Source code for

# 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 partial sensitivity of the functions."""

from __future__ import annotations

import itertools
import logging
from typing import TYPE_CHECKING

from matplotlib import pyplot
from numpy import absolute
from numpy import argsort
from numpy import array
from numpy import atleast_2d
from numpy import ndarray
from numpy import savetxt
from numpy import stack

from import OptPostProcessor
from gemseo.utils.string_tools import pretty_str
from gemseo.utils.string_tools import repr_variable

    from import Mapping

    from matplotlib.figure import Figure

LOGGER = logging.getLogger(__name__)

[docs] class VariableInfluence(OptPostProcessor): r"""First order variable influence analysis. This post-processing computes :math:`\frac{\partial f(x)}{\partial x_i}\left(x_i^* - x_i^{(0)}\right)` where :math:`x_i^{(0)}` is the initial value of the variable and :math:`x_i^*` is the optimal value of the variable. Options of the plot method are: - proportion of the total sensitivity to use as a threshold to filter the variables, - the use of a logarithmic scale, - the possibility to save the indices of the influential variables indices in a NumPy file. """ DEFAULT_FIG_SIZE = (20.0, 5.0) def _plot( self, level: float = 0.99, absolute_value: bool = False, log_scale: bool = False, save_var_files: bool = False, ) -> None: """ Args: level: The proportion of the total sensitivity to use as a threshold to filter the variables. absolute_value: Whether to plot the absolute value of the influence. log_scale: Whether to set the y-axis as log scale. save_var_files: Whether to save the influential variables indices to a NumPy file. """ # noqa: D205, D212, D415 function_names = self.optimization_problem.get_all_function_name() _, x_opt, _, _, _ = self.optimization_problem.get_optimum() x_0 = self.database.get_x_vect(1) absolute_value = log_scale or absolute_value names_to_sensitivities = {} evaluate = self.database.get_function_value for function_name in function_names: grad = evaluate(self.database.get_gradient_name(function_name), x_0) if grad is None: continue f_0 = evaluate(function_name, x_0) f_opt = evaluate(function_name, x_opt) if self._change_obj and function_name == self._neg_obj_name: grad = -grad function_name = self._obj_name if len(grad.shape) == 1: sensitivity = grad * (x_opt - x_0) sensitivity *= (f_opt - f_0) / sensitivity.sum() if absolute_value: sensitivity = absolute(sensitivity) names_to_sensitivities[function_name] = sensitivity else: for i, _grad in enumerate(grad): sensitivity = _grad * (x_opt - x_0) sensitivity *= (f_opt - f_0)[i] / sensitivity.sum() if absolute_value: sensitivity = absolute(sensitivity) names_to_sensitivities[repr_variable(function_name, i)] = ( sensitivity ) self._add_figure( self.__generate_subplots( names_to_sensitivities, level=level, log_scale=log_scale, save=save_var_files, ) ) def __get_quantile( self, sensitivity: ndarray, func: str, level: float = 0.99, save: bool = False, ) -> tuple[int, float]: """Get the number of variables explaining a fraction of the sensitivity. Args: sensitivity: The sensitivity. func: The function name. level: The quantile level. save: Whether to save the influential variables indices in a NumPy file. Returns: The number of influential variables and the absolute sensitivity w.r.t. the least influential variable. """ absolute_sensitivity = absolute(sensitivity) absolute_sensitivity_indices = argsort(absolute_sensitivity)[::-1] absolute_sensitivity = absolute_sensitivity[absolute_sensitivity_indices] variance = 0.0 total_variance = absolute_sensitivity.sum() * level n_variables = 0 while variance < total_variance and n_variables < len(absolute_sensitivity): variance += absolute_sensitivity[n_variables] n_variables += 1 influential_variables = absolute_sensitivity_indices[:n_variables] x_names = self._get_design_variable_names() " %s; %s", func, pretty_str([x_names[i] for i in influential_variables]), ) if save: names = [ [f"{name}${i}" for i in range(size)] for name, size in self.optimization_problem.design_space.variable_sizes.items() # noqa: E501 ] names = array(list(itertools.chain(*names))) file_name = f"{func}_influ_vars.csv" savetxt( file_name, stack((names[influential_variables], influential_variables)).T, fmt="%s", delimiter=" ; ", header="name ; index", ) self.output_files.append(file_name) return n_variables, absolute_sensitivity[n_variables - 1] def __generate_subplots( self, names_to_sensitivities: Mapping[str, ndarray], level: float = 0.99, log_scale: bool = False, save: bool = False, ) -> Figure: """Generate the gradients subplots from the data. Args: names_to_sensitivities: The output sensitivities w.r.t. the design variables. level: The proportion of the total sensitivity to use as a threshold to filter the variables. log_scale: Whether to set the y-axis as log scale. save: Whether to save the influential variables indices in a NumPy file. Returns: The gradients subplots. Raises: ValueError: If the `names_to_sensitivities` is empty. """ n_funcs = len(names_to_sensitivities) if not n_funcs: msg = "No gradients to plot at current iteration." raise ValueError(msg) n_cols = 2 n_rows = sum(divmod(n_funcs, n_cols)) if n_funcs == 1: n_cols = 1 fig, axes = pyplot.subplots( nrows=n_rows, ncols=n_cols, sharex=True, figsize=self.DEFAULT_FIG_SIZE ) axes = atleast_2d(axes) x_labels = self._get_design_variable_names() # This variable determines the number of variables to plot in the # x-axis. Since the data history can be edited by the user after the # problem was solved, we do not use something like opt_problem.dimension # because the problem dimension is not updated when the history is filtered. abscissas = range(len(next(iter(names_to_sensitivities.values())))) font_size = 12 rotation = 90 i = j = 0 "Output name; " "most influential variables to explain %s%% of the output variation ", level, ) for name, sensitivity in sorted(names_to_sensitivities.items()): axe = axes[i][j], sensitivity, color="blue", align="center") quantile, threshold = self.__get_quantile( sensitivity, name, level=level, save=save ) axe.set_title( f"{quantile} variables required " f"to explain {round(level * 100)}% of {name} variations" ) axe.set_xticks(abscissas) axe.set_xticklabels(x_labels, fontsize=font_size, rotation=rotation) axe.set_xlim(-1, len(sensitivity) + 1) axe.axhline(threshold, color="r") axe.axhline(-threshold, color="r") if log_scale: axe.set_yscale("log") # Update y labels spacing vis_labels = [ label for label in axe.get_yticklabels() if label.get_visible() is True ] pyplot.setp(vis_labels, visible=False) pyplot.setp(vis_labels[::2], visible=True) vis_xlabels = [ label for label in axe.get_xticklabels() if label.get_visible() is True ] if len(vis_xlabels) > 20: pyplot.setp(vis_xlabels, visible=False) pyplot.setp(vis_xlabels[:: int(len(vis_xlabels) / 10.0)], visible=True) if j == n_cols - 1: j = 0 i += 1 else: j += 1 if len(names_to_sensitivities) < n_rows * n_cols: axe = axes[i][j] axe.set_xticks(abscissas) axe.set_xticklabels(x_labels, fontsize=font_size, rotation=rotation) fig.suptitle( "Partial variation of the functions wrt design variables", fontsize=14 ) return fig