# Morris analysis¶

from __future__ import annotations

import pprint

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.morris.analysis import MorrisAnalysis

configure_logger()

<RootLogger root (INFO)>


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()


Then, we run sensitivity analysis of type MorrisAnalysis:

sensitivity_analysis = MorrisAnalysis([discipline], uncertain_space, n_samples=None)
sensitivity_analysis.compute_indices()

 WARNING - 08:55:22: No coupling in MDA, switching chain_linearize to True.
WARNING - 08:55:22: No coupling in MDA, switching chain_linearize to True.
INFO - 08:55:22:
INFO - 08:55:22: *** Start MorrisAnalysisSamplingPhase execution ***
INFO - 08:55:22: MorrisAnalysisSamplingPhase
INFO - 08:55:22:    Disciplines: _OATSensitivity
INFO - 08:55:22:    MDO formulation: MDF
INFO - 08:55:22: Running the algorithm lhs:
INFO - 08:55:22:     20%|██        | 1/5 [00:00<00:00, 55.75 it/sec]
INFO - 08:55:22:     40%|████      | 2/5 [00:00<00:00, 90.19 it/sec]
INFO - 08:55:22:     60%|██████    | 3/5 [00:00<00:00, 114.55 it/sec]
INFO - 08:55:22:     80%|████████  | 4/5 [00:00<00:00, 132.27 it/sec]
INFO - 08:55:22:    100%|██████████| 5/5 [00:00<00:00, 146.04 it/sec]
INFO - 08:55:22: *** End MorrisAnalysisSamplingPhase execution (time: 0:00:00.046215) ***

{'MU': {'y': [{'x1': array([-0.36000398]), 'x2': array([0.77781853]), 'x3': array([-0.70990541])}]}, 'MU_STAR': {'y': [{'x1': array([0.67947346]), 'x2': array([0.88906579]), 'x3': array([0.72694219])}]}, 'SIGMA': {'y': [{'x1': array([0.98724949]), 'x2': array([0.79064599]), 'x3': array([0.8074493])}]}, 'RELATIVE_SIGMA': {'y': [{'x1': array([1.45296254]), 'x2': array([0.88929976]), 'x3': array([1.11074761])}]}, 'MIN': {'y': [{'x1': array([0.0338188]), 'x2': array([0.11821721]), 'x3': array([8.72820113e-05])}]}, 'MAX': {'y': [{'x1': array([2.2360336]), 'x2': array([1.83987522]), 'x3': array([2.12052546])}]}}


The resulting indices are the empirical means and the standard deviations of the absolute output variations due to input changes.

pprint.pprint(sensitivity_analysis.indices)

{'MAX': {'y': [{'x1': array([2.2360336]),
'x2': array([1.83987522]),
'x3': array([2.12052546])}]},
'MIN': {'y': [{'x1': array([0.0338188]),
'x2': array([0.11821721]),
'x3': array([8.72820113e-05])}]},
'MU': {'y': [{'x1': array([-0.36000398]),
'x2': array([0.77781853]),
'x3': array([-0.70990541])}]},
'MU_STAR': {'y': [{'x1': array([0.67947346]),
'x2': array([0.88906579]),
'x3': array([0.72694219])}]},
'RELATIVE_SIGMA': {'y': [{'x1': array([1.45296254]),
'x2': array([0.88929976]),
'x3': array([1.11074761])}]},
'SIGMA': {'y': [{'x1': array([0.98724949]),
'x2': array([0.79064599]),
'x3': array([0.8074493])}]}}


The main indices corresponds to these empirical means (this main method can be changed with MorrisAnalysis.main_method):

pprint.pprint(sensitivity_analysis.main_indices)

{'y': [{'x1': array([0.67947346]),
'x2': array([0.88906579]),
'x3': array([0.72694219])}]}


and can be interpreted with respect to the empirical bounds of the outputs:

pprint.pprint(sensitivity_analysis.outputs_bounds)

{'y': [array([-1.00881748]), array([14.89344259])]}


We can also get the input parameters sorted by decreasing order of influence:

sensitivity_analysis.sort_parameters("y")

['x2', 'x3', 'x1']


We can use the method MorrisAnalysis.plot() to visualize the different series of indices:

sensitivity_analysis.plot("y", save=False, show=True, lower_mu=0, lower_sigma=0)

<Figure size 640x480 with 1 Axes>


Lastly, the sensitivity indices can be exported to a Dataset:

sensitivity_analysis.to_dataset()

GROUP MU MU_STAR SIGMA RELATIVE_SIGMA MIN MAX
VARIABLE y y y y y y
COMPONENT 0 0 0 0 0 0
x1 -0.360004 0.679473 0.987249 1.452963 0.033819 2.236034
x2 0.777819 0.889066 0.790646 0.889300 0.118217 1.839875
x3 -0.709905 0.726942 0.807449 1.110748 0.000087 2.120525

Total running time of the script: (0 minutes 0.462 seconds)

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