
    Ǆg5                     4   d dl Z d dlZd dlmZ d dlmZmZ d dlZd dlmZ d dl	m
Z
 d dlmZ d dlmZ d dlmZ d d	lmZ d
gZ e j(                  d      Zdej,                  dedej,                  fdZdej,                  dej,                  fdZ G d d
e      Zy)    N)Number)OptionalUnion)nan)constraints)ExponentialFamily)_precision_to_scale_tril)lazy_property)_sizeWishart   xpreturnc                 p   | j                  |dz
  dz        j                         sJ d       t        j                  | j	                  d      t        j
                  || j                  | j                        j                  d      j                  | j                  dz         z
        j                  d      S )N   r   z/Wrong domain for multivariate digamma function.dtypedevicer   )gtalltorchdigamma	unsqueezearanger   r   divexpandshapesum)r   r   s     c/home/mcse/projects/flask_80/flask-venv/lib/python3.12/site-packages/torch/distributions/wishart.py
_mvdigammar#      s    44Q!  "U$UU"==	B
,,q
9
=
=a
@
G
GRW
X	Y 
c"g    c                 t    | j                  t        j                  | j                        j                        S )N)min)clampr   finfor   eps)r   s    r"   _clamp_above_epsr*      s&    77u{{177+//700r$   c            
       2    e Zd ZdZej
                  ej
                  ej                   ej                  d      dZej
                  Z	dZ
dZ	 	 	 	 ddeej                  ef   deej                     deej                     d	eej                     f fd
Zd fd	Zed        Zed        Zed        Zed        Zed        Zed        Z ej6                         fdZ ej6                         dfdedej                  fdZd Zd Z ed        Z!d Z" xZ#S )r   a  
    Creates a Wishart distribution parameterized by a symmetric positive definite matrix :math:`\Sigma`,
    or its Cholesky decomposition :math:`\mathbf{\Sigma} = \mathbf{L}\mathbf{L}^\top`

    Example:
        >>> # xdoctest: +SKIP("FIXME: scale_tril must be at least two-dimensional")
        >>> m = Wishart(torch.Tensor([2]), covariance_matrix=torch.eye(2))
        >>> m.sample()  # Wishart distributed with mean=`df * I` and
        >>>             # variance(x_ij)=`df` for i != j and variance(x_ij)=`2 * df` for i == j

    Args:
        df (float or Tensor): real-valued parameter larger than the (dimension of Square matrix) - 1
        covariance_matrix (Tensor): positive-definite covariance matrix
        precision_matrix (Tensor): positive-definite precision matrix
        scale_tril (Tensor): lower-triangular factor of covariance, with positive-valued diagonal
    Note:
        Only one of :attr:`covariance_matrix` or :attr:`precision_matrix` or
        :attr:`scale_tril` can be specified.
        Using :attr:`scale_tril` will be more efficient: all computations internally
        are based on :attr:`scale_tril`. If :attr:`covariance_matrix` or
        :attr:`precision_matrix` is passed instead, it is only used to compute
        the corresponding lower triangular matrices using a Cholesky decomposition.
        'torch.distributions.LKJCholesky' is a restricted Wishart distribution.[1]

    **References**

    [1] Wang, Z., Wu, Y. and Chu, H., 2018. `On equivalence of the LKJ distribution and the restricted Wishart distribution`.
    [2] Sawyer, S., 2007. `Wishart Distributions and Inverse-Wishart Sampling`.
    [3] Anderson, T. W., 2003. `An Introduction to Multivariate Statistical Analysis (3rd ed.)`.
    [4] Odell, P. L. & Feiveson, A. H., 1966. `A Numerical Procedure to Generate a SampleCovariance Matrix`. JASA, 61(313):199-203.
    [5] Ku, Y.-C. & Bloomfield, P., 2010. `Generating Random Wishart Matrices with Fractional Degrees of Freedom in OX`.
    r   )covariance_matrixprecision_matrix
scale_trildfTNr/   r,   r-   r.   c                 x   |d u|d uz   |d uz   dk(  sJ d       t        d |||fD              }|j                         dk  rt        d      t        |t              rTt        j                  |j                  d d       }t        j                  ||j                  |j                        | _        nCt        j                  |j                  d d |j                        }|j                  |      | _        |j                  dd  }| j                  j                  |d   dz
        j                         rt        d	| d
|d   dz
   d      ||j                  |dz         | _        n7||j                  |dz         | _        n||j                  |dz         | _        t'        j(                  |d   dz
        | j*                  d<   | j                  j-                  |d         j                         rt/        j0                  d       t2        
| i  |||       t7        t9        | j:                              D 	cg c]  }	|	dz    
 c}	| _        ||| _        n7|%t
        j@                  jC                  |      | _        ntE        |      | _        t
        jF                  jH                  jK                  | j                  jM                  d      t        jN                  | jP                  d   | j>                  j                  | j>                  j                        j                  |dz         z
        | _)        y c c}	w )Nr   zTExactly one of covariance_matrix or precision_matrix or scale_tril may be specified.c              3   $   K   | ]  }|| 
 y wN ).0r   s     r"   	<genexpr>z#Wishart.__init__.<locals>.<genexpr>Y   s      
} 
s   r   zSscale_tril must be at least two-dimensional, with optional leading batch dimensionsr   r   zValue of df=z( expected to be greater than ndim - 1 = .)r   r   r/   z]Low df values detected. Singular samples are highly likely to occur for ndim - 1 < df < ndim.validate_argsr   r/   )*nextdim
ValueError
isinstancer   r   Sizer    tensorr   r   r/   broadcast_shapesr   leanyr.   r,   r-   r   greater_thanarg_constraintsltwarningswarnsuper__init__rangelen_batch_shape_batch_dims_unbroadcasted_scale_trillinalgcholeskyr	   distributionschi2Chi2r   r   _event_shape
_dist_chi2)selfr/   r,   r-   r.   r9   parambatch_shapeevent_shaper   	__class__s             r"   rJ   zWishart.__init__M   s    "-*D2HID(
 	gf	g   
')9:F
 
