
    9i                       S r SSKrSSKJr  SSKJrJrJrJrJ	r	J
r
  SSKrSSKJr  SSKJr  SSKrSSKrSSKJrJrJr  SS	KJrJrJrJrJrJrJrJ r J!r!J"r"J#r#J$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4  SS
KJ5r5J6r6  SSK7J8r9  SSKJ:r:  SSK;J<r<J=r=J>r>  SSK;J?r?J@r@JArAJBrB  SSKCJDrD  SSKCJErE  SSKFJGrG  SSKHJIrI  SSKJJKrK  S rL " S S5      rMSAS jrNS rO\ " S S5      5       rP\ " S S5      5       rQ " S S5      rR " S S5      rS " S  S!5      rTS" rU " S# S$5      rV " S% S&5      rW " S' S(5      rX " S) S*5      rY " S+ S,5      rZ " S- S.5      r[ " S/ S05      r\ " S1 S25      r] " S3 S45      r^ " S5 S65      r_ " S7 S85      r`S9 ra\R                  R                  S: 5       rd " S; S<5      re " S= S>5      rf " S? S@5      rgg)Bz8
Test functions for multivariate normal distributions.

    N)	dataclass)assert_allcloseassert_almost_equalassert_array_almost_equalassert_equalassert_array_lessassert_)raises   )check_distribution_rvs)_PSD_lnBmultivariate_normal_frozen)multivariate_normalmultivariate_hypergeommatrix_normalspecial_ortho_grouportho_grouprandom_correlationunitary_group	dirichletbetawishartmultinomial
invwishartchi2invgammanormuniformks_2sampkstestbinom	hypergeommultivariate_tcauchy
normaltestrandom_tableuniform_directionvonmises_fisherdirichlet_multinomialvonmises)_covariance
Covariance)	_norm_pdf)stats)tanhsinhcubaturequad)rombqmc_quaddblquadtplquad)multigammaln)check_random_state_property)_qsimvtv)patchc                     [         R                  " U 5      [         R                  " U5      p[        X/UQ70 UD6  [        U R                  UR                  5        g N)npasarrayr   r   shape)resrefargskwargss       c/var/www/html/land-doc-ocr/venv/lib/python3.13/site-packages/scipy/stats/tests/test_multivariate.pyassert_closerE   /   s=    zz#

3C.t.v.CII&    c                      \ rS rSrS r\R                  \R                  R                  \R                  R                  \R                  R                  S S.r\R                  " \" \5      5      r\R                  " / SQ5      / SQ/ SQ/ SQ/\R                  " / S	Q5      / S
Q/ SQ/ SQ/S.r\\SS \/ SQ   \SS S.r\R$                  R'                  S\SS 5      S 5       r\R$                  R'                  S\" \5      5      \R$                  R'                  S\5      S 5       5       r\R$                  R'                  SS\" 5       SS/5      \R$                  R'                  S\" \5      5      \R$                  R'                  S\5      S 5       5       5       r\R$                  R'                  S\" 5       S/5      \R$                  R'                  S\5      S 5       5       rS r\R$                  R5                  S5      S 5       rS rSrg) TestCovariance5   c                 L   Sn[         R                  " [        US9   [        R                  " [
        R                  " S5      5        S S S 5        Sn[         R                  " [        US9   [        R                  " [
        R                  " S5      [
        R                  " S5      S9  S S S 5        Sn[         R                  " [        US9   [        R                  " S5        S S S 5        S	n[         R                  " [        US9   [        R                  " [
        R                  " S5      5        S S S 5        S
n[         R                  " [        US9   [        R                  " S[
        R                  " S5      45        S S S 5        Sn[         R                  " [        US9   [        R                  " [
        R                  " S5      S45        S S S 5        Sn[         R                  " [        US9   [        R                  " / SQ[
        R                  " S5      45        S S S 5        g ! , (       d  f       GN= f! , (       d  f       GN= f! , (       d  f       GNt= f! , (       d  f       GN8= f! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       g = f)Nz:The input `precision` must be a square, two-dimensional...match   z0`precision.shape` must equal `covariance.shape`.   )
covariancez7The input `diagonal` must be a one-dimensional array...alpacaz9The input `cholesky` must be a square, two-dimensional...z4The input `eigenvalues` must be a one-dimensional...z,The input `eigenvectors` must be a square...z9The shapes of `eigenvalues` and `eigenvectors` must be...r   rM   rN   )pytestr
   
ValueErrorr,   CovViaPrecisionr=   oneseyeCovViaDiagonalCovViaCholeskyCovViaEigendecompositionselfmessages     rD   test_input_validation$TestCovariance.test_input_validation7   s   N]]:W5''
3 6 E]]:W5''q	bffQiH 6 L]]:W5&&x0 6 N]]:W5&&rwwqz2 6 I]]:W500(BFF1I1FG 6 A]]:W500"''!*h1GH 6 N]]:W500)RVVAY1GH 651 65 65 65 65 65 65 65sS   +H+*>H=I+I!-I3#-J3/J+
H:=
I
I!
I03
J
J
J#c                     [        U SS9$ )NTallow_singular)r   )xs    rD   <lambda>TestCovariance.<lambda>Y   s    %)!D%ArF   )Diagonal	PrecisionCholeskyEigendecompositionPSDrQ   )   r   rN   )r         )rN   rl      )r   r   rN   )rj   r   )rn   rj   r   r   r   r   )diagonal full rankzgeneral full rankzdiagonal singularzgeneral singularr   N)r   rn   rq   cov_type_namern   c                    [         R                  " / SQ5      n/ SQn[        [        SU 35      nU R                  U   n[        [
        SUR                  5        35      nU" U" U5      5      nU" U" U5      5      n[        U5      [        U5      L d   e[        UR                  U5      UR                  U5      5        g )NrQ   )rM   rj   CovViafrom_)
r=   diaggetattrr,   _covariance_preprocessingr-   lowertyper   whiten)	r[   rr   Arb   cov_typepreprocessingfactoryr@   rA   s	            rD   test_factoriesTestCovariance.test_factoriese   s    GGI;&(@A66}E*m.A.A.C-D&EFmA&'}Q'(CyDI%%%

