Loading picos/expressions/__init__.py +1 −0 Original line number Diff line number Diff line Loading @@ -47,6 +47,7 @@ from .exp_norm import Norm # noqa from .exp_nucnorm import NuclearNorm # noqa from .exp_powtrace import PowerTrace # noqa from .exp_quadratic import QuadraticExpression # noqa from .exp_quantentropy import QuantEntropy # noqa from .exp_specnorm import SpectralNorm # noqa from .exp_sqnorm import SquaredNorm # noqa from .exp_sumexp import SumExponentials # noqa Loading picos/expressions/exp_quantentropy.py 0 → 100644 +514 −0 Original line number Diff line number Diff line # ------------------------------------------------------------------------------ # 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:`QuantEntropy` and :class:`NegativeQuantEntropy`.""" # TODO: Common base class for QuantEntropy and NegativeQuantEntropy. import math import operator from collections import namedtuple import cvxopt import numpy from .. import glyphs from ..apidoc import api_end, api_start from ..caching import cached_selfinverse_unary_operator, cached_unary_operator from ..constraints import KullbackLeiblerConstraint from .data import convert_and_refine_arguments, convert_operands, cvx2np from .exp_affine import AffineExpression,ComplexAffineExpression from .expression import Expression, refine_operands, validate_prediction _API_START = api_start(globals()) # ------------------------------- class QuantEntropy(Expression): r"""Quantum entropy or negative quantum relative entropy of an affine expression. :Definition: Let :math:`X` be an :math:`n \times n`-dimensional symmetric and hermitian matrix, or their :attr:`special vectorization <.exp_biaffine.BiaffineExpression.svec>`. 1. If no additional expression :math:`Y` is given, this is the quantum entropy .. math:: -\operatorname{Tr}(X \log(X)). 2. If an additional affine expression :math:`Y` of same shape as :math:`x` is given, this is the negative quantum relative entropy .. math:: \operatorname{Tr}(X (\log(Y) - \log(X))) """ # -------------------------------------------------------------------------- # Initialization and factory methods. # -------------------------------------------------------------------------- @convert_and_refine_arguments("X", "Y", allowNone=True) def __init__(self, X, Y=None): """Construct an :class:`QuantEntropy`. :param X: The affine expression :math:`X`. :type X: ~picos.expressions.AffineExpression :param Y: An additional affine expression :math:`Y`. If necessary, PICOS will attempt to reshape or broadcast it to the shape of :math:`X`. :type Y: ~picos.expressions.AffineExpression """ if not isinstance(X, ComplexAffineExpression): raise TypeError("Can only take the matrix logarithm of a real " "or complex affine expression, not of {}.".format(type(X).__name__)) if not X.hermitian: raise TypeError("Can only take the matrix logarithm of a symmetric " "or hermitian expression, not of {}.".format(type(X).__name__)) if Y is not None: if not isinstance(Y, ComplexAffineExpression): raise TypeError("The additional parameter Y must be a real " "or complex affine expression, not {}.".format(type(Y).__name__)) if not Y.hermitian: raise TypeError("Can only take the matrix logarithm of a symmetric " "or hermitian expression, not of {}.".format(type(Y).__name__)) if X.shape != Y.shape and Y.shape != (1, 1): raise TypeError("The additional parameter Y must either be the " "same shape as X, or be a real scalar expression, not {}." .format(type(Y).__name__)) if Y.is1: Y = None self._X = X self._Y = Y if Y is None: typeStr = "Qauntum Entropy" symbStr = glyphs.neg(glyphs.trace(glyphs.mul(X.string, glyphs.log(X.string)))) else: typeStr = "Negative Quantum Relative Entropy" symbStr = glyphs.trace(glyphs.mul(X.string, glyphs.sub(glyphs.log(Y.string), glyphs.log(X.string)))) Expression.__init__(self, typeStr, symbStr) # -------------------------------------------------------------------------- # Abstract method implementations and method overridings, except _predict. # -------------------------------------------------------------------------- def _get_refined(self): if self._X.constant and (self._Y is None or self._Y.constant): return AffineExpression.from_constant(self.value, 1, self._symbStr) else: return self Subtype = namedtuple("Subtype", ("argdim", "y")) def _get_subtype(self): return self.Subtype(len(self._x), self._y is not None) def _get_value(self): x = numpy.ravel(cvx2np(self._x._get_value())) if self._y is None: s = -numpy.dot(x, numpy.log(x)) else: y = numpy.ravel(cvx2np(self._y._get_value())) s = numpy.dot(x, numpy.log(y / x)) return cvxopt.matrix(s) @cached_unary_operator def _get_mutables(self): if self._y is None: return self._x._get_mutables() else: return self._x._get_mutables().union(self._y.mutables) def _is_convex(self): return False def _is_concave(self): return True def _replace_mutables(self, mapping): return self.