Αi$SSKJr SSKJr SSKJr SSKrSSKJr SSK J r \(a SSKJ r SSK J r "S S \ R5rg) ) annotations)Sequence) TYPE_CHECKINGN) convert_dtype) distribution)Tensor) _DTypeLiteralc^\rSrSr%SrS\S'S\S'SU4SjjrSSjr\SS j5r \SS j5r /4SS jjr SS jr SS jr SSjrSSjrSSjrSrU=r$)Poissona! The Poisson distribution with occurrence rate parameter: `rate`. In probability theory and statistics, the Poisson distribution is the most basic discrete probability distribution defined on the nonnegative integer set, which is used to describe the probability distribution of the number of random events occurring per unit time. The probability mass function (pmf) is .. math:: pmf(x; \lambda) = \frac{e^{-\lambda} \cdot \lambda^x}{x!} In the above equation: * :math:`rate = \lambda`: is the mean occurrence rate. Args: rate(int|float|Tensor): The mean occurrence rate of Poisson distribution which should be greater than 0, meaning the expected occurrence times of an event in a fixed time interval. If the input data type is int or float, the data type of `rate` will be converted to a 1-D Tensor with paddle global default dtype. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import Poisson >>> paddle.set_device('cpu') >>> paddle.seed(100) >>> rv = Poisson(paddle.to_tensor(30.0)) >>> print(rv.sample([3])) Tensor(shape=[3], dtype=float32, place=Place(cpu), stop_gradient=True, [32., 27., 25.]) >>> print(rv.mean) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 30.) >>> print(rv.entropy()) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 3.11671519) >>> rv1 = Poisson(paddle.to_tensor([[30.,40.],[8.,5.]])) >>> rv2 = Poisson(paddle.to_tensor([[1000.,40.],[7.,10.]])) >>> print(rv1.kl_divergence(rv2)) Tensor(shape=[2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[864.80499268, 0. ], [0.06825146 , 1.53426409 ]]) rrater dtypec>[R"5UlURU5UlURR n[ TU]U5 gN)paddleget_default_dtyper _to_tensorr shapesuper__init__)selfr batch_shape __class__s [/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/poisson.pyrPoisson.__init__Ss=--/ OOD) iioo  %c[U[[45(a"[R"U/UR S9nU$[ UR 5UlU$)zQConvert the input parameters into tensors. Returns: Tensor: converted rate. r) isinstancefloatintr to_tensorrr)rr s rrPoisson._to_tensorZsK dUCL ) )##TF$**=D 'tzz2DJ rcUR$)z@Mean of poisson distribution. Returns: Tensor: mean value. r rs rmean Poisson.meangyyrcUR$)zHVariance of poisson distribution. Returns: Tensor: variance value. r%r&s rvariancePoisson.variancepr)rcf[U[5(d [S5e[U5n[UR5n[X-5n[ R "URUS9n[ R"5 [ R"U5sSSS5 $!,(df  g=f)aGenerate poisson samples of the specified shape. The final shape would be ``shape+batch_shape`` . Args: shape (Sequence[int], optional): Prepended shape of the generated samples. Returns: Tensor: Sampled data with shape `sample_shape` + `batch_shape`. z%sample shape must be Sequence object.)rN) rr TypeErrortuplerr broadcast_tor no_gradpoisson)rrr output_shape output_rates rsamplePoisson.sampleys{%**CD De D,,- U01 ))$))<H ^^ >>+.  