1szz!}5rF   matrix_typec                    SU SU S3nX R                   U   ;  a  [        R                  " U5        U R                  U   n[	        [
        SU 35      nU R                  U   n[        USS9nU" U" U5      5      n[        UR                  UR                  5        [        UR                  UR                  5        [        UR                  [        R                  " U5      R                  5        [        UR                  [        R                  " U5      5        [        R                   R#                  S5      n	U	R!                  SS9n
UR%                  U
5      nXR&                  -  n[        X-  X-  5        [)        US	5      (       a!  S
U;  a  [        UR+                  U5      U
5        U	R!                  SS9n
UR%                  U
5      nXR&                  -  n[        US-  R-                  SS9US-  R-                  SS95        [)        US	5      (       a!  S
U;  a  [        UR+                  U5      U
5        [)        US	5      (       aH  UR+                  [        R.                  " [1        U5      5      5      n[        UR2                  U-  U5        g g )Nru    does not support 	 matricesTr`      VGiVK rN   size	_colorizesingularrM   rl   rN   rM   rn   axis)
_cov_typesrR   skip	_matricesrx   r,   ry   r   rE   log_pdetr   rankr?   r=   r>   rO   randomdefault_rngr|   UhasattrcolorizesumrV   lenT)r[   r   rr   r\   r}   r~   r   psd
cov_objectrngrb   r@   rA   s                rD   test_covarianceTestCovariance.test_covariances   s    M?*<[M J  <<KK NN;';&(@A66}E1T* mA./
Z((#,,7Z__chh/Z%%rzz!}':':;Z**BJJqM: ii##$78JJAJ"%%iSY	*:{++
+0M,,S115 JJIJ&"%%ic1f\\r\*S!VLLbL,AB:{++
+0M,,S115 :{++%%bffSVn5Ca( ,rF   r   r   c                    SU SU S3nX0R                   U   ;  a  [        R                  " U5        U R                  U   n[	        [
        SU 35      nU R                  U   n/ SQnU" U" U5      5      n	[        n
[        XSS9n[        XSS9n[        R                  R                  S5      nUR                  XUS9n[        R                  R                  S5      nU
R                  XXS	9n[        R                  R                  S5      nU
" XUS
9R                  US9n[        U	[
        R                  5      (       aA  [        U[        R                  " U5      5        [        U[        R                  " U5      5        OL[!        UR"                  UR"                  5        [!        UR"                  UR"                  5        [        UU5        [        U
R%                  XU	5      UR%                  U5      5        [        UR%                  U5      UR%                  U5      5        [        U
R'                  XU	5      UR'                  U5      5        [        UR'                  U5      UR'                  U5      5        [        U
R)                  X5      UR)                  5       5        [        UR)                  5       UR)                  5       5        g )Nru   r   r   皙?皙?333333?Tr`   r   r   r   random_stateseed)r   rR   r   r   rx   r,   ry   r   r=   r   r   rvs
isinstance	CovViaPSDrE   squeezer   r?   pdflogpdfentropy)r[   r   r   rr   r\   r}   r~   r   meanr   mvndist0dist1r   rb   x1x2s                    rD   test_mvn_with_covariance'TestCovariance.test_mvn_with_covariance   s    M?*<[M J  <<KK NN;';&(@A66}EmA./
!#DDA#DTJii##$78##D$#7ii##$78WWTDWCii##$78,00d0;j+"7"788RZZ]+RZZ]+177+177+R SWWQj1599Q<@UYYq\599Q<0SZZ4ell1oFU\\!_ell1o6S[[2EMMODU]]_emmo6rF   c                 t   SnU R                   U   n[        [        SU 35      nU R                  U   n/ SQnU" U" U5      5      n[        n	[	        XtSS9n
[	        XxSS9n[
        R                  R                  S5      nUR	                  XtUS9n[        U	R                  XU5      U
R                  U5      5        [        UR                  U5      U
R                  U5      5        [        U	R                  XU5      U
R                  U5      5        [        UR                  U5      U
R                  U5      5        g )Nrp   ru   r   Tr`   r   r   )r   rx   r,   ry   r   r=   r   r   rE   cdflogcdf)r[   r   rr   r   r}   r~   r   r   r   r   r   r   r   rb   s                 rD   test_mvn_with_covariance_cdf+TestCovariance.test_mvn_with_covariance_cdf   s    +NN;';&(@A66}EmA./
!#DDA#DTJii##$78##D$#7SWWQj1599Q<@UYYq\599Q<0SZZ4ell1oFU\\!_ell1o6rF   c                     Sn[         R                  " [        US9   [        5         S S S 5        g ! , (       d  f       g = f)Nz7The `Covariance` class cannot be instantiated directly.rK   )rR   r
   NotImplementedErrorr-   rZ   s     rD   test_covariance_instantiation,TestCovariance.test_covariance_instantiation   s'    K]].g>L ?>>s   0
>zignore::RuntimeWarningc                 p   [         R                  " / SQ5      nUR                  S   n[         R                  " U5      n[        R
                  " [        SS9   [        X15      R                  5         S S S 5        Sn[         R                  R                  U5      n[         R                  R                  U5      n[        R                  " [         R                  R                  U5      5      n[        X75      nUR                  US9n	[        R                  " X7US9n
[        X5        g ! , (       d  f       N= f)N)r   rM   g:0yEr   zThe input matrix must be...rK   l   .ypGw r   )r=   rw   r?   zerosrR   r
   rS   r   r   r   r   r-   from_eigendecompositionlinalgeighr   )r[   r}   nr   r   rng1rng2covrvr@   rA   s              rD   test_gh9942TestCovariance.test_gh9942   s    
 GGM"GGAJxx{ ]]:-JK(,,. L #yy$$T*yy$$T*001BC +ff$f'!%%ddCS LKs   D''
D5c                 d   [         R                  " S5      n[        R                  " [         R                  " S5      [         R
                  " S5      45      n[        R                  R                  XS9nUR                  S S9n[        XA5        [        R                  R                  R                  [         R                  " SS/5      [         R                  " SS/SS//5      45      n[        R                  R                  XS9nUR                  S S9nUS   US   :w  d   eUS   US   :X  d   eg )	NrM   r   r   r         ?        g      y@r   r   )r=   rU   r-   r   r   rV   scipyr/   r   r   r   array)r[   r   r   distr   s        rD   test_gh19197TestCovariance.test_gh19197  s    
 wwqz00"((1+rvvay1IJ{{..D.BhhDh!Skk$$<<XXr2hB8b$Z*@!ABD{{..D.BhhDh!1va   1va   rF    )__name__
__module____qualname____firstlineno__r]   r=   rw   r   invcholeskyr   ry   r   list_all_covariance_typesr   r   rR   markparametrizer   r   tupler   r   r   filterwarningsr   r   __static_attributes__r   rF   rD   rH   rH   5   s	   I< .0WW.0iimm-/YY-?-?79yy~~)B	!C HHT*C%DE')wwy'9'0)Y&G&(ggi&8&0*i%HJI )>'<QR'@'<['I&;BC&@BJ
 [[_.CCR.HI6 J6 [[]DO<[[_.CD-) E =-)^ [[VdEGQ	%BC[[]DO<[[_.CD#7 E = D#7J [[Vegy%9:[[_.CD7 E ;70
 [[ 89 :,!rF   rH   c                    UR                  X 45      nXDR                  -  n[        R                  R	                  U5      u  pVU(       a  UR                  U S9S:  nSX'   U[        R                  " U5      -  UR                  -  nU$ )Nr   r   )r   r   r=   r   r   normalrw   )	dimevalsr   r   r}   _v	zero_eigsr   s	            rD   _random_covariancer     ss     	

C:A	CCA99>>!DAJJCJ(1,	
bggen
qss
"CJrF   c                     [         R                  R                  X 5      n[        R                  R                  U5      u  p#nU$ r<   )r=   r   randnr   r   svd)r   Musr   s        rD   _sample_orthonormal_matrixr   #  s1    
		Allq!GA!HrF   c                   ,  ^  \ rS rSr% Sr\\S'   \R                  \S'   \R                  \S'   \R                  \S'   \R                  \S'   \	\S'   \	\S	'   S
r
\	S
-  \S'   U 4S jr\SS j5       r\SS j5       r\SS j5       rS rS rS rS rSrU =r$ )
MVNProblemi)  a$  Instantiate a multivariate normal integration problem with special structure.

When covariance matrix is a correlation matrix where the off-diagonal entries
``covar[i, j] == lambdas[i]*lambdas[j]`` for ``i != j``, then the multidimensional
integral reduces to a simpler univariate integral that can be numerically integrated
easily.

The ``generate_*()`` classmethods provide a few options for creating variations
of this problem.

