# Source code for gemseo.problems.sellar.sellar

# 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
#
# 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: Charlie Vanaret
#                 Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
r"""The disciplines for the MDO problem proposed by Sellar et al. in.

Sellar, R., Batill, S., & Renaud, J. (1996).
Response surface based, concurrent subspace optimization
for multidisciplinary system design.
In 34th aerospace sciences meeting and exhibit (p. 714).

The MDO problem is written as follows:

.. math::

\begin{aligned}
\text{minimize the objective function }&obj=x_{local}^2 + x_{shared,2}
+y_1^2+e^{-y_2} \\
\text{with respect to the design variables }&x_{shared},\,x_{local} \\
\text{subject to the general constraints }
& c_1 \leq 0\\
& c_2 \leq 0\\
\text{subject to the bound constraints }
& -10 \leq x_{shared,1} \leq 10\\
& 0 \leq x_{shared,2} \leq 10\\
& 0 \leq x_{local} \leq 10.
\end{aligned}

where the coupling variables are

.. math::

\text{Discipline 1: } y_1 = \sqrt{x_{shared,1}^2 + x_{shared,2} +
x_{local} - 0.2\,y_2},

and

.. math::

\text{Discipline 2: }y_2 = |y_1| + x_{shared,1} + x_{shared,2}.

and where the general constraints are

.. math::

c_1 = 3.16 - y_1^2

c_2 = y_2 - 24

This module implements three disciplines to compute the different coupling variables,
constraints and objective:

- :class:.Sellar1:
this :class:.MDODiscipline computes :math:y_1
from :math:y_2, :math:x_{shared,1}, :math:x_{shared,2} and :math:x_{local}.
- :class:.Sellar2:
this :class:.MDODiscipline computes :math:y_2
from :math:y_1, :math:x_{shared,1} and :math:x_{shared,2}.
- :class:.SellarSystem:
this :class:.MDODiscipline computes both objective and constraints
from :math:y_1, :math:y_2, :math:x_{local} and :math:x_{shared,2}.
"""
from __future__ import annotations

from cmath import exp
from cmath import sqrt
from typing import Iterable

from numpy import array
from numpy import atleast_2d
from numpy import complex128
from numpy import ndarray
from numpy import ones
from numpy import zeros

from gemseo.core.discipline import MDODiscipline

Y_1 = "y_1"
Y_2 = "y_2"
X_SHARED = "x_shared"
X_LOCAL = "x_local"
OBJ = "obj"
C_1 = "c_1"
C_2 = "c_2"
R_1 = "r_1"
R_2 = "r_2"

[docs]def get_inputs(
names: Iterable[str] | None = None,
) -> dict[str, ndarray]:
"""Generate an initial solution for the MDO problem.

Args:
names: The names of the discipline inputs.

Returns:
The default values of the discipline inputs.
"""
inputs = {
X_LOCAL: array([0.0], dtype=complex128),
X_SHARED: array([1.0, 0.0], dtype=complex128),
Y_1: ones(1, dtype=complex128),
Y_2: ones(1, dtype=complex128),
}
if names is None:
return inputs
return {name: inputs[name] for name in names}

[docs]class SellarSystem(MDODiscipline):
"""The discipline to compute the objective and constraints of the Sellar problem."""

def __init__(self) -> None:
super().__init__()
self.input_grammar.update(["x_local", "x_shared", "y_1", "y_2"])
self.output_grammar.update(["obj", "c_1", "c_2"])
self.default_inputs = get_inputs()
self.re_exec_policy = self.RE_EXECUTE_DONE_POLICY

def _run(self) -> None:
x_local, x_shared, y_1, y_2 = self.get_inputs_by_name(
[X_LOCAL, X_SHARED, Y_1, Y_2]
)
obj = array([self.compute_obj(x_local, x_shared, y_1, y_2)], dtype=complex128)
c_1 = array([self.compute_c_1(y_1)], dtype=complex128)
c_2 = array([self.compute_c_2(y_2)], dtype=complex128)
self.store_local_data(obj=obj, c_1=c_1, c_2=c_2)

[docs]    @staticmethod
def compute_obj(
x_local: ndarray,
x_shared: ndarray,
y_1: ndarray,
y_2: ndarray,
) -> float:
"""Evaluate the objective :math:obj.

Args:
x_local: The design variables local to the first discipline.
x_shared: The shared design variables.
y_1: The coupling variable coming from the first discipline.
y_2: The coupling variable coming from the second discipline.

Returns:
The value of the objective :math:obj.
"""
return x_local[0] ** 2 + x_shared[1] + y_1[0] ** 2 + exp(-y_2[0])

[docs]    @staticmethod
def compute_c_1(
y_1: ndarray,
) -> float:
"""Evaluate the constraint :math:c_1.

Args:
y_1: The coupling variable coming from the first discipline.

