+
    iH                     V   ^ RI Ht ^ RIHt ^ RIHtHtHt ^ RIH	t	 ^ RI
Ht ^ RIHt ^ RIHtHt ^ RIHt ^ R	IHt ^ R
IHt ^ RIHt ^ RIHt ^ RIHt ^ RIHt ^ RIH t  ^ RI!H"t" ^ RI#H$t$H%t% ^ RI&H't' ^ RI(H)t)H*t* ^ RIH+t+ ^ RI,H-t- ^ RI.H/t/H0t0 ^ RI1H2t2 ^ RI3H4t4H5t5H6t6H7t7H8t8H9t9H:t: ^ RI;H<t<H=t=H>t>H?t?H@t@HAtBHCtCHDtEHFtFHGtGHHtHHItIHJtJ ^ RIKHLtLHMtMHNtNHOtO ^ RIPHQtQ ^ RIRHStSHTtT R tUR tVR tWR  tXR! tYR" tZR# t[R$ t\R% t]]OR& 4       t^R' t_R( t`]MR) 4       taR* tbR+ tcR, tdR- teR. tf]MR/ 4       tgR0# )1    )Product)Sum)Rationaloopi)Eq)S)symbols)RisingFactorial	factorial)
polar_lift)exp)sqrt)	Piecewise)besselk)gamma)eye)Determinant)Range)Interval
ProductSet)simplify)IndexedIndexedBase)comp)	integrate)MatrixMatrixSymbol)MatrixElement)densitymedianmarginal_distributionNormalLaplaceEsample)JointRVMultivariateNormalDistributionJointDistributionHandmadeMultivariateTNormalGamma$GeneralizedMultivariateLogGammaOmegaMultivariateBetaGeneralizedMultivariateLogGammaMultivariateEwensMultinomialNegativeMultinomialMultivariateNormalMultivariateLaplace)raisesXFAILskipslow)import_module)xyc                  
  a \        R ^^.^^ .^ ^..4      o\        R ^^.^^ .^ ^..4      p SV 8X  g   Q h\        S4      ! ^^4      ^^\        ,          ,          8X  g   Q hSP                  P
                  P                  \        \        P                  \        P                  4      8X  g   Q h\        \        V3R l4       \        R. RO. RO. RO. RO.4      p\        R\        ^^.4      \        ^^ .^ ^..4      4      p\        S4      ! \        \        4      \        V4      ! \        \        4      8X  g   Q h\        V^ ^4      ! ^^4      ^^\        ,          ,          8X  g   Q h\        \        V3R l4       \!        \        S4      ! \        \        4      \        \"        ) \"        3\        \"        ) \"        34      P%                  4       R8X  g   Q h\        R^^.\        ^ .^ \        ..4      p\        V4      ! ^ ^ 4      \'        ^\        ,          \        ,           ^\        ,          \        ,          ,          ) 4      ^\        ,          \)        \        \        ,          4      ,          ,          8X  g   Q h\        \        R 4       \+        RR	R	R
7      p\-        RV^4      p\-        RW4      p\        RWE4      p\        V4      \/        WE4      8X  g   Q h\        \0        V3R l4       ^p\-        RW4      p\-        RV^4      p\-        RV^4      p\        RWG4      p\        V4      p	V	! V4      P3                  V\5        ^4      V\        . RO4      V\        . RO4      /4      P7                  4       p
V	! ^ ^ ^ 4      P3                  V\5        ^4      V\        . RO4      /4      P7                  4       pV
\)        ^4      ^\        \9        R4      ,          ,          ,          8X  g   Q hV\)        ^4      ^\        \9        R4      ,          ,          ,          8X  g   Q h\+        RR	R	R
7      p\-        RW4      p\-        RV^4      p\-        RV^4      p\        RWG4      p\        V4      ! V4      p\;        \'        \        ^4      ^,          VP<                  VP<                  ,
