Coverage for picos/constraints/con_detrootn.py: 96.49%
57 statements
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1# ------------------------------------------------------------------------------
2# Copyright (C) 2012-2017 Guillaume Sagnol
3# Copyright (C) 2018-2019 Maximilian Stahlberg
4#
5# This file is part of PICOS.
6#
7# PICOS is free software: you can redistribute it and/or modify it under the
8# terms of the GNU General Public License as published by the Free Software
9# Foundation, either version 3 of the License, or (at your option) any later
10# version.
11#
12# PICOS is distributed in the hope that it will be useful, but WITHOUT ANY
13# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
14# A PARTICULAR PURPOSE. See the GNU General Public License for more details.
15#
16# You should have received a copy of the GNU General Public License along with
17# this program. If not, see <http://www.gnu.org/licenses/>.
18# ------------------------------------------------------------------------------
20"""Implementation of :class:`DetRootNConstraint`."""
22from collections import namedtuple
24from .. import glyphs
25from ..apidoc import api_end, api_start
26from .constraint import Constraint, ConstraintConversion
28_API_START = api_start(globals())
29# -------------------------------
32class DetRootNConstraint(Constraint):
33 """Lower bound on the :math:`n`-th root of a matrix determinant."""
35 class Conversion(ConstraintConversion):
36 """:math:`n`-th root of a matrix determinant constraint conversion."""
38 @classmethod
39 def predict(cls, subtype, options):
40 """Implement :meth:`~.constraint.ConstraintConversion.predict`."""
41 from ..expressions import LowerTriangularVariable
42 from . import (ComplexLMIConstraint, GeometricMeanConstraint,
43 LMIConstraint)
45 n = subtype.diag
46 r = (n * (n + 1)) // 2
48 yield (
49 "var", LowerTriangularVariable.make_var_type(dim=r, bnd=0), 1)
51 if subtype.complex:
52 yield ("con", ComplexLMIConstraint.make_type(diag=2*n), 1)
53 else:
54 yield ("con", LMIConstraint.make_type(diag=2*n), 1)
56 yield ("con", GeometricMeanConstraint.make_type(argdim=n), 1)
58 @classmethod
59 def convert(cls, con, options):
60 """Implement :meth:`~.constraint.ConstraintConversion.convert`."""
61 from ..modeling import Problem
62 from ..expressions import GeometricMean, LowerTriangularVariable
63 from ..expressions.algebra import block
65 n = con.detRootN.n
67 P = Problem()
68 L = LowerTriangularVariable("__L", n)
69 d = L.maindiag
70 D = d.diag
71 P.add_constraint(block([[con.detRootN.x, L], [L.T, D]]) >> 0)
72 P.add_constraint(GeometricMean(d) >= con.lowerBound)
73 return P
75 def __init__(self, detRootN, lowerBound):
76 """Construct a :class:`DetRootNConstraint`.
78 :param ~picos.expressions.DetRootN detRootN:
79 Constrained expression.
80 :param ~picos.expressions.AffineExpression lowerBound:
81 Lower bound on the expression.
82 """
83 from ..expressions import AffineExpression, DetRootN
85 assert isinstance(detRootN, DetRootN)
86 assert isinstance(lowerBound, AffineExpression)
87 assert len(lowerBound) == 1
89 self.detRootN = detRootN
90 self.lowerBound = lowerBound
92 super(DetRootNConstraint, self).__init__(detRootN._typeStr)
94 Subtype = namedtuple("Subtype", ("diag", "complex"))
96 def _subtype(self):
97 return self.Subtype(self.detRootN.n, self.detRootN.x.complex)
99 @classmethod
100 def _cost(cls, subtype):
101 n = subtype.diag
103 if subtype.complex:
104 return n**2 + 1
105 else:
106 return n*(n + 1)//2 + 1
108 def _expression_names(self):
109 yield "detRootN"
110 yield "lowerBound"
112 def _str(self):
113 return glyphs.ge(self.detRootN.string, self.lowerBound.string)
115 def _get_slack(self):
116 return self.detRootN.safe_value - self.lowerBound.safe_value
119# --------------------------------------
120__all__ = api_end(_API_START, globals())