Αi5SSKJr SSKrSSKrSSKJr SSKJr SSKJ r J r SSK r SSK J r Jr SSKJr SSKJr SS KJr SS KJr \ (a SS K Jr SS KJr S /rSrSSjrSSjrSSjrSSSjjr"SS \R@5r!g)) annotationsN)Sequence)reduce) TYPE_CHECKINGLiteral) check_type convert_dtype)Variable) distribution)Beta)in_dynamic_mode)Tensor) _DTypeLiteral LKJCholeskycp[R"[RURS9n[R "SUS-URS9n[R "URS5SU- S- -5n[R"USS9nXS- -S- [R"U5-U-$)zO Computes the multivariate log gamma function for input `a` and dimension `p`. dtypeaxis) paddle to_tensormathpirarangelgamma unsqueezesumlog)aprj gammaln_terms gammaln_sums `/var/www/html/banglarbhumi/venv/lib/python3.13/site-packages/paddle/distribution/lkj_cholesky.pymvlgammar)%s   $'' 1B aQagg.AMM!++b/QUaK"?@M**]4K QK!Ovzz"~ - ;;c[R"X4SS9n[R"X!S9n[R"USS9upEUR 5UR 54$)zc Returns the indices of the lower triangular part of an n x n matrix, including the k-th diagonal. int32rdiagonalT)as_tuple)ronestrilnonzeroflatten)nk full_matrix tril_matrixrowscolss r( tril_indicesr:0sM++qfG4K++k6K d;JD <<>4<<> ))r*c[R"[R"U5US9n[R"XR S55nU$)zt Extracts the lower triangular part of the input matrix or batch of matrices `x`, including the specified diagonal. r-bool)rr1 ones_like masked_selectastype)xr. tril_mask tril_elementss r(matrix_to_trilrC:s@ F,,Q/(CI((,<,rQ) matrW out_shaper4r8r9rAvec_lenvecs r(tril_matrix_to_vecrjjs  #2I " A byDI6$'>rd"QUG2NOOq!16==3CDJD t#IxAHqL)Q.G I##Iyy9I   s . 6 6y AC Jr*c^\rSrSr%SrS\S'S\S'S\S'S \S 'SSU4S jjjrSS jrSS jr/4SSjjr SSjr Sr U=r $)ra. The LKJCholesky class represents the LKJ distribution over Cholesky factors of correlation matrices. This class implements the LKJ distribution over Cholesky factors of correlation matrices, as described in Lewandowski, Kurowicka, and Joe (2009). It supports two sampling methods: "onion" and "cvine". Args: dim (int): The dimension of the correlation matrices. concentration (float, optional): The concentration parameter of the LKJ distribution. Default is 1.0. sample_method (str, optional): The sampling method to use, either "onion" or "cvine". Default is "onion". Example: .. code-block:: pycon >>> import paddle >>> dim = 3 >>> lkj = paddle.distribution.LKJCholesky(dim=dim) >>> sample = lkj.sample() >>> sample.shape paddle.Size([3, 3]) r concentrationrrintrSLiteral['onion', 'cvine'] sample_methodc >[5(dl[US[[[R R 4S5 [US[[[[[R R 4S5 URU5(a!X l [UR5Ul O2URU5uUl [R"5Ul XlUR S:d[#SUS35e[%UR [5(d['SUS35e[5(a3[R("URS:5(d [#S 5eX0lURR,nX4nURS UR S- --n[R."UR S - URRS 9nUS :Xab[R0"[R2"SURS 9U/5nUS -nUR5S5S U-- n [7X5UlOuUS:Xad[;[R<"S U-UR S - UR S - /55n UR5S5U - n [7X5UlO [#S5e[>T U]XE5 g)NrSrrmrz3Expected dim greater than or equal to 2. Found dim=.z)Expected dim to be an integer. Found dim=rz,The arg of `concentration` must be positive.?rronion)rrcvinez-`method` should be one of 'cvine' or 'onion'.)!r rrnr rpirValuefloatlisttuple_validate_argsrmr r _to_tensorget_default_dtyperSrd isinstance TypeErrorallrprFrrMrOr r _betarCresuper__init__) selfrSrmrp batch_shape event_shape marginal_concoffset beta_conc1 beta_conc0 offset_tril beta_conc __class__s r(rLKJCholesky.__init__sh   h 0 01   eXvzz/?/?