# -*- coding: utf-8 -*-
# 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
# 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
# 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 division, unicode_literals
from math import log
from typing import Optional, Sequence, Union
from numpy import argmax as np_argmax
from numpy import array, atleast_2d
from numpy import exp as np_exp
from numpy import max as np_max
from numpy import multiply, ndarray, ones
from numpy import sum as np_sum
from numpy import zeros
[docs]def ks_agg(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> float
"""Transform a vector of equalities into a Kreisselmeier–Steinhauser function.
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 multiplicative parameter in the exponential.
scale: The scaling factor for multiplying the constraints.
Returns:
The aggregated 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
)
[docs]def ks_agg_jac_v(
orig_val, # type: ndarray
orig_jac, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Aggregate inequality constraints.
Jacobian vector product of the constraints aggregation method for inequality
constraints.
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 aggregated function Jacobian vector product.
"""
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)
[docs]def ks_agg_jac(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Transform a vector of equalities into a scalar equivalent constraint.
Jacobian of the Constraints aggregation method for inequality constraints.
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 aggregated function Jacobian.
"""
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)
[docs]def iks_agg(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> float
"""Aggregate IKS Constraints for inequality constraints.
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 aggregated 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
[docs]def iks_agg_jac_v(
orig_val, # type: ndarray
orig_jac, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Aggregate inequality constraints.
Jacobian vector product of the IKS Constraints aggregation method for inequality
constraints.
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 aggregated function Jacobian vector product.
"""
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
[docs]def iks_agg_jac(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
rho=1e2, # type: float
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Jacobian of the IKS Constraints aggregation method for inequality constraints.
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 aggregated function Jacobian.
"""
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, # type: ndarray
full_size, # type: int
indices, # type: Sequence[int]
): # type: (...) -> 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
[docs]def sum_square_agg(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Transform a vector of equalities into a sum of squared constraints.
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 aggregated function.
"""
if indices is not None:
orig_val = orig_val[indices]
orig_val *= scale
return np_sum(orig_val ** 2)
[docs]def sum_square_agg_jac_v(
orig_val, # type: ndarray
orig_jac, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Transform a vector of equalities into a sum of squared constraints.
Jacobian vector product of the constraints aggregation method for equality
constraints.
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 aggregated function Jacobian vector product.
"""
if indices is not None:
orig_jac = orig_jac[indices, :]
orig_val = orig_val[indices]
orig_jac *= scale
orig_val *= scale
return 2 * np_sum(orig_jac * orig_val, axis=0)
[docs]def sum_square_agg_jac(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Transform a vector of equalities into a sum of squared constraints.
Jacobian of the constraints aggregation method for equality 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 aggregated function Jacobian.
"""
if indices is not None:
jac = zeros((1, orig_val.size))
jac[:, indices] = 2.0
else:
jac = 2 * ones((1, orig_val.size))
return jac
[docs]def max_agg(
orig_val, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> float
"""Transform a vector of equalities into a max of all values.
Constraints aggregation method for inequality 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 aggregated function.
"""
if indices is not None:
orig_val = orig_val[indices]
orig_val *= scale
return array([np_max(orig_val)])
[docs]def max_agg_jac_v(
orig_val, # type: ndarray
orig_jac, # type: ndarray
indices=None, # type: Optional[Sequence[int]]
scale=1.0, # type: Union[float, ndarray]
): # type: (...) -> ndarray
"""Transform a vector of equalities into the max of all the values.
Jacobian vector product of the max constraints aggregation method for inequality
constraints.
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 aggregated function.
"""
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, :]
