
    (ph                     P    S SK r S SKrS SKJr  S SKJr  S rS rS r	S r
S rS	 rg)
    N)special)primes_from_2_toc                 @    [        [        R                  " U 5      5      $ N)r   mathceil)ns    N/var/www/html/venv/lib/python3.13/site-packages/scipy/stats/tests/data/_mvt.py_primesr      s     DIIaL))    c                 .    [         R                  " X5      $ r   )r   gammaincinv)abs     r
   _gaminvr      s     q$$r   c                    [        S[        R                  " U5      5      n[        X#U-  XF-  5      u  pxn	[	        U5      n
Sn[        R
                  " X-  5      n[        R                  " U5      nSnSn[        R                  " [        SU
-  [        R                  " U
S-   5      -  S-  5      5      nUSS2[        R                  4   nSnSn[        U5       GH  nUR                  5       n[        R                  " X45      n[        U
5       GH^  n[        R                  " S[        R                  " UU   [        R                   " SUS-   5      -  UR#                  5       -   S5      -  S-
  5      nUS:X  a/  UnUS:  a&  [        R                  " S[%        UUS-  5      -  5      nO.['        UUU-  -   5      nUUS=== UUS2US-
  U24   U-  -  sss& UUSS24   nUR                  5       nUU   W-  U-
  nUR                  5       nU	U   U-  U-
  nSUUS:*  '   [        U5      S	:  n[)        UU   5      UU'   SUUS:*  '   [        U5      S	:  n[)        UU   5      UU'   UU-
  nUU-  nGMa     [        R*                  " U5      U-
  US-   -  nUU-   nUS-
  U-  US-   -  US-  -   nGM     [        R                  " U5      nX4$ )
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.

   
   r         N   i	   )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
   _qsimvtvrH      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$6N!   			!A4Kr   c                 .    [         R                  " U 5      $ r   )r   ndtr)zs    r
   r)   r)   v   s    <<?r   c                 .    [         R                  " U 5      $ r   )r   ndtri)r6   s    r
   r(   r(   z   s    ==r   c           	         Sn[         R                  " U R                  5      R                  n[	        U 5      oPR                  5       oaR                  5       orR                  5       n[         R                  " [         R                  " [         R                  " U5      S5      5      n	[        U5       HN  n
X   S:  d  M  USS2U
4==   X   -  ss'   XjSS24==   X   -  ss'   Xz==   X   -  ss'   X==   X   -  ss'   MP     [         R                  " US45      n[        R                  " S[        R                  -  5      n[        U5       GH  nUnSnSnSn[        X5       H  n
XjU
4   U:  d  M  [        R                  " [        XjU
4   S5      5      nU
S:  a  XjSU24   USU -  nXz   U-
  U-  nX   U-
  U-  n[        U5      [        U5      -
  nUU::  d  Mz  UnUnUnUnU
nM     X:  a  X}U/   X~U/'   XU/   XU/'   XmU4   XnU4'   XnSU24   R                  5       nXmSU24   XnSU24'   UXmSU24'   XnS-   S2U4   R                  5       nXnS-   S2U4   XnS-   S2U4'   UXnS-   S2U4'   XmS-   U2U4   R                  5       nXnUS-   U24   R                  XmS-   U2U4'   UR                  XnUS-   U24'   XUS-   -  :  Ga  XX4'   SXmUS-   S24'   [        US-   U5       HJ  n
XjU4   U-  XjU4'   XjUS-   U
S-   24   XjU4   XmS-   U
S-   2U4   R                  -  -
  XjUS-   U
S-   24'   ML     [!        U5      U:  aD  [         R"                  " WS-  * S-  5      [         R"                  " WS-  * S-  5      -
  UU-  -  X'   OWW-   S-  X'   US:  a  UX'   O
US:  a  UX'   XmSUS-   24==   U-  ss'   X}==   U-  ss'   X==   U-  ss'   OSXmS2U4'   X}   X   -   S-  X'   GM     XgU4$ )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   Nr   r   ir   )r   finfodtypeepsr   r"   r   maximumdiagr!   r#   r   pir   r)   Tr$   exp)Rr   r   eprQ   r	   r:   apbprE   r?   rB   sqtpkimckkdemr>   ciirD   rF   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   rH   r)   r(   r    r   r
   <module>ri      s1       -*%_F-r   