o * i?@sddlmZddlZddlmZddlmZddlZddlm Z ddl m Z er4ddlm Z ddl mZGd d d e jZdddZdddZdS)) annotationsN)Sequence) TYPE_CHECKING) convert_dtype) distribution)Tensor) _DTypeLiteralcseZdZUdZded<ded<ded<ded<ded < d#d$fd d Zed%ddZed%ddZgfd&ddZ gfd&ddZ d'ddZ d'ddZ d%ddZ d(d!d"ZZS))MultivariateNormala The Multivariate Normal distribution is a type multivariate continuous distribution defined on the real set, with parameter: `loc` and any one of the following parameters characterizing the variance: `covariance_matrix`, `precision_matrix`, `scale_tril`. Mathematical details The probability density function (pdf) is .. math:: p(X ;\mu, \Sigma) = \frac{1}{\sqrt{(2\pi)^k |\Sigma|}} \exp(-\frac{1}{2}(X - \mu)^{\intercal} \Sigma^{-1} (X - \mu)) In the above equation: * :math:`X`: is a k-dim random vector. * :math:`loc = \mu`: is the k-dim mean vector. * :math:`covariance_matrix = \Sigma`: is the k-by-k covariance matrix. Args: loc(int|float|Tensor): The mean of Multivariate Normal distribution. If the input data type is int or float, the data type of `loc` will be convert to a 1-D Tensor the paddle global default dtype. covariance_matrix(Tensor|None): The covariance matrix of Multivariate Normal distribution. The data type of `covariance_matrix` will be convert to be the same as the type of loc. precision_matrix(Tensor|None): The inverse of the covariance matrix. The data type of `precision_matrix` will be convert to be the same as the type of loc. scale_tril(Tensor|None): The cholesky decomposition (lower triangular matrix) of the covariance matrix. The data type of `scale_tril` will be convert to be the same as the type of loc. Examples: .. code-block:: python >>> import paddle >>> from paddle.distribution import MultivariateNormal >>> paddle.set_device("cpu") >>> paddle.seed(100) >>> rv = MultivariateNormal(loc=paddle.to_tensor([2.,5.]), covariance_matrix=paddle.to_tensor([[2.,1.],[1.,2.]])) >>> print(rv.sample([3, 2])) Tensor(shape=[3, 2, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[[-0.00339603, 4.31556797], [ 2.01385283, 4.63553190]], [[ 0.10132277, 3.11323833], [ 2.37435842, 3.56635118]], [[ 2.89701366, 5.10602522], [-0.46329355, 3.14768648]]]) >>> print(rv.mean) Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [2., 5.]) >>> print(rv.variance) Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=True, [1.99999988, 2. ]) >>> print(rv.entropy()) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 3.38718319) >>> rv1 = MultivariateNormal(loc=paddle.to_tensor([2.,5.]), covariance_matrix=paddle.to_tensor([[2.,1.],[1.,2.]])) >>> rv2 = MultivariateNormal(loc=paddle.to_tensor([-1.,3.]), covariance_matrix=paddle.to_tensor([[3.,2.],[2.,3.]])) >>> print(rv1.kl_divergence(rv2)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.55541301) rloc Tensor | Nonecovariance_matrixprecision_matrix scale_trilrdtypeNfloat | Tensorcs<t|_t|ttfrtj|g|jd}nt|j|_|dkr'| d}d|_ d|_ d|_ |du|du|dudkrBt d|dur{|dkrPt dtj||jd}t|jdd|jdd}|g||jd|jd|_ nm|dur|dkrt d tj||jd}t|jdd|jdd}|g||jd|jd|_ n4|dkrt d tj||jd}t|jdd|jdd}|g||jd|jd|_ |g|d|_|jjdd}|dur||_n|durtj||_nt||_t||dS) Nr)rzTExactly one of covariance_matrix or precision_matrix or scale_tril may be specified.zZscale_tril matrix must be at least two-dimensional, with optional leading batch dimensionszZcovariance_matrix must be at least two-dimensional, with optional leading batch dimensionszYprecision_matrix must be at least two-dimensional, with optional leading batch dimensions)paddleZget_default_dtyper isinstancefloatintZ to_tensorrdimreshaper r r ValueErrorcastZbroadcast_shapeshapeexpandr _unbroadcasted_scale_trillinalgcholeskyprecision_to_scale_trilsuper__init__)selfr r r rZ batch_shapeZ event_shape __class__s/home/app/PaddleOCR-VL-test/.venv_paddleocr/lib/python3.10/site-packages/paddle/distribution/multivariate_normal.pyr%es         zMultivariateNormal.