s B"" B0c URUR5RSS[UR5--5nUR U5n[ R"U5U-RS5*n[ R"[ R"UR[ R"SURS95URS9n[ R"X45$)a#Shannon entropy in nats. The entropy is .. math:: \mathcal{H}(X) = - \sum_{x \in \Omega} p(x) \log{p(x)} In the above equation: * :math:`\Omega`: is the support of the distribution. Returns: Tensor: Shannon entropy of poisson distribution. The data type is the same as `rate`. rgr)_enumerate_bounded_supportr reshapelenrlog_probrexpsumcast not_equalr"rmultiply)rvaluesr?proposedmasks rentropyPoisson.entropys 00;CC D3t//00 0 ==(ZZ)H499!<<{{    6++CtzzB **   x..rc ^^[RR5(a[R"[R"T5[R "STR S95(a*[R"[R"T55O[R"TTR S9n[R"[R"TSU--SS95n[R"SUTR S9nU$U4SjnU4Sjn[RRR"[R"T5[R "STR S95UU5n[R"[R"TSU--SS95n[R"SUTR S9nU$)aBGenerate a bounded approximation of the support. Approximately view Poisson r.v. as a Normal r.v. with mu = rate and sigma = sqrt(rate). Then by 30-sigma rule, generate a bounded approximation of the support. Args: rate (float): rate of one poisson r.v. Returns: Tensor: the bounded approximation of the support ?rint32rcX>[R"[R"T55$r)rsqrtmaxr%sr true_func5Poisson._enumerate_bounded_support..true_funcs{{6::d#344rcB>[R"STRS9$)NrKr)rr"rr&sr false_func6Poisson._enumerate_bounded_support..false_funcs''4::>>r)r frameworkin_dynamic_mode greater_equalrPr"rrO ones_likerBarangestaticnncond)rr s_maxupperrErQrTs`` rr<"Poisson._enumerate_bounded_supportsY    + + - -''JJt$f&6&6s$**&M FJJt,-%%d$**= JJv{{4"u*+FM 5 ?MM$$))$$JJt$f&6&6s$**&M EJJv{{4"u*+FMrcd[R"XRS9n[R"URR5R n[R "UR*U[R"UR5--[R"US-5- U*S9$)zLog probability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability. The data type is the same as `rate`. rr;)neginf) rrBrfinfor eps nan_to_numloglgamma)rvaluerds rr?Poisson.log_probs E4ll499??+//   &**TYY//0-- *+4   rcL[R"URU55$)zProbability density/mass function. Args: value (Tensor): The input tensor. Returns: Tensor: probability. The data type is the same as `rate`. )rr@r?)rrhs rprob Poisson.probszz$--.//rc>URUR:wa [S5e[R"[R"UR UR 55nUR U5n[R"U5n[R"SX@RS9RSS[UR5--5nURU5nURU5n[R"U5Xg- -RS5$)aThe KL-divergence between two poisson distributions with the same `batch_shape`. The probability density function (pdf) is .. math:: KL\_divergence\lambda_1, \lambda_2) = \sum_x p_1(x) \log{\frac{p_1(x)}{p_2(x)}} .. math:: p_1(x) = \frac{e^{-\lambda_1} \cdot \lambda_1^x}{x!} .. math:: p_2(x) = \frac{e^{-\lambda_2} \cdot \lambda_2^x}{x!} Args: other (Poisson): instance of ``Poisson``. Returns: Tensor, kl-divergence between two poisson distributions. The data type is the same as `rate`. zOKL divergence of two poisson distributions should share the same `batch_shape`.rrr8r:)r ValueErrorrrPmaximumr r<rZrr=r>r?r@rA)rotherrate_max support_maxa_maxcommon_support log_prob_1 log_prob_2s r kl_divergencePoisson.kl_divergences2   u00 0a ::fnnTYY CD55h?  ;'q%zzBJJ D3t//00 0 ]]>2 ^^N3  :&**ABGGJJr)rr )r float | TensorreturnNone)r ryrzr)rzr)rz Sequence[int]rzr)rhrrzr)rpr rzr)__name__ __module__ __qualname____firstlineno____doc____annotations__rrpropertyr'r+r5rHr<r?rkrw__static_attributes__ __classcell__)rs@rr r ss1f L & -//(/:'R ( 0&K&Krr ) __future__rcollections.abcrtypingrrpaddle.base.data_feederrpaddle.distributionrrpaddle._typing.dtype_liker Distributionr rrrs8#$ 1,7|Kl''|Kr