# Coverage for picos/expressions/exp_sumexp.py: 73.30%

## 191 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:SumExponentials."""

22import math

23import operator

24from collections import namedtuple

26import cvxopt

27import numpy

29from .. import glyphs

30from ..apidoc import api_end, api_start

31from ..caching import cached_property, cached_unary_operator

32from ..constraints import LogSumExpConstraint, SumExponentialsConstraint

33from .data import convert_and_refine_arguments, convert_operands, cvx2np

34from .exp_affine import AffineExpression

35from .expression import Expression, refine_operands, validate_prediction

37_API_START = api_start(globals())

38# -------------------------------

41class SumExponentials(Expression):

42 r"""Sum of elementwise exponentials of an affine expression.

44 :Definition:

46 Let :math:x be an :math:n-dimensional real affine expression.

48 1. If no additional expression :math:y is given, this is the sum of

49 elementwise exponentials

51 .. math::

53 \sum_{i = 1}^n \exp(\operatorname{vec}(x)_i).

55 2. If an additional affine expression :math:y of same shape as :math:x

56 is given, this is the sum of elementwise perspectives of exponentials

58 .. math::

60 \sum_{i = 1}^n \operatorname{vec}(y)_i \exp\left(

61 \frac{\operatorname{vec}(x)_i}{\operatorname{vec}(y)_i}\right).

63 .. warning::

65 When you pose an upper bound :math:t on a sum of elementwise

66 exponentials, then PICOS enforces :math:t \geq 0 through an auxiliary

67 constraint during solution search. When an additional expression

68 :math:y is given, PICOS enforces :math:y \geq 0 as well.

69 """

71 # --------------------------------------------------------------------------

72 # Initialization and factory methods.

73 # --------------------------------------------------------------------------

75 @convert_and_refine_arguments("x", "y", allowNone=True)

76 def __init__(self, x, y=None):

77 """Construct a :class:SumExponentials.

79 :param x: The affine expression :math:x.

80 :type x: ~picos.expressions.AffineExpression

81 :param y: An additional affine expression :math:y. If necessary, PICOS

82 will attempt to reshape or broadcast it to the shape of :math:x.

83 :type y: ~picos.expressions.AffineExpression

84 """

85 if not isinstance(x, AffineExpression):

86 raise TypeError("Can only sum the elementwise exponentials of a "

87 "real affine expression, not of {}.".format(x.string))

89 if y is not None:

90 if not isinstance(y, AffineExpression):

91 raise TypeError("The additional parameter y must be a real "

92 "affine expression, not {}.".format(y.string))

93 elif x.shape != y.shape:

96 if y.is1:

97 y = None

99 self._x = x

100 self._y = y

102 if len(x) == 1:

103 if y is None:

104 typeStr = "Exponential"

105 symbStr = glyphs.exp(x.string)

106 else:

107 typeStr = "Exponential Perspective"

108 symbStr = glyphs.mul(

109 y.string, glyphs.exp(glyphs.div(x.string, y.string)))

110 else:

111 if y is None:

112 typeStr = "Sum of Exponentials"

113 symbStr = glyphs.make_function("sum", "exp")(x.string)

114 else:

115 typeStr = "Sum of Exponential Perspectives"

116 symbStr = glyphs.sum(glyphs.mul(glyphs.slice(y.string, "i"),

117 glyphs.exp(glyphs.div(glyphs.slice(x.string, "i"),

118 glyphs.slice(y.string, "i")))))

120 Expression.__init__(self, typeStr, symbStr)

122 # --------------------------------------------------------------------------

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

124 # --------------------------------------------------------------------------

126 def _get_refined(self):

127 if self._x.constant and (self._y is None or self._y.constant):

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

129 else:

130 return self

132 Subtype = namedtuple("Subtype", ("argdim", "y"))

134 def _get_subtype(self):

135 return self.Subtype(len(self._x), self._y is not None)

137 def _get_value(self):

138 x = numpy.ravel(cvx2np(self._x._get_value()))

140 if self._y is None:

141 s = numpy.sum(numpy.exp(x))

142 else:

143 y = numpy.ravel(cvx2np(self._y._get_value()))

144 s = y.dot(numpy.exp(x / y))

146 return cvxopt.matrix(s)

148 @cached_unary_operator

149 def _get_mutables(self):

150 if self._y is None:

151 return self._x._get_mutables()

152 else:

153 return self._x._get_mutables().union(self._y.mutables)

155 def _is_convex(self):

156 return True

158 def _is_concave(self):

159 return False

161 def _replace_mutables(self, mapping):

162 return self.__class__(self._x._replace_mutables(mapping),

163 None if self._y is None else self._y._replace_mutables(mapping))

165 def _freeze_mutables(self, freeze):

166 return self.__class__(self._x._freeze_mutables(freeze),

167 None if self._y is None else self._y._freeze_mutables(freeze))

169 # --------------------------------------------------------------------------

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

171 # --------------------------------------------------------------------------

173 @classmethod

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

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

176 value = other.value

178 if not value:

179 return self

180 elif value > 0:

181 if self._y is None:

182 result = cls(self._x // math.log(value))

183 else:

184 result = cls(self._x // value, self._y // 1)

186 if forward:

188 else:

191 result._typeStr = "Offset " + result._typeStr

192 result._symbStr = string

194 return result

195 elif isinstance(other, cls):

196 assert forward, "Encountered __radd__ on equal types."

