Source code for gemseo.problems.analytical.rosenbrock

# -*- 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: Damien Guenot
#        :author: Francois Gallard
The Rosenbrock analytic problem
from __future__ import division, unicode_literals

import logging

from numpy import array, atleast_2d, ones, zeros
from scipy.optimize import rosen, rosen_der

from gemseo.algos.design_space import DesignSpace
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.core.discipline import MDODiscipline
from gemseo.core.function import MDOFunction

LOGGER = logging.getLogger(__name__)

[docs]class Rosenbrock(OptimizationProblem): r"""**Rosenbrock** :class:`.OptimizationProblem` uses the Rosenbrock objective function .. math:: f(x) = \sum_{i=2}^{n_x} 100(x_{i} - x_{i-1}^2)^2 + (1 - x_{i-1})^2 with the default :class:`.DesignSpace` :math:`[-0.2,0.2]^{n_x}`. """ def __init__(self, n_x=2, l_b=-2.0, u_b=2.0, scalar_var=False, initial_guess=None): """ The constructor initializes the Rosenbrock :class:`.OptimizationProblem` by defining the :class:`.DesignSpace` and the objective function. :param n_x: problem dimension :type n_x: int :param l_b: lower bound (common value to all variables) :type l_b: float :param u_b: upper bound (common value to all variables) :type u_b: float :param scalar_var: if True the design space will contain only scalar variables (as many as the problem dimension); if False the design space will contain a single multidimensional variable (whose size equals the problem dimension) :type scalar_var: bool :param initial_guess: initial guess for optimal solution :type initial_guess: numpy array """ design_space = DesignSpace() if scalar_var: args = ["x" + str(i) for i in range(1, n_x + 1)] for arg in args: design_space.add_variable(arg, l_b=l_b, u_b=u_b) else: args = ["x"] design_space.add_variable("x", size=n_x, l_b=l_b, u_b=u_b) if initial_guess is None: design_space.set_current_x(zeros(n_x)) else: design_space.set_current_x(initial_guess) super(Rosenbrock, self).__init__(design_space) expr = "sum(100*(x[1:] - x[:-1]**2)**2 + (1 - x[:-1])**2" self.objective = MDOFunction( rosen, name="rosen", f_type=MDOFunction.TYPE_OBJ, jac=rosen_der, expr=expr, args=args, )
[docs] def get_solution(self): """Return the theoretical optimal value. :returns: design variables values of optimized values, function value at optimum :rtype: numpy array """ x_opt = ones(self.design_space.dimension) f_opt = 0.0 return x_opt, f_opt
[docs]class RosenMF(MDODiscipline): r"""**RosenMF**, a multi-fidelity Rosenbrock :class:`.MDODiscipline`, returns the value: .. math:: \mathrm{fidelity} * \mathrm{Rosenbrock}(x) where both :math:`\mathrm{fidelity}` and :math:`x` are provided as input data. """ def __init__(self, dimension=2): """The constructor defines the default inputs of the :class:`.MDODiscipline`, namely the default design parameter values and the fidelity. :param dimension: problem dimension :type dimension: int """ super(RosenMF, self).__init__(auto_detect_grammar_files=True) self.default_inputs = {"x": zeros(dimension), "fidelity": array([1.0])} def _run(self): fidelity = self.local_data["fidelity"] x_val = self.local_data["x"] self.local_data["rosen"] = fidelity * rosen(x_val) def _compute_jacobian(self, inputs=None, outputs=None): x_val = self.local_data["x"] fidelity = self.local_data["fidelity"] self.jac = { "rosen": { "x": atleast_2d(fidelity * rosen_der(x_val)), "fidelity": atleast_2d(rosen(x_val)), } }