Source code for picos.expressions.exp_geomean

# ------------------------------------------------------------------------------
# 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 <>.
# ------------------------------------------------------------------------------

"""Implements :class:`GeometricMean`."""

import operator
from collections import namedtuple

import cvxopt
import numpy

from .. import glyphs
from ..apidoc import api_end, api_start
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 =**(1.0 / len(self._x)) return cvxopt.matrix(value) def _get_mutables(self): return self._x._get_mutables() def _is_convex(self): return False def _is_concave(self): return True # Only for nonnegative x. 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 _mul(cls, self, other, forward): if isinstance(other, AffineExpression) and other.constant: factor = other.safe_value if not factor: return elif factor == 1: return self elif factor > 0: if forward: string = glyphs.clever_mul(self.string, other.string) else: string = glyphs.clever_mul(other.string, self.string) product = cls(other*self._x) product._typeStr = "Scaled " + product._typeStr product._symbStr = string return product 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 GeometricMean._mul(self, other, True)
[docs] @convert_operands(scalarRHS=True) @refine_operands() def __rmul__(self, other): return GeometricMean._mul(self, other, False)
# -------------------------------------------------------------------------- # 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
[docs] @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())