__class__(self._x._replace_mutables(mapping), None if self._y is None else self._y._replace_mutables(mapping)) def _freeze_mutables(self, freeze): return self.__class__(self._x._freeze_mutables(freeze), None if self._y is None else self._y._freeze_mutables(freeze)) # -------------------------------------------------------------------------- # Python special method implementations, except constraint-creating ones. # -------------------------------------------------------------------------- @cached_selfinverse_unary_operator def __neg__(self): return NegativeEntropy(self._x, self._y) @convert_operands(scalarRHS=True) @refine_operands() def __add__(self, other): other_str = other.string if isinstance(other, AffineExpression): if other.is0: return self other = Entropy(other, other * math.e) if isinstance(other, Entropy): if self._y is None and other._y is None: entropy = Entropy(self._x.vec // other._x.vec) elif self._y is not None and other._y is None: one = AffineExpression.from_constant(1.0, (other.n, 1)) entropy = Entropy( self._x.vec // other._x.vec, self._y.vec // one) elif self._y is None and other._y is not None: one = AffineExpression.from_constant(1.0, (self.n, 1)) entropy = Entropy( self._x.vec // other._x.vec, one // other._y.vec) else: entropy = Entropy( self._x.vec // other._x.vec, self._y.vec // other._y.vec) entropy._symbStr = glyphs.clever_add(self.string, other_str) return entropy return Expression.__add__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __radd__(self, other): if isinstance(other, (AffineExpression, Entropy)): entropy = Entropy.__add__(self, other) if entropy is not self: entropy._symbStr = glyphs.clever_add(other.string, self.string) return entropy return Expression.__radd__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __sub__(self, other): if isinstance(other, (AffineExpression, NegativeEntropy)): return self + (-other) return Expression.__sub__(self, other) # -------------------------------------------------------------------------- # Methods and properties that return expressions. # -------------------------------------------------------------------------- @property def x(self): """The expression :math:`x`.""" return self._x @property def y(self): """The additional expression :math:`y`, or :obj:`None`.""" return self._y # -------------------------------------------------------------------------- # 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.__ge__: if issubclass(other.clstype, AffineExpression) \ and other.subtype.dim == 1: return KullbackLeiblerConstraint.make_type( argdim=subtype.argdim) return NotImplemented @convert_operands(scalarRHS=True) @validate_prediction @refine_operands() def __ge__(self, other): if isinstance(other, AffineExpression): return KullbackLeiblerConstraint(-self, -other) else: return NotImplemented class NegativeEntropy(Expression): r"""Negative or relative entropy of an affine expression. Relative entropy is also known as the Kullback-Leibler divergence. :Definition: Let :math:`x` be an :math:`n`-dimensional real affine expression. 1. If no additional expression :math:`y` is given, this is the negative entropy .. math:: \sum_{i = 1}^n \operatorname{vec}(x)_i \log(\operatorname{vec}(x)_i). 2. If an additional affine expression :math:`y` of same shape as :math:`x` is given, this is the relative entropy (or Kullback-Leibler divergence) .. math:: \sum_{i = 1}^n \operatorname{vec}(x)_i \log\left( \frac{\operatorname{vec}(x)_i}{\operatorname{vec}(y)_i} \right) = \sum_{i = 1}^n \operatorname{vec}(x)_i \left[ \log(\operatorname{vec}(x)_i) - \log(\operatorname{vec}(y)_i) \right]. .. warning:: When you pose an upper bound on this expression, then PICOS enforces :math:`x \geq 0` through an auxiliary constraint during solution search. When an additional expression :math:`y` is given, PICOS enforces :math:`y \geq 0` as well. """ # -------------------------------------------------------------------------- # Initialization and factory methods. # -------------------------------------------------------------------------- @convert_and_refine_arguments("x", "y", allowNone=True) def __init__(self, x, y=None): """Construct a :class:`NegativeEntropy`. :param x: The affine expression :math:`x`. :type x: ~picos.expressions.AffineExpression :param y: An additional affine expression :math:`y`. If necessary, PICOS will attempt to reshape or broadcast it to the shape of :math:`x`. :type y: ~picos.expressions.AffineExpression """ if not isinstance(x, AffineExpression): raise TypeError("Can only take the elementwise logarithm of a real " "affine expression, not of {}.".format(type(x).