# Source code for gemseo.algos.aggregation.core

# 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: Francois Gallard
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""Constraints aggregation core functions."""
from __future__ import annotations

from math import log
from typing import Sequence

from numpy import argmax as np_argmax
from numpy import array
from numpy import atleast_2d
from numpy import exp as np_exp
from numpy import full
from numpy import heaviside
from numpy import max as np_max
from numpy import multiply
from numpy import ndarray
from numpy import sum as np_sum
from numpy import zeros

# TODO: API: rename to compute_ks_agg
[docs]def ks_agg(
orig_val: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> float:
"""Transform a vector of constraint functions into a KS function.

The Kreisselmeier–Steinhauser function tends to the maximum operator
when the aggregation parameter tends to infinity.

Kreisselmeier G, Steinhauser R (1983)
Application of Vector Performance Optimization
to a Robust Control Loop Design for a Fighter Aircraft.
International Journal of Control 37(2):251–284,
doi:10.1080/00207179.1983.9753066

Graeme J. Kennedy, Jason E. Hicken,
Improved constraint-aggregation methods,
Computer Methods in Applied Mechanics and Engineering,
Volume 289,
2015,
Pages 332-354,
ISSN 0045-7825,
https://doi.org/10.1016/j.cma.2015.02.017.
(http://www.sciencedirect.com/science/article/pii/S0045782515000663)

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The aggregation parameter.
scale: The scaling factor for multiplying the constraints.

Returns:
The KS function value.
"""
if indices is not None:
orig_val = orig_val[indices]

orig_val *= scale
alpha = len(orig_val)
m = max(orig_val)

return (
m
+ (1.0 / rho) * log((1.0 / alpha) * sum(np_exp(rho * (orig_val + 1.0 - m))))
- 1.0
)

# TODO: API: rename to compute_total_ks_agg_jac
[docs]def ks_agg_jac_v(
orig_val: ndarray,
orig_jac: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of KS function with respect to constraint function inputs.

See :cite:kennedy2015improved and  :cite:kreisselmeier1983application.

Args:
orig_val: The original constraint values.
orig_jac: The original constraint jacobian.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of KS function with respect to constraint function inputs.
"""
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]

orig_jac *= scale
orig_val *= scale

m = max(orig_val)
div = np_sum(np_exp(rho * (orig_val + 1.0 - m)))
weights = np_exp(rho * (orig_val + 1.0 - m)).T / div
return np_sum(multiply(atleast_2d(weights).T, orig_jac), axis=0)

# TODO: API: rename to compute_partial_ks_agg_jac
[docs]def ks_agg_jac(
orig_val: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of KS function with respect to constraint functions.

See :cite:kennedy2015improved and  :cite:kreisselmeier1983application.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of KS function with respect to constraint functions.
"""
full_size = orig_val.size
if indices is not None:
orig_val = orig_val[indices]

orig_val *= scale

m = max(orig_val)
div = np_sum(np_exp(rho * (orig_val + 1.0 - m)))
weights = np_exp(rho * (orig_val + 1.0 - m)).T / div
der = atleast_2d(multiply(weights, scale))
return __filter_jac(der, full_size, indices)

# TODO: API: rename to compute_iks_agg
[docs]def iks_agg(
orig_val: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> float:
"""Transform a vector of constraint functions into an induces exponential function.

The induces exponential function (IKS) tends to the maximum operator when
the aggregation parameter tends to infinity.

See :cite:kennedy2015improved.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.

Returns:
The IKS function value.
"""
if indices is not None:
orig_val = orig_val[indices]

orig_val *= scale

m = max(orig_val)
iks = sum(orig_val * np_exp(rho * (orig_val + 1.0 - m)))
iks /= sum(np_exp(rho * (orig_val + 1.0 - m)))

return iks

# TODO: API: rename to compute_total_iks_agg_jac
[docs]def iks_agg_jac_v(
orig_val: ndarray,
orig_jac: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of IKS function with respect to constraints inputs.

See :cite:kennedy2015improved.

Args:
orig_val: The original constraint values.
orig_jac: The original constraint jacobian.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of IKS function with respect to constraints inputs.
"""
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]

orig_jac *= scale
orig_val *= scale

m = max(orig_val)

iks_num = sum(orig_val * np_exp(rho * (orig_val + 1.0 - m)))
iks_den = sum(np_exp(rho * (orig_val + 1.0 - m)))

iks_num_der = np_sum(
multiply(atleast_2d(np_exp(rho * (orig_val + 1.0 - m))).T, orig_jac), axis=0
)
iks_num_der += np_sum(
multiply(
atleast_2d(np_exp(rho * (orig_val + 1.0 - m)) * orig_val).T,
rho * orig_jac,
),
axis=0,
)
iks_den_der = np_sum(
multiply(atleast_2d(np_exp(rho * (orig_val + 1.0 - m))).T, rho * orig_jac),
axis=0,
)
return (-iks_den_der / iks_den**2) * iks_num + iks_num_der / iks_den

# TODO: API: rename to compute_partial_iks_agg_jac
[docs]def iks_agg_jac(
orig_val: ndarray,
indices: Sequence[int] | None = None,
rho: float = 1e2,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of IKS function with respect to constraints functions.