References
----------
.. [1] Tong, Y.L. "The Multivariate Normal Distribution".
       Springer-Verlag. p192. 1990.
ndimlowhighlambdascovar
target_val
target_errNtrue_valc                   > [         TU ]  5         Xl        X l        X0l        X@l        [        R                  " U R
                  U R
                  5      U l        [        R                  " U R                  S5        U R                  5         g Nr   )super__init__r   r   r   r   r=   outerr   fill_diagonalfind_target)r[   r   r   r   r   	__class__s        rD   r  MVNProblem.__init__F  s\    		XXdllDLL9

S)rF   c                    [         R                  R                  U5      n[         R                  " U[         R                  * 5      nUR                  S[         R                  " U5      US9nUR                  SSUS9nU " UUUUS9nU$ )zDRandom lambdas, random upper bounds, infinite lower bounds.
        r   r         r   r   r   r   r   r=   r   r   fullinfr   sqrtclsr   r   r   r   r   r[   s          rD   generate_semigeneralMVNProblem.generate_semigeneralQ  s{     ii##C(ggdRVVG${{3D{9++dCd+3	
 rF   c                 d   [         R                  R                  U5      n[         R                  " U[         R                  * 5      nUR                  S[         R                  " U5      US9n[         R                  " UR                  SS5      5      n[         R                  " X5      nU " UUUUS9nU$ )zVConstant off-diagonal covariance, random upper bounds, infinite lower bounds.
        r   r   r   r
  r  )r  r   r   r   r   sigmar   r[   s           rD   generate_constantMVNProblem.generate_constantb  s     ii##C(ggdRVVG${{3D{9C-.''$&	
 rF   c                     [         R                  " U[         R                  * 5      n[         R                  " U5      n[         R                  " S5      nU " UUUUS9nSUS-   -  Ul        U$ )zjOff-diagonal covariance of 0.5, negative orthant bounds.

True analytically-derived answer is 1/(ndim+1).
      ?r
  r   )r=   r  r  r   r  r   r  s          rD   generate_halvesMVNProblem.generate_halvest  s`     ggdRVVG$xx~''#,	
 T!VrF   c                     [        SSS9nUR                  U5        [        U R                  40 UD6u  U l        U l        g)z?Perform the simplified integral and store the results.
              "      "@abNdictupdater2   univariate_funcr   r   r[   kwdsds      rD   r  MVNProblem.find_target  s?     
 	
+/0D0D+J+J(rF   c           
         [         R                  " SU R                  S-  -
  5      n[         R                  " [        R
                  " U R                  U R                  USS2[         R                  4   -  -   U-  5      [        R
                  " U R                  U R                  USS2[         R                  4   -  -   U-  5      -
  SS9$ )zPThe parameter-specific term of the univariate integrand,
for separate plotting.
r   rM   Nr   )	r=   r  r   prodspecialndtrr   newaxisr   )r[   tdenoms      rD   _univariate_termMVNProblem._univariate_term  s     DLL!O+,wwLL$))dll1Q

]3C&CCuLMLL$((T\\!ArzzM2B%BBeKLM
 	
rF   c                     [         R                  " U5      n[         R                  " [        U5      U R	                  U5      -  5      $ )zUnivariate integrand.
        )r=   
atleast_1dr   norm_pdfr0  r[   r.  s     rD   r$  MVNProblem.univariate_func  s5     MM!zz(1+(=(=a(@@AArF   c                    SSK Jn  [        R                  " SSS5      nUR	                  U[        U5      SS9  UR	                  X R                  U5      SS9  UR	                  X R                  U5      S	S9  UR                  5         g
)QPlot the univariate integrand and its component terms for understanding.
        r   pyplotr  r    	$\phi(t)$label$f(t)$$f(t)*phi(t)$N)	
matplotlibr:  r=   linspaceplotr4  r0  r$  legendr[   pltr.  s      rD   plot_integrandMVNProblem.plot_integrand  so     	-KKc4(HQK|4))!,I>((+3CD

rF   )r   r   r   r   r   r   r   r   r<   )r   r   r   r   __doc__int__annotations__r=   ndarrayfloatr   r  classmethodr  r  r  r  r0  r$  rG  r   __classcell__)r  s   @rD   r   r   )  s     J
**::jjJJ #Hut|"	     "  $K	
B	 	rF   r   c                       \ rS rSr% Sr\\S'   \R                  \S'   \R                  \S'   \R                  \S'   \R                  \S'   \	\S'   \	\S	'   S
 r
\SS j5       rS rS rS rS rSrg)SingularMVNProblemi  a  Instantiate a multivariate normal integration problem with a special singular
covariance structure.

When covariance matrix is a correlation matrix where the off-diagonal entries
``covar[i, j] == -lambdas[i]*lambdas[j]`` for ``i != j``, and
``sum(lambdas**2 / (1+lambdas**2)) == 1``, then the matrix is singular, and
the multidimensional integral reduces to a simpler univariate integral that 
can be numerically integrated fairly easily.

The lower bound must be infinite, though the upper bounds can be general.

References
----------
.. [1] Kwong, K.-S. (1995). "Evaluation of the one-sided percentage points of the
       singular multivariate normal distribution." Journal of Statistical
       Computation and Simulation, 51(2-4), 121-135. doi:10.1080/00949659508811627
r   r   r   r   r   r   r   c                 B   Xl         X l        X0l        [        R                  " U[        R
                  * 5      U l        [        R                  " U R                  U R                  5      * U l        [        R                  " U R                  S5        U R                  5         g r   )r   r   r   r=   r  r  r   r  r   r  r  )r[   r   r   r   s       rD   r  SingularMVNProblem.__init__  sf    		774"&&)hht||T\\::

S)rF   Nc                 H   [         R                  R                  U5      nUR                  S[         R                  " U5      US9nUR                  [         R                  " US5      5      n[         R                  " USU-
  -  5      UR                  SS/US9-  nU " UUUS9nU$ )z/Singular lambdas, random upper bounds.
        r   r   r   r   r	  )r   r   r   )r=   r   r   r   r  r   r  choice)r  r   r   r   pr   r[   s          rD   generate_semiinfinite(SingularMVNProblem.generate_semiinfinite  s     ii##C({{3D{9MM"''$,-''!qs)$szz4+Dz'II

 rF   c                     [        SSS9nUR                  U5        [        U R                  40 UD6u  U l        U l        g )Nr  r  r  r!  r%  s      rD   r  SingularMVNProblem.find_target  s=    
 	