          ,          VR,          ,          V) V,           ,          4      \)        ^\        ,          V,          \?        V4      ,          4      ,          ^ ^ 4      pW8X  g   Q hR# )Ac                     < S ^,          # )    ms   ]/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/stats/tests/test_joint_rv.py<lambda>test_Normal.<locals>.<lambda>,   s	    qt    BCc                     < \        S 4      # N)r"   r@   s   rB   rC   rD   1   s    4Q7rE         ?Nc                  ,    \        R ^^.^^.^R..4      # )M)r#   r?   rE   rB   rC   rD   6   s    sQFaVaW4E FrE   nT)integerpositivemusigmaXc                     < \        S 4      # rI   )r!   r@   s   rB   rC   rD   =   s	    rE   SgobsN)   r>      rX   r   r   r   rX   r   r   r   rX   r   r   r   g      ?rN   ) r#   r2   r    r   pspacedistributionsetr   r	   Realsr4   
ValueErrorr   r9   r:   r"   r   r   evalfr   r   r
   r   r(   NotImplementedErrorsubsr   doitr   r   Tr   )r<   rO   prK   rR   rS   rT   rV   rW   	density_Xeval_aeval_bdensity_X_at_obsexpected_densityrA   s                 @rB   test_Normalrn   &   s   sQFaVaV,-A3A!Q!Q(89A6M61:aq!B$x'''88  $$
177AGG(DDDD
J$sI	9i@AAsVQF^VaVaV,<%=>A1:awqz!Q//// Aq)!Q/1ad8;;;
:78WQZ1%B3|a"b\BHHJcQQQsQFaVaV,-A1:asacAg!A%6#78!B$tAaCy.IIII
JFGTD1A	dAq	!B!'EsBA1:7BBBB
!23 	
A	dA	!B	dAq	!B
ua
#C3'A
Is^  "c!f
F9sF9$5"7 88< q!Q$$b#a&"fY6G%HINNPFT!WaHSM 112222T!WaHSM 112222TD1A	dA	!B	dAq	!B
ua
#C3'Aqz#$QqT!Vsuu%R0RC#I>?adQYR()	*+,a1 ///rE   c                     \        R ^ ^ .^^ .^ ^..^4      p \        V 4      ! ^^4      ^^\        ,          ,          8X  g   Q hV P                  P                  P
                  \        \        P                  \        P                  4      8X  g   Q h\        \        V 4      ! \        \        4      \        \        ) \        3\        \        ) \        34      P                  4       R8X  g   Q h\        \        R 4       \        R^^.\        ^ .^ \        ..^4      p\        V4      ! ^^4      ^^\        ,          \!        \        \        ,          4      ,          ,          8X  g   Q hR# )rg   rJ   c                  .    \        R ^^.^^.^R..^4      # )rg   rN   )r*   r?   rE   rB   rC   (test_MultivariateTDist.<locals>.<lambda>i   s     }S1a&Aq6Ar7:KQOrE   t2N)r*   r    r   r^   r_   r`   r   r	   ra   r   r9   r:   r   rc   r4   rb   r   )t1rr   s     rB   test_MultivariateTDistrt   c   s   	sQFaVaV$4a	8B2;1
AbD
))
)99!!%%AGGQWW)EEEEWR[A&RC	
RCeg% % %
:OP	taVq!fq!f%5q	9B2;q!1R4QqS	> 2222rE   c            
         \        \        R  4       \        R^^ .^^ .^ ^..4      p \        R^^ .^^ .^ ^..4      p\	        V 4      ! ^^4      \        ^4      \        ^ \        ^'4      4      ,          \        ,          8X  g   Q h\        R^^.\        ^ .^ \        ..4      p\	        V4      ! ^ ^4      \        ^\        ,          4      \        ^ \        ^^\        ,          ,           ^\        ,          ,           \        ,          4      4      ,          \        \        \        \        ,          4      ,          ,          8X  g   Q hV P                  P                  P                  \        \        P                   \        P                   4      8X  g   Q hV P                  P                  VP                  P                  8X  g   Q hR# )c                  ,    \        R ^^.^^.^^..4      # )rg   )r$   r?   rE   rB   rC   +test_multivariate_laplace.<locals>.<lambda>o   s    wsQFaVaV4DErE   LL2L1N)r4   rb   r$   r3   r    r   r   r   r   r9   r:   r^   r_   r`   r   r	   ra   )rx   ry   rz   s      rB   test_multivariate_laplacer{   n   sM   