198 if self._y is None and other._y is None:

199 result = cls(self._x.vec // other._x.vec)

200 elif self._y is not None and other._y is None:

201 one = AffineExpression.from_constant(1.0, (other.n, 1))

202 result = cls(self._x.vec // other._x.vec, self._y.vec // one)

203 elif self._y is None and other._y is not None:

204 one = AffineExpression.from_constant(1.0, (self.n, 1))

205 result = cls(self._x.vec // other._x.vec, one // other._y.vec)

206 else:

207 result = cls(

208 self._x.vec // other._x.vec, self._y.vec // other._y.vec)

212 return result

214 if forward:

216 else:

219 @convert_operands(scalarRHS=True)

220 @refine_operands()

224 @convert_operands(scalarRHS=True)

225 @refine_operands()

229 @classmethod

230 def _mul_div(cls, self, other, div, forward):

231 assert not div or forward

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

234 factor = other.safe_value

236 if not factor:

237 if div:

238 raise ZeroDivisionError(

239 "Cannot divide {} by zero.".format(self.string))

240 else:

241 return AffineExpression.zero()

242 elif factor == 1:

243 return self

244 elif factor > 0:

245 if div:

246 factor = 1 / factor

247 string = glyphs.div(self.string, other.string)

248 elif forward:

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

250 else:

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

253 if self._y is None:

254 result = cls(self._x + math.log(factor))

255 else:

256 result = cls(other*self._x, other*self._y)

258 result._typeStr = "Scaled " + result._typeStr

259 result._symbStr = string

261 return result

263 if div:

264 return Expression.__div__(self, other)

265 elif forward:

266 return Expression.__mul__(self, other)

267 else:

268 return Expression.__rmul__(self, other)

270 @convert_operands(scalarRHS=True)

271 @refine_operands()

272 def __mul__(self, other):

273 """Denote scaling from the right hand side."""

274 return SumExponentials._mul_div(self, other, div=False, forward=True)

276 @convert_operands(scalarRHS=True)

277 @refine_operands()

278 def __rmul__(self, other):

279 """Denote scaling from the left hand side."""

280 return SumExponentials._mul_div(self, other, div=False, forward=False)

282 @convert_operands(scalarRHS=True)

283 @refine_operands()

284 def __truediv__(self, other):

285 """Denote division by a constant scalar."""

286 return SumExponentials._mul_div(self, other, div=True, forward=True)

288 # --------------------------------------------------------------------------

289 # Methods and properties that return expressions.

290 # --------------------------------------------------------------------------

292 @property

293 def x(self):

294 """The expression :math:x."""

295 return self._x

297 @property

298 def y(self):

299 """The additional expression :math:y, or :obj:None."""

300 return self._y

302 @cached_property

303 def log(self):

304 """The logarithm of the expression."""

305 from . import LogSumExp

307 if self._y is not None:

308 raise NotImplementedError("May only take the logarithm of a sum of"

309 " exponentials, not of a sum of exponential perspectives.")

311 return LogSumExp(self._x)

313 # --------------------------------------------------------------------------

314 # Methods and properties that describe the expression.

315 # --------------------------------------------------------------------------

317 @property

318 def n(self):

319 """Length of :attr:x."""

320 return len(self._x)

322 # --------------------------------------------------------------------------

323 # Constraint-creating operators, and _predict.

324 # --------------------------------------------------------------------------

326 @classmethod

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

328 assert isinstance(subtype, cls.Subtype)

330 if relation == operator.__le__:

331 if issubclass(other.clstype, AffineExpression) \

332 and other.subtype.dim == 1:

333 return SumExponentialsConstraint.make_type(

334 argdim=subtype.argdim,

335 lse_representable=(not subtype.y and other.subtype.nonneg))

336 elif issubclass(other.clstype, SumExponentials):

337 if subtype.y or other.subtype.y:

338 return NotImplemented

340 if other.subtype.argdim != 1:

341 return NotImplemented

343 return LogSumExpConstraint.make_type(argdim=subtype.argdim)

345 return NotImplemented

347 @convert_operands(scalarRHS=True)

348 @validate_prediction

349 @refine_operands()

350 def __le__(self, other):

351 from . import LogSumExp

353 if isinstance(other, AffineExpression):

354 return SumExponentialsConstraint(self, other)

355 elif isinstance(other, SumExponentials):

356 if self._y is not None or other._y is not None:

357 raise NotImplementedError("Comparing two sums of exponentials "

358 "is not supported if either expression has the additional "

359 "perspectives parameter y set.")

361 if other.n != 1:

362 raise NotImplementedError("You may only upper bound a sum of "

363 "exponentials by a single exponential, not by another sum.")

365 return LogSumExp(self._x) <= other._x

366 else:

367 return NotImplemented

370# --------------------------------------

371__all__ = api_end(_API_START, globals())