
    \h"                         S SK Jr  S SKJr  S SKJr  S SK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JrJrJr  S S	KJrJr  S S
KJrJrJrJrJrJr  S SKJ r J!r!  S SK"J#r#  S r$S r%S r&S r'S r(S r)S r*S r+g)    )Product)pi)S)Dummysymbols)exp)sqrt)gamma)DeterminantMatrixTraceMatrixSymbol	MatrixSet)densitysample)MatrixGammaDistributionMatrixGammaMatrixPSpaceWishartMatrixNormalMatrixStudentT)raisesskip)import_modulec                     ^ [        SSSS/SS//5      m[        STSS5      n U R                  T:X  d   e[        [        U4S j5        g )N      Mc                      > [        ST SS5      $ )Nr   g333333?r   )r   r   s   c/var/www/auris/envauris/lib/python3.13/site-packages/sympy/stats/tests/test_matrix_distributions.py<lambda>#test_MatrixPSpace.<locals>.<lambda>   s    |CC;    )r   r   distributionr   
ValueError)MPr   s    @r!   test_MatrixPSpacer(      sK    11v1v&67A	c1a	#B??a
:;<r$   c                    ^
^^ [        SSSSS/SS//5      m
T
R                  R                  R                  [	        SS[
        R                  5      :X  d   e[        [        T
5      [        5      (       d   e[        SSS5      n [        [        [        [        S5      * S-  S/S[        S5      * S-  //5      U -  5      5      n[        T
5      " U 5      R                  5       US[        -  [!        [#        U 5      5      -  -  :X  d   e[        T
5      " SS/SS//5      R                  5       [!        S5      [        S5      -  S	[        -  -  :X  d   e[        SSS5      n [        S
SS5      n[        T
5      " X/5      R                  5       [        U S   * S-  US   S-  -
  5      S[        -  [!        U S   US   -  U S   US   -  -
  5      -  -  :X  d   e[%        SSS9u  p4[%        SSSS9n[        S
XU5      n[        SSS5      m[        SXU5      n[        SX4U5      n[        SSSSS/SS//5      m['        S5      n[        U* US-
  -  S-  -  XC* U-  -  -  [        [        SU-  US-  -  U-  5      5      -  [#        U5      U* -  -  [#        U5      X5S-  -
  [        S5      S-  -
  -  -  [)        [+        U* S-  U-   [        S5      S-  -   5      USU45      -  n	[        U5      " U5      R-                  U	5      (       d   e[/        [0        U
UU4S j5        [/        [2        U
4S j5        [/        [2        S 5        [/        [2        S 5        [/        [2        S 5        [/        [2        S 5        g )Nr   r   r   r   X         Y)r   r   )r   r   za bTpositivedr1   integerZSMM2M3kc                  ,   > [        TT -   5      " T5      $ )Nr   )r   r8   r5   s   r!   r"   "test_MatrixGamma.<locals>.<lambda>/   s    Q(:r$   c                  &   > [        T 5      " S5      $ Nr   r<   r    s   r!   r"   r=   0       wqz!}r$   c                  *    [        SSSSS/SS//5      $ Nr   r:   r   r   r   r    r$   r!   r"   r=   1       {3AAA7GHr$   c                  *    [        SSSSS/SS//5      $ )Nr   r:   r-   r   r   rC   rD   r$   r!   r"   r=   2   s    {3B!Q!Q8HIr$   c                  *    [        SSSSS/SS//5      $ rB   rC   rD   r$   r!   r"   r=   3   rE   r$   c                  (    [        SSSSS/S//5      $ rB   rC   rD   r$   r!   r"   r=   4   s    {3AA}Er$   )r   pspacer%   setr   r   Reals
isinstancer   r   r   r   r   r   doitr   r	   r   r   r   r   r
   dummy_eqr   NotImplementedErrorr&   )r*   numr/   abr2   r6   r7   r9   exprdr   r8   r5   s             @@@r!   test_MatrixGammarT      sT   CAAA/0A88  $$	!Q(@@@@gaj"9::::S!QA
eFadU1WaL1qteAg,78:;
<C1:a=3"T+a.-A(A#BBBB1:1v1v&',,.$q'#b'/2b52IIIIS!QAS!QA1:qf""$QtWHQJ4,B(CQrT$ !$$!D'!D'/ AKC FC )D D D D 54(DAdD1AS!AS!QA	dA	!B	T1	$B	T1a1a&1a&!1	2Bc
A!QUAq2a4y(UBqD"r(?13D-E *
 

b/QB
  +AqS1Q461A BCCJqbdQh1a 1a)D--E 2;q>""5))))
 :;
:,-
:HI
:IJ
:HI
:EFr$   c                  
