Scatter plot matrix

In this example, we illustrate the use of the ScatterPlotMatrix plot on the Sobieski’s SSBJ problem.

from __future__ import division, unicode_literals

from matplotlib import pyplot as plt

Import

The first step is to import some functions from the API and a method to get the design space.

from gemseo.api import configure_logger, create_discipline, create_scenario
from gemseo.problems.sobieski.core import SobieskiProblem

configure_logger()

Out:

<RootLogger root (INFO)>

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.

Create disciplines

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

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

Create design space

We also read the design space from the SobieskiProblem.

design_space = SobieskiProblem().read_design_space()

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.

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

Out:

    INFO - 14:42:10:
    INFO - 14:42:10: *** Start DOE Scenario execution ***
    INFO - 14:42:10: DOEScenario
    INFO - 14:42:10:    Disciplines: SobieskiPropulsion SobieskiAerodynamics SobieskiStructure SobieskiMission
    INFO - 14:42:10:    MDOFormulation: MDF
    INFO - 14:42:10:    Algorithm: OT_MONTE_CARLO
    INFO - 14:42:10: Optimization problem:
    INFO - 14:42:10:    Minimize: -y_4(x_shared, x_1, x_2, x_3)
    INFO - 14:42:10:    With respect to: x_shared, x_1, x_2, x_3
    INFO - 14:42:10:    Subject to constraints:
    INFO - 14:42:10:       g_1(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 14:42:10:       g_2(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 14:42:10:       g_3(x_shared, x_1, x_2, x_3) <= 0.0
    INFO - 14:42:10: Generation of OT_MONTE_CARLO DOE with OpenTurns
    INFO - 14:42:10: DOE sampling:   0%|          | 0/30 [00:00<?, ?it]
    INFO - 14:42:10: DOE sampling:   7%|▋         | 2/30 [00:00<00:00, 280.33 it/sec]
    INFO - 14:42:10: DOE sampling:  17%|█▋        | 5/30 [00:00<00:00, 133.71 it/sec]
    INFO - 14:42:10: DOE sampling:  27%|██▋       | 8/30 [00:00<00:00, 84.47 it/sec]
    INFO - 14:42:10: DOE sampling:  37%|███▋      | 11/30 [00:00<00:00, 63.58 it/sec]
    INFO - 14:42:10: DOE sampling:  47%|████▋     | 14/30 [00:00<00:00, 48.28 it/sec]
    INFO - 14:42:10: DOE sampling:  57%|█████▋    | 17/30 [00:00<00:00, 39.38 it/sec]
    INFO - 14:42:10: DOE sampling:  67%|██████▋   | 20/30 [00:00<00:00, 33.72 it/sec]
    INFO - 14:42:11: DOE sampling:  77%|███████▋  | 23/30 [00:01<00:00, 29.67 it/sec]
    INFO - 14:42:11: DOE sampling:  87%|████████▋ | 26/30 [00:01<00:00, 25.92 it/sec]
    INFO - 14:42:11: DOE sampling:  97%|█████████▋| 29/30 [00:01<00:00, 23.11 it/sec]
 WARNING - 14:42:11: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 14:42:11: DOE sampling: 100%|██████████| 30/30 [00:01<00:00, 22.32 it/sec]
    INFO - 14:42:11: Optimization result:
    INFO - 14:42:11: Objective value = 617.0803511313786
    INFO - 14:42:11: The result is not feasible.
    INFO - 14:42:11: Status: None
    INFO - 14:42:11: Optimizer message: None
    INFO - 14:42:11: Number of calls to the objective function by the optimizer: 30
    INFO - 14:42:11: Constraints values:
    INFO - 14:42:11:    g_1 = [-0.48945084 -0.2922749  -0.21769656 -0.18063263 -0.15912463 -0.07434699
    INFO - 14:42:11:  -0.16565301]
    INFO - 14:42:11:    g_2 = 0.010000000000000009
    INFO - 14:42:11:    g_3 = [-0.78174978 -0.21825022 -0.11408603 -0.01907799]
    INFO - 14:42:11: Design space:
    INFO - 14:42:11: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:42:11: | name     | lower_bound |        value        | upper_bound | type  |
    INFO - 14:42:11: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:42:11: | x_shared |     0.01    | 0.06294679971968815 |     0.09    | float |
    INFO - 14:42:11: | x_shared |    30000    |  42733.67550603654  |    60000    | float |
    INFO - 14:42:11: | x_shared |     1.4     |  1.663874765307306  |     1.8     | float |
    INFO - 14:42:11: | x_shared |     2.5     |  5.819410624921828  |     8.5     | float |
    INFO - 14:42:11: | x_shared |      40     |  69.42919736071644  |      70     | float |
    INFO - 14:42:11: | x_shared |     500     |  1221.859441367615  |     1500    | float |
    INFO - 14:42:11: | x_1      |     0.1     |  0.1065122508792764 |     0.4     | float |
    INFO - 14:42:11: | x_1      |     0.75    |   1.09882806437771  |     1.25    | float |
    INFO - 14:42:11: | x_2      |     0.75    |   1.07969581180922  |     1.25    | float |
    INFO - 14:42:11: | x_3      |     0.1     |  0.4585171784931197 |      1      | float |
    INFO - 14:42:11: +----------+-------------+---------------------+-------------+-------+
    INFO - 14:42:11: *** DOE Scenario run terminated ***

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

Post-process scenario

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

Tip

Each post-processing method requires different inputs and offers a variety of customization options. Use the API function get_post_processing_options_schema() to print a table with the options for any post-processing algorithm. Or refer to our dedicated page: Options for Post-processing algorithms.

design_variables = ["x_shared", "x_1", "x_2", "x_3"]
scenario.post_process(
    "ScatterPlotMatrix",
    save=False,
    show=False,
    variables_list=design_variables + ["-y_4"],
)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()
plot history scatter matrix

Total running time of the script: ( 0 minutes 5.451 seconds)

Gallery generated by Sphinx-Gallery