# -*- 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 - API and implementation and/or documentation
# :author: Francois Gallard
# :author: Damien Guenot
# OTHER AUTHORS - MACROSCOPIC CHANGES
"""Plot the derivatives of the functions."""
from __future__ import division, unicode_literals
import logging
from typing import Dict, Iterable, Mapping
from matplotlib import pyplot
from matplotlib.figure import Figure
from numpy import arange, atleast_2d, ndarray
from gemseo.post.opt_post_processor import OptPostProcessor
LOGGER = logging.getLogger(__name__)
[docs]class GradientSensitivity(OptPostProcessor):
"""Histograms of the derivatives of objective and constraints.
The plot method considers the derivatives at the last iteration. The iteration can
be changed.
"""
DEFAULT_FIG_SIZE = (10.0, 10.0)
def _plot(
self,
iteration=-1, # type: int
scale_gradients=False, # type: bool
): # type: (...) -> None
"""
Args:
iteration: The iteration to plot the sensitivities;
if negative, use the optimum.
scale_gradients: If True, normalize each gradient
w.r.t. the design variables.
"""
if iteration == -1:
x_ref = self.opt_problem.solution.x_opt
else:
x_ref = self.opt_problem.database.get_x_by_iter(iteration)
grad_dict = self.__get_grad_dict(x_ref, scale_gradients=scale_gradients)
x_names = self._generate_x_names()
fig = self.__generate_subplots(
x_names,
x_ref,
grad_dict,
scale_gradients=scale_gradients,
)
self._add_figure(fig)
def __get_grad_dict(
self,
x_ref, # type: ndarray
scale_gradients=False, # type: bool
): # type: (...) -> Dict[str,ndarray]
"""Create a gradient dictionary from a given iteration.
Scale it if necessary.
Args:
x_ref: The reference value for x.
scale_gradients: If True, normalize each gradient
w.r.t. the design variables.
Returns:
The gradients of the outputs
indexed by the names of the output,
e.g. 'output_name' for a mono-dimensional output,
or 'output_name_i' for the i-th component of a multi-dimensional output.
"""
all_funcs = self.opt_problem.get_all_functions_names()
scale_func = self.opt_problem.design_space.unnormalize_vect
grad_dict = {}
for func in all_funcs:
grad = self.database.get_f_of_x("@{}".format(func), x_ref)
if grad is not None:
if len(grad.shape) == 1:
if scale_gradients:
grad = scale_func(grad, minus_lb=False)
grad_dict[func] = grad
else:
n_f, _ = grad.shape
for i in range(n_f):
if scale_gradients:
grad[i, :] = scale_func(grad[i, :], minus_lb=False)
grad_dict["{}_{}".format(func, i)] = grad[i, :]
return grad_dict
@classmethod
def __generate_subplots(
cls,
x_names, # type: Iterable[str]
x_ref, # type: ndarray
grad_dict, # type: Mapping[str, ndarray]
scale_gradients=False, # type: bool
): # type: (...)-> Figure
"""Generate the gradients subplots from the data.
Args:
x_names: The variables names.
x_ref: The reference value for x.
grad_dict: The gradients to plot.
scale_gradients: If True, normalize the gradients w.r.t. the design variables.
Returns:
The gradients subplots.
Raises:
ValueError: If `grad_dict` is empty.
"""
n_funcs = len(grad_dict)
if n_funcs == 0:
raise ValueError("No gradients to plot at current iteration!")
nrows = n_funcs // 2
if 2 * nrows < n_funcs:
nrows += 1
ncols = 2
fig, axes = pyplot.subplots(
nrows=nrows,
ncols=2,
sharex=True,
sharey=False,
figsize=cls.DEFAULT_FIG_SIZE,
)
i = 0
j = -1
axes = atleast_2d(axes)
n_subplots = len(axes) * len(axes[0])
abscissa = arange(len(x_ref))
x_labels = [str(x_id) for x_id in x_names]
for func, grad in sorted(grad_dict.items()):
j += 1
if j == ncols:
j = 0
i += 1
axe = axes[i][j]
axe.bar(abscissa, grad, color="blue", align="center")
axe.set_title(func)
axe.set_xticklabels(x_labels, fontsize=12, rotation=90)
axe.set_xticks(abscissa)
# Update y labels spacing
vis_labels = [
label for label in axe.get_yticklabels() if label.get_visible() is True
]
pyplot.setp(vis_labels[::2], visible=False)
if len(grad_dict) < n_subplots:
# xlabel must be written with the same fontsize on the 2 columns
j += 1
# if j == ncols: Seems impossible to reach
# j = 0
# i += 1
axe = axes[i][j]
axe.set_xticklabels(x_labels, fontsize=12, rotation=90)
axe.set_xticks(abscissa)
if scale_gradients:
fig.suptitle(
"Derivatives of objective and constraints"
+ " with respect to design variables.\n \nNormalized Design Space.",
fontsize=14,
)
else:
fig.suptitle(
"Derivatives of objective and constraints"
+ " with respect to design variables",
fontsize=14,
)
return fig
