# Source code for picos.expressions.exp_logsumexp

# ------------------------------------------------------------------------------
# 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:LogSumExp."""

import operator
from collections import namedtuple

import cvxopt
import numpy

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_property
from ..constraints import LogSumExpConstraint
from .data import convert_and_refine_arguments, convert_operands, cvx2np
from .exp_affine import AffineExpression
from .expression import Expression, refine_operands, validate_prediction

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

[docs]class LogSumExp(Expression):
r"""Logarithm of the sum of elementwise exponentials of an expression.

:Definition:

For an :math:n-dimensional real affine expression :math:x, this is the
logarithm of the sum of elementwise exponentials

.. math::

\log\sum_{i = 1}^n \exp(\operatorname{vec}(x)_i).
"""

# --------------------------------------------------------------------------
# Initialization and factory methods.
# --------------------------------------------------------------------------

[docs]    @convert_and_refine_arguments("x")
def __init__(self, x):
"""Construct a :class:LogSumExp.

:param x: The affine expression :math:x.
:type x: ~picos.expressions.AffineExpression
"""
if not isinstance(x, AffineExpression):
raise TypeError("Can only form the logarithm of the sum of "
"elementwise exponentials of a real affine expression, not of "
"{}.".format(type(x).__name__))

self._x = x

typeStr = "Logarithm of Sum of Exponentials"
symbStr = glyphs.make_function("log", "sum", "exp")(x.string)

Expression.__init__(self, typeStr, symbStr)

# --------------------------------------------------------------------------
# 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)
elif len(self._x) == 1:
return self._x  # Don't carry the string for an identity.
else:
return self

Subtype = namedtuple("Subtype", ("argdim"))

def _get_subtype(self):
return self.Subtype(len(self._x))

def _get_value(self):
x = numpy.ravel(cvx2np(self._x._get_value()))
s = numpy.log(numpy.sum(numpy.exp(x)))
return cvxopt.matrix(s)

def _get_mutables(self):
return self._x._get_mutables()

def _is_convex(self):
return True

def _is_concave(self):
return False

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
if isinstance(other, AffineExpression):
if other.is0:
return self

lse = cls(self._x + other)

if forward:
else:

return lse

if forward:
else:

[docs]    @convert_operands(scalarRHS=True)
@refine_operands()

[docs]    @convert_operands(scalarRHS=True)
@refine_operands()

[docs]    @convert_operands(scalarRHS=True)
@refine_operands()
def __sub__(self, other):
if isinstance(other, AffineExpression):
if other.is0:
return self

lse = LogSumExp(self._x - other)
lse._symbStr = glyphs.clever_sub(self.string, other.string)

return lse

return Expression.__sub__(self, other)

# --------------------------------------------------------------------------
# Methods and properties that return expressions.
# --------------------------------------------------------------------------

@property
def x(self):
"""The expression :math:x."""
return self._x

[docs]    @cached_property
def exp(self):
"""The elementwise sum of exponentials of :math:x."""
from . import SumExponentials
return SumExponentials(self._x)

# --------------------------------------------------------------------------
# Methods and properties that describe the expression.
# --------------------------------------------------------------------------

@property
def n(self):
"""Length of :attr:x."""
return len(self._x)

# --------------------------------------------------------------------------
# Constraint-creating operators, and _predict.
# --------------------------------------------------------------------------

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

if relation == operator.__le__:
if issubclass(other.clstype, AffineExpression) \
and other.subtype.dim == 1:
return LogSumExpConstraint.make_type(subtype.argdim)

return NotImplemented

[docs]    @convert_operands(scalarRHS=True)
@validate_prediction
@refine_operands()
def __le__(self, other):
if isinstance(other, AffineExpression):
return LogSumExpConstraint(self, other)
else:
return NotImplemented

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