+/0D0D+J+J(rF   c           	         [         R                  " SU R                  S-  -   5      n[         R                  " [        R
                  " U R                  SU R                  -  US S 2[         R                  4   -  -
  U-  5      SS9n[         R                  " [        R
                  " U R                  * SU R                  -  US S 2[         R                  4   -  -   U-  5      SS9nUSU R                  -  U-  -
  R                  $ )Nr   rM   y              ?r   rn   )
r=   r  r   r*  r+  r,  r   r-  r   real)r[   r.  r/  i1i2s        rD   r0  #SingularMVNProblem._univariate_term  s    DLL!O+,WWLL$))boa2::6F&FF%OP
 WWLL499*r$,,qBJJ7G'GG5PQ
 b499_r))///rF   c                     [         R                  " U5      n[        U5      U R                  U5      -  R	                  5       $ r<   )r=   r3  r4  r0  r   r5  s     rD   r$  "SingularMVNProblem.univariate_func  s3    MM!d33A66??AArF   c                 4   SSK Jn  [        R                  " SSS5      nUR	                  U[        U5      SS9  UR	                  X R                  U5      SS9  UR	                  X R                  U5      S	S9  UR                  S
S5        UR                  5         g)r8  r   r9  r  r  r;  r<  r=  r?  r@  皙皙?N)
rA  r:  r=   rB  rC  r4  r0  r$  ylimrD  rE  s      rD   rG  !SingularMVNProblem.plot_integrand  s}     	-KKc4(HQK|4))!,I>((+3CDs