__name__)) if y is not None: if not isinstance(y, AffineExpression): raise TypeError("The additional parameter y must be a real " "affine expression, not {}.".format(type(x).__name__)) elif x.shape != y.shape: y = y.reshaped_or_broadcasted(x.shape) if y.is1: y = None self._x = x self._y = y if y is None: typeStr = "Negative Entropy" if len(x) == 1: symbStr = glyphs.mul(x.string, glyphs.log(x.string)) else: symbStr = glyphs.dotp(x.string, glyphs.log(x.string)) else: typeStr = "Relative Entropy" if len(x) == 1: symbStr = glyphs.mul( x.string, glyphs.log(glyphs.div(x.string, y.string))) else: symbStr = glyphs.dotp(x.string, glyphs.sub(glyphs.log(x.string), glyphs.log(y.string))) Expression.__init__(self, typeStr, symbStr) # -------------------------------------------------------------------------- # Abstract method implementations and method overridings, except _predict. # -------------------------------------------------------------------------- def _get_refined(self): if self._x.constant and (self._y is None or self._y.constant): return AffineExpression.from_constant(self.value, 1, self._symbStr) else: return self Subtype = namedtuple("Subtype", ("argdim", "y")) def _get_subtype(self): return self.Subtype(len(self._x), self._y is not None) def _get_value(self): x = numpy.ravel(cvx2np(self._x._get_value())) if self._y is None: s = numpy.dot(x, numpy.log(x)) else: y = numpy.ravel(cvx2np(self._y._get_value())) s = numpy.dot(x, numpy.log(x / y)) return cvxopt.matrix(s) @cached_unary_operator def _get_mutables(self): if self._y is None: return self._x._get_mutables() else: return self._x._get_mutables().union(self._y.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), None if self._y is None else self._y._replace_mutables(mapping)) def _freeze_mutables(self, freeze): return self.__class__(self._x._freeze_mutables(freeze), None if self._y is None else self._y._freeze_mutables(freeze)) # -------------------------------------------------------------------------- # Python special method implementations, except constraint-creating ones. # -------------------------------------------------------------------------- @cached_selfinverse_unary_operator def __neg__(self): return Entropy(self._x, self._y) @convert_operands(scalarRHS=True) @refine_operands() def __add__(self, other): other_str = other.string if isinstance(other, AffineExpression): if other.is0: return self other = NegativeEntropy(other, other / math.e) if isinstance(other, NegativeEntropy): if self._y is None and other._y is None: negent = NegativeEntropy(self._x.vec // other._x.vec) elif self._y is not None and other._y is None: one = AffineExpression.from_constant(1.0, (other.n, 1)) negent = NegativeEntropy( self._x.vec // other._x.vec, self._y.vec // one) elif self._y is None and other._y is not None: one = AffineExpression.from_constant(1.0, (self.n, 1)) negent = NegativeEntropy( self._x.vec // other._x.vec, one // other._y.vec) else: negent = NegativeEntropy( self._x.vec // other._x.vec, self._y.vec // other._y.vec) negent._symbStr = glyphs.clever_add(self.string, other_str) return negent return Expression.__add__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __radd__(self, other): if isinstance(other, (AffineExpression, NegativeEntropy)): negent = NegativeEntropy.__add__(self, other) if negent is not self: negent._symbStr = glyphs.clever_add(other.string, self.string) return negent return Expression.__radd__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __sub__(self, other): if isinstance(other, (AffineExpression, Entropy)): return self + (-other) return Expression.__sub__(self, other) # -------------------------------------------------------------------------- # Methods and properties that return expressions. # -------------------------------------------------------------------------- @property def x(self): """The expression :math:`x`.""" return self._x @property def y(self): """The additional expression :math:`y`, or :obj:`None`.""" return self._y # -------------------------------------------------------------------------- # 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 KullbackLeiblerConstraint.make_type( argdim=subtype.argdim) return NotImplemented @convert_operands(scalarRHS=True) @validate_prediction @refine_operands() def __le__(self, other): if isinstance(other, AffineExpression): return KullbackLeiblerConstraint(self, other) else: return NotImplemented # -------------------------------------- __all__ = api_end(_API_START, globals()) Loading
