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 - API and implementation and/or documentation
#        :author: Francois Gallard
#        :author: Damien Guenot
"""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 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], 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