rF   )r   r   r   r   r   r   r   r<   )r   r   r   r   rI  rJ  rK  r=   rL  rM  r  rN  rW  r  r0  r$  rG  r   r   rF   rD   rQ  rQ    sq    " J
**::jjJJ  K0B
rF   rQ  c                      \ rS rSrS rS rS rS rS rS r	S r
S	 rS
 rS rS rS rS rS r\R&                  R)                  S\R,                  " S5      \R0                  " SS/5      /5      S 5       rS rS rS rS rS rS rS r S r!S r"S r#S r$S r%S  r&S! r'\R&                  RP                  \R&                  R)                  S"SS#/5      S$ 5       5       r)S% r*\R&                  R)                  S"\+" SS&5      5      \R&                  R)                  S'S(S)/5      S* 5       5       r,\R&                  R)                  S"\+" SS+5      5      \R&                  R)                  S'S(S)/5      S, 5       5       r-\R&                  R)                  S"\+" S-S+5      5      \R&                  R)                  S'S(S./5      S/ 5       5       r.S0 r/S1 r0\R&                  R)                  S2S35      S4 5       r1S5 r2\R&                  R)                  S6\Rf                  " S75      \Rf                  " S85      /5      S9 5       r4\R&                  R)                  S:\Rf                  " S;5      \Rf                  " S<5      \Rf                  " S=5      /5      S> 5       r5S? r6S@ r7SA r8SBr9gC)DTestMultivariateNormali
  c                 \   [         R                  " S5      n[         R                  " S5      n[        [        [
        R                  SX5        [        [        [
        R                  SX5        [        [        [
        R                  SX5        [        [        [
        R                  SX5        g )NrN   rM   r   r   r   r   rM   )r=   arangeidentityassert_raisesrS   r   r   r   )r[   mur   s      rD   test_input_shape'TestMultivariateNormal.test_input_shape  sp    YYq\kk!nj"5"9"962Kj"5"9"99bNj"5"9"962Kj"5"9"99bNrF   c                    [         R                  R                  S5        Su  pn[        R                  " XU5      n[        UR                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " [         R                  R                  S5      5      n[        R                  " XU5      n[        UR                  S5        Su  pn[        R                  " XU5      n[        UR                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " [         R                  R                  S5      5      n[        R                  " XU5      n[        UR                  S5        g )N  )      ?g333333?      @r   rj   )
r=   r   r   r   r   r   r   r   absr   )r[   rb   r   r   r   r   s         rD   test_scalar_values)TestMultivariateNormal.test_scalar_values  s*   
		t %!%%as3SXXq! IIOOAyyq!ffRYY__Q'(!%%as3SXXq! %!%%as3SXXq! IIOOAyyq!ffRYY__Q'(!%%as3SXXq!rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " [         R                  R                  S5      5      n[
        R                  " XU5      n[
        R                  " XU5      n[        U[         R                  " U5      5        g Nrs  rj   )
r=   r   r   r   rv  r   r   r   r   logr[   rb   r   r   d1d2s         rD   test_logpdf"TestMultivariateNormal.test_logpdf.      
		tIIOOAyyq!ffRYY__Q'( ''5 $$Qc2BFF2J'rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[        R
                  " U5      n[        R                  " U5      n[        R
                  " US S5      n[        R                  " US S5      n[        U[         R                  " U5      5        [        U[         R                  " U5      5        g Nrs  rj   r   )	r=   r   r   r   r   r   r   r   r{  r[   rb   r}  r~  d3d4s         rD   test_logpdf_default_values1TestMultivariateNormal.test_logpdf_default_values8       			tIIOOA ''* $$Q' ''43 $$Qa0BFF2J'BFF2J'rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " [         R                  R                  S5      5      n[
        R                  " XU5      n[
        R                  " XU5      n[        U[         R                  " U5      5        g rz  )
r=   r   r   r   rv  r   r   r   r   r{  r|  s         rD   test_logcdf"TestMultivariateNormal.test_logcdfE  r  rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[        R
                  " U5      n[        R                  " U5      n[        R
                  " US S5      n[        R                  " US S5      n[        U[         R                  " U5      5        [        U[         R                  " U5      5        g r  )	r=   r   r   r   r   r   r   r   r{  r  s         rD   test_logcdf_default_values1TestMultivariateNormal.test_logcdf_default_valuesO  r  rF   c                    [         R                  R                  S5        Sn[         R                  R                  U5      n[	        SUS-   5       Hl  n[         R                  R                  X5      n[         R
                  " XDR                  5      n[        X%SS9n[        UR                  R                  U5        Mn     g )Nrs  rl   r   Tr`   )r=   r   r   r   rangedotr   r   r   r   r   )r[   r   r   expected_rankr   r   distns          rD   	test_rank TestMultivariateNormal.test_rank\  s    
		tyyq!"1a!e_M		1A&&CC.C'$GE))..>	 -rF   c           	         [        SS5       GH  n[        R                  R                  U5      n[        SU5       GH  n[        R                  R                  X35      n[        R                  " XDR
                  5      n[        R                  " X45      nXVS U2S U24'   [        R                  " U5      nUS U US U& [        U5      n[        R                  " U[        R                  " XhR
                  5      5      n	[        R                  " X5      n
[        [        R                  " U5      USS9n[        [        R                  " U5      USS9n[        [        R                  " U5      U	SS9n[        UR                  R                  U5        [        UR                  R                  U5        [        UR                  R                  U5        UR                  US U 5      nUR                  U5      nUR                  U
5      n[        X5        [        UU5        UR                  US U 5      nUR                  U5      nUR                  U
5      n[        UU5        [        UU5        XS S 2S4   -   nUR                  U5      nUR                  U5      n[        US5        [        U[        R                  * 5        GM     GM     g )Nr   rj   Tr`   rn   r   )r  r=   r   r   r  r   r   r   r   r   r   r   r   r   r   r  )r[   r   zkr   cov_kkcov_nnrb   r   cov_rrydistn_kkdistn_nndistn_rrpdf_kkpdf_nnpdf_rr	logpdf_kk	logpdf_nn	logpdf_rry_orthpdf_rr_orthlogpdf_rr_orths                          rD   test_degenerate_distributions4TestMultivariateNormal.test_degenerate_distributionsg  s2   q!A		"A1a[IIOOA)33 1&)!'rr2A2v HHQK"1"1 /q1266&###67FF1L /rxx{F>BD.rxx{F>BD.rxx{F>BDX0055q9X0055q9X0055q9!ae,!a!a//$OOAbqE2	$OOA.	$OOA.		95	95 q"uX&ll62!)!8 [#.^bffW5] ! rF   c           	      h   Sn[        SS5       GH  n[        SU5       GH
  n[        R                  " U5      n[        U5      S S 2S U24   n[        R                  " XUR
                  5      n[        R                  " XFUS9n[        R                  " XtUSS9n[        UR                  U5        [        R                  " US:  5      (       d   e[        R                  " XtUSS9n	[        U	R                  U5        [        R                  " U	[        R                  * :  5      (       a  GM   e   GM"     g )	N
   rM   rk   r   r   r   r   T)r   r   ra   r   )r  r=   r   r   r  r   r   r   r   r   r   allr   r  )
r[   r  r   rmnr   vrXr   r   s
             rD   test_degenerate_array,TestMultivariateNormal.test_degenerate_array  s     q!A1a[XXa[.q1!RaR%8VVAss^'++!D)--ab=ACSXXq)vvcCi((((,33ABCGIV[[!,vvfw.//// ! rF   c                 <   SnSnSn[         R                  " X-  5      nX#-   n[         R                  " XU4[        S9n[         R                  " Xd5        SXc* S 2U* S 24'   [        [        R                  R                  U5      S5        [        [        R                  R                  US U2S U24   5      [         R                  5        [        [         R                  R                  US U2S U24   5      SU45        [        U5      n[        UR                  U5        g )Ng     @@d   rM   dtyper   r   )r=   expr   rM  r  r   r   r   detr  r   slogdetr   r   )r[   large_total_lognposnzerolarge_entryr   r   r   s           rD   test_large_pseudo_determinant4TestMultivariateNormal.test_large_pseudo_determinant  s    
 !ff_34LhhvU+
* !FGeVW 	U\\%%c*A.U\\%%c%4%$,&78"&&A		))#eteUdUl*;<O,	. 3io6rF   c                 :   [         R                  R                  S5      nSnUR                  X"5      n[         R                  " X3R