 99;?e  b&!**U[["%56Kll2U[[NDG00Sb1A288LKii,DGkk"#&77::k"o)*..0rd"J;WY?[\K\J]]^_  !#ll;+ABDO*%*\\+2H%ID")$)LLx1G$HD!%0%=%=k"oPQ>Q%RT"77::k"o&**,MMo 	kO.3C8I8I4J.KLa!eHL!-7D**-2\\-B-BCT-UD*-EFV-WD*  --2277!!"%,,%%b)88>>99@@ &u,-. 8 	
 Ms   8L7c                 "   | j                  t        |      }t        j                  |      }|| j                  z   }| j
                  j                  |      |_        | j                  j                  |      |_        t        t        |            D cg c]  }|dz    
 c}|_
        d| j                  v r | j                  j                  |      |_        d| j                  v r | j                  j                  |      |_        d| j                  v r | j                  j                  |      |_        t        j                  j                   j#                  |j                  j%                  d      t        j&                  | j                  d   |j
                  j(                  |j
                  j*                        j                  |dz         z
        |_        t.        t        |c  || j                  d	
       | j2                  |_        |S c c}w )Nr   r,   r.   r-   r   r   r   r:   Fr8   )_get_checked_instancer   r   r?   rZ   rO   r   r/   rK   rL   rN   __dict__r,   r.   r-   rR   rS   rT   r   r   r   r   rV   rI   rJ   _validate_args)rW   rY   	_instancenew	cov_shaper   r[   s         r"   r   zWishart.expand   s   (()<jj-$"2"22	(,(F(F(M(Mi(X%,-23{3C-DEQU8E$--/$($:$:$A$A)$LC!4==(!__33I>CN.#'#8#8#?#?	#JC  ,,1166  $,,$$R(77==88?? &u,-. 7 	
 	gs$[$2B2BRW$X!00
/ Fs   Hc                 f    | j                   j                  | j                  | j                  z         S r2   )rO   r   rM   rU   rW   s    r"   r.   zWishart.scale_tril   s/    --44 1 11
 	
r$   c                     | j                   | j                   j                  dd      z  j                  | j                  | j                  z         S )Nr6   r   )rO   	transposer   rM   rU   rd   s    r"   r,   zWishart.covariance_matrix   sH     **,,66r2>?
&""T%6%66
7	8r$   c                 (   t        j                  | j                  d   | j                  j                  | j                  j
                        }t        j                  || j                        j                  | j                  | j                  z         S )Nr   )r   r   )	r   eyerU   rO   r   r   cholesky_solver   rM   )rW   identitys     r"   r-   zWishart.precision_matrix   sx    99b!11880066

 ##Hd.L.LMTT 1 11
 	
r$   c                 l    | j                   j                  | j                  dz         | j                  z  S )Nr   r   )r/   viewrM   r,   rd   s    r"   meanzWishart.mean   s+    ww||D--67$:P:PPPr$   c                     | j                   | j                  j                  d   z
  dz
  }t        ||dk  <   |j	                  | j
                  dz         | j                  z  S )Nr   r   r   rl   )r/   r,   r    r   rm   rM   )rW   factors     r"   modezWishart.mode   sY    41177;;a?!v{{{4,,v569O9OOOr$   c                     | j                   }|j                  dd      }| j                  j                  | j                  dz         |j                  d      t        j                  d||      z   z  S )Nr6   r   dim1dim2rl   r   z...i,...j->...ij)r,   diagonalr/   rm   rM   powr   einsum)rW   Vdiag_Vs      r"   variancezWishart.variance   sb    """-ww||D--67EE!Hu||$6GG
 	
r$   c                    | j                   d   }t        | j                  j                  |      j	                               j                  dd      }t        j                  ||d      \  }}t        j                  t        j                  |      | j                  z   t        ||dz
  z  dz        fz   |j                  |j                        |d||f<   | j                  |z  }||j                  dd      z  S )	Nr   r6   rs   )offsetr   r   r   .)rU   r*   rV   rsamplesqrt
diag_embedr   tril_indicesrandnr?   rM   intr   r   rO   rf   )rW   sample_shaper   noiseijchols          r"   _bartlett_samplingzWishart._bartlett_sampling   s    b! !OO##L1668

