# Coverage for picos/expressions/exp_geomean.py: 89.66%

## 87 statements

, created at 2023-03-26 07:46 +0000

1# ------------------------------------------------------------------------------

2# Copyright (C) 2019 Maximilian Stahlberg

3# Based on the original picos.expressions module by Guillaume Sagnol.

4#

5# This file is part of PICOS.

6#

7# PICOS is free software: you can redistribute it and/or modify it under the

9# Foundation, either version 3 of the License, or (at your option) any later

10# version.

11#

12# PICOS is distributed in the hope that it will be useful, but WITHOUT ANY

13# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR

14# A PARTICULAR PURPOSE. See the GNU General Public License for more details.

15#

16# You should have received a copy of the GNU General Public License along with

17# this program. If not, see <http://www.gnu.org/licenses/>.

18# ------------------------------------------------------------------------------

20"""Implements :class:GeometricMean."""

22import operator

23from collections import namedtuple

25import cvxopt

26import numpy

28from .. import glyphs

29from ..apidoc import api_end, api_start

30from ..constraints import GeometricMeanConstraint

31from .data import convert_and_refine_arguments, convert_operands, cvx2np

32from .exp_affine import AffineExpression

33from .expression import Expression, refine_operands, validate_prediction

35_API_START = api_start(globals())

36# -------------------------------

39class GeometricMean(Expression):

40 r"""Geometric mean of an affine expression.

42 :Definition:

44 For an :math:n-dimensional affine expression :math:x with

45 :math:x \geq 0, the geometric mean is given as

47 .. math::

49 \left(\prod_{i = 1}^n x_i \right)^{\frac{1}{n}}.

51 .. warning::

53 When you pose a lower bound on a geometric mean, then PICOS enforces

54 :math:x \geq 0 through an auxiliary constraint during solution search.

55 """

57 # --------------------------------------------------------------------------

58 # Initialization and factory methods.

59 # --------------------------------------------------------------------------

61 @convert_and_refine_arguments("x")

62 def __init__(self, x):

63 """Construct a :class:GeometricMean.

65 :param x: The affine expression to form the geometric mean of.

66 :type x: ~picos.expressions.AffineExpression

67 """

68 if not isinstance(x, AffineExpression):

69 raise TypeError("Can only form the geometrtic mean of a real affine"

70 " expression, not of {}.".format(type(x).__name__))

72 self._x = x

74 Expression.__init__(

75 self, "Geometric Mean", glyphs.make_function("geomean")(x.string))

77 # --------------------------------------------------------------------------

78 # Abstract method implementations and method overridings, except _predict.

79 # --------------------------------------------------------------------------

81 def _get_refined(self):

82 if self._x.constant:

83 return AffineExpression.from_constant(self.value, 1, self._symbStr)

84 elif len(self._x) == 1:

85 return self._x.renamed(self._symbStr)

86 else:

87 return self

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

91 def _get_subtype(self):

92 return self.Subtype(len(self._x))

94 def _get_value(self):

95 value = self._x._get_value()

96 value = numpy.prod(cvx2np(value))**(1.0 / len(self._x))

97 return cvxopt.matrix(value)

99 def _get_mutables(self):

100 return self._x._get_mutables()

102 def _is_convex(self):

103 return False

105 def _is_concave(self):

106 return True # Only for nonnegative x.

108 def _replace_mutables(self, mapping):

109 return self.__class__(self._x._replace_mutables(mapping))

111 def _freeze_mutables(self, freeze):

112 return self.__class__(self._x._freeze_mutables(freeze))

114 # --------------------------------------------------------------------------

115 # Python special method implementations, except constraint-creating ones.

116 # --------------------------------------------------------------------------

118 @classmethod

119 def _mul(cls, self, other, forward):

120 if isinstance(other, AffineExpression) and other.constant:

121 factor = other.safe_value

123 if not factor:

124 return AffineExpression.zero()

125 elif factor == 1:

126 return self

127 elif factor > 0:

128 if forward:

129 string = glyphs.clever_mul(self.string, other.string)

130 else:

131 string = glyphs.clever_mul(other.string, self.string)

133 product = cls(other*self._x)

134 product._typeStr = "Scaled " + product._typeStr

135 product._symbStr = string

137 return product

139 if forward:

140 return Expression.__mul__(self, other)

141 else:

142 return Expression.__rmul__(self, other)

144 @convert_operands(scalarRHS=True)

145 @refine_operands()

146 def __mul__(self, other):

147 return GeometricMean._mul(self, other, True)

149 @convert_operands(scalarRHS=True)

150 @refine_operands()

151 def __rmul__(self, other):

152 return GeometricMean._mul(self, other, False)

154 # --------------------------------------------------------------------------

155 # Methods and properties that return modified copies.

156 # --------------------------------------------------------------------------

158 @property

159 def x(self):

160 """The expression under the mean."""

161 return self._x

163 # --------------------------------------------------------------------------

164 # Constraint-creating operators, and _predict.

165 # --------------------------------------------------------------------------

167 @classmethod

168 def _predict(cls, subtype, relation, other):

169 assert isinstance(subtype, cls.Subtype)

171 if relation == operator.__ge__:

172 if issubclass(other.clstype, AffineExpression) \

173 and other.subtype.dim == 1:

174 return GeometricMeanConstraint.make_type(subtype.argdim)

176 return NotImplemented

178 @convert_operands(scalarRHS=True)

179 @validate_prediction

180 @refine_operands()

181 def __ge__(self, other):

182 if isinstance(other, AffineExpression):

183 return GeometricMeanConstraint(self, other)

184 else:

185 return NotImplemented

188# --------------------------------------

189__all__ = api_end(_API_START, globals())