                  5      nUR                  U5      nUR                  SSU5      n[        R                  " XeU5      n[        R                  " XeU5      n[        S5       Hh  n	[        S5       HV  n
[        R                  " XiU
4   XT5      n[        XX4   5        [        R                  " XiU
4   XT5      n[        XX4   SS9  MX     Mj     g )Nrs  rl   rM   rN   MbP?rtol)r=   r   RandomStater   r  r   r   r   r   r  r   )r[   r   r   datar   r   r  desired_pdfdesired_cdfijactuals               rD   test_broadcasting(TestMultivariateNormal.test_broadcasting  s    ii##D) yyffT66"yy| IIaA *--as;)--as;qA1X,00a4$DAC(89,00a4$DAC(8tD  rF   c                 *   [         R                  " SSS5      nSu  p#US-  n[        R                  " XU5      n[        R                  " XU5      n[        XV5        [        R                  " XU5      n[        R                  " XU5      n[        XV5        g )Nr   rM   r  )333333??r  )r=   rB  r   r   r   r   r   )r[   rb   r   r   scaler}  r~  s          rD   test_normal_1D%TestMultivariateNormal.test_normal_1D  sz     KK1b!	SXXau% $$Qc2XXau% $$Qc2rF   c                 6   [         R                  " SS/5      n[         R                  " SS/SS//5      nSnSUS-
  -  n[         R                  " S	SU5      n[         R                  " XU5      u  pg[         R                  " X3S
45      nXhS S 2S S 2S	4'   XxS S 2S S 2S4'   [
        R                  " XU5      n	[        XS	S9n
[        XSS9n[        R                  " XQS	   US   S-  S9n[        R                  " XQS   US   S-  S9n[        XSSS9  [        XSSS9  g )Nru  g      @r  r   333333?i  rk   r   r   rM   r   r   r   locr  )r   r   {Gz?r  atol)
r=   r   rB  meshgridemptyr   r   r3   r   r   )r[   r   r   r   deltar   xvyvposr   margin_xmargin_ygauss_xgauss_ys                 rD   test_marginalization+TestMultivariateNormal.test_marginalization  s    xxc
#hhS	C9-.QUKK1a Q"hhay!Aq!GAq!G!%%c5 ++ ((1q'Tc1AB((1q'Tc1AB4@4@rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " [         R                  R                  S5      5      n[        X#5      n[        UR                  U5      [
        R                  " XU5      5        [        UR                  U5      [
        R                  " XU5      5        [        UR                  U5      [
        R                  " XU5      5        [        UR                  U5      [
        R                  " XU5      5        g rz  )r=   r   r   r   rv  r   r   r   r   r   r   )r[   rb   r   r   norm_frozens        rD   test_frozen"TestMultivariateNormal.test_frozen  s    
		tIIOOAyyq!ffRYY__Q'()$4*,?,C,CAS,QR**1-+221C@	B*,?,C,CAS,QR**1-+221C@	BrF   rO   rM   r   c                    [         R                  " S5      n[         R                  " S5      n[        X!5      n[         R                  " UR
                  U5      (       d   e[         R                  " UR                  U5      (       d   eg )NrM   rM   )r=   rU   rV   r   allcloser   r   )r[   rO   r   cov_should_ber  s        rD   2test_frozen_multivariate_normal_exposes_attributesITestMultivariateNormal.test_frozen_multivariate_normal_exposes_attributes  s`     wwt}q	)$;{{;++T2222{{;??M::::rF   c           
         [         R                  R                  S5        Sn[         R                  R                  X5      n[         R                  " X"R
                  5      n[        R                  R                  U5      u  pE[         R                  " US5      nSUS'   SUS'   [         R                  " U[         R                  " [         R                  " U5      UR
                  5      5      nSn[        X6S	9n[        UR                  US	9n[        UR                  [         R                  " [         R                   " US S 5      5      5        [        UR                  * UR                  5        g )
Nrs  rm   r  r   r   Hz>rn   h㈵>)cond)r=   r   r   r   r  r   r   r   r   r  rw   r   pinvr   r   r   r{  )	r[   r   rb   r   r   r   r  r   psd_pinvs	            rD   test_pseudodet_pinv*TestMultivariateNormal.test_pseudodet_pinv$  s     			tIIOOA!ffQn||  %GGAsO!"ffQrwwqz133/0 3"t, 	bffRVVAcrF^&<= 	x'8'89rF   c                 >    / SQ/ SQ/n[        [        [        U5        g )NrQ   rl   rj   rk   rn  rS   r   r[   r   s     rD   test_exception_nonsquare_cov3TestMultivariateNormal.test_exception_nonsquare_cov>  s    )$j$,rF   c                     SS/S[         R                  //n[        [        [        U5        SS/S[         R
                  //n[        [        [        U5        g )Nr   r   )r=   nanrn  rS   r   r  )r[   cov_nancov_infs      rD   test_exception_nonfinite_cov3TestMultivariateNormal.test_exception_nonfinite_covB  sF    q6Arvv;'j$0q6Arvv;'j$0rF   c                 >    SS/SS//n[        [        [        U5        g )Nr   r   rn   r  r  s     rD   test_exception_non_psd_cov1TestMultivariateNormal.test_exception_non_psd_covH  s     1v2wj$,rF   c                    [         R                  R                  S5        [         R                  R                  S5      n[         R                  R                  S5      n[         R                  " S5      n[         R
                  R                  n[        U[        X#5        [        U[        R                  XU5        [        U[        R                  XU5        [        U[        R                  XU5        [        U[        R                  XU5        SS/SS//nSn[        R                  " [         R
                  R                  US9   [        US9  S S S 5        g ! , (       d  f       g = f)	Nrs  rj   )rj   rj   r   r   z0When `allow_singular is False`, the input matrixrK   r   )r=   r   r   r   rU   r   LinAlgErrorrn  r   r   r   r   r   rR   r
   )r[   rb   r   r   emsgs         rD   test_exception_singular_cov2TestMultivariateNormal.test_exception_singular_covL  s    
		tIIOOAyyq!ggfoII!!a,d8a,00!3?a,33QcBa,00!3?a,33QcB Bx"b"@]]29900<C( =<<s   
E
E'c                 0   [         R                  " / SQ5      n[         R                  " SSS5      nSU-  S-
  nU[         R                  " U5      -   n[         R                  " X#U/5      R                  n[         R                  " / SQS5      n[         R                  " / SQ/ S	Q/ S
Q/S5      n[
        R                  " XVU5      n[        XSS9  [         R                  " / SQ5      n	[
        R                  " XVU5      n
[        XSS9  [         R                  " / SQ5      n[         R                  " X#/5      R                  n[         R                  " SS/S5      n[         R                  " SS/SS//S5      n[
        R                  " XU5      n[        XSS9  g )N)g0Q-?gox'V?g[S, t?gDB?gc_.?r   rM   rj   rN   )r   rN   rM   r'  r   rM   r   )rM   rj   r  )r   r  rN   绽|=r  )gwk:E]?g̙Z?g0?gL8?gAG*?gh㈵>)gIى?gG?gƏ)?gėh?gEE?r   r  )	r=   r   rB  cosr   r   r   r   r   )r[   r_pdfrb   r  r  r  r   r   r   r_cdfr   r_cdf2r2mean2cov2cdf2s                   rD   test_R_values$TestMultivariateNormal.test_R_values_  sQ     6 7 KK1a EAIq	MHHaAY!!xx	3'hh	:z:C@!%%as3/  6 7 "%%as3.  3 4 XXqf!Q%xx!Q!Q(#."&&r$740rF   c                     [         R                  " S5      n[         R                  " S5      n[        XSS9nUR                  5       n[	        USS/5        g )NrM   rM   rM   Tr`   r   )r=   r   r   r   r   )r[   r   rO   modelsamples        rD   ,test_multivariate_normal_rvs_zero_covarianceCTestMultivariateNormal.test_multivariate_normal_rvs_zero_covariance  sB    xx{XXf%
#DTJVaV$rF   c                    SnSn[         R                  " [        R                  " U5      SUS9n[	        UR
                  X45        [         R                  " S [        R                  " SS/SS//5      US9n[	        UR
                  US45        [        SSS9nUR                  U5      n[	        UR
                  U45        g )	Ni,  rl   r   r  rM   r   r   r   )r   r   r=   r   r   r?   r   )r[   Nr'  r#  r   s        rD   test_rvs_shape%TestMultivariateNormal.test_rvs_shape  s     $((bhhqkqqIV\\A6*$((d-/XX2wQ6H-I./1 	V\\Aq6*QA.qV\\A5)rF   c                 ~   [         R                  R                  S5      nSnUR                  U5      nUR                  X"5      n[         R                  " XDR
                  5      nSn[        R                  " X5XaS9n[        [         R                  " UR
                  5      USS9  [        UR                  S5      USS9  g )N  rN     r   r   r  r   )r=   r   r  r   r  r   r   r   r   r   r   )r[   r   r   r   r   r   r   r#  s           rD   test_large_sample(TestMultivariateNormal.test_large_sample  s     ii##D)yy|IIaOffQn$((DKvxx(#D9A48rF   c                 h   [         R                  R                  S5      nSnUR                  U5      nUR                  X"5      n[         R                  " XDR
