Αi SSKJr SSKrSSKrSSKJr SSKrSSKrSSK J r SSK J r \(aSSK Jr SSKJr SSKJrJr "S S \ 5rg) ) annotationsN) TYPE_CHECKING) framework)TransformedDistribution)Sequence)Tensor) TransformUniformc^\rSrSr%SrS\S'S\S'S\S'S\S 'SU4S jjr\SS j5r\SS j5r \SS j5r SSjr SSjr SSjr SSjr/4SSjjr/4SSjjrSrU=r$)Gumbel"aThe Gumbel distribution with location `loc` and `scale` parameters. Mathematical details The probability density function (pdf) is .. math:: pdf(x; mu, sigma) = exp(-(x - mu) / sigma - exp(-(x - mu) / sigma)) / sigma In the above equation: * :math:`loc = \mu`: is the mean. * :math:`scale = \sigma`: is the std. Args: loc(int|float|tensor): The mean of gumbel distribution.The data type is int, float, tensor. scale(int|float|tensor): The std of gumbel distribution.The data type is int, float, tensor. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution.gumbel import Gumbel >>> # Gumbel distributed with loc=0, scale=1 >>> dist = Gumbel(paddle.full([1], 0.0), paddle.full([1], 1.0)) >>> # doctest: +SKIP >>> print(dist.sample([2])) Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.40484068], [3.19400501]]) >>> print(dist.rsample([2])) Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[-0.95093185], [ 0.32422572]]) >>> # doctest: -SKIP >>> value = paddle.full([1], 0.5) >>> print(dist.prob(value)) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.33070430]) >>> print(dist.log_prob(value)) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [-1.10653067]) >>> print(dist.cdf(value)) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [0.54523921]) >>> print(dist.entropy()) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.57721567]) rlocscaler base_distztuple[Transform, ...] transformsc >[U[R[R[ R R45(d[S[U535e[U[R[R[ R R45(d[S[U535e[U[R5(a[ R"SUS9n[U[R5(a[ R"SUS9nURUR:wa%[ R"X/5uUl UlOXsUl Ul[R "SS9n[ R"R%[ R&"UR[)UR*55[ R&"UR[)SUR,- 555UlSUl[2TU]iUR.UR05 g)Nz5Expected type of loc is Real|Variable|Value, but got z7Expected type of scale is Real|Variable|Value, but got )shape fill_valuefloat32)dtype) isinstancenumbersRealrVariablepaddlepirValue TypeErrortypefullrbroadcast_tensorsrrnpfinfo distributionr full_likefloattinyepsrrsuper__init__)selfrrr% __class__s Z/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/gumbel.pyr,Gumbel.__init__cs ',, 2 2FJJ4D4DE  GS {S  GLL)"4"4fjj6F6FG  I$u+W  c7<< ( (++B37C eW\\ * *KKbU;E 99 ##)#;#;SL#I DHdj#& DHdjy),,44   TXXuUZZ'8 9   TXXuQ]'; <   9cVURUR[R--$)uMean of distribution The mean is .. math:: mean = \mu + \sigma * γ In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. * :math:`γ`: is the euler's constant. Returns: Tensor: mean value. )rrr$ euler_gammar-s r/mean Gumbel.means (xx$**r~~555r1c [R"URR[R [R -UR RS9n[R"UR S5U-S- $)zVariance of distribution. The variance is .. math:: variance = \sigma^2 * \pi^2 / 6 In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: The variance value. rrr) rr"rrmathpirrpow)r-temps r/varianceGumbel.variances[${{((..ww(**""  zz$**a(4/!33r1cB[R"UR5$)zStandard deviation of distribution The standard deviation is .. math:: stddev = \sqrt{\sigma^2 * \pi^2 / 6} In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: std value )rsqrtr?r4s r/stddev Gumbel.stddevs {{4==))r1clURURURR5- URRURR5- n[R "U[R "U5- 5URRUR5- $)zProbability density/mass function Args: value (Tensor): The input tensor. Returns: Tensor: probability.The data type is same with value. )rastyperrrexp)r-valueys r/prob Gumbel.probszXX TXX^^4 4 8I8I HHNN9  zz!fjjm+,tzz/@/@/IIIr1cL[R"URU55$)zLog probability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability.The data type is same with value. )rlogrJr-rHs r/log_probGumbel.log_probszz$))E*++r1c[R"[R"XRRUR5- *UR RUR5- 5*5$)zCumulative distribution function. Args: value (Tensor): value to be evaluated. Returns: Tensor: cumulative probability of value. )rrGrrFrrrNs r/cdf Gumbel.cdfs[zz ZZ((//%++667**##EKK01   r1cj[R"UR5S-[R-$)zHEntropy of Gumbel distribution. Returns: Entropy of distribution. r)rrMrr$r3r4s r/entropyGumbel.entropys%zz$**%)BNN::r1c[R"5 URU5sSSS5 $!,(df  g=f)zSample from ``Gumbel``. Args: shape (Sequence[int], optional): The sample shape. Defaults to []. Returns: Tensor: A tensor with prepended dimensions shape.The data type is float32. N)rno_gradrsample)r-rs r/sample Gumbel.samples&^^ <<&  s1 ?c L[RR5n[RR[R"UR R SURRS9[R"UR 5*5n[RRURUR *5nURURURURURRU55555$)zreparameterized sample Args: shape (Sequence[int], optional): 1D `int32`. Shape of the generated samples. Defaults to []. Returns: Tensor: A tensor with prepended dimensions shape.The data type is float32. rr8)rr& ExpTransformAffineTransformr"rrrr ones_likeforwardinverse_baserZ)r-r exp_transaffine_trans_1affine_trans_2s r/rYGumbel.rsample s''446 ,,<< KKjj&&1DHHNN   djj ) )    ,,<< HHtzzk %%   &&%%djj&7&7&>?   r1)rrrr)rfloat | TensorrrgreturnNone)rhr)rHrrhr)rz Sequence[int]rhr)__name__ __module__ __qualname____firstlineno____doc____annotations__r,propertyr5r?rCrJrOrRrUrZrY__static_attributes__ __classcell__)r.s@r/r r "s9v K M%%!:F66*442**"J , ;-/ '.0  r1r ) __future__rr;rtypingrnumpyr$r paddle.baser,paddle.distribution.transformed_distributionrcollections.abcrrpaddle.distributionr r r rr1r/rzs:#   !P(6B $B r1