picos/expressions/__init__.py +1 −0 Original line number Diff line number Diff line Loading @@ -47,6 +47,7 @@ from .exp_norm import Norm # noqa from .exp_nucnorm import NuclearNorm # noqa from .exp_powtrace import PowerTrace # noqa from .exp_quadratic import QuadraticExpression # noqa from .exp_quantentropy import QuantEntropy # noqa from .exp_specnorm import SpectralNorm # noqa from .exp_sqnorm import SquaredNorm # noqa from .exp_sumexp import SumExponentials # noqa Loading
picos/expressions/exp_quantentropy.py 0 → 100644 +514 −0 Original line number Diff line number Diff line # ------------------------------------------------------------------------------ # 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:`QuantEntropy` and :class:`NegativeQuantEntropy`.""" # TODO: Common base class for QuantEntropy and NegativeQuantEntropy. import math import operator from collections import namedtuple import cvxopt import numpy from .. import glyphs from ..apidoc import api_end, api_start from ..caching import cached_selfinverse_unary_operator, cached_unary_operator from ..constraints import KullbackLeiblerConstraint from .data import convert_and_refine_arguments, convert_operands, cvx2np from .exp_affine import AffineExpression,ComplexAffineExpression from .expression import Expression, refine_operands, validate_prediction _API_START = api_start(globals()) # ------------------------------- class QuantEntropy(Expression): r"""Quantum entropy or negative quantum relative entropy of an affine expression. :Definition: Let :math:`X` be an :math:`n \times n`-dimensional symmetric and hermitian matrix, or their :attr:`special vectorization <.exp_biaffine.BiaffineExpression.svec>`. 1. If no additional expression :math:`Y` is given, this is the quantum entropy .. math:: -\operatorname{Tr}(X \log(X)). 2. If an additional affine expression :math:`Y` of same shape as :math:`x` is given, this is the negative quantum relative entropy .. math:: \operatorname{Tr}(X (\log(Y) - \log(X))) """ # -------------------------------------------------------------------------- # Initialization and factory methods. # -------------------------------------------------------------------------- @convert_and_refine_arguments("X", "Y", allowNone=True) def __init__(self, X, Y=None): """Construct an :class:`QuantEntropy`. :param X: The affine expression :math:`X`. :type X: ~picos.expressions.AffineExpression :param Y: An additional affine expression :math:`Y`. If necessary, PICOS will attempt to reshape or broadcast it to the shape of :math:`X`. :type Y: ~picos.expressions.AffineExpression """ if not isinstance(X, ComplexAffineExpression): raise TypeError("Can only take the matrix logarithm of a real " "or complex affine expression, not of {}.".format(type(X).__name__)) if not X.hermitian: raise TypeError("Can only take the matrix logarithm of a symmetric " "or hermitian expression, not of {}.".format(type(X).__name__)) if Y is not None: if not isinstance(Y, ComplexAffineExpression): raise TypeError("The additional parameter Y must be a real " "or complex affine expression, not {}.".format(type(Y).__name__)) if not Y.hermitian: raise TypeError("Can only take the matrix logarithm of a symmetric " "or hermitian expression, not of {}.".format(type(Y).__name__)) if X.shape != Y.shape and Y.shape != (1, 1): raise TypeError("The additional parameter Y must either be the " "same shape as X, or be a real scalar expression, not {}." .format(type(Y).__name__)) if Y.is1: Y = None self._X = X self._Y = Y if Y is None: typeStr = "Qauntum Entropy" symbStr = glyphs.neg(glyphs.trace(glyphs.mul(X.string, glyphs.log(X.string)))) else: typeStr = "Negative Quantum Relative Entropy" symbStr = glyphs.trace(glyphs.mul(X.string, glyphs.sub(glyphs.log(Y.string), glyphs.log(X.string)))) Expression.__init__(self, typeStr, symbStr) # -------------------------------------------------------------------------- # Abstract method implementations and method overridings, except _predict. # -------------------------------------------------------------------------- def _get_refined(self): if self._X.constant and (self._Y is None or self._Y.constant): return AffineExpression.from_constant(self.value, 1, self._symbStr) else: return self Subtype = namedtuple("Subtype", ("argdim", "y")) def _get_subtype(self): return self.Subtype(len(self._x), self._y is not None) def _get_value(self): x = numpy.ravel(cvx2np(self._x._get_value())) if self._y is None: s = -numpy.dot(x, numpy.log(x)) else: y = numpy.ravel(cvx2np(self._y._get_value())) s = numpy.dot(x, numpy.log(y / x)) return cvxopt.matrix(s) @cached_unary_operator def _get_mutables(self): if self._y is None: return self._x._get_mutables() else: return self._x._get_mutables().union(self._y.mutables) def _is_convex(self): return False def _is_concave(self): return True def _replace_mutables(self, mapping): return self.