Source code for picos.expressions.cone_soc

# ------------------------------------------------------------------------------
# Copyright (C) 2019 Maximilian Stahlberg
# Based on the original picos.expressions module by Guillaume Sagnol.
# 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 <>.
# ------------------------------------------------------------------------------

"""Implements :class:`SecondOrderCone`."""

import operator
from collections import namedtuple

from .. import glyphs
from ..apidoc import api_end, api_start
from ..constraints import SOCConstraint
from .cone import Cone
from .exp_affine import AffineExpression

_API_START = api_start(globals())
# -------------------------------

[docs]class SecondOrderCone(Cone): r"""The second order cone. .. _lorentz: Also known as the quadratic, :math:`2`-norm, Lorentz, or ice cream cone. For :math:`n \in \mathbb{Z}_{\geq 2}`, represents the convex cone .. math:: \mathcal{Q}^n = \left\{ x \in \mathbb{R}^n ~\middle|~ x_1 \geq \sqrt{\sum_{i = 2}^n x_i^2} \right\}. :Dual cone: The second order cone as defined above is self-dual. """
[docs] def __init__(self, dim=None): """Construct a second order cone.""" if dim and dim < 2: raise ValueError("The minimal dimension for {} is {}." .format(self.__class__.__name__, 2)) typeStr = "Second Order Cone" symbStr = glyphs.set(glyphs.sep( glyphs.col_vectorize("t", "x"), glyphs.le(glyphs.norm("x"), "t"))) Cone.__init__(self, dim, typeStr, symbStr)
def _get_mutables(self): return frozenset() def _replace_mutables(self): return self Subtype = namedtuple("Subtype", ("dim",)) def _get_subtype(self): return self.Subtype(self.dim) @classmethod def _predict(cls, subtype, relation, other): from .uncertain import UncertainAffineExpression assert isinstance(subtype, cls.Subtype) if relation == operator.__rshift__: if issubclass(other.clstype, (AffineExpression, UncertainAffineExpression)) \ and not subtype.dim or subtype.dim == other.subtype.dim \ and other.subtype.dim >= 2: if issubclass(other.clstype, UncertainAffineExpression): raise NotImplementedError("Cannot predict the outcome " "of constraining an uncertain affine expression to the " "second order cone.") return SOCConstraint.make_type(other.subtype.dim - 1) return Cone._predict_base(cls, subtype, relation, other) def _rshift_implementation(self, element): from .uncertain import ConicPerturbationSet, UncertainAffineExpression if isinstance(element, (AffineExpression, UncertainAffineExpression)): self._check_dimension(element) if len(element) < 2: raise TypeError("Elements of the second order cone must be " "at least two-dimensional.") element = element.vec if isinstance(element, AffineExpression): return SOCConstraint(element[1:], element[0]) else: if isinstance(element.universe, ConicPerturbationSet): # Unpredictable case: Outcome depends on whether slices of # the element remain uncertain. return abs(element[1:]) <= element[0] # Handle scenario uncertainty for all cones. return Cone._rshift_base(self, element) @property def dual_cone(self): """Implement :attr:`.cone.Cone.dual_cone`.""" return self
# -------------------------------------- __all__ = api_end(_API_START, globals())