Source code for

# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry,
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# 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
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 import RobustnessQuantifier
from import OptPostProcessor

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 = 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