__class__(self._x._replace_mutables(mapping), None if self._y is None else self._y._replace_mutables(mapping)) def _freeze_mutables(self, freeze): return self.__class__(self._x._freeze_mutables(freeze), None if self._y is None else self._y._freeze_mutables(freeze)) # -------------------------------------------------------------------------- # Python special method implementations, except constraint-creating ones. # -------------------------------------------------------------------------- @cached_selfinverse_unary_operator def __neg__(self): return NegativeEntropy(self._x, self._y) @convert_operands(scalarRHS=True) @refine_operands() def __add__(self, other): other_str = other.string if isinstance(other, AffineExpression): if other.is0: return self other = Entropy(other, other * math.e) if isinstance(other, Entropy): if self._y is None and other._y is None: entropy = Entropy(self._x.vec // other._x.vec) elif self._y is not None and other._y is None: one = AffineExpression.from_constant(1.0, (other.n, 1)) entropy = Entropy( self._x.vec // other._x.vec, self._y.vec // one) elif self._y is None and other._y is not None: one = AffineExpression.from_constant(1.0, (self.n, 1)) entropy = Entropy( self._x.vec // other._x.vec, one // other._y.vec) else: entropy = Entropy( self._x.vec // other._x.vec, self._y.vec // other._y.vec) entropy._symbStr = glyphs.clever_add(self.string, other_str) return entropy return Expression.__add__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __radd__(self, other): if isinstance(other, (AffineExpression, Entropy)): entropy = Entropy.__add__(self, other) if entropy is not self: entropy._symbStr = glyphs.clever_add(other.string, self.string) return entropy return Expression.__radd__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __sub__(self, other): if isinstance(other, (AffineExpression, NegativeEntropy)): return self + (-other) return Expression.__sub__(self, other) # -------------------------------------------------------------------------- # Methods and properties that return expressions. # -------------------------------------------------------------------------- @property def x(self): """The expression :math:`x`.""" return self._x @property def y(self): """The additional expression :math:`y`, or :obj:`None`.""" return self._y # -------------------------------------------------------------------------- # 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.__ge__: if issubclass(other.clstype, AffineExpression) \ and other.subtype.dim == 1: return KullbackLeiblerConstraint.make_type( argdim=subtype.argdim) return NotImplemented @convert_operands(scalarRHS=True) @validate_prediction @refine_operands() def __ge__(self, other): if isinstance(other, AffineExpression): return KullbackLeiblerConstraint(-self, -other) else: return NotImplemented class NegativeEntropy(Expression): r"""Negative or relative entropy of an affine expression. Relative entropy is also known as the Kullback-Leibler divergence. :Definition: Let :math:`x` be an :math:`n`-dimensional real affine expression. 1. If no additional expression :math:`y` is given, this is the negative entropy .. math:: \sum_{i = 1}^n \operatorname{vec}(x)_i \log(\operatorname{vec}(x)_i). 2. If an additional affine expression :math:`y` of same shape as :math:`x` is given, this is the relative entropy (or Kullback-Leibler divergence) .. math:: \sum_{i = 1}^n \operatorname{vec}(x)_i \log\left( \frac{\operatorname{vec}(x)_i}{\operatorname{vec}(y)_i} \right) = \sum_{i = 1}^n \operatorname{vec}(x)_i \left[ \log(\operatorname{vec}(x)_i) - \log(\operatorname{vec}(y)_i) \right]. .. warning:: When you pose an upper bound on this expression, then PICOS enforces :math:`x \geq 0` through an auxiliary constraint during solution search. When an additional expression :math:`y` is given, PICOS enforces :math:`y \geq 0` as well. """ # -------------------------------------------------------------------------- # Initialization and factory methods. # -------------------------------------------------------------------------- @convert_and_refine_arguments("x", "y", allowNone=True) def __init__(self, x, y=None): """Construct a :class:`NegativeEntropy`. :param x: The affine expression :math:`x`. :type x: ~picos.expressions.AffineExpression :param y: An additional affine expression :math:`y`. If necessary, PICOS will attempt to reshape or broadcast it to the shape of :math:`x`. :type y: ~picos.expressions.AffineExpression """ if not isinstance(x, AffineExpression): raise TypeError("Can only take the elementwise logarithm of a real " "affine expression, not of {}.".format(type(x).