Αi?SSKJr SSKrSSKJr SSKJr SSKrSSKJ r SSK J r \(a SSKJ r SSK Jr "S S \ R5rS S jrSS jrg)) annotationsN)Sequence) TYPE_CHECKING) convert_dtype) distribution)Tensor) _DTypeLiteralc^\rSrSr%SrS\S'S\S'S\S'S\S'S \S 'SSU4S jjjr\SS j5r\SS j5r /4SSjjr /4SSjjr SSjr SSjr SSjrSSjrSrU=r$)MultivariateNormala4 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 dtypec>[R"5Ul[U[[ 45(a![R "U/URS9nO[UR5UlUR5S:aURS5nSUl SUl SUl USLUSL-USL-S:wa [S5eUbUR5S:a [S5e[R"X@RS9n[R"UR SSUR SS5nUR#/UQUR SPUR SP5Ul GOLUbUR5S:a [S 5e[R"X RS9n[R"UR SSUR SS5nUR#/UQUR SPUR SP5Ul OUR5S:a [S 5e[R"X0RS9n[R"UR SSUR SS5nUR#/UQUR SPUR SP5Ul UR#/UQSP5UlUR$R SSnUbX@lO8Ub%[R(R+U5UlO[-U5Ul[.TU]aXV5 g) 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/python3.13/site-packages/paddle/distribution/multivariate_normal.pyr+MultivariateNormal.__init__esE--/ cE3< ( (""C5 ;C&syy1DJ 779q=++d#C!% $ T )j.D E D (  f   !~~!# = ZzzBJ 00  "%syy"~K)//J+Jz//3JZ5E5Eb5IJDO * $$&* =!' ,=ZZ P  00!'',ciinK&7%=%= %++B/&++B/&D " ##%) = &{{+;::N  00 &&s+SYYs^K%5$;$; $**2.%**2.%D !::0 0R01hhnnRS)  !-7 *  *-3]]-C-C!.D *.E .D * 2cUR$)zLMean of Multivariate Normal distribution. Returns: Tensor: mean value. )r r,s r0meanMultivariateNormal.means xxr2c[R"UR5RS5R UR UR -5$)zTVariance of Multivariate Normal distribution. Returns: Tensor: variance value. r)rsquarer&sumr% _batch_shape _event_shaper4s r0varianceMultivariateNormal.variances? MM$88 9 SW VD%%(9(99 : r2c[R"5 URU5sSSS5 $!,(df  g=f)aGenerate Multivariate Normal samples of the specified shape. The final shape would be ``sample_shape + batch_shape + event_shape``. Args: shape (Sequence[int], optional): Prepended shape of the generated samples. Returns: Tensor, Sampled data with shape `sample_shape` + `batch_shape` + `event_shape`. The data type is the same as `self.loc`. N)rno_gradrsample)r,r$s r0sampleMultivariateNormal.samples&^^ <<&  s1 ?c^[U[5(d [S5eURU5n[R "[R "US9URS9nUR[R"URURS55RS5-$)r?z%sample shape must be Sequence object.)r$rr) rr TypeError _extend_shaperr"normalrr matmulr& unsqueezesqueeze)r,r$ output_shapeepss r0rAMultivariateNormal.rsamples%**CD D))%0 kk&--l;4::Nxx&--  * *CMM",= '"+ r2ct[R"XRS9nXR- n[ UR U5nUR R SSS9R5RS5nSURS[R"S[R-5-U--U- $)zLog probability density function. Args: value (Tensor): The input tensor. Returns: Tensor: log probability. The data type is the same as `self.loc`. rrraxis1axis2grr) rr"rr batch_mahalanobisr&diagonallogr9r;mathpi)r,valuediffM half_log_dets r0log_probMultivariateNormal.log_probs E4xx d< MM  + +  + + 5 5h ? MM   5 XBbX ) SW  (  + +TXX -A    [#4#4Q#778 9 r2)r&rrr rr)NNN)r zfloat | Tensorrrrrrr)returnr)r$z Sequence[int]rur)rWrrur)rlr rur)__name__ __module__ __qualname____firstlineno____doc____annotations__r+propertyr5r<rBrAr[r_rers__static_attributes__ __classcell__)r/s@r0r r s?B K$$##  ,0*.$( U3 U3)U3( U3 " U3U3n    -/ '.0" . 0/<7 7 r2r c[RR[R"US55n[R"US5n[ [ [ UR555nUSUSsUS'US'[R"X#5n[R"URSURS9n[RRXESS9nU$)zConvert precision matrix to scale tril matrix Args: P (Tensor): input precision matrix Returns: Tensor: scale tril matrix )rrrrrFupper) rr'r(fliprhrircr$rjeyertriangular_solve)PLftmproL_invIdLs r0r)r)is    Ax 8 9B ++b( #CE#cii.)*H!)"x|HRL(2,   S +E AGGBKqww /B &&u&>A Hr2cURSnURSSn[U5nUR5S- nXE- nXe-nUSU--nURSUn [URSSURUS5HupXU -U 4- n M X4- n UR U 5n[ [ U55[ [ XhS55-[ [ US-US55-U/-n URU 5nUR SX"45n UR SU RSU45nURS5n[RRXSS 9RS5RS5nUR5nUR URSS5n[ [ U55n[ U5HnUUU-UU-/- nM URU5nUR U5$) 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)rrrFr)r$rcrzipr rhrirjrr'rpowr9t)bLbxnbx_batch_shape bx_batch_dims bL_batch_dimsouter_batch_dimsold_batch_dimsnew_batch_dims bx_new_shapesLsx permute_dimsflat_Lflat_x flat_x_swapM_swaprY permuted_Mpermute_inv_dimsi reshaped_Ms r0rRrR|s  AXXcr]N'MFFHqLM$4%5N%M(99N88--.LbhhsmRXX.>r%BCr2& DDL L !B U# $% u%q9 : ; u%)>1= > ?    l #B ZZQ #F ZZV\\!_a0 1F""9-K &&v%&H Q R  A288CR=)JE"234 = !-1>A3EFF"%%J   n --r2)rrrur)rrrrrur) __future__rrUcollections.abcrtypingrrpaddle.base.data_feederrpaddle.distributionrrpaddle._typing.dtype_liker Distributionr r)rRr2r0rsD# $ 1,7I 22I X  &7.r2