# ------------------------------------------------------------------------------
# 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:`Logarithm`."""
import math
import operator
from collections import namedtuple
import cvxopt
from .. import glyphs
from ..apidoc import api_end, api_start
from ..constraints import LogConstraint
from .data import convert_and_refine_arguments, convert_operands
from .exp_affine import AffineExpression
from .expression import Expression, refine_operands, validate_prediction
_API_START = api_start(globals())
# -------------------------------
[docs]class Logarithm(Expression):
r"""Logarithm of a scalar affine expression.
:Definition:
For a real scalar affine expression :math:`x`, this is :math:`\log(x)`.
.. warning::
When you pose a lower bound on a logarithm :math:`\log(x)`, then PICOS
enforces :math:`x \geq 0` through an auxiliary constraint during
solution search.
"""
# --------------------------------------------------------------------------
# Initialization and factory methods.
# --------------------------------------------------------------------------
[docs] @convert_and_refine_arguments("x")
def __init__(self, x):
"""Construct a :class:`Logarithm`.
:param x: The scalar affine expression :math:`x`.
:type x: ~picos.expressions.AffineExpression
"""
if not isinstance(x, AffineExpression):
raise TypeError("Can only take the logarithm of a real affine "
"expression, not of {}.".format(type(x).__name__))
elif not x.scalar:
raise TypeError("Can only take the logarithm of a scalar expression"
"but {} is shaped {}.".format(x.string, glyphs.shape(x.shape)))
self._x = x
Expression.__init__(self, "Logarithm", glyphs.log(x.string))
# --------------------------------------------------------------------------
# Abstract method implementations and method overridings, except _predict.
# --------------------------------------------------------------------------
def _get_refined(self):
if self._x.constant:
return AffineExpression.from_constant(self.value, 1, self._symbStr)
else:
return self
Subtype = namedtuple("Subtype", ())
def _get_subtype(self):
return self.Subtype()
def _get_value(self):
value = cvxopt.matrix(self._x._get_value()) # Must be dense for log.
return cvxopt.log(value)
def _get_mutables(self):
return self._x._get_mutables()
def _is_convex(self):
return False
def _is_concave(self):
return True
def _replace_mutables(self, mapping):
return self.__class__(self._x._replace_mutables(mapping))
def _freeze_mutables(self, freeze):
return self.__class__(self._x._freeze_mutables(freeze))
# --------------------------------------------------------------------------
# Python special method implementations, except constraint-creating ones.
# --------------------------------------------------------------------------
@classmethod
def _add(cls, self, other, forward):
if isinstance(other, AffineExpression) and other.constant:
if other.is0:
return self
log = cls(self._x * math.exp(other.value))
log._typeStr = "Offset " + log._typeStr
if forward:
log._symbStr = glyphs.clever_add(self.string, other.string)
else:
log._symbStr = glyphs.clever_add(other.string, self.string)
return log
if forward:
return Expression.__add__(self, other)
else:
return Expression.__radd__(self, other)
[docs] @convert_operands(scalarRHS=True)
@refine_operands()
def __add__(self, other):
return Logarithm._add(self, other, True)
[docs] @convert_operands(scalarRHS=True)
@refine_operands()
def __radd__(self, other):
return Logarithm._add(self, other, False)
[docs] @convert_operands(scalarRHS=True)
@refine_operands()
def __sub__(self, other):
if isinstance(other, AffineExpression) and other.constant:
log = Logarithm(self._x / math.exp(other.value))
log._typeStr = "Offset " + log._typeStr
log._symbStr = glyphs.clever_sub(self.string, other.string)
return log
return Expression.__sub__(self, other)
@classmethod
def _mul(cls, self, other, forward):
from . import Entropy, NegativeEntropy
if isinstance(other, AffineExpression):
if other.is0:
return AffineExpression.zero()
elif other.is1:
return self
elif other.equals(self._x):
return NegativeEntropy(self._x)
elif other.equals(-self._x):
return Entropy(self._x)
if forward:
return Expression.__mul__(self, other)
else:
return Expression.__rmul__(self, other)
[docs] @convert_operands(scalarRHS=True)
@refine_operands()
def __mul__(self, other):
return Logarithm._mul(self, other, True)
[docs] @convert_operands(scalarRHS=True)
@refine_operands()
def __rmul__(self, other):
return Logarithm._mul(self, other, False)
# --------------------------------------------------------------------------
# Methods and properties that return expressions.
# --------------------------------------------------------------------------
@property
def x(self):
"""The expression :math:`x`."""
return self._x
@property
def exp(self):
"""The exponential of the logarithm, equal to :math:`x`."""
return self._x
# --------------------------------------------------------------------------
# Constraint-creating operators, and _predict.
# --------------------------------------------------------------------------
@classmethod
def _predict(cls, subtype, relation, other):
assert isinstance(subtype, cls.Subtype)
if relation == operator.__ge__:
if issubclass(other.clstype, AffineExpression) \
and other.subtype.dim == 1:
return LogConstraint.make_type()
return NotImplemented
[docs] @convert_operands(scalarRHS=True)
@validate_prediction
@refine_operands()
def __ge__(self, other):
if isinstance(other, AffineExpression):
return LogConstraint(self, other)
else:
return NotImplemented
# --------------------------------------
__all__ = api_end(_API_START, globals())