                  5      n[        X55      n[        UR                  5       [        R                  " X55      5        [         R                  R                  U5      S   nSU[         R                  " S[         R                  -  5      S-   -  [         R                  " [         R                  " U5      5      -   -  n[        XR                  5       5        g )Nr+  rN   r   r  rM   r   )r=   r   r  r   r  r   r   r   r   r   eigr{  pir   )	r[   r   r   r   r   r   r   eigsdesireds	            rD   test_entropy#TestMultivariateNormal.test_entropy  s    ii##D)yy|IIaOffQn + 	BJJL*=*E*Ed*PQ yy}}S!!$1q255y 1A 56t9MMNGZZ\2rF   c                     [         R                  " / SQ5      nSn[        [         R                  " [	        U5      5      U5        g )Nr   r   r   r  )r=   r   r   r  r   )r[   alphar3  s      rD   test_lnBTestMultivariateNormal.test_lnB  s,    #BFF4;/9rF   c                 r   [         R                  R                  S5      nSS/n[         R                  " S5      nUR                  S5      S-  S-
  nUR                  S5      S-  S-
  n[        R
                  " XRX4S9n[        R
                  " XRU5      n[        R
                  " XBU5      n[         R                  " USSS	24   USS	S24   4S
S9n	[         R                  " USS	S24   USSS	24   4S
S9n
[        R
                  " XU5      n[        R
                  " XU5      nXx-   U-
  U-
  n[        Xm5        g )N   FYc@Y r   rM   )rl   rN   rM   rk   rN   lower_limit.r   rn   r   )r=   r   r   rV   r   r   concatenater   )r[   r   r   r   r  r   cdf1cdf2acdf2bab1ab2cdf2ab1cdf2ab2r  s                 rD    test_cdf_with_lower_limit_arrays7TestMultivariateNormal.test_cdf_with_lower_limit_arrays  s*   ii##$781vffQiJJy!!#a'JJy!!#a'"&&qC#''5#''5nnaQqSk1S!A#X;7bAnnaQqSk1S!A#X;7bA%))#S9%))#S9}w&0#rF   c           	      >   [         R                  R                  S5      nUR                  S5      nUR                  S5      nX3R                  -  nUR                  S5      S-  S-
  nUR                  S5      S-  S-
  n[        R
                  " XRX4S9n[	        X#5      R                  XTS9n[         R                  " [        R                  " XRX4S95      n[         R                  " [	        X#5      R                  XTS95      n	[        XvSS9  [        XSS9  [        XSS9  g )	Nr<  rN   rN   rN   rM   rN   rk   r=  -C6?r  )	r=   r   r   r   r   r   r  r   r   )
r[   r   r   r   r  r   r@  r  cdf3cdf4s
             rD   %test_cdf_with_lower_limit_consistency<TestMultivariateNormal.test_cdf_with_lower_limit_consistency  s    ii##$78zz!}jj EEkJJvq 1$JJvq 1$"&&qC"4-11!1Cvv)00#MNvv)$4;;A;MN...rF   c                    [         R                  " S5      n[         R                  " S5      n/ SQ/ SQ/ SQ/ SQ/n/ SQ/ SQ/ SQ/ SQ/n[         R                  " / SQ5      n[        R
                  " X1X$S9n[        XfS   U-  5        g )	NrN   r7  ro   r   r   r   r   r   r   r   rn   rn   r   r=  r   r=   r   rV   r   r   r   r   )r[   r   r   r   r  expected_signsr   s          rD   test_cdf_signs%TestMultivariateNormal.test_cdf_signs  si    xx{ffQi	9i8	9i8.1!%%asBVN23rF   r   rN   c                    [         R                  R                  S5      nUR                  X4S9nUR                  U-  nUR                  US9n[        XTS9nUR                  SSU4S9nUR                  U5      n[        S/U-  US9n	[        U	R                  [         R                  * /U-  Xu-
  5      R                  n
[        XSS	9  g )
N{   r   r   rN   )r   r   r   r   gh㈵>r  )r=   r   r   r   r   r   r   r1   r   r  estimater   )r[   r   r   r  r   mr   rb   r   dist_icdf_is              rD   test_cdf_vs_cubature+TestMultivariateNormal.test_cdf_vs_cubature  s     ii##C(KKd\K*ccAgKKTK""3KKBQdWK5hhqk$1#d(<rvvgYt^QU;DD.rF   c                     [        SS5       Hd  n[        R                  " X4S5      n[        R                  " US5        [	        S/U-  US9n[        UR                  S/U-  5      SSU-   -  SS9  Mf     g )	NrM      r  r   r   r  -C6
?r  )r  r=   r  r  r   r   r   )r[   r   r   r   s       rD   test_cdf_known%TestMultivariateNormal.test_cdf_known  so    !RLD''4,,CS"%&s4xS9D!T"b4i 	 !rF   r  r   l   >[= l	   HVqKWs.!) c                 Z   [         R                  R                  U5      n[        R	                  X#S9nUR
                  [         R                  * :H  R                  5       (       d   e[        S/U-  UR                  S9nUR                  UR                  US9n[        XdR                  SS9  g Nr   r   r   r   r   rd  r  )r=   r   r   r   r  r   r  r  r   r   r   r   r   r   r[   r   r   r   caser   cdf_vals          rD   test_cdf_vs_univariate-TestMultivariateNormal.test_cdf_vs_univariate+  s     ii##D)..D.BRVVG#((****"DdjjA((499#(.t<rF      c                 Z   [         R                  R                  U5      n[        R	                  X#S9nUR
                  [         R                  * :H  R                  5       (       d   e[        S/U-  UR                  S9nUR                  UR                  US9n[        XdR                  SS9  g rh  )r=   r   r   r   r  r   r  r  r   r   r   r   r   r   rk  s          rD   test_cdf_vs_univariate_2/TestMultivariateNormal.test_cdf_vs_univariate_26  s     ii##D)+++?RVVG#((****"DdjjA((499#(.t<rF   rl   l	   HVqKWs.!) c                    [         R                  R                  U5      n[        R	                  X#S9nUR
                  [         R                  * :H  R                  5       (       d   e[        S/U-  UR                  SSUR                  R                  S   -  S9nUR                  UR                  US9n[        XdR                  SS9  g )	Nri  r   T'  )r   r   ra   maxptsrj  r  r  )r=   r   r   rQ  rW  r   r  r  r   r   r?   r   r   r   r   rk  s          rD   test_cdf_vs_univariate_singular6TestMultivariateNormal.test_cdf_vs_univariate_singularA  s    
 ii##D)!77T7KRVVG#((****"DdjjQU*01A1A!1D*D
 ((499#(.t<rF   c                    [         R                  " S[         R                  " / SQ5      -  5      n[        R                  " U5      nSn[
        R                  " [        US9   [        R                  " SS/U5        S S S 5        [
        R                  " [        US9   [        SS/U5        S S S 5        / SQn[        R                  " U/ SQU5      n[        [        R                  " XBS9U5        [        R                  " U/ S	QU5      n[        [        R                  " USUS9U5        g ! , (       d  f       N= f! , (       d  f       N= f)
Nr   rQ   z7`cov` represents a covariance matrix in 3 dimensions...rK   r   )r  r  r  ro   r  r7  )r=   rw   r   r,   rT   rR   r
   rS   r   r   r   r   )r[   Pr   r\   rb   rA   s         rD   test_mean_cov$TestMultivariateNormal.test_mean_covQ  s    GGA++, 003
K]]:W5''A
; 6 ]]:W5A
3 6 !%%aJ?(,,Q?E!%%aJ?(,,QzBCH 65 65s   !D*D;*
D8;
E	c                     SS/nSn[         R                  " [        US9   [        R                  " U5        S S S 5        g ! , (       d  f       g = f)Nr   rN   z`x` must be two-dimensional.rK   )rR   r
   rS   r   fit)r[   r  	error_msgs      rD   test_fit_wrong_fit_data_shape4TestMultivariateNormal.test_fit_wrong_fit_data_shaped  s8    1v2	]]:Y7##D) 877s   A  
Ar   )rN   rj   c                 &   [         R                  R                  S5      nUR                  SU45      n[        R                  " U5      u  pE[         R
                  " USS9[         R                  " UR                  SS9pv[        XFSS9  [        XWSS9  g )	N   @,Q| r  r   r   )ddofV瞯<r  r  )	r=   r   r   r   r~  r   r   r   r   )r[   r   r   rb   mean_estcov_estmean_refcov_refs           rD   test_fit_correctness+TestMultivariateNormal.test_fit_correctnessj  sq    ii##$45JJSz"/33A6GGAA.qss0C'7u5rF   c                     [         R                  " SS5      nSn[         R                  " S5      n[        R                  " XUS9u  pE[        XB5        [        XS5        g )N)rM   r   rN   r   )fix_meanfix_cov)r=   r  
atleast_2dr   r~  r   )r[   r  
mean_fixed	cov_fixedr   r   s         rD   test_fit_both_parameters_fixed5TestMultivariateNormal.test_fit_both_parameters_fixeds  sL    wwvq!
MM"%	'++D4=?	T&S$rF   r  r!  rN   c                     Sn[         R                  " [        US9   [        R                  " [
        R                  " S5      US9  S S S 5        g ! , (       d  f       g = f)Nzd`fix_mean` must be a one-dimensional array the same length as the dimensionality of the vectors `x`.rK   rM   r  rR   r
   rS   r   r~  r=   rV   )r[   r  r  s      rD   "test_fit_fix_mean_input_validation9TestMultivariateNormal.test_fit_fix_mean_input_validation|  s<    C]]:S1##BFF1IA 211   *A
Ar  r  )rN   rM   )rl   rl   c                     Sn[         R                  " [        US9   [        R                  " [
