\;j2^ddlZddlZddlZddlmZddlmZGddejZ y)N) framework) distributionceZdZdZfdZedZedZedZdZ dZ dZ d Z d Z dd Zd Zd ZdZxZS)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) ct|tjtjfst dt |t|tjtjfst dt |t|tjrtjd|}t|tjrtjd|}t|jdkDst|jdkDr>|j|jk(r%tj||g\|_ |_n||c|_ |_t|A|jjy)Nz/Expected type of loc is Real|Variable, but got z1Expected type of scale is Real|Variable, but got shape fill_valuer) isinstancenumbersRealrVariable TypeErrortypepaddlefulllenr dtypebroadcast_tensorslocscalesuper__init__)selfrr __class__s dG:\00. PROJECTS\API\Inventory\templateJSON\kerjaOCR\Lib\site-packages\paddle/distribution/laplace.pyrzLaplace.__init__8s# i.@.@ABA$s)M %',, 0B0B!CDCDK=Q  c7<< (++B37C eW\\ *KKbU;E  q C NQ$6 II $#)#;#;S%L#I DHdj#& DHdj (c|jS)zTMean of distribution. Returns: Tensor: The mean value. )rrs rmeanz Laplace.meanRs xxrc d|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?)rr s rstddevzLaplace.stddev[s $**$$rc8|jjdS)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 rvariancezLaplace.variancems {{q!!rcRt|tjrtjd|}|j |j j k7r*tj||j j }t|j jdkDs:t|jjdkDst|jdkDr1tj|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. rr r) r r rrrrrcastrr rr)rvaluerrs r_validate_valuezLaplace._validate_values eW\\ *KKbU;E ;;$**** *KKtzz'7'78E    !A %488>>"Q&5;;!# & 8 84::u-! C4::CE5  rc|j|\}}}tjd|z }|tj||z |z z S)aLog probability density/mass function. The log_prob is .. math:: log\_prob(value) = \frac{-log(2 * \sigma) - |value - \mu|}{\sigma} In the above equation: * :math:`loc = \mu`: is the location parameter. * :math:`scale = \sigma`: is the scale parameter. Args: value (Tensor|Scalar): The input value, can be a scalar or a tensor. Returns: Tensor: The log probability, whose data type is same with value. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> value = paddle.to_tensor(0.1) >>> m.log_prob(value) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -0.79314721) r%)r+rlogabs)rr*rr log_scales rlog_probzLaplace.log_probsM>!007UEZZE ** 6::eck2U:::rcLdtjd|jzzS)amEntropy of Laplace distribution. The entropy is: .. math:: entropy() = 1 + log(2 * \sigma) In the above equation: * :math:`scale = \sigma`: is the scale parameter. Returns: The entropy of distribution. Examples: .. code-block:: python >>> import paddle >>> m = paddle.distribution.Laplace(paddle.to_tensor(0.0), paddle.to_tensor(1.0)) >>> m.entropy() Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.69314718) r%)rr-rr s rentropyzLaplace.entropys 26::a$**n---rc|j|\}}}d||z jztj||z j |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) ?)r+signrexpm1r.)rr*rriterms rcdfz Laplace.cdfsj<!007UE s{  " #llUS[--//%78 9  U{rc|j|\}}}|dz }|||jztjd|j 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) r5)r+r6rlog1pr.)rr*rrterms ricdfz Laplace.icdfsR:!007UEs{Ud[[]*V\\"txxz/-JJJJrct|tr|n t|}tj5|j |cdddS#1swYyxYw)azGenerate samples of the specified shape. Args: shape(tuple[int]): The shape of generated samples. 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)r tuplerno_gradrsample)rr s rsamplezLaplace.sample"s:&$E51uU| ^^ <<&  s A  Ac |j}|j|}tj|t t j dd|dz zd|dz z |jj}|j|j|jztj|j zz S)azReparameterized sample. Args: shape(tuple[int]): The shape of generated samples. Returns: Tensor: A sample tensor that fits the Laplace distribution. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(2023) >>> m = paddle.distribution.Laplace(paddle.to_tensor([0.0]), paddle.to_tensor([1.0])) >>> m.rsample((1,)) # Laplace distributed with loc=0, scale=1 Tensor(shape=[1, 1], dtype=float32, place=Place(cpu), stop_gradient=True, [[1.31554604]]) r2r%g?)r minmaxr) _get_eps _extend_shaperuniformfloatnp nextafterrrrr6r<r.)rr epsrJs rrBzLaplace.rsample9s(mmo""5)..bll2q)*S1W4cAg ((..   xx$**w||~5 [[]N9    rcd}|jjtjk(s'|jjtjk(rd}|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<)rrrfloat64 complex128)rrNs rrHzLaplace._get_epsYs= HHNNfnn ,xx~~!2!22C rcF|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]) r2)rrr.rexpr-)rother var_ratiotterm1term2s r kl_divergencezLaplace.kl_divergencems~RKK$**, JJtxx%))+ ,fjj!djj99A=L 9%u}q  r)r)__name__ __module__ __qualname____doc__rpropertyr!r#r'r+r0r3r9r>rCrBrHrY __classcell__)rs@rrrs{>)4%%""""!6";H.6%N KD'. @(.!rr) r numpyrLr paddle.baserpaddle.distributionr Distributionrrrrrds* !,C!l''C!r