# ------------------------------------------------------------------------------
# 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:`SumExponentialsConstraint`."""
import math
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 SumExponentialsConstraint(Constraint):
"""Upper bound on a sum of exponentials."""
[docs] class ConicConversion(ConstraintConversion):
"""Sum of exponentials 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.theSum.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((u[i] // y[i] // x[i]) << ExponentialCone())
return P
[docs] class LogSumExpConversion(ConstraintConversion):
"""Sum of exponentials to logarithm of the sum constraint conversion."""
[docs] @classmethod
def predict(cls, subtype, options):
"""Implement :meth:`~.constraint.ConstraintConversion.predict`."""
from . import LogSumExpConstraint
n = subtype.argdim
if subtype.lse_representable:
yield ("con", LogSumExpConstraint.make_type(argdim=n), 1)
else:
# HACK: Return the input constraint type.
# TODO: Handle partial subtype support differently, e.g. by
# introducing ConstraintConversion.supports.
yield ("con", SumExponentialsConstraint.make_type(*subtype), 1)
[docs] @classmethod
def convert(cls, con, options):
"""Implement :meth:`~.constraint.ConstraintConversion.convert`."""
from ..expressions import LogSumExp
from ..modeling import Problem
x = con.numerator
b = con.upperBound
P = Problem()
if con.lse_representable:
P.add_constraint(LogSumExp(x) <= math.log(b.value))
else:
# HACK: See predict.
P.add_constraint(con)
return P
[docs] def __init__(self, theSum, upperBound):
"""Construct a :class:`SumExponentialsConstraint`.
:param ~picos.expressions.SumExponentials theSum:
Constrained expression.
:param ~picos.expressions.AffineExpression upperBound:
Upper bound on the expression.
"""
from ..expressions import AffineExpression, SumExponentials
assert isinstance(theSum, SumExponentials)
assert isinstance(upperBound, AffineExpression)
assert len(upperBound) == 1
self.theSum = theSum
self.upperBound = upperBound
super(SumExponentialsConstraint, self).__init__(theSum._typeStr)
@property
def numerator(self):
"""The :math:`x` of the sum."""
return self.theSum.x
[docs] @cached_property
def denominator(self):
"""The :math:`y` of the sum, or :math:`1`."""
if self.theSum.y is None:
from ..expressions import AffineExpression
return AffineExpression.from_constant(1, self.theSum.x.shape)
else:
return self.theSum.y
@property
def lse_representable(self):
"""Whether this can be converted to a logarithmic constraint."""
if self.theSum.y is not None:
return False
if not self.upperBound.constant:
return False
if self.upperBound.value < 0:
return False
return True
Subtype = namedtuple("Subtype", ("argdim", "lse_representable"))
def _subtype(self):
return self.Subtype(self.theSum.n, self.lse_representable)
@classmethod
def _cost(cls, subtype):
# NOTE: Twice the argument dimension due to the denominator.
return 2*subtype.argdim + 1
def _expression_names(self):
yield "theSum"
yield "upperBound"
def _str(self):
return glyphs.le(self.theSum.string, self.upperBound.string)
def _get_slack(self):
return self.upperBound.safe_value - self.theSum.safe_value
# --------------------------------------
__all__ = api_end(_API_START, globals())