# ------------------------------------------------------------------------------
# Copyright (C) 2012-2017 Guillaume Sagnol
# 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:`GeometricMeanConstraint`."""
import math
from collections import namedtuple
from .. import glyphs
from ..apidoc import api_end, api_start
from .constraint import Constraint, ConstraintConversion
_API_START = api_start(globals())
# -------------------------------
[docs]class GeometricMeanConstraint(Constraint):
"""Lower bound on a geometric mean."""
[docs] class RSOCConversion(ConstraintConversion):
"""Geometric mean to rotated second order cone constraint conversion."""
[docs] @classmethod
def predict(cls, subtype, options):
"""Implement :meth:`~.constraint.ConstraintConversion.predict`."""
from ..expressions import RealVariable
from . import RSOCConstraint
j = subtype.argdim - 1
k = int(math.log(j, 2))
l = j + k - "{:b}".format(j - 2**k).count("1")
yield ("var", RealVariable.make_var_type(dim=1, bnd=0), l - 1)
yield ("con", RSOCConstraint.make_type(argdim=1), l)
# TODO: Refactor to be human readable.
[docs] @classmethod
def convert(cls, con, options):
"""Implement :meth:`~.constraint.ConstraintConversion.convert`."""
from ..expressions.algebra import rsoc
from ..modeling import Problem
geoMean = con.geoMean
lowerBound = con.lowerBound
P = Problem()
x = geoMean.x
m = len(x)
lm = [[i] for i in range(m - 1, -1, -1)]
K = []
depth = 0
u = {}
while len(lm) > 1:
depth += 1
nlm = []
while lm:
i1 = lm.pop()[-1]
if lm:
i2 = lm.pop()[0]
else:
i2 = 'x'
nlm.insert(0, (i2, i1))
k = str(depth) + ':' + str(i1) + '-' + str(i2)
K.append(k)
u[k] = P.add_variable('__u[' + k + ']', 1)
lm = nlm
root = K[-1]
maxd = int(K[-1].split(':')[0])
P.remove_variable(u[root].name) # TODO: Update for new expressions.
u[root] = lowerBound
for k in K:
i1 = int(k.split('-')[0].split(':')[1])
i2 = k.split('-')[1]
if i2 != 'x':
i2 = int(i2)
if k[:2] == '1:':
if i2 != 'x':
P.add_constraint((x[i1] & x[i2] & u[k]) << rsoc())
else:
P.add_constraint((x[i1] & lowerBound & u[k]) << rsoc())
else:
d = int(k.split(':')[0])
if i2 == 'x' and d < maxd:
k2pot = [ki for ki in K
if ki.startswith(str(d - 1) + ':')
and int(ki.split(':')[1].split('-')[0]) >= i1]
k1 = k2pot[0]
if len(k2pot) == 2:
k2 = k2pot[1]
P.add_constraint((u[k1] & u[k2] & u[k]) << rsoc())
else:
P.add_constraint(
(u[k1] & lowerBound & u[k]) << rsoc())
else:
k1 = [ki for ki in K
if ki.startswith(str(d - 1) + ':' + str(i1))][0]
k2 = [ki for ki in K if ki.startswith(str(d - 1) + ':')
and ki.endswith('-' + str(i2))][0]
P.add_constraint((u[k1] & u[k2] & u[k]) << rsoc())
return P
[docs] def __init__(self, geoMean, lowerBound):
"""Construct a :class:`GeometricMeanConstraint`.
:param ~picos.expressions.GeometricMean lhs:
Constrained expression.
:param ~picos.expressions.AffineExpression lowerBound:
Lower bound on the expression.
"""
from ..expressions import AffineExpression, GeometricMean
assert isinstance(geoMean, GeometricMean)
assert isinstance(lowerBound, AffineExpression)
assert len(lowerBound) == 1
self.geoMean = geoMean
self.lowerBound = lowerBound
super(GeometricMeanConstraint, self).__init__(geoMean._typeStr)
Subtype = namedtuple("Subtype", ("argdim",))
def _subtype(self):
return self.Subtype(len(self.geoMean.x))
@classmethod
def _cost(cls, subtype):
return subtype.argdim + 1
def _expression_names(self):
yield "geoMean"
yield "lowerBound"
def _str(self):
return glyphs.ge(self.geoMean.string, self.lowerBound.string)
def _get_slack(self):
return self.geoMean.safe_value - self.lowerBound.safe_value
# --------------------------------------
__all__ = api_end(_API_START, globals())