# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This work is licensed under a BSD 0-Clause License.
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# 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
"""
Comparing sensitivity indices
=============================
"""

from __future__ import annotations

from gemseo import configure_logger
from gemseo.problems.uncertainty.ishigami.ishigami_discipline import IshigamiDiscipline
from gemseo.problems.uncertainty.ishigami.ishigami_space import IshigamiSpace
from gemseo.uncertainty.sensitivity.correlation_analysis import CorrelationAnalysis
from gemseo.uncertainty.sensitivity.morris_analysis import MorrisAnalysis

configure_logger()

# %%
# In this example,
# we consider the Ishigami function :cite:`ishigami1990`
#
# .. math::
#
#    f(x_1,x_2,x_3)=\sin(x_1)+7\sin(x_2)^2+0.1x_3^4\sin(x_1)
#
# implemented as an :class:`.Discipline` by the :class:`.IshigamiDiscipline`.
# It is commonly used
# with the independent random variables :math:`X_1`, :math:`X_2` and :math:`X_3`
# uniformly distributed between :math:`-\pi` and :math:`\pi`
# and defined in the :class:`.IshigamiSpace`.
discipline = IshigamiDiscipline()
uncertain_space = IshigamiSpace()

# %%
# We would like to carry out two sensitivity analyses,
# e.g. a first one based on correlation coefficients
# and a second one based on the Morris methodology,
# and compare the results,
#
# Firstly,
# we create a :class:`.CorrelationAnalysis` and compute the sensitivity indices:
correlation = CorrelationAnalysis()
correlation.compute_samples([discipline], uncertain_space, 10)
correlation.compute_indices()

# %%
# Then,
# we create an :class:`.MorrisAnalysis` and compute the sensitivity indices:
morris = MorrisAnalysis()
morris.compute_samples([discipline], uncertain_space, 10)
morris.compute_indices()

# %%
# Lastly,
# we compare these analyses
# with the graphical method :meth:`.BaseSensitivityAnalysis.plot_comparison`,
# either using a bar chart:
morris.plot_comparison(correlation, "y", use_bar_plot=True, save=False, show=True)

# %%
# or a radar plot:
morris.plot_comparison(correlation, "y", use_bar_plot=False, save=False, show=True)

# %%
# .. tip::
#
#    The comparison method can use plotly to generate an interactive web-based figure.
#    Just set the execution option ``file_format`` to ``"html"``.