Source code for picos.expressions.exp_logsumexp

# 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:`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, cached_unary_operator
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) @cached_unary_operator def _get_variables(self): return self._x.variables def _is_convex(self): return True def _is_concave(self): return False 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): log = LogSumExp(self._x + other) log._symbStr = glyphs.clever_add(self.string, other.string) return log else: return NotImplemented @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): log = LogSumExp(self._x - other) log._symbStr = glyphs.clever_sub(self.string, other.string) return log else: return NotImplemented # -------------------------------------------------------------------------- # Methods and properties that return expressions. # -------------------------------------------------------------------------- @property def x(self): """The expression :math:`x`.""" return self._x @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 @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())