:EFaVq!fq!f-.A	TAq6QFQF+;	<B1:as1vgab&::2====	1vAA/	0B2;q!AaCD!ac'AaC-!2344baclCD D D88  $$
177AGG(DDDD88  BII$:$::::rE   c            	      R   \        R ^^^^4      p \        V 4      ! ^^4      ^ \        R4      ,          \        \        4      ,          8X  g   Q hV P
                  P                  P                  \        \        P                  \        ^ \        4      4      8X  g   Q h\        \        R 4       \        V ^ 4      ! ^4      ^\        ^
4      ,          \!        \#        ^^4      4      ,          ^
\        \        4      ,          \!        \#        ^^4      4      ,          ,          8X  g   Q h\        V \$        4      ! ^4      \        \#        R^4      4      ^,          8X  g   Q h\        V ^ ^.4      ! \&        4      \&        ^,          \        \&        ) ^,          4      ,          ^,          8X  g   Q hR# )Gc                       \        R ^^^R4      # )r}   rN   )r+   r?   rE   rB   rC   "test_NormalGamma.<locals>.<lambda>~   s    k#q!Q;rE   NrN   )r+   r    r   r   r   r^   r_   r`   r   r	   ra   r   r   r4   rb   r"   r   r   r:   r9   )ngs    rB   test_NormalGammar   z   s0   	S!Q1	%B2;q!3r7
48 333399!!%%AGGXa_)MMMM
:;< Q'*	$r(
5!Q(("T"X+eHQN6K*KLM M M Q'*c(2q/.B3.FFFF QqE*1-Ac1"Q$i1CCCCrE   c                    aaaaaaaaaaaaaaa \         P                  p \        ^W V .V ^W .W ^V .W V ^..4      o^. RO. ROuooo\        RRR7      w  rr4\        RRR7      p\	        RSSSS4      p\        RVSSS4      pRp\        \        V4      ! WW44      4      V8X  g   Q hR	p	\        \        V4      ! WW44      4      V	8X  g   Q hR
p
\        \        Wf^ ,          4      ! V4      4      V
8X  g   Q h\        ^W ..4      o\        ^W V .V ^^V .W ^V .W V ^..4      o\        ^W V .V ^^V .W ^V .W V ^..4      o\        RRRR7      o^^S^.oS^^^.o\        ^W W .V ^W V .W ^W .W V ^V .W W ^..4      o. ROo\        ^..4      o^.;oo\        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVVV3R l4       \        \        VVV3R l4       R# )rX   zy_1:5T)realdrQ   r}   Gdzd**4*Sum(4*24**(-n - 4)*(1 - d)**n*exp((n + 4)*(y_1 + 2*y_2 + 3*y_3 + 4*y_4) - exp(y_1) - exp(2*y_2)/2 - exp(3*y_3)/3 - exp(4*y_4)/4)/(gamma(n + 1)*gamma(n + 4)**3), (n, 0, oo))z5*2**(2/3)*5**(1/3)*Sum(4*24**(-n - 4)*(-2**(2/3)*5**(1/3)/4 + 1)**n*exp((n + 4)*(y_1 + 2*y_2 + 3*y_3 + 4*y_4) - exp(y_1) - exp(2*y_2)/2 - exp(3*y_3)/3 - exp(4*y_4)/4)/(gamma(n + 1)*gamma(n + 4)**3), (n, 0, oo))/64ay  5*2**(2/3)*5**(1/3)*exp(4*y_1)*exp(-exp(y_1))*Integral(exp(-exp(4*G[3])/4)*exp(16*G[3])*Integral(exp(-exp(3*G[2])/3)*exp(12*G[2])*Integral(exp(-exp(2*G[1])/2)*exp(8*G[1])*Sum((-1/4)**n*(-4 + 2**(2/3)*5**(1/3))**n*exp(n*y_1)*exp(2*n*G[1])*exp(3*n*G[2])*exp(4*n*G[3])/(24**n*gamma(n + 1)*gamma(n + 4)**3), (n, 0, oo)), (G[1], -oo, oo)), (G[2], -oo, oo)), (G[3], -oo, oo))/5308416v_fFrQ   r   c                  "   < \        R SSS S4      # r}   GMVLGO)lrR   omega_f1vs   rB   rC   Btest_GeneralizedMultivariateLogGammaDistribution.<locals>.