# Comparing sensitivity indices¶

from __future__ import annotations

from gemseo.uncertainty.sensitivity.correlation.analysis import CorrelationAnalysis
from gemseo.uncertainty.sensitivity.morris.analysis import MorrisAnalysis
from gemseo.uncertainty.use_cases.ishigami.ishigami_discipline import IshigamiDiscipline
from gemseo.uncertainty.use_cases.ishigami.ishigami_space import IshigamiSpace


In this example, we consider the Ishigami function [IH90]

$f(x_1,x_2,x_3)=\sin(x_1)+7\sin(x_2)^2+0.1x_3^4\sin(x_1)$

implemented as an MDODiscipline by the IshigamiDiscipline. It is commonly used with the independent random variables $$X_1$$, $$X_2$$ and $$X_3$$ uniformly distributed between $$-\pi$$ and $$\pi$$ and defined in the 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 CorrelationAnalysis and compute the sensitivity indices:

correlation = CorrelationAnalysis([discipline], uncertain_space, 10)
correlation.compute_indices()

{<Method.KENDALL: 'Kendall'>: {'y': [{'x1': array([0.55555556]), 'x2': array([0.02222222]), 'x3': array([-0.11111111])}]}, <Method.PCC: 'PCC'>: {'y': [{'x1': array([0.84696461]), 'x2': array([0.68814608]), 'x3': array([-0.29846394])}]}, <Method.PEARSON: 'Pearson'>: {'y': [{'x1': array([0.685388]), 'x2': array([0.09681897]), 'x3': array([-0.23027298])}]}, <Method.PRCC: 'PRCC'>: {'y': [{'x1': array([0.90374102]), 'x2': array([0.76539572]), 'x3': array([-0.02232206])}]}, <Method.SPEARMAN: 'Spearman'>: {'y': [{'x1': array([0.74545455]), 'x2': array([0.04242424]), 'x3': array([-0.09090909])}]}, <Method.SRC: 'SRC'>: {'y': [{'x1': array([0.94001308]), 'x2': array([0.55748872]), 'x3': array([-0.16157012])}]}, <Method.SRRC: 'SRRC'>: {'y': [{'x1': array([1.06252802]), 'x2': array([0.60167726]), 'x3': array([-0.00959941])}]}, <Method.SSRC: 'SSRC'>: {'y': [{'x1': array([0.88362459]), 'x2': array([0.31079367]), 'x3': array([0.0261049])}]}}


Then, we create an MorrisAnalysis and compute the sensitivity indices:

morris = MorrisAnalysis([discipline], uncertain_space, 10)
morris.compute_indices()

{'MU': {'y': [{'x1': array([0.73532408]), 'x2': array([-0.05115399]), 'x3': array([-1.6024484])}]}, 'MU_STAR': {'y': [{'x1': array([0.76770333]), 'x2': array([2.09435091]), 'x3': array([1.6024484])}]}, 'SIGMA': {'y': [{'x1': array([0.76770333]), 'x2': array([2.09435091]), 'x3': array([1.58984353])}]}, 'RELATIVE_SIGMA': {'y': [{'x1': array([1.]), 'x2': array([1.]), 'x3': array([0.99213399])}]}, 'MIN': {'y': [{'x1': array([0.03237925]), 'x2': array([2.04319692]), 'x3': array([0.01260487])}]}, 'MAX': {'y': [{'x1': array([1.50302741]), 'x2': array([2.14550491]), 'x3': array([3.19229192])}]}}


Lastly, we compare these analyses with the graphical method SensitivityAnalysis.plot_comparison(), either using a bar chart:

morris.plot_comparison(correlation, "y", use_bar_plot=True, save=False, show=True)

<gemseo.post.dataset.bars.BarPlot object at 0x7f00988c0700>


morris.plot_comparison(correlation, "y", use_bar_plot=False, save=False, show=True)

<gemseo.post.dataset.radar_chart.RadarChart object at 0x7f00b6a77a60>