Kennedy, Graeme J., and Jason E. Hicken.
"Improved constraint-aggregation methods."
Computer Methods in Applied Mechanics and Engineering
289 (2015): 332-354.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
rho: The multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of IKS function with respect to constraints functions.
"""
full_size = orig_val.size
if indices is not None:
orig_val = orig_val[indices]

orig_val *= scale

m = max(orig_val)

iks_num = sum(orig_val * np_exp(rho * (orig_val + 1.0 - m)))
iks_den = sum(np_exp(rho * (orig_val + 1.0 - m)))

iks_num_der = atleast_2d(np_exp(rho * (orig_val + 1.0 - m)))
iks_num_der += rho * atleast_2d(np_exp(rho * (orig_val + 1.0 - m)) * orig_val)
iks_den_der = rho * atleast_2d(np_exp(rho * (orig_val + 1.0 - m)))
iks_d = atleast_2d((-iks_den_der / iks_den**2) * iks_num + iks_num_der / iks_den)

iks_d = multiply(iks_d, scale)

return __filter_jac(iks_d, full_size, indices)

def __filter_jac(
orig_jac: ndarray,
full_size: int,
indices: Sequence[int],
) -> ndarray:
"""Filters the Jacobian according to the indices.

Args:
orig_jac: The original Jacobian.
full_size: The size of the full flatten Jacobian array.
indices: The array of indices to filter.

Returns:
The filtered Jacobian.
"""
if indices is not None:
jac = zeros((1, full_size))
jac[:, indices] = orig_jac
return jac

return orig_jac

# TODO: API: rename to compute_sum_square_agg
[docs]def sum_square_agg(
orig_val: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Transform a vector of constraint functions into a sum squared function.

The sum squared function is the sum of the squares of the input vector components.

Args:
orig_val: The input vector.
indices: The indices to generate a subset of the outputs to aggregate.
If None, scale all the constraint values.
scale: The scaling factor for multiplying the constraints.

Returns:
The sum squared function value.
"""
if indices is not None:
orig_val = orig_val[indices]
return np_sum(scale * orig_val**2)

# TODO: API: rename to compute_total_sum_square_agg_jac
[docs]def sum_square_agg_jac_v(
orig_val: ndarray,
orig_jac: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of squared sum function with respect to constraints inputs.

Args:
orig_val: The original constraint values.
orig_jac: The original constraint jacobian.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of squared sum function with respect to constraints inputs.
"""
orig_jac = atleast_2d(orig_jac)
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]

return np_sum((2 * scale * orig_val).flatten() * orig_jac.T, axis=1)

# TODO: API: rename to compute_partial_sum_square_agg_jac
[docs]def sum_square_agg_jac(
orig_val: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of squared sum function with respect to constraints.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of squared sum function with respect to constraints.
"""
if indices is not None:
jac = zeros((1, orig_val.size))
jac[:, indices] = 2.0 * scale * orig_val[indices]
else:
jac = full((1, orig_val.size), 2.0) * atleast_2d(scale * orig_val)

return jac

# TODO: API: rename to compute_max_agg
[docs]def max_agg(
orig_val: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> float:
"""Transform a vector of constraints into a max of all values.

The maximum function is not differentiable for all input values.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The maximum value.
"""
if indices is not None:
orig_val = orig_val[indices]
orig_val *= scale
return array([np_max(orig_val)])

# TODO: API: rename to compute_max_agg_jac
[docs]def max_agg_jac_v(
orig_val: ndarray,
orig_jac: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of max function with respect to constraints inputs.

Args:
orig_val: The original constraint values.
orig_jac: The original constraint jacobian.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of max function with respect to constraints inputs.
"""
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]
orig_jac *= scale
orig_val *= scale
i_max = np_argmax(orig_val)

return atleast_2d(orig_jac)[i_max, :]

[docs]def compute_sum_positive_square_agg(
orig_val: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Transform a vector of constraint functions into a positive sum squared function.

The positive sum squared function is the sum of the squares of the input vector
components that are positive.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, scale all the constraint values.
scale: The scaling factor for multiplying the constraints.

Returns:
The positive sum squared function value.
"""
if indices is not None:
orig_val = orig_val[indices]
return np_sum(scale * (orig_val**2) * heaviside(orig_val, 0))

[docs]def compute_total_sum_square_positive_agg_jac(
orig_val: ndarray,
orig_jac: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of positive sum squared function w.r.t. constraints inputs.

Args:
orig_val: The original constraint values.
orig_jac: The original constraint jacobian.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of positive sum squared function w.r.t. constraints inputs.
"""
orig_jac = atleast_2d(orig_jac)
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]
return np_sum(
(2 * scale * orig_val * heaviside(orig_val, 0)).flatten() * orig_jac.T,
axis=1,
)

[docs]def compute_partial_sum_positive_square_agg_jac(
orig_val: ndarray,
indices: Sequence[int] | None = None,
scale: float | ndarray = 1.0,
) -> ndarray:
"""Compute the Jacobian of positive sum squared function w.r.t. constraints.

Args:
orig_val: The original constraint values.
indices: The indices to generate a subset of the outputs to aggregate.
If None, aggregate all the outputs.
scale: The scaling factor for multiplying the constraints.

Returns:
The Jacobian of positive sum squared function w.r.t. constraints.
"""
if indices is not None:
jac = zeros((1, orig_val.size))
jac[:, indices] = (
2.0 * scale * orig_val[indices] * heaviside(orig_val[indices], 0.0)
)
else:
jac = atleast_2d(2 * scale * orig_val * heaviside(orig_val, 0.0))

return jac