Source code for picos.expressions.exp_logarithm

# 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:`Logarithm`."""

import math
import operator
from collections import namedtuple

import cvxopt

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_unary_operator
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) @cached_unary_operator def _get_variables(self): return self._x.variables def _is_convex(self): return False def _is_concave(self): return True def _replace_variables(self, var_map): return self.__class__(self._x._replace_variables(var_map)) # -------------------------------------------------------------------------- # Python special method implementations, except constraint-creating ones. # -------------------------------------------------------------------------- @convert_operands(scalarRHS=True) @refine_operands() def __add__(self, other): if isinstance(other, AffineExpression): if not other.constant: raise NotImplementedError("You may only add a constant term to " "a nonconstant PICOS logarithm.") log = Logarithm(self._x * math.exp(other.value)) log._typeStr = "Offset " + log._typeStr log._symbStr = glyphs.clever_add(self.string, other.string) return log @convert_operands(scalarRHS=True) @refine_operands() def __radd__(self, other): if isinstance(other, AffineExpression): log = self.__add__(other) # NOTE: __add__ always creates a fresh expression. log._symbStr = glyphs.clever_add(other.string, self.string) return log else: return NotImplemented @convert_operands(scalarRHS=True) @refine_operands() def __sub__(self, other): if isinstance(other, AffineExpression): if not other.constant: raise NotImplementedError("You may only substract a constant " "term from a nonconstant PICOS logarithm.") log = Logarithm(self._x / math.exp(other.value)) log._typeStr = "Offset " + log._typeStr log._symbStr = glyphs.clever_sub(self.string, other.string) return log @convert_operands(scalarRHS=True) @refine_operands() def __mul__(self, other): from . import Entropy, NegativeEntropy if isinstance(other, AffineExpression): if other.is0: return AffineExpression.zero() elif other.is1: # NOTE: We could return self here, but this is more consistent # with other expressions' __mul__ methods. return Logarithm(self._x) elif other.equals(self._x): return NegativeEntropy(self._x) elif other.equals(-self._x): return Entropy(self._x) else: raise NotImplementedError( "You may multiply {} only with {}, 0, or 1." .format(self.string, glyphs.plsmns(self._x.string))) else: return NotImplemented @convert_operands(scalarRHS=True) @refine_operands() def __rmul__(self, other): if isinstance(other, AffineExpression): return self.__mul__(other) else: return NotImplemented # -------------------------------------------------------------------------- # 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 @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())