Returns:
The value of the constraint :math:c_1.
"""
return 3.16 - y_1[0] ** 2

[docs]    @staticmethod
def compute_c_2(
y_2: ndarray,
) -> float:
"""Evaluate the constraint :math:c_2.

Args:
y_2: The coupling variable coming from the second discipline.

Returns:
The value of the constraint :math:c_2.
"""
return y_2[0] - 24.0

def _compute_jacobian(
self,
inputs: Iterable[str] | None = None,
outputs: Iterable[str] | None = None,
) -> None:
self._init_jacobian(inputs, outputs, with_zeros=True)
x_local, _, y_1, y_2 = self.get_inputs_by_name([X_LOCAL, X_SHARED, Y_1, Y_2])
self.jac[C_1][Y_1] = atleast_2d(array([-2.0 * y_1]))
self.jac[C_2][Y_2] = ones((1, 1))
self.jac[OBJ][X_LOCAL] = atleast_2d(array([2.0 * x_local[0]]))
self.jac[OBJ][X_SHARED] = atleast_2d(array([0.0, 1.0]))
self.jac[OBJ][Y_1] = atleast_2d(array([2.0 * y_1[0]]))
self.jac[OBJ][Y_2] = atleast_2d(array([-exp(-y_2[0])]))

[docs]class Sellar1(MDODiscipline):
"""The discipline to compute the coupling variable :math:y_1."""

def __init__(self) -> None:
super().__init__()
self.input_grammar.update(["x_local", "x_shared", "y_2"])
self.output_grammar.update(["y_1"])
self.default_inputs = get_inputs(self.input_grammar.keys())

def _run(self) -> None:
x_local, x_shared, y_2 = self.get_inputs_by_name([X_LOCAL, X_SHARED, Y_2])

# functional form
y_1_out = array([self.compute_y_1(x_local, x_shared, y_2)], dtype=complex128)
self.store_local_data(y_1=y_1_out)

[docs]    @staticmethod
def compute_y_1(
x_local: ndarray,
x_shared: ndarray,
y_2: ndarray,
) -> float:
"""Evaluate the first coupling equation in functional form.

Args:
x_local: The design variables local to first discipline.
x_shared: The shared design variables.
y_2: The coupling variable coming from the second discipline.

Returns:
The value of the coupling variable :math:y_1.
"""
return sqrt(x_shared[0] ** 2 + x_shared[1] + x_local[0] - 0.2 * y_2[0])

def _compute_jacobian(
self,
inputs: Iterable[str] | None = None,
outputs: Iterable[str] | None = None,
) -> None:
self._init_jacobian(inputs, outputs, with_zeros=True)
x_local, x_shared, y_2 = self.get_inputs_by_name([X_LOCAL, X_SHARED, Y_2])

inv_denom = 1.0 / (self.compute_y_1(x_local, x_shared, y_2))
self.jac[Y_1] = {}
self.jac[Y_1][X_LOCAL] = atleast_2d(array([0.5 * inv_denom]))
self.jac[Y_1][X_SHARED] = atleast_2d(
array([x_shared[0] * inv_denom, 0.5 * inv_denom])
)
self.jac[Y_1][Y_2] = atleast_2d(array([-0.1 * inv_denom]))

[docs]class Sellar2(MDODiscipline):
"""The discipline to compute the coupling variable :math:y_2."""

def __init__(self) -> None:
super().__init__()
self.input_grammar.update(["x_shared", "y_1"])
self.output_grammar.update(["y_2"])
self.default_inputs = get_inputs(self.input_grammar.keys())

def _run(self) -> None:
x_shared, y_1 = self.get_inputs_by_name([X_SHARED, Y_1])

self.store_local_data(
y_2=array([self.compute_y_2(x_shared, y_1)], dtype=complex128)
)

def _compute_jacobian(
self,
inputs: Iterable[str] | None = None,
outputs: Iterable[str] | None = None,
) -> None:
self._init_jacobian(inputs, outputs, with_zeros=True)
y_1 = self.get_inputs_by_name(Y_1)
self.jac[Y_2] = {}
self.jac[Y_2][X_LOCAL] = zeros((1, 1))
self.jac[Y_2][X_SHARED] = ones((1, 2))
if y_1[0] < 0.0:
self.jac[Y_2][Y_1] = -ones((1, 1))
elif y_1[0] == 0.0:
self.jac[Y_2][Y_1] = zeros((1, 1))
else:
self.jac[Y_2][Y_1] = ones((1, 1))

[docs]    @staticmethod
def compute_y_2(
x_shared: ndarray,
y_1: ndarray,
) -> float:
"""Evaluate the second coupling equation in functional form.

Args:
x_shared: The shared design variables.
y_1: The coupling variable coming from the first discipline.

Returns:
The value of the coupling variable :math:y_2.
"""
out = x_shared[0] + x_shared[1]
if y_1[0].real == 0:
y_2 = out
elif y_1[0].real > 0:
y_2 = y_1[0] + out
else:
y_2 = -y_1[0] + out
return y_2