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 

8# terms of the GNU General Public License as published by the Free Software 

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# ------------------------------------------------------------------------------ 

19 

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

21 

22import operator 

23from collections import namedtuple 

24 

25import cvxopt 

26import numpy 

27 

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 

34 

35_API_START = api_start(globals()) 

36# ------------------------------- 

37 

38 

39class GeometricMean(Expression): 

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

41 

42 :Definition: 

43 

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

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

46 

47 .. math:: 

48 

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

50 

51 .. warning:: 

52 

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 """ 

56 

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

58 # Initialization and factory methods. 

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

60 

61 @convert_and_refine_arguments("x") 

62 def __init__(self, x): 

63 """Construct a :class:`GeometricMean`. 

64 

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__)) 

71 

72 self._x = x 

73 

74 Expression.__init__( 

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

76 

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

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

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

80 

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 

88 

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

90 

91 def _get_subtype(self): 

92 return self.Subtype(len(self._x)) 

93 

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) 

98 

99 def _get_mutables(self): 

100 return self._x._get_mutables() 

101 

102 def _is_convex(self): 

103 return False 

104 

105 def _is_concave(self): 

106 return True # Only for nonnegative x. 

107 

108 def _replace_mutables(self, mapping): 

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

110 

111 def _freeze_mutables(self, freeze): 

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

113 

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

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

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

117 

118 @convert_operands(scalarRHS=True) 

119 @refine_operands() 

120 def __mul__(self, other): 

121 if isinstance(other, AffineExpression): 

122 if not other.constant: 

123 raise NotImplementedError("You may only multiply a nonconstant " 

124 "PICOS geometric mean with a constant term.") 

125 

126 if other.value < 0: 

127 raise NotImplementedError("You may only multiply a nonconstant " 

128 "PICOS geometric mean with a nonnegative term.") 

129 

130 mean = GeometricMean(other.value * self._x) 

131 mean._typeStr = "Scaled " + mean._typeStr 

132 mean._symbStr = glyphs.clever_mul(self.string, other.string) 

133 return mean 

134 else: 

135 return NotImplemented 

136 

137 @convert_operands(scalarRHS=True) 

138 @refine_operands() 

139 def __rmul__(self, other): 

140 if isinstance(other, AffineExpression): 

141 mean = self.__mul__(other) 

142 # NOTE: __mul__ always creates a fresh expression. 

143 mean._symbStr = glyphs.clever_mul(other.string, self.string) 

144 return mean 

145 else: 

146 return NotImplemented 

147 

148 # -------------------------------------------------------------------------- 

149 # Methods and properties that return modified copies. 

150 # -------------------------------------------------------------------------- 

151 

152 @property 

153 def x(self): 

154 """The expression under the mean.""" 

155 return self._x 

156 

157 # -------------------------------------------------------------------------- 

158 # Constraint-creating operators, and _predict. 

159 # -------------------------------------------------------------------------- 

160 

161 @classmethod 

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

163 assert isinstance(subtype, cls.Subtype) 

164 

165 if relation == operator.__ge__: 

166 if issubclass(other.clstype, AffineExpression) \ 

167 and other.subtype.dim == 1: 

168 return GeometricMeanConstraint.make_type(subtype.argdim) 

169 

170 return NotImplemented 

171 

172 @convert_operands(scalarRHS=True) 

173 @validate_prediction 

174 @refine_operands() 

175 def __ge__(self, other): 

176 if isinstance(other, AffineExpression): 

177 return GeometricMeanConstraint(self, other) 

178 else: 

179 return NotImplemented 

180 

181 

182# -------------------------------------- 

183__all__ = api_end(_API_START, globals())