Source code for picos.constraints.con_detrootn

# coding: utf-8

# ------------------------------------------------------------------------------
# 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
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"""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 n = con.detRootN.n P = Problem() L = LowerTriangularVariable("__L", n) d = L.maindiag D = d.diag P.add_constraint((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.value - self.lowerBound.value
# -------------------------------------- __all__ = api_end(_API_START, globals())