  ^ [        SSSS/SS//5      mTR                  R                  R                  [	        SS[
        R                  5      :X  d   e[        SSS5      n [        [        [        [        S5      * S-  S/S[        S5      * S-  //5      U -  5      5      n[        T5      " U 5      R                  5       U[        U 5      -  S[        -  -  :X  d   e[        T5      " SS/SS//5      R                  5       [        S5      S	[        -  -  :X  d   e[        S
SS9n[        SSSS9n[        SX35      n[        SX35      n[        SX%5      m[!        S5      nSU* U-  S-  -  [        U* US-
  -  S-  -  -  [        [        [        S5      S-  * US-  -  U-  5      5      -  [        U5      U* S-  -  -  [        U5      U* S-  US-  -   [        S5      S-  -
  -  -  [#        [%        U* S-  US-  -   [        S5      S-  -   5      USU45      -  n[        T5      " U5      R'                  U5      (       d   e[)        [*        U4S j5        [)        [*        S 5        [)        [*        S 5        [)        [*        S 5        g )NW   r   r   r   r*      r-      nTr0   r2   r3   r/   r6   r9   r+   r:   c                  &   > [        T 5      " S5      $ r?   r<   )rV   s   r!   r"   test_Wishart.<locals>.<lambda>G   r@   r$   c                  (    [        SSSS/SS//5      $ )NrV   r:   r   r   r   rD   r$   r!   r"   r\   H       wsB!Q!Q0@Ar$   c                  (    [        SSSS/SS//5      $ )NrV   r:   r   r   r   r^   rD   r$   r!   r"   r\   I   r_   r$   c                  &    [        SSSS/S//5      $ )NrV   r   r   r   r^   rD   r$   r!   r"   r\   J   s    wsQ!Q!>r$   )r   rI   r%   rJ   r   r   rK   r   r   r   r   r   rM   r   r   r   r   r   r
   rN   r   r&   )	r*   term1rZ   r2   r/   r6   r9   rS   rV   s	           @r!   test_Wishartrc   6   sa   Q!Q!Q()A88  $$	!Q(@@@@S!QAf!uQwlQ1aL9:1<=>E1:a=5;q>#92b5#AAAA1:1v1v&',,.#b'1R4.@@@d#AdD1AS!A	dA	!BQAc
A1QKaRQZ\**3uqtAvYrBx5G5I/J , "o1)!nBqD1Q3J1a r!taczAaDF':!;aAYGHE 1:a=!!%((((
:,-
:AB
:AB
:>?r$   c                    ^	 [        SSS//S/SS/SS//5      m	T	R                  R                  R                  [	        SS[
        R                  5      :X  d   e[        SSS5      n [        [        [        [        S5      S-  [        S5      * S-  /[        S5      * S-  [        S5      S-  //5      [        S	/S
//5      U R                  -   -  [        [        S5      S-  //5      -  [        S	S
//5      U -   -  5      * S-  5      n[        T	5      " U 5      R                  5       [        S5      U-  S[        -  -  :X  d   e[        T	5      " SS//5      R                  5       [        S5      [        [        S5      * S-  5      -  S[        -  -  :X  d   e[!        SSSS9u  p#[        SX"5      n[        SX35      n[        SX25      n[        SX25      n[        SXeU5      m	S[        -  U* U-  S-  -  [        [        US-  UR                  * UR                  -   -  US-  -  U* U-   -  5      * S-  5      -  [#        U5      U* S-  -  -  [#        U5      U* S-  -  -  n[        T	5      " U5      R                  5       U:X  d   e[%        [&        U	4S j5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        [%        [&        S 5        g )Nr   rW      r+   r   r   r*   r,   rX      rY   zd nTr3   SM2SM1LMr/   r:   c                  &   > [        T 5      " S5      $ r?   r<   r    s   r!   r"   #test_MatrixNormal.<locals>.