# 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 annotations
import logging
from typing import Iterable
from typing import Mapping
from matplotlib import pyplot
from matplotlib.figure import Figure
from numpy import arange
from numpy import atleast_2d
from numpy import ndarray
from gemseo.post.opt_post_processor import OptPostProcessor
LOGGER = logging.getLogger(__name__)
[docs]class GradientSensitivity(OptPostProcessor):
"""Derivatives of the objective and constraints at a given iteration."""
DEFAULT_FIG_SIZE = (10.0, 10.0)
def _plot(
self,
iteration: int | None = None,
scale_gradients: bool = False,
) -> None:
"""
Args:
iteration: The iteration to plot the sensitivities.
Can use either positive or negative indexing,
e.g. ``4`` for the 5-th iteration
or ``-2`` for the penultimate one.
If ``None``, use the iteration of the optimum.
scale_gradients: If True, normalize each gradient
w.r.t. the design variables.
"""
if iteration is None:
design_value = self.opt_problem.solution.x_opt
else:
design_value = self.opt_problem.database.get_x_by_iter(iteration)
fig = self.__generate_subplots(
self._generate_x_names(),
design_value,
self.__get_output_gradients(design_value, scale_gradients=scale_gradients),
scale_gradients=scale_gradients,
)
self._add_figure(fig)
def __get_output_gradients(
self,
design_value: ndarray,
scale_gradients: bool = False,
) -> dict[str, ndarray]:
"""Return the gradients of all the output variable at a given design value.
Args:
design_value: The value of the design vector.
scale_gradients: Whether to normalize the gradients
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.
"""
function_names = self.opt_problem.get_all_functions_names()
scale_gradient = self.opt_problem.design_space.unnormalize_vect
function_names_to_gradients = {}
for function_name in function_names:
gradient_value = self.database.get_f_of_x(f"@{function_name}", design_value)
if gradient_value is None:
continue
if gradient_value.ndim == 1:
if scale_gradients:
gradient_value = scale_gradient(gradient_value, minus_lb=False)
function_names_to_gradients[function_name] = gradient_value
continue
for i, _gradient_value in enumerate(gradient_value):
if scale_gradients:
_gradient_value = scale_gradient(_gradient_value, minus_lb=False)
function_names_to_gradients[f"{function_name}_{i}"] = _gradient_value
return function_names_to_gradients
def __generate_subplots(
self,
design_names: Iterable[str],
design_value: ndarray,
gradients: Mapping[str, ndarray],
scale_gradients: bool = False,
) -> Figure:
"""Generate the gradients subplots from the data.
Args:
design_names: The names of the design variables.
design_value: The reference value for x.
gradients: The gradients to plot indexed by the output names.
scale_gradients: Whether to normalize the gradients
w.r.t. the design variables.
Returns:
The gradients subplots.
Raises:
ValueError: If `gradients` is empty.
"""
n_gradients = len(gradients)
if n_gradients == 0:
raise ValueError("No gradients to plot at current iteration!")
n_cols = 2
n_rows = sum(divmod(n_gradients, n_cols))
fig, axes = pyplot.subplots(
nrows=n_rows,
ncols=n_cols,
sharex=True,
sharey=False,
figsize=self.DEFAULT_FIG_SIZE,
)
axes = atleast_2d(axes)
abscissa = arange(len(design_value))
if self._change_obj:
gradients[self._obj_name] = -gradients.pop(self._standardized_obj_name)
i = j = 0
font_size = 12
rotation = 90
for output_name, gradient_value in sorted(gradients.items()):
axe = axes[i][j]
axe.bar(abscissa, gradient_value, color="blue", align="center")
axe.set_title(output_name)
axe.set_xticklabels(design_names, fontsize=font_size, rotation=rotation)
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 j == n_cols - 1:
j = 0
i += 1
else:
j += 1
if j == n_cols - 1:
axe = axes[i][j]
axe.set_xticklabels(design_names, fontsize=font_size, rotation=rotation)
axe.set_xticks(abscissa)
title = (
"Derivatives of objective and constraints with respect to design variables"
)
if scale_gradients:
fig.suptitle(f"{title}\n\nNormalized design space.", fontsize=14)
else:
fig.suptitle(title, fontsize=14)
return fig
