# ------------------------------------------------------------------------------
# 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:`DetRootNConstraint`."""
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 DetRootNConstraint(Constraint):
"""Lower bound on the :math:`n`-th root of a matrix determinant."""
[docs] class Conversion(ConstraintConversion):
""":math:`n`-th root of a matrix determinant constraint conversion."""
[docs] @classmethod
def predict(cls, subtype, options):
"""Implement :meth:`~.constraint.ConstraintConversion.predict`."""
from ..expressions import LowerTriangularVariable
from . import (ComplexLMIConstraint, GeometricMeanConstraint,
LMIConstraint)
n = subtype.diag
r = (n * (n + 1)) // 2
yield (
"var", LowerTriangularVariable.make_var_type(dim=r, bnd=0), 1)
if subtype.complex:
yield ("con", ComplexLMIConstraint.make_type(diag=2*n), 1)
else:
yield ("con", LMIConstraint.make_type(diag=2*n), 1)
yield ("con", GeometricMeanConstraint.make_type(argdim=n), 1)
[docs] @classmethod
def convert(cls, con, options):
"""Implement :meth:`~.constraint.ConstraintConversion.convert`."""
from ..modeling import Problem
from ..expressions import GeometricMean, LowerTriangularVariable
from ..expressions.algebra import block
n = con.detRootN.n
P = Problem()
L = LowerTriangularVariable("__L", n)
d = L.maindiag
D = d.diag
P.add_constraint(block([[con.detRootN.x, L], [L.T, D]]) >> 0)
P.add_constraint(GeometricMean(d) >= con.lowerBound)
return P
[docs] def __init__(self, detRootN, lowerBound):
"""Construct a :class:`DetRootNConstraint`.
:param ~picos.expressions.DetRootN detRootN:
Constrained expression.
:param ~picos.expressions.AffineExpression lowerBound:
Lower bound on the expression.
"""
from ..expressions import AffineExpression, DetRootN
assert isinstance(detRootN, DetRootN)
assert isinstance(lowerBound, AffineExpression)
assert len(lowerBound) == 1
self.detRootN = detRootN
self.lowerBound = lowerBound
super(DetRootNConstraint, self).__init__(detRootN._typeStr)
Subtype = namedtuple("Subtype", ("diag", "complex"))
def _subtype(self):
return self.Subtype(self.detRootN.n, self.detRootN.x.complex)
@classmethod
def _cost(cls, subtype):
n = subtype.diag
if subtype.complex:
return n**2 + 1
else:
return n*(n + 1)//2 + 1
def _expression_names(self):
yield "detRootN"
yield "lowerBound"
def _str(self):
return glyphs.ge(self.detRootN.string, self.lowerBound.string)
def _get_slack(self):
return self.detRootN.safe_value - self.lowerBound.safe_value
# --------------------------------------
__all__ = api_end(_API_START, globals())