
    ȅiW                     x    S SK r S SKrS SKJrJrJr  S SKJr  S SKJr  S SK	J
r
  S SKJrJr  S/r " S S\5      rg)	    N)infnanTensor)constraints)Distribution)broadcast_all)_Number_sizeCauchyc            	       L  ^  \ rS rSrSr\R                  \R                  S.r\R                  r	Sr
 SS\\-  S\\-  S\S-  S	S4U 4S
 jjjrSU 4S jjr\S	\4S j5       r\S	\4S j5       r\S	\4S j5       r\R*                  " 5       4S\S	\4S jjrS rS rS rS rSrU =r$ )r      a  
Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of
independent normally distributed random variables with means `0` follows a
Cauchy distribution.

Example::

    >>> # xdoctest: +IGNORE_WANT("non-deterministic")
    >>> m = Cauchy(torch.tensor([0.0]), torch.tensor([1.0]))
    >>> m.sample()  # sample from a Cauchy distribution with loc=0 and scale=1
    tensor([ 2.3214])

Args:
    loc (float or Tensor): mode or median of the distribution.
    scale (float or Tensor): half width at half maximum.
)locscaleTNr   r   validate_argsreturnc                   > [        X5      u  U l        U l        [        U[        5      (       a+  [        U[        5      (       a  [
        R                  " 5       nOU R                  R                  5       n[        TU ]%  XCS9  g )Nr   )
r   r   r   
isinstancer	   torchSizesizesuper__init__)selfr   r   r   batch_shape	__class__s        T/home/james-whalen/.local/lib/python3.13/site-packages/torch/distributions/cauchy.pyr   Cauchy.__init__&   s[      -S8$*c7##
5'(B(B**,K((--/KB    c                 &  > U R                  [        U5      n[        R                  " U5      nU R                  R                  U5      Ul        U R                  R                  U5      Ul        [        [        U]#  USS9  U R                  Ul	        U$ )NFr   )
_get_checked_instancer   r   r   r   expandr   r   r   _validate_args)r   r   	_instancenewr   s       r   r"   Cauchy.expand3   st    ((;jj-((//+.JJ%%k2	fc#Ku#E!00
r   c                     [         R                  " U R                  5       [        U R                  R
                  U R                  R                  S9$ N)dtypedevice)r   full_extended_shaper   r   r)   r*   r   s    r   meanCauchy.mean<   5    zz  "Ctxx~~dhhoo
 	
r   c                     U R                   $ N)r   r-   s    r   modeCauchy.modeB   s    xxr   c                     [         R                  " U R                  5       [        U R                  R
                  U R                  R                  S9$ r(   )r   r+   r,   r   r   r)   r*   r-   s    r   varianceCauchy.varianceF   r0   r   sample_shapec                     U R                  U5      nU R                  R                  U5      R                  5       nU R                  X0R                  -  -   $ r2   )r,   r   r%   cauchy_r   )r   r8   shapeepss       r   rsampleCauchy.rsampleL   sC    $$\2hhll5!))+xx#

***r   c                     U R                   (       a  U R                  U5        [        R                  " [        R                  5      * U R
                  R                  5       -
  XR                  -
  U R
                  -  S-  R                  5       -
  $ )N   )r#   _validate_samplemathlogpir   r   log1pr   values     r   log_probCauchy.log_probQ   sj    !!%(XXdggjjnn!TZZ/A5<<>?	
r   c                     U R                   (       a  U R                  U5        [        R                  " XR                  -
  U R
                  -  5      [        R                  -  S-   $ Ng      ?)r#   rA   r   atanr   r   rB   rD   rF   s     r   cdf
Cauchy.cdfZ   sF    !!%(zz588+tzz9:TWWDsJJr   c                     [         R                  " [        R                  US-
  -  5      U R                  -  U R
                  -   $ rK   )r   tanrB   rD   r   r   rF   s     r   icdfCauchy.icdf_   s0    yyECK01DJJ>IIr   c                     [         R                  " S[         R                  -  5      U R                  R                  5       -   $ )N   )rB   rC   rD   r   r-   s    r   entropyCauchy.entropyb   s)    xxDGG$tzz~~'777r   r2   )__name__
__module____qualname____firstlineno____doc__r   realpositivearg_constraintssupporthas_rsampler   floatboolr   r"   propertyr.   r3   r6   r   r   r
   r=   rH   rM   rQ   rU   __static_attributes____classcell__)r   s   @r   r   r      s   $ *..9M9MNOGK &*	Ce^C ~C d{	C
 
C C 
f 
 

 f   
& 
 

 -2JJL +E +V +

K
J8 8r   )rB   r   r   r   r   torch.distributionsr    torch.distributions.distributionr   torch.distributions.utilsr   torch.typesr	   r
   __all__r    r   r   <module>rl      s4      " " + 9 3 & *T8\ T8r   