Coverage for picos/expressions/exp_logarithm.py: 74.14%

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:`Logarithm`.""" 

21 

22import math 

23import operator 

24from collections import namedtuple 

25 

26import cvxopt 

27 

28from .. import glyphs 

29from ..apidoc import api_end, api_start 

30from ..constraints import LogConstraint 

31from .data import convert_and_refine_arguments, convert_operands 

32from .exp_affine import AffineExpression 

33from .expression import Expression, refine_operands, validate_prediction 

34 

35_API_START = api_start(globals()) 

36# ------------------------------- 

37 

38 

39class Logarithm(Expression): 

40 r"""Logarithm of a scalar affine expression. 

41 

42 :Definition: 

43 

44 For a real scalar affine expression :math:`x`, this is :math:`\log(x)`. 

45 

46 .. warning:: 

47 

48 When you pose a lower bound on a logarithm :math:`\log(x)`, then PICOS 

49 enforces :math:`x \geq 0` through an auxiliary constraint during 

50 solution search. 

51 """ 

52 

53 # -------------------------------------------------------------------------- 

54 # Initialization and factory methods. 

55 # -------------------------------------------------------------------------- 

56 

57 @convert_and_refine_arguments("x") 

58 def __init__(self, x): 

59 """Construct a :class:`Logarithm`. 

60 

61 :param x: The scalar affine expression :math:`x`. 

62 :type x: ~picos.expressions.AffineExpression 

63 """ 

64 if not isinstance(x, AffineExpression): 

65 raise TypeError("Can only take the logarithm of a real affine " 

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

67 elif not x.scalar: 

68 raise TypeError("Can only take the logarithm of a scalar expression" 

69 "but {} is shaped {}.".format(x.string, glyphs.shape(x.shape))) 

70 

71 self._x = x 

72 

73 Expression.__init__(self, "Logarithm", glyphs.log(x.string)) 

74 

75 # -------------------------------------------------------------------------- 

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

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

78 

79 def _get_refined(self): 

80 if self._x.constant: 

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

82 else: 

83 return self 

84 

85 Subtype = namedtuple("Subtype", ()) 

86 

87 def _get_subtype(self): 

88 return self.Subtype() 

89 

90 def _get_value(self): 

91 value = cvxopt.matrix(self._x._get_value()) # Must be dense for log. 

92 return cvxopt.log(value) 

93 

94 def _get_mutables(self): 

95 return self._x._get_mutables() 

96 

97 def _is_convex(self): 

98 return False 

99 

100 def _is_concave(self): 

101 return True 

102 

103 def _replace_mutables(self, mapping): 

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

105 

106 def _freeze_mutables(self, freeze): 

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

108 

109 # -------------------------------------------------------------------------- 

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

111 # -------------------------------------------------------------------------- 

112 

113 @classmethod 

114 def _add(cls, self, other, forward): 

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

116 if other.is0: 

117 return self 

118 

119 log = cls(self._x * math.exp(other.value)) 

120 log._typeStr = "Offset " + log._typeStr 

121 

122 if forward: 

123 log._symbStr = glyphs.clever_add(self.string, other.string) 

124 else: 

125 log._symbStr = glyphs.clever_add(other.string, self.string) 

126 

127 return log 

128 

129 if forward: 

130 return Expression.__add__(self, other) 

131 else: 

132 return Expression.__radd__(self, other) 

133 

134 @convert_operands(scalarRHS=True) 

135 @refine_operands() 

136 def __add__(self, other): 

137 return Logarithm._add(self, other, True) 

138 

139 @convert_operands(scalarRHS=True) 

140 @refine_operands() 

141 def __radd__(self, other): 

142 return Logarithm._add(self, other, False) 

143 

144 @convert_operands(scalarRHS=True) 

145 @refine_operands() 

146 def __sub__(self, other): 

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

148 log = Logarithm(self._x / math.exp(other.value)) 

149 log._typeStr = "Offset " + log._typeStr 

150 log._symbStr = glyphs.clever_sub(self.string, other.string) 

151 

152 return log 

153 

154 return Expression.__sub__(self, other) 

155 

156 @classmethod 

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

158 from . import Entropy, NegativeEntropy 

159 

160 if isinstance(other, AffineExpression): 

161 if other.is0: 

162 return AffineExpression.zero() 

163 elif other.is1: 

164 return self 

165 elif other.equals(self._x): 

166 return NegativeEntropy(self._x) 

167 elif other.equals(-self._x): 

168 return Entropy(self._x) 

169 

170 if forward: 

171 return Expression.__mul__(self, other) 

172 else: 

173 return Expression.__rmul__(self, other) 

174 

175 @convert_operands(scalarRHS=True) 

176 @refine_operands() 

177 def __mul__(self, other): 

178 return Logarithm._mul(self, other, True) 

179 

180 @convert_operands(scalarRHS=True) 

181 @refine_operands() 

182 def __rmul__(self, other): 

183 return Logarithm._mul(self, other, False) 

184 

185 # -------------------------------------------------------------------------- 

186 # Methods and properties that return expressions. 

187 # -------------------------------------------------------------------------- 

188 

189 @property 

190 def x(self): 

191 """The expression :math:`x`.""" 

192 return self._x 

193 

194 @property 

195 def exp(self): 

196 """The exponential of the logarithm, equal to :math:`x`.""" 

197 return self._x 

198 

199 # -------------------------------------------------------------------------- 

200 # Constraint-creating operators, and _predict. 

201 # -------------------------------------------------------------------------- 

202 

203 @classmethod 

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

205 assert isinstance(subtype, cls.Subtype) 

206 

207 if relation == operator.__ge__: 

208 if issubclass(other.clstype, AffineExpression) \ 

209 and other.subtype.dim == 1: 

210 return LogConstraint.make_type() 

211 

212 return NotImplemented 

213 

214 @convert_operands(scalarRHS=True) 

215 @validate_prediction 

216 @refine_operands() 

217 def __ge__(self, other): 

218 if isinstance(other, AffineExpression): 

219 return LogConstraint(self, other) 

220 else: 

221 return NotImplemented 

222 

223 

224# -------------------------------------- 

225__all__ = api_end(_API_START, globals())