zj3ddlmZddlZddlmZddlZddlZddlm Z ddl m Z er ddl m Z ddlmZGdd e jZdS) ) annotationsN) TYPE_CHECKING) framework) distribution)Sequence)TensorceZdZUdZded<ded<dfd Zedd Zedd Zedd Z ddZ ddZ ddZ ddZ ddZgfddZgfddZd dZd!dZxZS)"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) rlocscalefloat | TensorreturnNonecXt|tjtjt jjfstdt|t|tjtjt jjfstdt|t|tjrt j d|}t|tjrt j d|}t|j dkst|j dkr4|j |j kr$t j||g\|_|_n||c|_|_t#|jj dS)Nz/Expected type of loc is Real|Variable, but got z1Expected type of scale is Real|Variable, but got shape fill_valuer) isinstancenumbersRealrVariablepaddlepirValue TypeErrortypefulllenrdtypebroadcast_tensorsr r super__init__)selfr r __class__s k/lsinfo/ai/hellotax_ai/data_center/backend/venv/lib/python3.11/site-packages/paddle/distribution/laplace.pyr#zLaplace.__init__Bsx ', 2FJ4DE   M$s))MM  GL)"4fj6FG   QDKKQQ  c7< ( ( 8+B3777C eW\ * * <KbU;;;E   q C NNQ$6$6 I $ $#)#;S%L#I#I DHdjj#& DHdj (((((c|jS)zTMean of distribution. Returns: Tensor: The mean value. )r r$s r&meanz Laplace.mean`s xr'cd|jzS)zStandard deviation. The stddev is .. math:: stddev = \sqrt{2} * \sigma In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: The std value. g;f?)r r)s r&stddevzLaplace.stddevis $*$$r'c6|jdS)aVariance of distribution. The variance is .. math:: variance = 2 * \sigma^2 In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: Tensor: The variance value. )r,powr)s r&variancezLaplace.variance{s {q!!!r'valuetuple[Tensor, Tensor, Tensor]ct|tjrtjd|}|j|jjkrtj||jj}t|jj dks5t|j j dkst|j dkr&tj |j |j|g\}}}n|j |j}}|||fS)aHArgument dimension check for distribution methods such as `log_prob`, `cdf` and `icdf`. Args: value (Tensor|Scalar): The input value, which can be a scalar or a tensor. Returns: loc, scale, value: The broadcasted loc, scale and value, with the same dimension and data type. rrr) rrrrrr r castrrr r!)r$r1r r s r&_validate_valuezLaplace._validate_values eW\ * * <KbU;;;E ;$** * *Ktz'788E   ! !A % %48>""Q&&5;!## & 84:u-!! C4:CE5  r'c||\}}}tjd|z }|tj||z |z z S)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.)r5rlogabs)r$r1r r log_scales r&log_probzLaplace.log_probsR>!0077UEZE *** 6:eck22U:::r'c@dtjd|jzzS)amEntropy of Laplace distribution. The entropy is: .. math:: entropy() = 1 + log(2 * \sigma) In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: The entropy of distribution. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.entropy() Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.69314718) r.)rr7r r)s r&entropyzLaplace.entropys26:a$*n----r'c||\}}}d||z ztj||z  |z z}d|z S)aZCumulative 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) ?)r5signrexpm1r8)r$r1r r items r&cdfz Laplace.cdfst<!0077UE s{  "" #lUS[--///%788 9 Tzr'c||\}}}|dz }|||ztjd|zzz S)a`Inverse Cumulative distribution function. The icdf is .. math:: cdf^{-1}(value)= \mu - \sigma * sign(value - 0.5) * ln(1 - 2 * |value-0.5|) In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor): The value to be evaluated. Returns: Tensor: The cumulative probability of value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.icdf(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -1.60943794) r?)r5r@rlog1pr8)r$r1r r terms r&icdfz Laplace.icdfsZ:!0077UEs{Ud[[]]*V\"txxzz/-J-JJJJr'r Sequence[int]ct|tr|nt|}tj5||cdddS#1swxYwYdS)aGenerate 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$rs r&samplezLaplace.sample2s($E511CuU|| ^   ' '<<&& ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 'sAA #A c |}||}tj|t t jdd|dz zd|dz z |jj}|j|j | ztj | zz S)aReparameterized 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 r r r@rFr8)r$repsrUs r&rMzLaplace.rsampleJs*mmoo""5)).bl2q))**S1W4cAg (.     x$*w||~~5 [[]]N9 9    r'rVcvd}|jjtjks|jjtjkrd}|S)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 r rfloat64 complex128)r$rYs r&rSzLaplace._get_epsks6 HNfn , ,x~!222C r'otherc|j|jz }tj|j|jz }|jtj| |jz z|z|jz }tj|}||zdz S)aCalculate the KL divergence KL(self || other) with two Laplace instances. The kl_divergence between two Laplace distribution is .. math:: KL\_divergence(\mu_0, \sigma_0; \mu_1, \sigma_1) = 0.5 (ratio^2 + (\frac{diff}{\sigma_1})^2 - 1 - 2 \ln {ratio}) .. math:: ratio = \frac{\sigma_0}{\sigma_1} .. math:: diff = \mu_1 - \mu_0 In the above equation: * :math:`loc = \mu`: is the location parameter of self. * :math:`scale = \sigma`: is the scale parameter of self. * :math:`loc = \mu_1`: is the location parameter of the reference Laplace distribution. * :math:`scale = \sigma_1`: is the scale parameter of the reference Laplace distribution. * :math:`ratio`: is the ratio between the two distribution. * :math:`diff`: is the difference between the two distribution. Args: other (Laplace): An instance of Laplace. Returns: Tensor: The kl-divergence between two laplace distributions. Examples: .. code-block:: python >>> import paddle >>> m1 = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m2 = paddle.distribution.Laplace(paddle.to_tensor([1.0]), paddle.to_tensor([0.5])) >>> m1.kl_divergence(m2) Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True, [1.04261160]) r<)r rr8r expr7)r$r] var_ratiotterm1term2s r& kl_divergencezLaplace.kl_divergencessRK$*, Jtx%)+ , ,fj!dj999A=L 9%%u}q  r')r r r r rr)rr)r1r rr2)r1r rr)rrIrr)rrV)r]r rr)__name__ __module__ __qualname____doc____annotations__r#propertyr*r,r0r5r:r=rCrHrNrMrSrd __classcell__)r%s@r&r r s>KKKMMM))))))<X%%%X%""""X""!!!!:";";";";H....6%%%%N K K K KD-/'''''0.0     B(.!.!.!.!.!.!.!.!r'r ) __future__rrtypingrnumpyrWr paddle.baserpaddle.distributionrcollections.abcrr Distributionr rr'r&rss#"""""  !!!!!!,,,,,,((((((N!N!N!N!N!l'N!N!N!N!N!r'