@     } - -!. &}':':;DJ#'??=#A T 113DJxx1}EcU!L DHHc**GuANO O   ::d001455 !OPP*((.. j **SDHHqL-AA  HHqL$$**  G #]]d&,,7@F #J&004sV|CJj5DJ g %(##C&L488a<A2NOK&//3kAIi3DJLM M 2r*cURRU5RS5n[R"UR U5UR S9RS5nX3RSSS9- nUSSS2SS24n/[URSS5QSPURP7n[R"XdR S 9n[R"Xu/SS 9n[R"U5U-n[R"UR 5R n [R""S[R$"US -SS 9- U S 9R5n U[R&"U 5- nU$) zGenerate a sample using the "onion" method. Args: sample_shape (tuple): The shape of the samples to be generated. Returns: w (Tensor): The Cholesky factor of the sampled correlation matrix. rrT)rkeepdim.rNrcrErr)min)rsampler rrandn _extend_shaperr1normrzrFrSrOrMsqrtfinfotinyclipr! diag_embed) rrVyu_normal u_hypersphereu_hypersphere_other zero_shapezero_rowweps diag_elemss r(_onionLKJCholesky._onionsC JJ  l + 5 5b 9<<   | ,AGG $r(  !==b$=#GG ,CQJ7Du]00"56DD488D <!>CHMMO  V  z **r*cURRU5RS5nSU-S- nURS:XaURS5nURURS- -S-nU[ [ R US5-n[URR5S:waXPRRS-nURU45n[UURUUUS5n[R"UR5Rn[R "USU-SU- S9nUS-n[R""[R$"SU- 5SS9n SS/U R&S- -SS/-n [R(R*R-U SS S24U S S S 9n U[R."URSURS5- nX{-nU$) zGenerate a sample using the "cvine" method. Args: sample_shape (tuple): The shape of the samples to be generated. Returns: r (Tensor): The Cholesky factor of the sampled correlation matrix. rrrrcr)rmax)rS.Nconstant?)padmodevalue)rrr rSrrGrHlenrmrFrQrarrrrrcumprodrndimnn functionalreye) rrV beta_samplepartial_correlationrTrUrrzz1m_cumprod_sqrt pad_widthz1m_cumprod_sqrt_shifteds r(_cvineLKJCholesky._cvinesjj'' 5??C +o1 88q="5"?"?"C 88txx!|,1 6(,, a#HH t!!'' (A - //55b9 9M199=:JK0  HH      ll;,,-22 KK+"s(!c' K qD!>>&++a!e*<"EF.33a78Aq6A #)99#7#7#;#; S#2#X & $<$   VZZ  % %b )+>+D+DR+H    (r*cx[U[5(d [S5eURS:XaUR U5nOUR U5n[ U5nURURR5 URURUR/5 URU5$)z6Generate a sample using the specified sampling method.z%sample shape must be Sequence object.rt) r~rrrprrryextendrmrFrSrQ)rrVresrYs r(rLKJCholesky.sample?s,11CD D    (++l+C++l+CL) D..445TXXtxx01{{<((r*cb[R"USSSS9SSS24n[R"SURS-URR S 9nSURS- R S5-UR-U- n[R"U[R"U5-SS 9nURS- nURS U--n[R"U5U-n[US - U5nS U-[R"[R5-n X-U- n XJ- $) aUCompute the log probability density of the given Cholesky factor under the LKJ distribution. Args: value (Tensor): The Cholesky factor of the correlation matrix for which the log probability density is to be computed. Returns: log_prob (Tensor): The log probability density of the given Cholesky factor under the LKJ distribution. rrrc)raxis1axis2.rNrrrrs) rr.rrSrmrr r!r"rr)rr) rrrorderunnormalized_log_pdfdm1alpha denominator numerator pi_constantnormalize_terms r(log_probLKJCholesky.log_probOs__U1BbI G  aAT5G5G5M5MNT''!+66r::TXXEM &zz FJJz* *  hhl""S3Y.mmE*S0 US[#. Ci$((477"33 %0;>#44r*)rrmrSrrp)rrrt)rSrnrmrxrproreturnNone)rVz Sequence[int]rr)rrrr) __name__ __module__ __qualname____firstlineno____doc____annotations__rrrrr__static_attributes__ __classcell__)rs@r(rrs,  H,,"3: B3 B3B31 B3  B3B3H$L7r46) #5#5r*)r)r)rfrrWrnrr)" __future__rrrGcollections.abcr functoolsrtypingrrrpaddle.base.data_feederrr paddle.base.frameworkr paddle.distributionr paddle.distribution.betar paddle.frameworkr rpaddle._typing.dtype_liker__all__r)r:rCrarj Distributionrrr*r(rsr# $) =*,),7 /<*DE$N,r5,++r5r*