12-dimensional g-function

To be compared with results from “An effective screening design for sensitivity analysis of large models”, Campolongo et al, 2007

Initially we have to import the necessary modules.

import shutil
from UQpy.run_model.model_execution.PythonModel import PythonModel
from UQpy.run_model.RunModel import RunModel
from UQpy.distributions import Uniform
from UQpy.sensitivity import MorrisSensitivity
import matplotlib.pyplot as plt

Set-up problem with g-function.

a_values = [0.001, 89.9, 5.54, 42.10, 0.78, 1.26, 0.04, 0.79, 74.51, 4.32, 82.51, 41.62]
na = len(a_values)

model = PythonModel(model_script='local_pfn.py', model_object_name='gfun_sensitivity', delete_files=True,
                    a_values=a_values, var_names=['X{}'.format(i) for i in range(na)])
runmodel_object = RunModel(model=model)

dist_object = [Uniform(), ] * na

sens = MorrisSensitivity(runmodel_object=runmodel_object,
                         distributions=dist_object,
                         n_levels=20,
                         maximize_dispersion=True)
sens.run(n_trajectories=10)

print(['a{}={}'.format(i + 1, ai) for i, ai in enumerate(a_values)])

fig, ax = plt.subplots()
ax.scatter(sens.mustar_indices, sens.sigma_indices)
for i, (mu, sig) in enumerate(zip(sens.mustar_indices, sens.sigma_indices)):
    ax.text(x=mu + 0.01, y=sig + 0.01, s='X{}'.format(i + 1))
ax.set_xlabel(r'$\mu^{\star}$', fontsize=14)
ax.set_ylabel(r'$\sigma$', fontsize=14)
ax.set_title('Morris sensitivity indices', fontsize=16)
plt.show()

['a1=0.001', 'a2=89.9', 'a3=5.54', 'a4=42.1', 'a5=0.78', 'a6=1.26', 'a7=0.04', 'a8=0.79', 'a9=74.51', 'a10=4.32', 'a11=82.51', 'a12=41.62']