# Source code for picos.expressions.set_simplex

# ------------------------------------------------------------------------------
# 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
# 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:Simplex."""

import operator
from collections import namedtuple

from .. import glyphs
from ..apidoc import api_end, api_start
from ..constraints import SimplexConstraint
from .data import convert_and_refine_arguments
from .exp_affine import AffineExpression, Constant
from .set import Set

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

[docs]class Simplex(Set):
r"""A (truncated, symmetrized) real simplex.

:Definition:

Let :math:r \in \mathbb{R}_{\geq 0} the specified radius and
:math:n \in \mathbb{Z}_{\geq 1} an arbitrary dimensionality.

1.  Without truncation and symmetrization, this is the nonnegative simplex

.. math::

\{x \in \mathbb{R}^n_{\geq 0} \mid \sum_{i = 1}^n x_i \leq r\}.

For :math:r = 1, this is the standard (unit) :math:n-simplex.

2.  With truncation but without symmetrization, this is the nonnegative
simplex intersected with the :math:\infty-norm unit ball

.. math::

\{
x \in \mathbb{R}^n_{\geq 0}
\mid
\sum_{i = 1}^n x_i \leq r \land x \leq 1
\}.

For :math:r \leq 1, this equals case (1).

3.  With symmetrization but without truncation, this is the :math:1-norm
ball of radius :math:r

.. math::

\{x \in \mathbb{R}^n \mid \sum_{i = 1}^n |x_i| \leq r\}.

4.  With both symmetrization and truncation, this is the convex polytope

.. math::

\{
x \in \mathbb{R}
\mid
\sum_{i = 1}^n |x_i| \leq r \land 0 \leq x \leq 1
\}.

For :math:r \leq 1, this equals case (3).
"""

"""Construct a :class:Simplex.

float or ~picos.expressions.AffineExpression
"""
raise TypeError("A simplex' radius must be given as a real affine "
raise TypeError("A simplex' radius must be scalar, not of shape {}."

truncated = False

unit = "Unit " if radius.is1 else ""
if not truncated and not symmetrized:
typeStr = "{}Simplex".format(unit)
symbStr = glyphs.set(glyphs.sep(glyphs.ge(var, 0),
elif truncated and not symmetrized:
typeStr = "Box-Truncated {}Simplex".format(unit)
symbStr = glyphs.set(glyphs.sep(glyphs.le(0, glyphs.le(var, 1)),
elif not truncated and symmetrized:
typeStr = "{}1-norm Ball".format(unit)
symbStr = glyphs.set(glyphs.sep(var,
else:  # truncated and symmetrized
typeStr = "Box-Truncated {}1-norm Ball".format(unit)
symbStr = glyphs.set(glyphs.sep(glyphs.le(-1, glyphs.le(var, 1)),

self._truncated   = truncated
self._symmetrized = symmetrized

Set.__init__(self, typeStr, symbStr)

@property

@property
def truncated(self):
r"""Whether this is intersected with the unit :math:\infty-ball."""
return self._truncated

@property
def symmetrized(self):
"""Wether the simplex is mirrored onto all orthants."""
return self._symmetrized

def _get_mutables(self):

def _replace_mutables(self, mapping):
self._truncated, self._symmetrized)

Subtype = namedtuple("Subtype", ("truncated", "symmetrized"))

def _get_subtype(self):
return self.Subtype(self._truncated, self._symmetrized)

@classmethod
def _predict(cls, subtype, relation, other):
assert isinstance(subtype, cls.Subtype)

if relation == operator.__rshift__:
if issubclass(other.clstype, AffineExpression):
return SimplexConstraint.make_type(
argdim=other.subtype.dim,
truncated=subtype.truncated,
symmetrized=subtype.symmetrized)

return NotImplemented

def _rshift_implementation(self, element):
if isinstance(element, AffineExpression):
return SimplexConstraint(self, element)
else:
return NotImplemented

# --------------------------------------
__all__ = api_end(_API_START, globals())