__init__returncCs|jS)zdMean of Multivariate Normal distribution. Returns: Tensor: mean value. )r r&r)r)r*meanszMultivariateNormal.meancCs t|jd|j|jS)zlVariance of Multivariate Normal distribution. Returns: Tensor: variance value. r)rZsquarer sumr _batch_shape _event_shaper,r)r)r*variances zMultivariateNormal.variancer Sequence[int]cCs6t ||WdS1swYdS)Generate Multivariate Normal samples of the specified shape. The final shape would be ``sample_shape + batch_shape + event_shape``. Args: shape (Sequence[int], optional): Prepended shape of the generated samples. Returns: Tensor, Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`. The data type is the same as `self.loc`. N)rZno_gradrsample)r&rr)r)r*samples $zMultivariateNormal.samplecCsTt|ts td||}tjtj|d|jd}|jt |j | d dS)r3z%sample shape must be Sequence object.)rrr) rr TypeErrorZ _extend_shaperrnormalrr matmulr Z unsqueezeZsqueeze)r&rZ output_shapeZepsr)r)r*r4s   zMultivariateNormal.rsamplevaluecCsftj||jd}||j}t|j|}|jjdddd}d|j dt dt j ||S)zLog probability density function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability. The data type is the same as `self.loc`. rrrZaxis1Zaxis2grr) rrrr batch_mahalanobisr diagonallogr.r0mathpi)r&r9diffM half_log_detr)r)r*log_probs   zMultivariateNormal.log_probcCst||S)zProbability density function. Args: value (Tensor): The input tensor. Returns: Tensor: probability. The data type is the same as `self.loc`. )rexprC)r&r9r)r)r*probs zMultivariateNormal.probcCs^|jjdddd}d|jddtdtj|}t|jdkr)|S| |jS)aShannon entropy in nats. The entropy is .. math:: \mathcal{H}(X) = \frac{n}{2} \log(2\pi) + \log {\det A} + \frac{n}{2} In the above equation: * :math:`\Omega`: is the support of the distribution. Returns: Tensor, Shannon entropy of Multivariate Normal distribution. The data type is the same as `self.loc`. rrr:?rg?r) r r<r=r.r0r>r?lenr/r)r&rBHr)r)r*entropys  zMultivariateNormal.entropyothercCs|j|jkr|j|jkrtd|jjdddd}|jjdddd}ttt |jj }|d|d|d<|d<t |j|j |}t |j|j |}t j||jdddd}|t|j|j|j7}||d||jdS)a^The KL-divergence between two poisson distributions with the same `batch_shape` and `event_shape`. The probability density function (pdf) is .. math:: KL\_divergence(\lambda_1, \lambda_2) = \log(\det A_2) - \log(\det A_1) -\frac{n}{2} +\frac{1}{2}[tr [\Sigma_2^{-1} \Sigma_1] + (\mu_1 - \mu_2)^{\intercal} \Sigma_2^{-1} (\mu_1 - \mu_2)] Args: other (MultivariateNormal): instance of Multivariate Normal. Returns: Tensor, kl-divergence between two Multivariate Normal distributions. The data type is the same as `self.loc`. zmKL divergence of two Multivariate Normal distributions should share the same `batch_shape` and `event_shape`.rrr:rFr)r/r0rr r<r=r.listrangerGrrr8 transposer!Zsolver;r )r&rJZhalf_log_det_1Zhalf_log_det_2new_permZ cov_mat_1Z cov_mat_2Z expectationr)r)r* kl_divergence/sJ     z MultivariateNormal.kl_divergence)NNN)r rr r r r rr )r+r)rr2r+r)r9rr+r)rJr r+r)__name__ __module__ __qualname____doc____annotations__r%propertyr-r1r5r4rCrErIrO __classcell__r)r)r'r*r s* AW      r Prr+cCstjt|d}t|d}ttt|j}|d|d|d<|d<t||}tj |jd|j d}tjj ||dd}|S)zConvert precision matrix to scale tril matrix Args: P (Tensor): input precision matrix Returns: Tensor: scale tril matrix )rrrrrFupper) rr!r"fliprKrLrGrrMeyertriangular_solve)rWZLftmprNZL_invZIdLr)r)r*r#is  r#bLbxcCs|jd}|jdd}t|}|d}||}||}|d|}|jd|} t|jdd|j|dD] \} } | | | | f7} q:| |f7} || }tt|tt||dtt|d|d|g} || }|d||f} |d| jd|f}|d}tj j | |dd  d d}| }||jdd}tt|}t|D] }|||||g7}q||}||S) aa Computes the squared Mahalanobis distance of the Multivariate Normal distribution with cholesky decomposition of the covariance matrix. Accepts batches for both bL and bx. Args: bL (Tensor): scale trial matrix (batched) bx (Tensor): difference vector(batched) Returns: Tensor: squared Mahalanobis distance rNrrrr)rrrFrX)rrGrziprrKrLrMrr!r\powr.t)r_r`nZbx_batch_shapeZ bx_batch_dimsZ bL_batch_dimsZouter_batch_dimsZold_batch_dimsZnew_batch_dimsZ bx_new_shapeZsLsxZ permute_dimsZflat_LZflat_xZ flat_x_swapZM_swaprAZ permuted_MZpermute_inv_dimsiZ reshaped_Mr)r)r*r;|sJ   &        r;)rWrr+r)r_rr`rr+r) __future__rr>collections.abcrtypingrrZpaddle.base.data_feederrZpaddle.distributionrrZpaddle._typing.dtype_liker Distributionr r#r;r)r)r)r*s        N