<lambda>]   r@   r$   c                  :    [        SSS/SS/SS//SS/SS//5      $ Nr   r   r   r   r   rD   r$   r!   r"   rm   ^   1    |C!Q1a&1a&9IQPQFUVXYTZK[\r$   c                  :    [        SSS/SS/SS//SS/SS//5      $ ro   rp   rD   r$   r!   r"   rm   _   rq   r$   c                  :    [        SSS/SS/SS//SS/SS//5      $ ro   rp   rD   r$   r!   r"   rm   `   rq   r$   c                  8    [        SSS/SS/S//SS/SS//5      $ ro   rp   rD   r$   r!   r"   rm   a   s-    |C!Q1a&1#!QRSUVQWHXYr$   c                  8    [        SSS/SS/SS//SS/S//5      $ ro   rp   rD   r$   r!   r"   rm   b   s-    |C!Q1a&1a&9IQPQFUVTW=Yr$   c                  6    [        SSS//SS/SS//SS//5      $ ro   rp   rD   r$   r!   r"   rm   c   s)    |C1a&QFQF;KqRSfXVr$   c                  ,    [        SSS//S/SS//5      $ ro   rp   rD   r$   r!   r"   rm   d   s    |C1a&A3!QIr$   )r   rI   r%   rJ   r   r   rK   r   r   r   r   Tr   rM   r	   r   r   r   r   r&   )
r*   rb   r2   rZ   ri   rj   rk   r/   rS   r   s
            @r!   test_MatrixNormalry   L   s   SAq6(QC1a&1a&)9:A88  $$	!Q(@@@@S!QAv1a!A$q1QqTE!GQqT!V3DEFRD2$< 133&((.1az(:;<BRH:<NQR<RT U UUVW XE1:a=DGu#4be#<<<<1:1vh$$&$q'#qteAg,*>2*FFFF546DA
ua
#C
ua
#C	dA	!BS!AS"3'ArTaRT!VS%b	BDD5133;(?b	(IB3QR7(S #
 "

"  1%&&1#&6!A&>?E1:a=5(((
:,-
:\]
:\]
:\]
:YZ
:YZ
:VW
:IJr$   c                    ^
 [        SSSS//SS/SS//S/5      m
T
R                  R                  R                  [	        SS[
        R                  5      :X  d   e[        SSS5      n [        S-  [        [        S//5      5      S-  -  [        [        SS/SS//5      5      S	-  -  [        [        [        S5      S-  //5      [        S
S//5      U -   -  [        [        S5      S-  [        S5      * S-  /[        S5      * S-  [        S5      S-  //5      -  [        S
/S//5      U R                  -   -  [        S//5      -   5      S-  -  n[        T
5      " U 5      U:X  d   e[        SSS9nSu  p4[        SXD5      n[        SX35      n[        SX45      n[        SX45      n[        SX'XV5      m
[        US-  S-   5      [        [        S//5      US-  U* U-   -  US-  -  UR                  * UR                  -   -  -   5      U* S-  S-
  -  -  [        [        US-  5      -  [        [        U5      5      -  [        U5      -  -  n	[        T
5      " U5      U	:X  d   e[!        ["        U
4S j5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        [!        ["        S 5        g )Nr   r   rW   re   r   r+   r*   g      g      rf   rg   r,   vTr0   )r   r   OmegaSigmaLocationr/   r:   c                  &   > [        T 5      " S5      $ r?   r<   r    s   r!   r"   %test_MatrixStudentT.<locals>.<lambda>|   r@   r$   c            	      <    [        SSSS/SS/SS//SS/SS//5      $ ro   r   rD   r$   r!   r"   r   }   5    ~c1q!f1v1v>NRSUVQWZ[]^Y_P`ar$   c            	      <    [        SSSS/SS/SS//SS/SS//5      $ ro   r   rD   r$   r!   r"   r   ~   r   r$   c            	      <    [        SSSS/SS/SS//SS/SS//5      $ ro   r   rD   r$   r!   r"   r      r   r$   c            	      :    [        SSSS/SS/S//SS/SS//5      $ ro   r   rD   r$   r!   r"   r      s0    ~c1q!f1vsmqRSfWXZ[V\M]^r$   c                  8    [        SSSS/SS/SS//S/S//5      $ ro   r   rD   r$   r!   r"   r      s/    ~c1q!f1v1v>NRSQTWXVYPZ[r$   c                  8    [        SSSS//SS/SS//SS//5      $ ro   r   rD   r$   r!   r"   r      s.    ~c11vh!Q!Q@PTUWXSYRZ[r$   c                  .    [        SSSS//S/SS//5      $ ro   r   rD   r$   r!   r"   r      s    ~c11vhq!fXNr$   c                  2    [        SSSS/SS/SS//S/5      $ )Nr   r:   r   r   r   r+   r   rD   r$   r!   r"   r      s&    ~c21vAA?ORSQTUr$   )r   rI   r%   rJ   r   r   rK   r   r   r   r   rx   r   r   r
   r	   r   r&   )r*   Dr{   rZ   pr|   r}   r~   r/   rS   r   s             @r!   test_MatrixStudentTr   f   s   sAAx1a&1a&)9A3?A88  $$	!Q(@@@@S!QA
t{6A3%=1d;;k&STVWRX[\^_Z`QaJb>c? 	1
| 4Rz8JQ8N O"(1Q4!8adUQY*?1Q4%!)QqTTUXAV)W"X!Y(.rd|(<qss(B!DFLqcUm!T UXYZ	ZA 1:a=Ad#ADA!'E!'EJ-HS!AsA6A!A#'N;vse}ur{XIPQM7RSX[]S^7^aiakak`knonqnq`q7r'rswxvxyzvz}~v~ac
]4E 233K4FFHE 1:a=E!!!
