+
    0i                     R    ^ RI t ^ RIt^ RIHt ^ RIHt R tR tR t	R t
R tR	 tR# )
    N)special)primes_from_2_toc                 @    \        \        P                  ! V 4      4      # N)r   mathceil)ns   &Y/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/stats/tests/data/_mvt.py_primesr      s     DIIaL))    c                 .    \         P                  ! W4      # r   )r   gammaincinv)abs   &&r
   _gaminvr      s     q$$r   c                   \        ^\        P                  ! V4      4      p\        W#V,          WF,          4      w  rxp	\	        V4      p
^
p\        P
                  ! W,          4      p\        P                  ! V4      p^ p^ p\        P                  ! \        ^V
,          \        P                  ! V
^,           4      ,          ^,          4      4      pVR\        P                  3,          pRpRp\        V4       EF]  pVP                  4       p\        P                  ! W34      p\        V
4       EF  p\        P                  ! ^\        P                  ! VV,          \        P                   ! ^V^,           4      ,          VP#                  4       ,           ^4      ,          ^,
          4      pV^ 8X  d9   TpV^ 8  d/   \        P                  ! ^\%        VV^,          4      ,          4      pMF\'        VVV,          ,           4      pVVR;;; VVR1V^,
          V13,          V,          ,          uuu% VVR3,          pVP                  4       pVV,          X,          V,
          pVP                  4       pV	V,          V,          V,
          p^ VVR8*  &   \        V4      ^	8  p\)        VV,          4      VV&   ^ VVR8*  &   \        V4      ^	8  p\)        VV,          4      VV&   VV,
          pVV,          pEK  	  \        P*                  ! V4      V,
          V^,           ,          pVV,           pV^,
          V,          V^,           ,          V^,          ,           pEK`  	  \        P                  ! V4      pW3# )a  Estimates the multivariate t CDF using randomized QMC

Parameters
----------
m : int
    The number of points
nu : float
    Degrees of freedom
sigma : ndarray
    A 2D positive semidefinite covariance matrix
a : ndarray
    Lower integration limits
b : ndarray
    Upper integration limits.
rng : Generator
    Pseudorandom number generator

Returns
-------
p : float
    The estimated CDF.
e : float
    An absolute error estimate.

NNNNi)maxr   sqrt_chlrpslenr   nponesr   lognewaxisrangecopyzerosabsmodarangerandomr   _Phinv_Phimean) mnusigmar   r   rngsnchazbzr	   NPonpepsqcdcSvpsixrysiaidbitls    &&&&&&                          r
   _qsimvtvrC      s   P 
Q		"	BWUbD!$-G
E
AA		!#ARWWQZQA	1TXXac]*1,-	.BBq"**}4E 	A4b1XWWYBHHaV,qAq!RYYq!A#%6 6 EqII!KLAAv6'!RT"2 23A1qt8$!"AB!AI**1a4Bbggi!beAgl	APRSTPUVWPWZ\P\2AbBhK#b'A+RtBrF|quAbBhK#b'A+RtBrF|quQBR"W  WWR[1_q1u%1q5qq1uaiQ6G!Q$6N!   			!A4Kr   c                 .    \         P                  ! V 4      # r   )r   ndtr)zs   &r
   r$   r$   v   s    <<?r   c                 .    \         P                  ! V 4      # r   )r   ndtri)r1   s   &r
   r#   r#   z   s    ==r   c           	     j
   Rp\         P                  ! V P                  4      P                  p\	        V 4      qPP                  4       qaP                  4       qrP                  4       p\         P                  ! \         P                  ! \         P                  ! V4      ^ 4      4      p	\        V4       F  p
W,          ^ 8  g   K  VRV
3;;,          W,          ,          uu&   WjR3;;,          W,          ,          uu&   Wz;;,          W,          ,          uu&   W;;,          W,          ,          uu&   K  	  \         P                  ! V^34      p\        P                  ! ^\        P                  ,          4      p\        V4       EF  pTp^ p^p^ p\        W4       F  p
WjV
3,          V8  g   K  \        P                  ! \        WjV
3,          ^ 4      4      pV
^ 8  d   WjRV13,          VRV ,          pWz,          V,
          V,          pW,          V,
          V,          p\        V4      \        V4      ,
          pVV8:  g   K  TpTpTpTpT
pK  	  W8  Ed   W}V.,          W~V.&   WV.,          WV.&   WmV3,          WnV3&   WnRV13,          P                  4       pWmRV13,          WnRV13&   VWmRV13&   Wn^,           R1V3,          P                  4       pWn^,           R1V3,          Wn^,           R1V3&   VWn^,           R1V3&   Wm^,           V1V3,          P                  4       pWnV^,           V13,          P                  Wm^,           V1V3&   VP                  WnV^,           V13&   WV^,           ,          8  Ed   WW3&   ^ WmV^,           R13&   \        V^,           V4       F~  p
WjV3,          V,          WjV3&   WjV^,           V
^,           13,          WjV3,          Wm^,           V
^,           1V3,          P                  ,          ,
          WjV^,           V
^,           13&   K  	  \!        V4      V8  da   \         P"                  ! X^,          ) ^,          4      \         P"                  ! X^,          ) ^,          4      ,
          VV,          ,          W&   M)XX,           ^,          W&   VR8  d   VW&   MV^
8  d   VW&   WmRV^,           13;;,          V,          uu&   W};;,          V,          uu&   W;;,          V,          uu&   M&^ WmR1V3&   W},          W,          ,           ^,          W&   EK  	  WgV3# )z
Computes permuted and scaled lower Cholesky factor c for R which may be
singular, also permuting and scaling integration limit vectors a and b.
g|=r   Ni)r   finfodtypeepsr   r   r   maximumdiagr   r   r   pir   r$   Tr   exp)Rr   r   eprL   r	   r5   apbpr@   r:   r=   sqtpkimckkdemr9   ciir?   rA   deambmts   &&&                      r
   r   r   ~   s(   
 
B
((177


CAAFFH668b&&(R

SUSZSZ[\S]_`Ha@bA1X4!8adGqtOGQ!tW_WEQTME25AD=5  	!QA1TWW9!5$1Xaqa!qAAw}iiAdGQ0q5a2A2h2A.!eAgs]"%'3BT"Xd2h=N9CRsbr"2  6W+BAwKRB[rq'{aSTPTg!F)bqb&	 Aa2A2h!F)1RaR%Q$%)!!#AAdeQhKQ!tuby\qa45!8A#b&!)!!#AA!A#b&jMOOQs2vqy\UVUXUXQ1Q3r6z]QqS>adG1!W:1Q3]qD'#+Q$qAaC!G}qAwqSTQTUVWXUXQXZ[Q[}G^7^qAaC!G} #3x"}Avax(2662q5&(+;;SIR1}8AD"WAD!A#gJ#Jru|uRUc\UAb!eH"%"%-!2!$; < "9r   )r   numpyr   scipyr   scipy.stats._qmcr   r   r   rC   r$   r#   r    r   r
   <module>rd      s1       -*%_F-r   