 or -1. It is the normalized covariance between the two quantities: .. math:: R_{xy}=\frac {\sum \limits _{i=1}^n(x_i-{\bar{x}})(y_i-{\bar{y}})}{ns_{x}s_{y}} =\frac {\sum \limits _{i=1}^n(x_i-{\bar{x}})(y_i-{\bar{y}})}{\sqrt {\sum \limits _{i=1}^n(x_i-{\bar{x}})^{2}\sum \limits _{i=1}^n(y_i-{\bar{y}})^{2}}} The **Correlations** post-processing builds scatter plots of correlated variables among design variables, output functions, and constraints. The plot method considers all variable correlations greater than 95%. A different threshold value and/or a sublist of variable names can be passed as options. .. GENERATED FROM PYTHON SOURCE LINES 64-68 Create disciplines ------------------ Then, we instantiate the disciplines of the Sobieski's SSBJ problem: Propulsion, Aerodynamics, Structure and Mission .. GENERATED FROM PYTHON SOURCE LINES 68-77 .. code-block:: default disciplines = create_discipline( [ "SobieskiPropulsion", "SobieskiAerodynamics", "SobieskiStructure", "SobieskiMission", ] ) .. GENERATED FROM PYTHON SOURCE LINES 78-81 Create design space ------------------- We also read the design space from the :class:.SobieskiProblem. .. GENERATED FROM PYTHON SOURCE LINES 81-83 .. code-block:: default design_space = SobieskiProblem().design_space .. GENERATED FROM PYTHON SOURCE LINES 84-91 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 91-103 .. code-block:: default scenario = create_scenario( disciplines, formulation="MDF", objective_name="y_4", maximize_objective=True, design_space=design_space, ) scenario.set_differentiation_method("user") for constraint in ["g_1", "g_2", "g_3"]: scenario.add_constraint(constraint, "ineq") scenario.execute({"algo": "SLSQP", "max_iter": 10}) .. rst-class:: sphx-glr-script-out Out: .. code-block:: none INFO - 10:04:23: INFO - 10:04:23: *** Start MDOScenario execution *** INFO - 10:04:23: MDOScenario INFO - 10:04:23: Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission INFO - 10:04:23: MDO formulation: MDF INFO - 10:04:23: Optimization problem: INFO - 10:04:23: minimize -y_4(x_shared, x_1, x_2, x_3) INFO - 10:04:23: with respect to x_1, x_2, x_3, x_shared INFO - 10:04:23: subject to constraints: INFO - 10:04:23: g_1(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:04:23: g_2(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:04:23: g_3(x_shared, x_1, x_2, x_3) <= 0.0 INFO - 10:04:23: over the design space: INFO - 10:04:23: +----------+-------------+-------+-------------+-------+ INFO - 10:04:23: | name | lower_bound | value | upper_bound | type | INFO - 10:04:23: +----------+-------------+-------+-------------+-------+ INFO - 10:04:23: | x_shared | 0.01 | 0.05 | 0.09 | float | INFO - 10:04:23: | x_shared | 30000 | 45000 | 60000 | float | INFO - 10:04:23: | x_shared | 1.4 | 1.6 | 1.8 | float | INFO - 10:04:23: | x_shared | 2.5 | 5.5 | 8.5 | float | INFO - 10:04:23: | x_shared | 40 | 55 | 70 | float | INFO - 10:04:23: | x_shared | 500 | 1000 | 1500 | float | INFO - 10:04:23: | x_1 | 0.1 | 0.25 | 0.4 | float | INFO - 10:04:23: | x_1 | 0.75 | 1 | 1.25 | float | INFO - 10:04:23: | x_2 | 0.75 | 1 | 1.25 | float | INFO - 10:04:23: | x_3 | 0.1 | 0.5 | 1 | float | INFO - 10:04:23: +----------+-------------+-------+-------------+-------+ INFO - 10:04:23: Solving optimization problem with algorithm SLSQP: INFO - 10:04:23: ... 0%| | 0/10 [00:00 0.95 .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 3.706 seconds) .. _sphx_glr_download_examples_post_process_plot_correlations.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_correlations.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: plot_correlations.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _