Source code for picos.expressions.set_soc

# coding: utf-8

# ------------------------------------------------------------------------------
# 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 <http://www.gnu.org/licenses/>.
# ------------------------------------------------------------------------------

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

import operator
from collections import namedtuple

from .. import glyphs
from ..apidoc import api_end, api_start
from ..constraints import SOCConstraint
from .data import convert_operands
from .exp_affine import AffineExpression
from .expression import refine_operands, validate_prediction
from .set import Set

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


[docs]class SecondOrderCone(Set): 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): """Construct a second order cone.""" typeStr = "Second Order Cone" symbStr = glyphs.set(glyphs.sep( glyphs.col_vectorize("t", "x"), glyphs.le(glyphs.norm("x"), "t"))) Set.__init__(self, typeStr, symbStr)
def _get_variables(self): return set() def _replace_variables(self): return self Subtype = namedtuple("Subtype", ()) def _get_subtype(self): return self.Subtype() @classmethod def _predict(cls, subtype, relation, other): assert isinstance(subtype, cls.Subtype) if relation == operator.__rshift__: if issubclass(other.clstype, AffineExpression): if other.subtype.dim >= 2: return SOCConstraint.make_type(other.subtype.dim - 1) return NotImplemented @convert_operands() @validate_prediction @refine_operands() def __rshift__(self, element): if isinstance(element, AffineExpression): if len(element) < 2: raise TypeError("Elements of the second order cone must be " "at least two-dimensional.") element = element.vec return SOCConstraint(element[1:], element[0]) else: return NotImplemented
# -------------------------------------- __all__ = api_end(_API_START, globals())