<lambda>       vc8Q2>rE   c                  "   < \        R SSS S4      # r   r   )r   rR   omega_f2r   s   rB   rC   r      r   rE   c                  "   < \        R SSS S4      # r   r   )r   rR   omega_f3r   s   rB   rC   r      r   rE   c                  "   < \        R SSS S4      # r   r   )r   rR   omegar   s   rB   rC   r      s    vc5#q"=rE   c                  "   < \        R SSS S4      # r   r   )l_frR   r   r   s   rB   rC   r      s    vc5!S"=rE   c                  "   < \        R SSS S4      # r   r   )r   m_fr   r   s   rB   rC   r      s    vc5!Q<rE   c                  "   < \        R SSS S4      # r   r   )r   rR   omega_f4r   s   rB   rC   r      r   rE   c                  "   < \        R SSS S4      # r   r   )l_f1rR   r   r   s   rB   rC   r      s    vc5!T2>rE   c                  "   < \        R SSS S4      # r   r   )l_f5mu_f5omega_f5r   s   rB   rC   r      s    vc8QeDrE   c                  6   < \        R \        ^^4      SS S4      # r   )GMVLGr   )r   rR   r   s   rB   rC   r      s    uS(1a.!QCrE   N)rX   r>   rY      )rX   r>   rY   r      )r	   Halfr   r
   r   r   strr    r"   r4   rb   )hy_1y_2y_3y_4deltar}   r   denddenmargr   r   r   r   r   rR   r   r   r   r   r   r   r   r   r   s              @@@@@@@@@@@@@@@rB   0test_GeneralizedMultivariateLogGammaDistributionr      s|   	AQaLA\Aq\Aq\# $E <HAq" t4CcC$'EsE1a$A	tUAq"	%B:D wr{3S./4777XC wqz#C-.#555"D $Q!-c23t;;;1yk"H1|Aq\Aq\Aq\# $H 1|Aq\Aq\Aq\# $H %%d
3Caa.C1a.C1A!_Aq_Aq!_A!_	& 'H
 Dse}H3ED
:>?
:>?
:>?
:=>
:=>
:<=
:>?
:>?
:DE
:CDrE   c                  Z  aaaa \        R RR7      w  oo\        R RRR7      w  oo\        RSS.4      p \        RSS4      p\        V 4      ! ^^4      \        ^4      S^,
          ,          \	        SS,           4      ,          \	        S4      \	        S4      ,          ,          8X  g   Q h\        V^ 4      ! ^4      \        ^4      S^,
          ,          \	        SS,           4      ,          S\	        S4      ,          \	        S4      ,          ,          8X  g   Q h\        \        VV3R l4       \        \        VV3R l4       \        \        R	 4       \        \        VV3R
 l4       V P                  P                  P                  \        \        ^ ^4      \        ^ ^4      4      8X  g   Q hR# )za1, a2Tr   Fr   rF   rG   c                      < \        R S S.4      # b1r-   )a1_fa2s   rB   rC   'test_MultivariateBeta.<locals>.<lambda>   s    /tRjArE   c                      < \        R S S.4      # b2r   )a1a2_fs   rB   rC   r      s    /r4jArE   c                      \        R ^ ^ .4      # )b3r   r?   rE   rB   rC   r      s    /q!f=rE   c                      < \        R S S.4      # )b4r   )r   r   s   rB   rC   r      s    /tTlCrE   N)r
   r-   r    r	   r   r"   r4   rb   r^   r_   r`   r   r   )mbmb_cr   r   r   r   s     @@@@rB   test_MultivariateBetar      sD   X-FBE=JD$	#Bx	(BCR(D2;q!!rAvuR"W~ =!&r59!4!6 6 6 6 q)!,!rAvuR"W~0M13E"IeBi1G1I I I I
:AB
:AB
:=>
:CD99!!%%HQNHQPQN)SSSSrE   c                  *  a	 \        R RR7      w  rp\        RRR7      o	\        RRRR7      p\        R^V4      p\        V4      ! V^ ,          V^,          V^,          4      \        ^^V^,          ) ,          ,          ^V^,          ) ,          ,          W^ ,          ,          ,          W^,          ,          ,          W^,          ,          ,          W^,           ,          V^,           ,          \	        V^ ,          4      ,          \	        V^,          4      ,          \	        