:,-
:ab
:ab
:ab
:^_
:[\
:[\
:NO
:UVr$   c                    ^ [        SSS//S/SS/SS//5      [        SSSS/SS//5      /n Sn[        S	5      nU(       d  [        S
5        g U  HD  n[	        X1S9nU H2  n[        U5      UR                  R                  R                  ;   a  M2   e   MF     [        SSSSS/SS//5      m[        [        U4S j5        g )Nr   rW   re   r+   r   r   rV   r   scipyz3Scipy not installed. Abort tests for _sample_scipy.sizec                     > [        T SS9$ Nr,   r   r   r    s   r!   r"   #test_sample_scipy.<locals>.<lambda>       F11,=r$   r   r   r   r   r   r   rI   r%   rJ   r   r   rO   )distribs_scipyr   r   r*   sampssamr   s         @r!   test_sample_scipyr      s    SAq6(QC1a&1a&)9:Q!Q!Q()N
 D'"EBCA1(Ec{ahh&;&;&?&????    QQFQF#34"$=>r$   c                    ^ [        SSS/SS//SS/SS//SS/SS//5      [        S	S
SS/SS//5      /n Sn[        S5      nU(       d  [        S5        g U  HE  n[	        X1SS9nU H2  n[        U5      UR                  R                  R                  ;   a  M2   e   MG     [        SSSSS/SS//5      m[        [        U4S j5        g )Nr   rW   re   r,   r+   r   r   r   rV   rh   pymcz4PyMC is not installed. Abort tests for _sample_pymc.)r   libraryc                     > [        T SS9$ r   r   r    s   r!   r"   "test_sample_pymc.<locals>.<lambda>   r   r$   r   )distribs_pymcr   r   r*   r   r   r   s         @r!   test_sample_pymcr      s    SAq6Aq6*aVaV,<1v1v>NOQ!Q!Q()M D DCDA18Ec{ahh&;&;&?&????   QQFQF#34"$=>r$   c                     [        SSS/SS//SS/SS//SS/SS//5      n / S	QnU H  n [        U5      nU(       ay  / / / pen[        U S
USS9n[        U S
USS9n[        U S
USS9n[        S
5       H?  nXG   XW   :H  R	                  5       (       d   eXW   Xg   :g  R	                  5       (       a  M?   e   M  M     g ! [
         a     M  f = f)Nr   rW   re   r,   r+   r   r   r   )r   numpyr   
   )r   r   seed)r   r   r   rangeallrO   )r*   	librarieslibimported_libs0s1s2is           r!   test_sample_seedr      s    SAq6Aq6*aVaV,<1v1v>NOA*I	(-LRAB!<AB!<AB!<rAERUN//1111ERUN//1111 #   # 		s   BB;0B;;
C	C	N),sympy.concrete.productsr   sympy.core.numbersr   sympy.core.singletonr   sympy.core.symbolr   r   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr	   'sympy.functions.special.gamma_functionsr
   sympy.matricesr   r   r   r   r   sympy.statsr   r    sympy.stats.matrix_distributionsr   r   r   r   r   r   sympy.testing.pytestr   r   sympy.externalr   r(   rT   rc   ry   r   r   r   r   rD   r$   r!   <module>r      sc    + ! " . 6 9 9 N N 'R R - (=G@@,K4W@?$?"r$   