Αi3SSKJr SSKrSSKJr SSKrSSKrSSKJ r SSK J r \(a SSK J r SSKJr "SS \ R5rg) ) annotationsN) TYPE_CHECKING) framework) distribution)Sequence)Tensorc^\rSrSr%SrS\S'S\S'SU4Sjjr\SSj5r\SSj5r \SS j5r SS jr SS jr SS jr SS jrSSjr/4SSjjr/4SSjjrSSjrSSjrSrU=r$)Laplacea@ Creates a Laplace distribution parameterized by :attr:`loc` and :attr:`scale`. Mathematical details The probability density function (pdf) is .. math:: pdf(x; \mu, \sigma) = \frac{1}{2 * \sigma} * e^{\frac{-|x - \mu|}{\sigma}} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: loc (scalar|Tensor): The mean of the distribution. scale (scalar|Tensor): The scale of the distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.sample() # Laplace distributed with loc=0, scale=1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.31554604) rlocscalec>[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"SUS9n[UR5S:d[UR5S:a?URUR:Xa%[ R"X/5uUlUlOXsUlUl["TU]IURR5 g)Nz/Expected type of loc is Real|Variable, but got z1Expected type of scale is Real|Variable, but got shape fill_valuer) isinstancenumbersRealrVariablepaddlepirValue TypeErrortypefulllenrdtypebroadcast_tensorsr r super__init__)selfr r __class__s [/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/laplace.pyr!Laplace.__init__BsK ',, 2 2FJJ4D4DE  A$s)M  GLL)"4"4fjj6F6FG  CDK=Q  c7<< ( (++B37C eW\\ * *KKbU;E  q C NQ$6 II $#)#;#;SL#I DHdj#& DHdj (cUR$)z>"Q&5;;!# & 8 84::u-! C4::5  r&cURU5up#n[R"SU-5*nU[R"X- 5U- - $)aLog probability density/mass function. The log_prob is .. math:: log\_prob(value) = \frac{-log(2 * \sigma) - |value - \mu|}{\sigma} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor|Scalar): The input value, can be a scalar or a tensor. Returns: Tensor: The log probability, whose data type is same with value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.log_prob(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -0.79314721) r/)r6rlogabs)r"r5r r log_scales r$log_probLaplace.log_probsI>!007EZZE ** 6::ek2U:::r&cNS[R"SUR-5-$)aEntropy of Laplace distribution. The entropy is: .. math:: entropy() = 1 + log(2 * \sigma) In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: The entropy of distribution. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.entropy() Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.69314718) r/)rr9r r(s r$entropyLaplace.entropys 26::a$**n---r&cURU5up#nSX- R5-[R"X- R 5*U- 5-nSU- $)aCumulative distribution function. The cdf is .. math:: cdf(value) = 0.5 - 0.5 * sign(value - \mu) * e^\frac{-|(\mu - \sigma)|}{\sigma} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor): The value to be evaluated. Returns: Tensor: The cumulative probability of value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.cdf(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 0.54758132) ?)r6signrexpm1r:)r"r5r r items r$cdf Laplace.cdfsd<!007E {  " #llU[--//%78 9 Tzr&cURU5up#nUS- nX#UR5-[R"SUR 5-5-- $)aInverse Cumulative distribution function. The icdf is .. math:: cdf^{-1}(value)= \mu - \sigma * sign(value - 0.5) * ln(1 - 2 * |value-0.5|) In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor): The value to be evaluated. Returns: Tensor: The cumulative probability of value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.icdf(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -1.60943794) rC)r6rDrlog1pr:)r"r5r r terms r$icdf Laplace.icdfsN:!007Es{d[[]*V\\"txxz/-JJJJr&c[U[5(aUO [U5n[R"5 UR U5sSSS5 $!,(df  g=f)a7Generate samples of the specified shape. Args: shape(Sequence[int], optional): The shape of generated samples. Defaults to []. Returns: Tensor: A sample tensor that fits the Laplace distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.sample() # Laplace distributed with loc=0, scale=1 Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.31554604) N)rtuplerno_gradrsample)r"rs r$sampleLaplace.sample2s=($E511uU| ^^ <<&  s A A!c UR5nURU5n[R"U[ [ R "SS55US- -SUS- - URRS9nURURUR5-[R"UR5*5-- $)a7Reparameterized sample. Args: shape(Sequence[int], optional): The shape of generated samples. Defaults to []. Returns: Tensor: A sample tensor that fits the Laplace distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m.rsample((1,)) # Laplace distributed with loc=0, scale=1 Tensor(shape=[1, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.31554604]]) r?r/g?)rminmaxr) _get_eps _extend_shaperuniformfloatnp nextafterr rr rDrKr:)r"repsr[s r$rRLaplace.rsampleJs*mmo""5)..bll2q)*S1W4cAg ((..   xx$**w||~5 [[]N9    r&cSnURR[R:Xd(URR[R:XaSnU$)z Get the eps of certain data type. Note: Since paddle.finfo is temporarily unavailable, we use hard-coding style to get eps value. Returns: Float: An eps value by different data types. gy>gǝ<)r rrfloat64 complex128)r"r_s r$rYLaplace._get_epsks= HHNNfnn ,xx~~!2!22C r&cJURUR- n[R"URUR- 5nUR[R"U*UR- 5-U-UR- n[R "U5nXE-S- $)aCalculate the KL divergence KL(self || other) with two Laplace instances. The kl_divergence between two Laplace distribution is .. math:: KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\frac{diff}{\sigma_1})^2 - 1 - 2 \ln {ratio}) .. math:: ratio = \frac{\sigma_0}{\sigma_1} .. math:: diff = \mu_1 - \mu_0 In the above equation: * :math:`loc = \mu`: is the location parameter of self. * :math:`scale = \sigma`: is the scale parameter of self. * :math:`loc = \mu_1`: is the location parameter of the reference Laplace distribution. * :math:`scale = \sigma_1`: is the scale parameter of the reference Laplace distribution. * :math:`ratio`: is the ratio between the two distribution. * :math:`diff`: is the difference between the two distribution. Args: other (Laplace): An instance of Laplace. Returns: Tensor: The kl-divergence between two laplace distributions. Examples: .. code-block:: python >>> import paddle >>> m1 = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m2 = paddle.distribution.Laplace(paddle.to_tensor([1.0]), paddle.to_tensor([0.5])) >>> m1.kl_divergence(m2) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.04261160]) r?)r rr:r expr9)r"other var_ratiotterm1term2s r$ kl_divergenceLaplace.kl_divergences|RKK$**, JJtxx%))+ ,fjj!djj99A=L 9%}q  r&)r r )r float | Tensorr rnreturnNone)ror)r5rnroztuple[Tensor, Tensor, Tensor])r5rnror)rz Sequence[int]ror)ror\)rgr ror)__name__ __module__ __qualname____firstlineno____doc____annotations__r!propertyr)r,r1r6r<r@rGrMrSrRrYrl__static_attributes__ __classcell__)r#s@r$r r s> K M)<%%""""!#! &!:";H.6%N KD-/'0.0 B(.!.!r&r ) __future__rrtypingrnumpyr]r paddle.baserpaddle.distributionrcollections.abcrr Distributionr rr&r$rs9#  !,(N!l''N!r&