V^,          4      ,          ,          \        V^ ,          ^V^,          ,          ,           ^V^,          ,          ,           ^4      3R4      8X  g   Q h\        WD^,          4      ! V^,          4      \        ^^V^,          ) ,          ,          W^,          ,          ,          V^,           V^,           ,          \	        V^,          4      ,          ,          \        ^V^,          ,          ^,           ^4      3R4      8X  g   Q h\        \        V	3R l4       VP                  P                  P                  \        \        ^ ^^4      \        ^ ^^4      \        ^ ^^4      4      8X  g   Q h\        RW4      p\        R	4      p\        R
4      w  rg\        \	        V 4      \        WV,          ,          V^,           W6,          ) ,          ,          \	        W6,          4      ,          V^ V ^,
          34      ,          \!        W4      ,          \        V \#        V^,           W7,          ,          V^ V ^,
          34      4      3R4      p\        V4      ! V4      P%                  V4      '       g   Q hR# )z	n theta iTr   t_fnegativeza_1:4)rQ   rP   r%   c                     < \        R ^S 4      # )e1)r/   )theta_fs   rB   rC   (test_MultivariateEwens.<locals>.<lambda>   s    0q'BrE   azj, kNr   T)r
   r/   r    r   r   r   r"   r4   rb   r^   r_   r`   r   r   r   r   r   r   dummy_eq)
rO   thetair   ededsjkr   r   s
            @rB   test_MultivariateEwensr      s   +5KAa ed+GDD9A	35	)B2;qtQqT1Q4(IqadU|A1J7N,1Q4K888=t8DDIQ4K8P-2AI->	-J,5adO.<<EadO.L,5adO.<8= ?A1!A$,-adFB345?7	78
 :C-D D D D !U+AaD1Y!qte*49Q4KA@BG!)5:QYB@@I!A$BPAQ 57q1vz14E@G IR6S S S S :BC99!!%%E!QN,1!QNE!QN*L L L L C
*CCA6?DA
Yq\'%1+q1u6F*FQT?+1q5M#+ ++:5+DEq#q1uadlQ1q5M2356?AC 3<?##C((((rE   c            	        aaa	a
aaa \        R RRR7      w  orr#\        RRR7      w  o	ooo\        RRR7      w  o
o\        RSS	SSS.4      p\        R^S	SS4      p\        p\        V4      ! WW#4      \	        S	V ,          SV,          ,          SV,          ,          SV,          ,          V! S4      ,          V! V 4      V! V4      ,          V! V4      ,          V! V4      ,          ,          \        SW,           V,           V,           4      3R4      8X  g   Q h\        WU^ ,          4      ! V 4      P                  V ^4      ^S	,          S^,          ,          ^S	,          S,          S,          ,           ^S	,          S^,          ,          ,           8X  g   Q h\        \        V	V
VV3R	 l4       \        \        VV	VVV3R
 l4       \        \        V3R l4       R# )zn, x1, x2, x3, x4TnonnegativerP   p1, p2, p3, p4r   z	p1_f, n_fr   rM   rG   c                  &   < \        R ^S SSS.4      # r   r0   p1p1_fp2p3s   rB   rC   "test_Multinomial.<locals>.<lambda>   s    {4RR4FGrE   c                  &   < \        R S SSSS.4      # r   r   )n_fr   r   r   p4s   rB   rC   r      s    {4r2r26FGrE   c                  $   < \        R S RRRR4      # )r         ?皙?333333?皙?r   )rO   s   rB   rC   r      s    {4Cc3GrE   Nr   )
r
   r0   r   r    r   r   r"   re   r4   rb   )x1x2x3x4rM   rG   frO   r   r   r   r   r   r   s          @@@@@@@rB   test_Multinomialr      s    3tTArr-=NBBd3ID#CRR,-ACBB'AA1:bb%BF2r6M"b&4HR4O,-aD5123B%"+ae2CAbE2I5K,.q"'B,2C,D4FGP*R R R R !aD)"-222q9<=bDQJ<=bDGBJ=G<=bDQJ=GG G G :GH
:GGH
