# ------------------------------------------------------------------------------
# Copyright (C) 2018-2019 Maximilian Stahlberg
#
# This file is part of PICOS.
#
# PICOS is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
#
# PICOS 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 General Public License for more details.
#
# You should have received a copy of the GNU General Public License along with
# this program. If not, see <http://www.gnu.org/licenses/>.
# ------------------------------------------------------------------------------
"""Implementation of :class:`ExpConeConstraint`."""
from collections import namedtuple
import numpy
from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from .constraint import Constraint
_API_START = api_start(globals())
# -------------------------------
[docs]class ExpConeConstraint(Constraint):
r"""Exponential cone membership constraint.
An exponential cone constraint stating that :math:`(x, y, z)` fulfills
:math:`x \geq y e^{\frac{z}{y}} \land x > 0 \land y > 0`.
"""
[docs] def __init__(self, element, customString=None):
"""Construct an :class:`ExpConeConstraint`.
:param ~picos.expressions.AffineExpression element:
Three-dimensional expression representing the vector
:math:`(x, y, z)`.
:param str customString:
Optional string description.
"""
from ..expressions import AffineExpression
assert isinstance(element, AffineExpression)
assert len(element) == 3
self.element = element
super(ExpConeConstraint, self).__init__(
"Exponential Cone", customString, printSize=False)
x = property(lambda self: self.element[0])
y = property(lambda self: self.element[1])
z = property(lambda self: self.element[2])
Subtype = namedtuple("Subtype", ())
def _subtype(self):
return self.Subtype()
@classmethod
def _cost(cls, subtype):
return 3
def _expression_names(self):
yield "element"
def _str(self):
return glyphs.ge(self.element[0].string,
glyphs.mul(self.element[1].string, glyphs.exp(glyphs.div(
self.element[2].string, self.element[1].string))))
def _get_size(self):
return (3, 1)
def _get_slack(self):
x = self.element.safe_value
# TODO: Also consider x_1 > 0 and x_2 > 0 by projecting x on the cone's
# surface and measuring the distance between the projection and x.
return x[0] - x[1] * numpy.exp(x[2] / x[1])
# --------------------------------------
__all__ = api_end(_API_START, globals())