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 division, unicode_literals

import logging
from math import sqrt

import matplotlib.pyplot as plt
from matplotlib.figure import Figure
from numpy import zeros
from numpy.random import normal

from import RobustnessQuantifier
from import OptPostProcessor

LOGGER = logging.getLogger(__name__)

[docs]class Robustness(OptPostProcessor): """Uncertainty quantification at the optimum. Compute the quadratic approximations of all the output functions, propagate analytically a normal distribution centered on the optimal design variables with a standard deviation which is a percentage of the mean passed in option (default: 1%) and plot the corresponding output boxplot. """ DEFAULT_FIG_SIZE = (8.0, 5.0) SR1_APPROX = "SR1" def _plot( self, stddev=0.01, # type: float ): # type: (...) -> None """ Args: stddev: The standard deviation of the inputs as fraction of x bounds. """ self._add_figure(self.__boxplot(stddev)) def __boxplot( self, stddev=0.01, # type: float ): # type: (...) -> Figure """Plot the Hessian of the function. Args: stddev: The standard deviation of the inputs as fraction of x bounds. Returns: A plot of the Hessian of the function. """ 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(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(figsize=self.DEFAULT_FIG_SIZE) fig.suptitle( "Box plot of the optimization functions " "with normalized stddev {}".format(stddev) ) plt.boxplot(data, showfliers=False, labels=funcs_names) return fig