:GHrE   c                  X  a	a
aaa \        R RRR7      w  o	rr#\        RRR7      w  o
oop\        RRR7      o\        R^S
SSV.4      p\        R^R	R
R4      p\        p\        p\	        \        V4      ! WW#4      S
V ,          SV,          ,          SV,          ,          WC,          ,          S
) S,
          S,
          V,
          ^,           ^,          ,          V! W,           V,           V,           ^,           4      ,          ^V! V 4      ,          V! V4      ,          V! V4      ,          V! V4      ,          ,          ,
          4      \        P                  J g   Q h\        \        Wf^ ,          4      ! ^4      P                  4       RR4      '       g   Q h\        \        V
VVV3R l4       \        \        V	3R l4       VP                  P                  P                  \!        \#        ^ \$        ^4      \#        ^ \$        ^4      \#        ^ \$        ^4      \#        ^ \$        ^4      4      8X  g   Q hR# )zk0, x1, x2, x3, x4Tr   r   r   r   r   rK   rG   r   皙?r   gQ?{Gz?c                  &   < \        R ^S SSS.4      # r   r1   r   s   rB   rC   *test_NegativeMultinomial.<locals>.<lambda>  s    24RR<NOrE   c                  $   < \        R S RRRR4      # )r   r   r   r   r   )k0s   rB   rC   r     s    24S#sCPrE   N)r
   r1   r   r   r   r    r	   Zeror   r"   rc   r4   rb   r^   r_   r`   r   r   r   )r   r   r   r   r   rK   rG   gr   r   r   r   r   r   s            @@@@@rB   test_NegativeMultinomialr     s    !54QUVB-=NBB6D)DCRR$45ACCc2AAAGAJrr.F2r6M"b& '"rB);a)?!(CCAbgGGG E AbE'!B%-"-ae355 69:@ @ @ %a1.q17794EEEE
:OP
:PQ88  $$
5B?!ROU1b!_eAr1o)G G G GrE   c                  n   \        R ^ ^ .^^ .^ ^..^4      p \        W ^,          4      ! \        4      p\        ^4      \        ^,          ^,          ^,           ,          ^\	        \        ^,          ^,          ^,           4      \        ^4      ^,          ,          ,          ,          pW8X  g   Q V4       h\        \        V ^4      ! \        4      \        \        ) \        34      ^8X  g   Q h\        R . RO. RO. RO. RO.^4      p\        \        V^ 4      ! ^4      P                  4       RR4      '       g   Q hR# )rg   r   r   Nr]   rZ   r[   r\   )
r*   r"   r9   r   r   r	   r   r   r   rc   )rg   gotansts       rB   &test_JointPSpace_marginal_distributionr    s    cAq6QFQF#3Q7A
Q4
(
+C
q'1a46A:
*QT!VaZ"81Q46"B B
CC:s:*1a03a"b\BaGGGc9y)Y&GKA%a+A.446SAAAArE   c                  \   R  R 4       w  r\        V ^,          ) ^,          V ,           V^,          ^,          ,
          \        P                  ,
          4      ^\        ,          ,          p\	        RV4      p\        V4      ! ^^4      \        R4      ^\        ,          ,          8X  g   Q h\        VP                  P                  \        4      '       g   Q h\        V^ 4      ! ^4      \        ^4      \        \        R^4      4      ,          ^\        \        4      ,          ,          8X  g   Q hR# )c              3   :   "   T F  p\        R V4      x  K  	  R# 5ir9   Nr   .0r   s   & rB   	<genexpr>test_JointRV.<locals>.<genexpr>!       .v!gc1oov   r9   NrX   r>   rN   )r   r	   r   r   r'   r    
isinstancer^   r_   r)   r"   r   r   )r   r   pdfrT   s       rB   test_JointRVr     s    .v.FB
r1ufQhmb!eAg%.
