Source code for gemseo.post.robustness

# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.

# Contributors:
#    INITIAL AUTHORS - initial API and implementation and/or initial
#                           documentation
#        :author: Damien Guenot
#        :author: Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""
Box plots to quantify optimum robustness
****************************************
"""
from __future__ import absolute_import, division, unicode_literals

from math import sqrt

import matplotlib.pyplot as plt
import numpy.random as npr
from future import standard_library
from numpy import zeros

from gemseo.post.core.robustness_quantifier import RobustnessQuantifier
from gemseo.post.opt_post_processor import OptPostProcessor

standard_library.install_aliases()
from gemseo import LOGGER

[docs]class Robustness(OptPostProcessor):
"""
The **Robustness** post processing
performs a quadratic approximation from an optimization history,
and plot the results as cuts of the approximation
computes the quadratic approximations of all the output functions,
propagate analytically a normal distribution centered on the optimal
design variable with a standard deviation which is a percentage
of the mean passed in option (default: 1%)
and plot the corresponding output boxplot.

It is possible either to save the plot, to show the plot or both.
"""

SR1_APPROX = "SR1"

def _plot(
self, save=True, show=False, stddev=0.01, file_path="boxplot", extension="pdf"
):
"""
Builds the plot and saves it

:param function: function name to build quadratic approximation
:type function: bool
:param show: if True, displays the plot windows
:type show: bool
:param save: if True, exports plot to pdf
:type save: bool
:param file_path: the base paths of the files to export
:type file_path: str
:param stddev: standard deviation of inputs as fraction of x bounds
:type stddev: float
:param share_y: if True, all Y axis are the same,
useful to comare sensitivities
:type share_y: bool
:param extension: file extension
:type extension: str
"""
fig = self.__boxplot(stddev)
self._save_and_show(
fig, save=save, show=show, file_path=file_path, extension=extension
)

def __boxplot(self, stddev=0.01):
"""
Plots the Hessian of the function

:param stddev : standard deviation of inputs as fraction of x bounds
"""
robustness = RobustnessQuantifier(self.database, "SR1")
n_x = self.opt_problem.get_dimension()
cov = zeros((n_x, n_x))
upper_bounds = self.opt_problem.design_space.get_upper_bounds()
lower_bounds = self.opt_problem.design_space.get_lower_bounds()
bounds_range = upper_bounds - lower_bounds
cov[list(range(n_x)), list(range(n_x))] = (stddev * (bounds_range)) ** 2

data = []
funcs_names = []
for func in self.opt_problem.get_all_functions():
func_name = func.name
dim = func.dim
for i in range(dim):
b0_mat = zeros((n_x, n_x))
robustness.compute_approximation(
funcname=func_name,
at_most_niter=int(1.5 * n_x),
func_index=i,
b0_mat=b0_mat,
)
x_ref = robustness.x_ref
mean = robustness.compute_expected_value(x_ref, cov)
var = robustness.compute_variance(x_ref, cov)
if var > 0:  # Otherwise normal doesnt work
data.append(npr.normal(loc=mean, scale=sqrt(var), size=500))
legend = func_name
if dim > 1:
legend += "_" + str(i + 1)
funcs_names.append(legend)

fig = plt.figure()
fig.suptitle(
"Box plot of the optimization functions "
+ "with normalized stddev "
+ str(stddev)
)
plt.boxplot(data, showfliers=False, labels=funcs_names)

return fig