# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This work is licensed under a BSD 0-Clause License.
#
# Permission to use, copy, modify, and/or distribute this software
# for any purpose with or without fee is hereby granted.
#
# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL
# WARRANTIES WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL
# THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT,
# OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING
# FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
# NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
# WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
#        :author: François Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""
Analytical test case # 2
========================
"""
#############################################################################
# In this example, we consider a simple optimization problem to illustrate
# algorithms interfaces and optimization libraries integration.
#
# Imports
# -------
from gemseo.algos.design_space import DesignSpace
from gemseo.algos.doe.doe_factory import DOEFactory
from gemseo.algos.opt.opt_factory import OptimizersFactory
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.api import configure_logger
from gemseo.api import execute_post
from gemseo.core.mdofunctions.mdo_function import MDOFunction
from matplotlib import pyplot as plt
from numpy import cos
from numpy import exp
from numpy import ones
from numpy import sin

configure_logger()


#############################################################################
# Define the objective function
# -----------------------------
# We define the objective function :math:`f(x)=\sin(x)-\exp(x)`
# using a :class:`.MDOFunction` defined by the sum of :class:`.MDOFunction` objects.
f_1 = MDOFunction(sin, name="f_1", jac=cos, expr="sin(x)")
f_2 = MDOFunction(exp, name="f_2", jac=exp, expr="exp(x)")
objective = f_1 - f_2

#############################################################################
# .. seealso::
#
#    The following operators are implemented: addition, subtraction and multiplication.
#    The minus operator is also defined.
#
# Define the design space
# -----------------------
# Then, we define the :class:`.DesignSpace` with |g|.
design_space = DesignSpace()
design_space.add_variable("x", 1, l_b=-2.0, u_b=2.0, value=-0.5 * ones(1))

#############################################################################
# Define the optimization problem
# -------------------------------
# Then, we define the :class:`.OptimizationProblem` with |g|.
problem = OptimizationProblem(design_space)
problem.objective = objective

#############################################################################
# Solve the optimization problem using an optimization algorithm
# --------------------------------------------------------------
# Finally, we solve the optimization problems with |g| interface.
#
# Solve the problem
# ^^^^^^^^^^^^^^^^^
opt = OptimizersFactory().execute(problem, "L-BFGS-B", normalize_design_space=True)

print("Optimum = ", opt)

#############################################################################
# Note that you can get all the optimization algorithms names:
algo_list = OptimizersFactory().algorithms
print("Available algorithms ", algo_list)

#############################################################################
# Save the optimization results
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
# We can serialize the results for further exploitation.
problem.export_hdf("my_optim.hdf5")

#############################################################################
# Post-process the results
# ^^^^^^^^^^^^^^^^^^^^^^^^
execute_post(problem, "OptHistoryView", show=False, save=False)
# Workaround for HTML rendering, instead of ``show=True``
plt.show()

#############################################################################
# .. note::
#
#    We can also save this plot using the arguments :code:`save=False`
#    and :code:`file_path='file_path'`.

#############################################################################
# Solve the optimization problem using a DOE algorithm
# ----------------------------------------------------
# We can also see this optimization problem as a trade-off
# and solve it by means of a design of experiments (DOE).
opt = DOEFactory().execute(problem, "lhs", n_samples=10, normalize_design_space=True)
print("Optimum = ", opt)