/2
6CSA1:as2w"~---ahh++-FGGGG A&q)T!WS"a5I-I1TRTX:-VVVVrE   c                      \        R \        \        .^^ .^ ^..4      p \        \	        V ^,          4      4      \        8X  g   Q hR# r<   N)r#   r9   r:   r   r%   r@   s    rB   test_expectationr  )  s<    sQFaVaV,-AAadG!!!rE   c                  x    \        R \        \        .^^ .^ ^..4      p \        V 4      \        \        38X  g   Q hR# r  )r#   r9   r:   r%   r@   s    rB   test_joint_vector_expectationr  .  s5    sQFaVaV,-AQ4Aq6>>rE   c                    a \        R ^^.^^.^^..4      \        R. R	O4      \        R^2. R
O4      .p ^p\        R4      pV'       g   \	        R4       R# V  FI  p\        W1RR7      pV F3  p\        V4      VP                  P                  P                  9   d   K3  Q h	  KK  	  \        R^RRR4      o\        \        V3R l4       R# )rM   rF   rK   r   numpyz6Numpy is not installed. Abort tests for _sample_numpy.sizelibraryc                     < \        S R R7      # )r  r  r&   N_cs   rB   rC   #test_sample_numpy.<locals>.<lambda>D  s    F3,HrE   N)r   r      2      )r   r   r   g      ?g333333?)r2   r-   r0   r8   r6   r&   tupler^   r_   r`   r1   r4   rd   )distribs_numpyr  r  rT   sampssamr"  s         @rB   test_sample_numpyr+  4  s    3A!Q!Q(8934C89N
 D'"EEFA19ESzQXX%:%:%>%>>>>    "#q#sC8"$HIrE   c                  l  a	 \        R ^ ^ .RR.RR..4      \        R. R
O4      \        R^. RO4      .p ^p\        R4      pV'       g   \	        R4       R	# V  F  p\        W1R7      p\        VRR7      pV F3  p\        V4      VP                  P                  P                  9   d   K3  Q h	  \        ^4       FR  p\        ^4       F@  p\        WW,          V,          4      VP                  P                  P                  9   d   K@  Q h	  KT  	  K  	  \        R^RRR4      o	\        \        V	3R l4       R	# )rM   r   g?rF   rK   scipyz3Scipy not installed. Abort tests for _sample_scipy.)r  c                     < \        S 4      # rI   r   r!  s   rB   rC   #test_sample_scipy.<locals>.<lambda>\  s	    F3KrE   Nr   r   r$  r   r   r   r   )r>   r>   )r2   r-   r0   r8   r6   r&   r'  r^   r_   r`   ranger1   r4   rd   )
distribs_scipyr  r-  rT   r)  samps2r*  r   r   r"  s
            @rB   test_sample_scipyr5  G  s   3A#us|(DEl+C01N D'"EBCA1(EAF+FSzQXX%:%:%>%>>>> 1XqA 1.!((2G2G2K2KKKK "    "#q#sC8"$78rE   c                    a \        R ^^.^^ .^ ^..4      \        R. R	O4      \        R^. R
O4      .p ^p\        R4      pV'       g   \	        R4       R# V  FW  p\        W1RR7      pV FA  p\        VP                  4       4      VP                  P                  P                  9   d   KA  Q h	  KY  	  \        R^RRR4      o\        \        V3R l4       R# )rM   rF   rK   r   pymcz4PyMC is not installed. Abort tests for _sample_pymc.r  c                     < \        S R R7      # )r7  r  r   r!  s   rB   rC   "test_sample_pymc.<locals>.<lambda>o  s    F3,GrE   Nr0  r1  )r2   r-   r0   r8   r6   r&   r'  flattenr^   r_   r`   r1   r4   rd   )distribs_pymcr  r7  rT   r)  r*  r"  s         @rB   test_sample_pymcr<  _  s    3A!Q!Q(89l+C01M
 D DCDA18ES[[]+qxx/D/D/H/HHHH   "#q#sC8"$GHrE   c                     R  R 4       w  r\        V ^,          ) ^,          V ,           V^,          ^,          ,
          \        P                  ,
          4      ^\        ,          ,          p\	        RV4      p. ROpV Fu  p \        V4      pV'       d_   . . . rp\        V^
V^ R7      p\        V^
V^ R7      p\        V^
V^R7      p	\        Wx8H  4      '       g   Q h\        W8g  4      '       g   Q hKu  Kw  	  R#   \         d     K  i ; i)c              3   :   "   T F  p\        R V4      x  K  	  R# 5ir  r  r	  s   & rB   r  #test_sample_seed.<locals>.<genexpr>s  r  r  r9   )r  r  seedNr  )r-  r  r7  )	r   r	   r   r   r'   r8   r&   allrd   )
r   r   r  rT   	librarieslibimported_libs0s1s2s
             rB   test_sample_seedrH  r  s    .v.FB
r1ufQhmb!eAg%.
