\;j{nddlZddlmZddlmZddlmZddlmZGddejZ d dZ y) N)check_variable_and_dtype) LayerHelper)exponential_family)in_dynamic_modecreZdZdZfdZedZedZd dZdZ dZ dZ ed Z d Z xZS) Dirichletab Dirichlet distribution with parameter "concentration". The Dirichlet distribution is defined over the `(k-1)-simplex` using a positive, lenght-k vector concentration(`k > 1`). The Dirichlet is identically the Beta distribution when `k = 2`. For independent and identically distributed continuous random variable :math:`\boldsymbol X \in R_k` , and support :math:`\boldsymbol X \in (0,1), ||\boldsymbol X|| = 1` , The probability density function (pdf) is .. math:: f(\boldsymbol X; \boldsymbol \alpha) = \frac{1}{B(\boldsymbol \alpha)} \prod_{i=1}^{k}x_i^{\alpha_i-1} where :math:`\boldsymbol \alpha = {\alpha_1,...,\alpha_k}, k \ge 2` is parameter, the normalizing constant is the multivariate beta function. .. math:: B(\boldsymbol \alpha) = \frac{\prod_{i=1}^{k} \Gamma(\alpha_i)}{\Gamma(\alpha_0)} :math:`\alpha_0=\sum_{i=1}^{k} \alpha_i` is the sum of parameters, :math:`\Gamma(\alpha)` is gamma function. Args: concentration (Tensor): "Concentration" parameter of dirichlet distribution, also called :math:`\alpha`. When it's over one dimension, the last axis denotes the parameter of distribution, ``event_shape=concentration.shape[-1:]`` , axes other than last are condsider batch dimensions with ``batch_shape=concentration.shape[:-1]`` . Examples: .. code-block:: python >>> import paddle >>> dirichlet = paddle.distribution.Dirichlet(paddle.to_tensor([1., 2., 3.])) >>> print(dirichlet.entropy()) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, -1.24434423) >>> print(dirichlet.prob(paddle.to_tensor([.3, .5, .6]))) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 10.80000019) c|jdkr td||_t||j dd|j ddy)Nz:`concentration` parameter must be at least one dimensional)dim ValueError concentrationsuper__init__shape)selfr __class__s fG:\00. PROJECTS\API\Inventory\templateJSON\kerjaOCR\Lib\site-packages\paddle/distribution/dirichlet.pyrzDirichlet.__init__GsW     "L + ,,Sb1=3F3Frs3KLcV|j|jjddz S)zbMean of Dirichelt distribution. Returns: Mean value of distribution. r Tkeepdim)rsumrs rmeanzDirichlet.meanPs+!!D$6$6$:$:2t$:$LLLrc|jjdd}|j||jz z|jd|dzzz S)zjVariance of Dirichlet distribution. Returns: Variance value of distribution. r Trr )rrpow)rconcentration0s rvariancezDirichlet.varianceYsZ++//D/A""nt7I7I&IJ   q !^a%7 8  rct|tr|n t|}t|jj |j |S)zSample from dirichlet distribution. Args: shape (Sequence[int], optional): Sample shape. Defaults to empty tuple. ) isinstancetuple _dirichletrexpand _extend_shape)rrs rsamplezDirichlet.samplees? $E51uU|$,,33D4F4Fu4MNOOrcJtj|j|S)zProbability density function(PDF) evaluated at value. Args: value (Tensor): Value to be evaluated. Returns: PDF evaluated at value. )paddleexplog_probrvalues rprobzDirichlet.probnszz$--.//rc&tj||jdz zjdtj|jjdztj|jjdz S)zpLog of probability densitiy function. Args: value (Tensor): Value to be evaluated. ?r )r)logrrlgammar,s rr+zDirichlet.log_probystZZ $"4"4s": ; @ @ DmmD..22267 8mmD../33B7 8 rc|jjd}|jjd}tj|jjdtj|z ||z tj |zz |jdz tj |jzjdz S)zbEntropy of Dirichlet distribution. Returns: Entropy of distribution. r r0)rrrr)r2digamma)rrks rentropyzDirichlet.entropys ++//3    $ $R ( MM$,, - 1 1" 5mmN+ ,>!V^^N%CC D##c)V^^Dr^s1<02,E="44E=Pr