# Copyright 2021 IRT Saint ExupĂ©ry, https://www.irt-saintexupery.com
#
# This work is licensed under a BSD 0-Clause License.
#
# Permission to use, copy, modify, and/or distribute this software
# for any purpose with or without fee is hereby granted.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL
# WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL
# THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT,
# OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING
# FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
# NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
# WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
# Contributors:
# INITIAL AUTHORS - initial API and implementation and/or initial
# documentation
# :author: Matthias De Lozzo
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""
Correlations
============
In this example, we illustrate the use of the :class:`.Correlations` plot
on the Sobieski's SSBJ problem.
"""
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
# %%
# Import
# ------
# The first step is to import some high-level functions
# and a method to get the design space.
configure_logger()
# %%
# 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.
# %%
# Create disciplines
# ------------------
# Then, we instantiate the disciplines of the Sobieski's SSBJ problem:
# Propulsion, Aerodynamics, Structure and Mission
disciplines = create_discipline(
[
"SobieskiPropulsion",
"SobieskiAerodynamics",
"SobieskiStructure",
"SobieskiMission",
]
)
# %%
# Create design space
# -------------------
# We also create the :class:`.SobieskiDesignSpace`.
design_space = SobieskiDesignSpace()
# %%
# 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.
scenario = create_scenario(
disciplines,
formulation="MDF",
objective_name="y_4",
maximize_objective=True,
design_space=design_space,
)
scenario.set_differentiation_method()
for constraint in ["g_1", "g_2", "g_3"]:
scenario.add_constraint(constraint, "ineq")
scenario.execute({"algo": "SLSQP", "max_iter": 10})
# %%
# Post-process scenario
# ---------------------
# Lastly, we post-process the scenario by means of the :class:`.Correlations`
# plot which provides scatter plots of correlated variables among design
# variables, outputs functions and constraints any of the constraint or
# objective functions w.r.t. optimization iterations or sampling snapshots.
# This method requires the list of functions names to plot.
# %%
# .. tip::
#
# Each post-processing method requires different inputs and offers a variety
# of customization options. Use the API 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`.
scenario.post_process("Correlations", save=False, show=True)