# coding: utf-8
# ------------------------------------------------------------------------------
# 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:`KullbackLeiblerConstraint`."""
from collections import namedtuple
from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from .constraint import Constraint, ConstraintConversion
_API_START = api_start(globals())
# -------------------------------
[docs]class KullbackLeiblerConstraint(Constraint):
"""Upper bound on a Kullback-Leibler divergence.
This is the upper bound on a negative or relative entropy, both represented
by :class:`~picos.expressions.NegativeEntropy`.
"""
[docs] class ExpConeConversion(ConstraintConversion):
"""Kullback-Leibler to exponential cone constraint conversion."""
[docs] @classmethod
def predict(cls, subtype, options):
"""Implement :meth:`~.constraint.ConstraintConversion.predict`."""
from ..expressions import RealVariable
from . import AffineConstraint, ExpConeConstraint
n = subtype.argdim
yield ("var", RealVariable.make_var_type(dim=n, bnd=0), 1)
yield ("con", AffineConstraint.make_type(dim=1, eq=False), 1)
yield ("con", ExpConeConstraint.make_type(), n)
[docs] @classmethod
def convert(cls, con, options):
"""Implement :meth:`~.constraint.ConstraintConversion.convert`."""
from ..expressions import ExponentialCone
from ..modeling import Problem
x = con.numerator
y = con.denominator
n = con.divergence.n
b = con.upperBound
P = Problem()
u = P.add_variable("__u", n)
P.add_constraint((u | 1) >= -b)
for i in range(n):
P.add_constraint((y[i] // x[i] // u[i]) << ExponentialCone())
return P
[docs] def __init__(self, divergence, upperBound):
"""Construct a :class:`KullbackLeiblerConstraint`.
:param ~picos.expressions.NegativeEntropy divergence:
Constrained expression.
:param ~picos.expressions.AffineExpression upperBound:
Upper bound on the expression.
"""
from ..expressions import AffineExpression, NegativeEntropy
assert isinstance(divergence, NegativeEntropy)
assert isinstance(upperBound, AffineExpression)
assert len(upperBound) == 1
self.divergence = divergence
self.upperBound = upperBound
super(KullbackLeiblerConstraint, self).__init__(divergence._typeStr)
@property
def numerator(self):
"""The :math:`x` of the divergence."""
return self.divergence.x
@cached_property
def denominator(self):
"""The :math:`y` of the divergence, or :math:`1`."""
from ..expressions import AffineExpression
if self.divergence.y is None:
return AffineExpression.from_constant(1, self.divergence.x.shape)
else:
return self.divergence.y
Subtype = namedtuple("Subtype", ("argdim",))
def _subtype(self):
return self.Subtype(len(self.numerator))
@classmethod
def _cost(cls, subtype):
# NOTE: Twice the argument dimension due to the denominator.
return 2*subtype.argdim + 1
def _expression_names(self):
yield "divergence"
yield "upperBound"
def _str(self):
return glyphs.le(self.divergence.string, self.upperBound.string)
def _get_slack(self):
return self.upperBound.value - self.divergence.value
# --------------------------------------
__all__ = api_end(_API_START, globals())