*"2*
& 	 !!!Qr21 ;;JJ|$t'8'88CQUa<P;RR++<<
c1ai
 --5dnnR,,,r$   r   r   c                    |"t         j                  j                         rdnd}t        j                  |      }| j	                  |      }| j
                  j                  |      }| j                  r|j                  | j                        }t         j                  j                         r~t        |      D ]n  }| j	                  |      }t        j                  |||      }| j
                  j                  |       }| j                  sT|j                  | j                        }p |S |j                         rt        j                  d       t        |      D ]  }| j	                  ||   j                        }|||<   | j
                  j                  |       }| j                  r|j                  | j                        }|||j!                         <   |j                         r |S  |S )a  
        .. warning::
            In some cases, sampling algorithm based on Bartlett decomposition may return singular matrix samples.
            Several tries to correct singular samples are performed by default, but it may end up returning
            singular matrix samples. Singular samples may return `-inf` values in `.log_prob()`.
            In those cases, the user should validate the samples and either fix the value of `df`
            or adjust `max_try_correction` value for argument in `.rsample` accordingly.
           
   zSingular sample detected.)r   _C_get_tracing_stater?   r   supportcheckrM   amaxrN   rK   whererC   rG   rH   r    clone)rW   r   max_try_correctionsampleis_singular_
sample_newis_singular_news           r"   r~   zWishart.rsample   s    %&+hh&A&A&Czz,/((6 ll((0%**4+;+;<K88&&(-. E!44\B
[*fE#||11&99$$"-"2"243C3C"DKE2   9:12 
A!%!8!8[9Q9W9W!XJ*4F;''+||'9'9*'E&EO((*9*>*>t?O?O*P7FK 1 1 34&??,
 r$   c                 4   | j                   r| j                  |       | j                  }| j                  d   }| |t        z  dz  | j
                  j                  dd      j                         j                  d      z   z  t        j                  |dz  |      z
  ||z
  dz
  dz  t        j                  j                  |      j                  z  z   t        j                  || j
                        j                  dd      j                  d      dz  z
  S )Nr   r   r6   rs   r   r   )r<   )r_   _validate_sampler/   rU   _log_2rO   rv   logr!   r   mvlgammarP   slogdet	logabsdetri   )rW   valuenur   s       r"   log_probzWishart.log_prob#  s   !!%(WWb!CF
Q0099r9KR nnR!Vq)* AvzQ!5!5e!<!F!FFG ""5$*H*HIX2BX'SRS[	
r$   c                 l   | j                   }| j                  d   }| j                  }|dz   |t        z  dz  | j                  j                  dd      j                         j                  d      z   z  t        j                  |dz  |      z   ||z
  dz
  dz  t        |dz  |      z  z
  ||z  dz  z   S )Nr   r   r   r6   rs   r   )r/   rU   r,   r   rO   rv   r   r!   r   r   r#   )rW   r   r   ry   s       r"   entropyzWishart.entropy8  s    WWb!""UF
Q0099r9KR nnR!Vq)* AvzQBFa!889 1fqj		
r$   c                 n    | j                   }| j                  d   }| j                   dz  ||z
  dz
  dz  fS )Nr   r   r   )r/   rU   r-   )rW   r   r   s      r"   _natural_paramszWishart._natural_paramsI  sA    WWb!%%%)BFQJ!+;;;r$   c                     | j                   d   }||dz   dz  z   t        j                  j                  d|z        j                   t
        |z  z   z  t        j                  ||dz   dz  z   |      z   S )Nr   r   r   r6   r   )rU   r   rP   r   r   r   r   )rW   r   yr   s       r"   _log_normalizerzWishart._log_normalizerO  sr    b!QUaK\\!!"q&)333fqj@
NN1A{?a01 	1r$   )NNNNr2   )$__name__
__module____qualname____doc__r   positive_definitelower_choleskyrD   rE   r   has_rsample_mean_carrier_measurer   r   Tensorr   r   rJ   r   r
   r.   r,   r-   propertyrn   rq   r{   r?   r   r   r~   r   r   r   r   __classcell__)r[   s   @r"   r   r   "   s   B )::'99!00&k&&q)	O ++GK
 5937-1E
%,,&'E
 $ELL1E
 #5<<0	E

 U\\*E
N@ 
 

 8 8 
 
 Q Q P P
 
 
 /9ejjl -$ %/EJJLT2!2	2h
*
" < <
1r$   )mathrG   numbersr   typingr   r   r   r   torch.distributionsr   torch.distributions.exp_familyr   'torch.distributions.multivariate_normalr	   torch.distributions.utilsr
   torch.typesr   __all__r   r   r   r   r#   r*   r   r3   r$   r"   <module>r      s       "   + < L 3  +	!%,, 3 5<< 1 1 1
q1 q1r$   