Source code for picos.expressions.exp_geomean

# 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:`GeometricMean`."""

import operator
from collections import namedtuple

import cvxopt
import numpy

from .. import glyphs
from ..apidoc import api_end, api_start
from ..caching import cached_unary_operator
from ..constraints import GeometricMeanConstraint
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 GeometricMean(Expression): r"""Geometric mean of an affine expression. :Definition: For an :math:`n`-dimensional affine expression :math:`x` with :math:`x \geq 0`, the geometric mean is given as .. math:: \left(\prod_{i = 1}^n x_i \right)^{\frac{1}{n}}. .. warning:: When you pose a lower bound on a geometric mean, 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:`GeometricMean`. :param x: The affine expression to form the geometric mean of. :type x: ~picos.expressions.AffineExpression """ if not isinstance(x, AffineExpression): raise TypeError("Can only form the geometrtic mean of a real affine" " expression, not of {}.".format(type(x).__name__)) self._x = x Expression.__init__( self, "Geometric Mean", glyphs.make_function("geomean")(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) elif len(self._x) == 1: return self._x.renamed(self._symbStr) else: return self Subtype = namedtuple("Subtype", ("argdim")) def _get_subtype(self): return self.Subtype(len(self._x)) def _get_value(self): value = self._x._get_value() value = numpy.prod(cvx2np(value))**(1.0 / len(self._x)) return cvxopt.matrix(value) @cached_unary_operator def _get_variables(self): return self._x.variables def _is_convex(self): return False def _is_concave(self): return True # Only for nonnegative x. 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 __mul__(self, other): if isinstance(other, AffineExpression): if not other.constant: raise NotImplementedError("You may only multiply a nonconstant " "PICOS geometric mean with a constant term.") if other.value < 0: raise NotImplementedError("You may only multiply a nonconstant " "PICOS geometric mean with a nonnegative term.") mean = GeometricMean(other.value * self._x) mean._typeStr = "Scaled " + mean._typeStr mean._symbStr = glyphs.clever_mul(self.string, other.string) return mean else: return NotImplemented @convert_operands(scalarRHS=True) @refine_operands() def __rmul__(self, other): if isinstance(other, AffineExpression): mean = self.__mul__(other) # NOTE: __mul__ always creates a fresh expression. mean._symbStr = glyphs.clever_mul(other.string, self.string) return mean else: return NotImplemented # -------------------------------------------------------------------------- # Methods and properties that return modified copies. # -------------------------------------------------------------------------- @property def x(self): """The expression under the mean.""" 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 GeometricMeanConstraint.make_type(subtype.argdim) return NotImplemented @convert_operands(scalarRHS=True) @validate_prediction @refine_operands() def __ge__(self, other): if isinstance(other, AffineExpression): return GeometricMeanConstraint(self, other) else: return NotImplemented
# -------------------------------------- __all__ = api_end(_API_START, globals())