__name__)) if y is not None: if not isinstance(y, AffineExpression): raise TypeError("The additional parameter y must be a real " "affine expression, not {}.".format(type(x).__name__)) elif x.shape != y.shape: y = y.reshaped_or_broadcasted(x.shape) if y.is1: y = None self._x = x self._y = y if y is None: typeStr = "Negative Entropy" if len(x) == 1: symbStr = glyphs.mul(x.string, glyphs.log(x.string)) else: symbStr = glyphs.dotp(x.string, glyphs.log(x.string)) else: typeStr = "Relative Entropy" if len(x) == 1: symbStr = glyphs.mul( x.string, glyphs.log(glyphs.div(x.string, y.string))) else: symbStr = glyphs.dotp(x.string, glyphs.sub(glyphs.log(x.string), glyphs.log(y.string))) Expression.__init__(self, typeStr, symbStr) # -------------------------------------------------------------------------- # Abstract method implementations and method overridings, except _predict. # -------------------------------------------------------------------------- def _get_refined(self): if self._x.constant and (self._y is None or self._y.constant): return AffineExpression.from_constant(self.value, 1, self._symbStr) else: return self Subtype = namedtuple("Subtype", ("argdim", "y")) def _get_subtype(self): return self.Subtype(len(self._x), self._y is not None) def _get_value(self): x = numpy.ravel(cvx2np(self._x._get_value())) if self._y is None: s = numpy.dot(x, numpy.log(x)) else: y = numpy.ravel(cvx2np(self._y._get_value())) s = numpy.dot(x, numpy.log(x / y)) return cvxopt.matrix(s) @cached_unary_operator def _get_mutables(self): if self._y is None: return self._x._get_mutables() else: return self._x._get_mutables().union(self._y.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), None if self._y is None else self._y._replace_mutables(mapping)) def _freeze_mutables(self, freeze): return self.__class__(self._x._freeze_mutables(freeze), None if self._y is None else self._y._freeze_mutables(freeze)) # -------------------------------------------------------------------------- # Python special method implementations, except constraint-creating ones. # -------------------------------------------------------------------------- @cached_selfinverse_unary_operator def __neg__(self): return Entropy(self._x, self._y) @convert_operands(scalarRHS=True) @refine_operands() def __add__(self, other): other_str = other.string if isinstance(other, AffineExpression): if other.is0: return self other = NegativeEntropy(other, other / math.e) if isinstance(other, NegativeEntropy): if self._y is None and other._y is None: negent = NegativeEntropy(self._x.vec // other._x.vec) elif self._y is not None and other._y is None: one = AffineExpression.from_constant(1.0, (other.n, 1)) negent = NegativeEntropy( self._x.vec // other._x.vec, self._y.vec // one) elif self._y is None and other._y is not None: one = AffineExpression.from_constant(1.0, (self.n, 1)) negent = NegativeEntropy( self._x.vec // other._x.vec, one // other._y.vec) else: negent = NegativeEntropy( self._x.vec // other._x.vec, self._y.vec // other._y.vec) negent._symbStr = glyphs.clever_add(self.string, other_str) return negent return Expression.__add__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __radd__(self, other): if isinstance(other, (AffineExpression, NegativeEntropy)): negent = NegativeEntropy.__add__(self, other) if negent is not self: negent._symbStr = glyphs.clever_add(other.string, self.string) return negent return Expression.__radd__(self, other) @convert_operands(scalarRHS=True) @refine_operands() def __sub__(self, other): if isinstance(other, (AffineExpression, Entropy)): return self + (-other) return Expression.__sub__(self, other) # -------------------------------------------------------------------------- # Methods and properties that return expressions. # -------------------------------------------------------------------------- @property def x(self): """The expression :math:`x`.""" return self._x @property def y(self): """The additional expression :math:`y`, or :obj:`None`.""" return self._y # -------------------------------------------------------------------------- # 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 KullbackLeiblerConstraint.make_type( argdim=subtype.argdim) return NotImplemented @convert_operands(scalarRHS=True) @validate_prediction @refine_operands() def __le__(self, other): if isinstance(other, AffineExpression): return KullbackLeiblerConstraint(self, other) else: return NotImplemented # -------------------------------------- __all__ = api_end(_API_START, globals())