/2
6CSA*I
	(-LRAB!<AB!<AB!<28}}$}28}}$}   # 		s   ?A/C66DDc                  J   \        R ^ ^ .^ ^ .^ ^ ..4      p \        R ^ ^ .^ ^ .^ ^ ..4      p\        R ^ ^ .^ ^ .^ ^..4      pW8X  g   Q hRpV F  p \        V4      pV'       d   \        V ^VR7      p\        V^VR7      p\        V^VR7      p\	        VP                  4       4      \	        VP                  4       4      8X  g   Q hV FA  p	\	        V	P                  4       4      VP                  P                  P                  9   d   KA  Q h	  K  K  	  R#   \         d     K  i ; i)r9   r  N)r-  r  
r#   r2   r8   r&   r'  r:  r^   r_   r`   rd   
rA   rO   rh   rB  r  rD  rF  rG  s3ss
             rB   test_issue_21057rN    s#   sQFaVaV,-A3A!Q!Q(89AsQFaVaV,-A6M6"I
	(1LAAw7AAw7AAw7RZZ\*eBJJL.AAAAA -1F1F1J1JJJJ    # 		   B2DDD"!D"c                  J   \        R ^ ^ .^ ^ .^ ^ ..4      p \        R ^ ^ .^ ^ .^ ^ ..4      p\        R ^ ^ .^ ^ .^ ^..4      pW8X  g   Q hRpV F  p \        V4      pV'       d   \        V ^VR7      p\        V^VR7      p\        V^VR7      p\	        VP                  4       4      \	        VP                  4       4      8X  g   Q hV FA  p	\	        V	P                  4       4      VP                  P                  P                  9   d   KA  Q h	  K  K  	  R#   \         d     K  i ; i)r9   r  N)r7  rJ  rK  s
             rB   test_issue_21057_pymcrQ    s#   sQFaVaV,-A3A!Q!Q(89AsQFaVaV,-A6M6I
	(1LAAw7AAw7AAw7RZZ\*eBJJL.AAAAA -1F1F1J1JJJJ    # 		rO  N)hsympy.concrete.productsr   sympy.concrete.summationsr   sympy.core.numbersr   r   r   sympy.core.relationalr   sympy.core.singletonr	   sympy.core.symbolr
   (sympy.functions.combinatorial.factorialsr   r   $sympy.functions.elementary.complexesr   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   sympy.functions.special.besselr   'sympy.functions.special.gamma_functionsr   sympy.matrices.denser   &sympy.matrices.expressions.determinantr   sympy.sets.fancysetsr   sympy.sets.setsr   r   sympy.simplify.simplifyr   sympy.tensor.indexedr   r   r   sympy.integrals.integralsr   sympy.matricesr   r   "sympy.matrices.expressions.matexprr   sympy.statsr    r!   r"   r#   r$   r%   r&   sympy.stats.joint_rv_typesr'   r(   r)   r*   r+   r,   r   r-   r.   r   r/   r0   r1   r2   r3   sympy.testing.pytestr4   r5   r6   r7   sympy.externalr8   	sympy.abcr9   r:   rn   rt   r{   r   r   r   r   r   r   r  r  r  r  r+  r5  r<  rH  rN  rQ  r?   rE   rB   <module>rm     s   + ) 1 1 $ " % Q ; 6 9 : 2 9 $ > & 2 , 7 # / / < Z Z Z% % % % ; : ( :0z3	;D8EvT )>I&G$ B BW"
  
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