x-j?ddlmZddlZddlmZddlmZddlZddlm Z ddl m Z er ddlm Z ddl mZGd d e jZddZddZdS)) annotationsN)Sequence) TYPE_CHECKING) convert_dtype) distribution)Tensor) _DTypeLiteralceZdZUdZded<ded<ded<ded<ded < ddfd ZeddZeddZgfddZ gfddZ ddZ ddZ ddZ ddZxZS) 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_trilr dtypeNfloat | Tensorctj|_t|tt frtj|g|j}nt|j|_|dkr| d}d|_ d|_ d|_ |du|duz|duzdkrtd||dkrtdtj||j}tj|jdd|jdd}|g||jd|jd|_ nQ||dkrtd tj||j}tj|jdd|jdd}|g||jd|jd|_ n|dkrtd tj||j}tj|jdd|jdd}|g||jd|jd|_ |g|d|_|jjdd}|||_n;|%tj||_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)paddleget_default_dtyper isinstancefloatint to_tensorrdimreshaperrr ValueErrorcastbroadcast_shapeshapeexpandr _unbroadcasted_scale_trillinalgcholeskyprecision_to_scale_trilsuper__init__)selfr rrr batch_shape event_shape __class__s g/var/www/html/banglarbhumi/venv/lib/python3.11/site-packages/paddle/distribution/multivariate_normal.pyr+zMultivariateNormal.__init__es-// cE3< ( ( 2"C5 ;;;CC&sy11DJ 7799q==++d##C!% $ T )j.D E D (   f   !~~!## = ZtzBBBJ 0 "%sy"~K)//J+Jz/3JZ5Eb5IJDOO * $$&&** =!' ,=TZ P P P  0!',cinK&7%=%= %+B/&+B/&&D " " ##%%)) = &{+;4:NNN  0 &ss+SYss^K%5$;$; $*2.%*2.%%D !::0 0R011hnRSS)  !-7D * *  *-3]-C-C!..D * *.E ..D * k22222returnc|jS)zdMean of Multivariate Normal distribution. Returns: Tensor: mean value. )r r,s r0meanzMultivariateNormal.means xr1ctj|jd|j|jzS)zlVariance of Multivariate Normal distribution. Returns: Tensor: variance value. r)rsquarer&sumr% _batch_shape _event_shaper4s r0variancezMultivariateNormal.variances< M$8 9 9 SWW VD%(99 : : r1r$ Sequence[int]ctj5||cdddS#1swxYwYdS)Generate Multivariate Normal samples of the specified shape. The final shape would be ``sample_shape + batch_shape + event_shape``. Args: shape (Sequence[int], optional): Prepended shape of the generated samples. Returns: Tensor, Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`. The data type is the same as `self.loc`. N)rno_gradrsample)r,r$s r0samplezMultivariateNormal.samples^   ' '<<&& ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 's 6::c`t|tstd||}t jt j||j}|jt j |j | d dzS)r>z%sample shape must be Sequence object.)r$rr) rr TypeError _extend_shaperr"normalrr matmulr& unsqueezesqueeze)r,r$ output_shapeepss r0r@zMultivariateNormal.rsamples%** ECDD D))%00 k&-l;;;4:NNNx&-  *CMM",=,=  '"++ r1valuechtj||j}||jz }t |j|}|jddd}d|j dtjdtj zz|zz|z S)zLog probability density function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability. The data type is the same as `self.loc`. rrraxis1axis2grr) rr"rr batch_mahalanobisr&diagonallogr8r:mathpi)r,rKdiffM half_log_dets r0log_probzMultivariateNormal.log_probs E444tx d >  M  +  + 5 5h ? ?  M   9 5 5 XBbX ) ) SWW  (  +TX -A     [4#4Q#778 9 r1)NNN)r rrr rr rr )r2r)r$r<r2r)rKrr2r)rar r2r)__name__ __module__ __qualname____doc____annotations__r+propertyr5r;rAr@rXr[r`rm __classcell__)r/s@r0r r si??BKKK$$$$#### ,0*.$( U3U3U3U3U3U3U3nX    X  -/ ' ' ' ' '.0"    . 0 0 0 0////<7 7 7 7 7 7 7 7 r1r Prr2ctjtj|d}tj|d}t t t |j}|d|dc|d<|d<tj||}tj |jd|j }tj ||d}|S)zConvert precision matrix to scale tril matrix Args: P (Tensor): input precision matrix Returns: Tensor: scale tril matrix )rrrrrFupper) rr'r(fliprcrdr^r$reeyertriangular_solve)ruLftmpriL_invIdLs r0r)r)is    Ax 8 8 9 9B +b( # #CE#ci..))**H!)"x|HRL(2,  S( + +E AGBKqw / / /B &&ub&>>A Hr1bLbxc|jd}|jdd}t|}|dz }||z }||z}|d|zz}|jd|} t|jdd|j|dD]\} } | | | z| fz } | |fz } || }t t |t t ||dzt t |dz|dz|gz} || }|d||f} |d| jd|f}|d}tj | |d  d d}| }||jdd}t t |}t |D]}|||z||zgz }||}||S) aa Computes the squared Mahalanobis distance of the Multivariate Normal distribution with cholesky decomposition of the covariance matrix. Accepts batches for both bL and bx. Args: bL (Tensor): scale trial matrix (batched) bx (Tensor): difference vector(batched) Returns: Tensor: squared Mahalanobis distance rNrrrr)rrrFrw)r$r^rzipr rcrdrerr'r{powr8t)rrnbx_batch_shape bx_batch_dims bL_batch_dimsouter_batch_dimsold_batch_dimsnew_batch_dims bx_new_shapesLsx permute_dimsflat_Lflat_x flat_x_swapM_swaprV permuted_Mpermute_inv_dimsi reshaped_Ms r0rPrP|sy  AXcrc]N''MFFHHqLM$}4% 5N%M(99N8---.LbhssmRX.>r.A%BCC''Br2& QDL L ! !B U# $ $%% u%~q99 : : ; u%)>1== > > ?    l # #B ZZQ # #F ZZV\!_a0 1 1F""9--K &&v{%&HH Q R  A28CRC=))JE"23344 = ! !GG-1>A3EFF%%J   n - --r1)rurr2r)rrrrr2r) __future__rrScollections.abcrtypingrrpaddle.base.data_feederrpaddle.distributionrrpaddle._typing.dtype_liker Distributionr r)rPr1r0rs#""""" $$$$$$ 111111,,,,,,8777777I I I I I 2I I I X     &7.7.7.7.7.7.r1