# 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
# 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
# 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 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 gemseo.post.core.robustness_quantifier import RobustnessQuantifier
from gemseo.post.opt_post_processor 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.
"""

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 = 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