        R                  " S5      US9  S S S 5        g ! , (       d  f       g = f)Nzn`fix_cov` must be a two-dimensional square array of same side length as the dimensionality of the vectors `x`.rK   rN   r  r  )r[   r  r  s      rD   +test_fit_fix_cov_input_validation_dimensionBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimension  s=     ]]:S1##BFF1Iw? 211r  c                     Sn[         R                  " [        US9   [        R                  " SS/SS//5      n[
        R                  " [        R                  " S5      US9  S S S 5        g ! , (       d  f       g = f)Nz2`fix_cov` must be symmetric positive semidefinite.rK   r   r   r	  rM   r  )rR   r
   rS   r=   r   r   r~  rV   )r[   r  r  s      rD   *test_fit_fix_cov_not_positive_semidefiniteATestMultivariateNormal.test_fit_fix_cov_not_positive_semidefinite  sT    H	]]:Y7hhR2s)45G##BFF1Iw? 877s   AA++
A9c                    [         R                  R                  S5      nUR                  S5      nUR                  S5      n[         R                  " X3R                  5      n[
        R                  " X$SUS9n[
        R                  " U5      u  pg[
        R                  " XVUS9R                  5       n[
        R                  " XRS9u  p[        X5        [
        R                  " XYU
S9R                  5       nX:  d   eUR                  S5      nS[         R                  " X3R                  5      -  nX-   n[
        R                  " UU	US9R                  5       nX:  d   eg )	Nr  rN   rJ  r  r   r   r   r   r   r  :0yE>)r=   r   r   r  r   r   r   r~  r   r   r   )r[   r   r  r}   r   samples	mean_freecov_free	logp_freemean_fixcov_fixlogp_fixr]  cov_perturbedlogp_perturbeds                  rD   test_fit_fix_mean(TestMultivariateNormal.test_fit_fix_mean  s4   ii##$45jjmJJvffQn%))s#7:<155g>	'..w3;==@SU 	/33GJX#&--g29;;>35 	 ### JJv266!SS>!-44W:B9FH 8;su 	 (((rF   c                    [         R                  R                  S5      nUR                  S5      nUR                  S5      n[         R                  " X3R                  5      n[
        R                  " X$SUS9n[
        R                  " U5      u  pg[
        R                  " XVUS9R                  5       n[
        R                  " XTS9u  p[        U	[         R                  " USS	95        [        X5        [
        R                  " XYU
S9R                  5       nX:  d   eU	S
UR                  S5      -  -   n[
        R                  " UUU
S9R                  5       nX:  d   eg )Nr  rN   rJ  r  r  r   r  r   r   r  )r=   r   r   r  r   r   r   r~  r   r   r   r   )r[   r   r  r}   r   r  r  r  r  r  r  r  mean_perturbedr  s                 rD   test_fit_fix_cov'TestMultivariateNormal.test_fit_fix_cov  s6   ii##$45jjmJJvffQn%))s/2F155g>	'..w3;==@SU 	/33GIXrwwwQ78W"&--g29;;>35 	 ### "D3::a=$88-44W:H9@B 8;su 	 (((rF   r   N):r   r   r   r   rp  rw  r  r  r  r  r  r  r  r  r  r  r  r  rR   r   r   r=   rV   r-   from_diagonalr  r  r   r  r	  r  r  r$  r(  r-  r4  r9  rG  rO  rW  slowr`  re  r  rn  rr  rw  r{  r  r  r  r   r  r  r  r  r  r   r   rF   rD   rh  rh  
  s   O"6((((	?26h0,70E0 A2B [[FF1I$$aV,	
;;:4-1-)&>1@%*"9"3$:$(/$	4 [[[[VaV,
/ - 
/
 [[VU1b\2[[Vj2T%UV= W 3= [[VU1b\2[[Vj2T%UV= W 3= [[VU1b\2[[Vj2T%UV= W 3=I&* [[UF+6 ,6% [[Z"((6*:*,((5/*; <B<B [[Y%)+&)9)+&)9); <@<@@):)rF   rh  c                   D    \ rS rSrS rS rS rS rS rS r	S r
S	 rS
rg)TestMatrixNormali  c           
      0   SnSn[         R                  " X4S5      nS[         R                  " U5      -  [         R                  " X4S5      -   nS[         R                  " U5      -  [         R                  " X"4S5      -   n[        [        [
        [         R                  " S5      5        [        [        [
        U[         R                  " S5      U5        [        [        [
        X4[         R                  " S5      5        [        [        [
        X4U5        [        [        [
        X5U5        [        [        [
        UR                  XE5        [         R                  R                  n[        U[
        R                  X4[         R                  " X"45      5        [        U[
        R                  U[         R                  " X45      U5        [        U[
        X4[         R                  " X"45      5        [        U[
        U[         R                  " X45      U5        g )Nrl   rN   r   r  ffffff?)rj   rl   rN   r  )r=   r  rm  rn  rS   r   r   r   r   r  r   rU   )r[   num_rowsnum_colsr   r   Vr  s          rD   test_bad_inputTestMatrixNormal.test_bad_input  sm   GGX'-"++h''"''82F*LL"++h''"''82F*LL 	j-'1BCj-BHHRL!Dj-rxx|Dj-q9j-q9j-a;II!!a**BGGX$89	;a**(!56	; 	abggx6J.KLa277H3G+H!LrF   c                 d   SnSn[         R                  " X4S5      nS[         R                  " U5      -  [         R                  " X4S5      -   nS[         R                  " U5      -  [         R                  " X"4S5      -   n[         R                  " X45      n[         R                  " US45      n[         R                  " SU45      n[         R                  " U5      n	[         R                  " U5      n
[         R                  " S5      n[	        [
        R                  " X4US9R                  X45        [	        [
        R                  " US9R                  X45        [	        [
        R                  " US	9R                  US45        [	        [
        R                  " US
9R                  SU45        [	        [
        R                  " X5S9R                  X45        [	        [
        R                  " X4S9R                  X45        [	        [
        R                  " XES9R                  X45        [	        [        US9R                  U	5        [	        [        US9R                  U
5        [	        [        US	9R                  U5        [	        [        US	9R                  U5        [	        [        US
9R                  U5        [	        [        US
9R                  U5        [	        [        X4S9R                  U
5        [	        [        X5S9R                  U	5        [	        [        XES9R                  U5        g )Nrl   rN   r   r  r  r   r   rowcovcolcov)r   )r  )r  )r   r  )r   r  )r  r  )r=   r  rm  r   r   r   r   r?   r  r  r   )r[   r  r  r   r   r  ZZrZcIrIcI1s               rD   test_default_inputs$TestMatrixNormal.test_default_inputs  ss   GGX'-"++h''"''82F*LL"++h''"''82F*LLHHh)*XXxm$XXq(m$[["[["[[^]&&ABHH)	+]&&A.44)	+]&&a066]	$]&&a066]	$]&&A8>>)	+]&&A8>>)	+]&&a:@@)	+ 	]*1126]*1126]!,1126]!,33R8]!,1126]!,33R8]4;;R@]4;;R@]!6;;Q?rF   c                     SnSn[         R                  " X4S5      n[         R                  " US5      nSn[         R                  " US5      nSn[         R                  " U5      n[         R                  " U5      n	[        [	        X4US9R
                  SU-  5        [        [	        X4US9R                  SU	-  5        [        [	        X5US9R
                  SU-  5        [        [	        X5US9R                  SU	-  5        g )Nrl   rN   r   r   r   r  )r=   r  rm  r   r   r  r  )
r[   r  r  r   UvUsVvVsr  r  s
             rD   test_covariance_expansion*TestMatrixNormal.test_covariance_expansion  s    GGX(#.WWXs#WWXs#[["[["]R@GGV	]R@GGV	]R@GGV	]R@GGV	rF   c           	         [        SS5       GH@  n[        SS5       GH+  n[        R                  " X4S5      nS[        R                  " U5      -  [        R                  " X4S5      -   nS[        R                  " U5      -  [        R                  " X"4S5      -   n[	        X4US9nUR                  SS9n[        R
                  " X4USS	9n[        Xx5        UR                  SS9n	UR                  U	5      n
[        R                  " XXES9n[        X5        UR                  U	5      n[        R                  " XXES9n[        X5        GM.     GMC     g )
Nr   rj   r   r  r  r  rs  r   )r   r  r  r   )	r  r=   r  rm  r   r   r   r   r   )r[   r  r  r   r   r  frozenrvs1rvs2r  pdf1pdf2logpdf1logpdf2s                 rD   test_frozen_matrix_normal*TestMatrixNormal.test_frozen_matrix_normal&  s   qA1QZGGQE3'"++a.(277A5#+>>"++a.(277A5#+>>&ABzztz4$((a!6:<T(JJDJ1zz!}$((1GT( --*'..qMW.)   rF   c                 6   [        SS5       GH  n[        SS5       GHs  n[        R                  " X4S5      nS[        R                  " U5      -  [        R                  " X4S5      -   nS[        R                  " U5      -  [        R                  " X"4S5      -   n[	        X4US9nUR                  SS9nUR                  U5      nUR                  U5      n	UR                  5       n
UR                  R                  5       nUR                  R                  5       n[        R                  " XT5      n[        R                  " XUS	9n[        R                  " XUS	9n[        R                  " XS	9n[        XS
S9  [        XS
S9  [        U
U5        GMv     GM     g )Nr   rj   r   r  r  r  rs  r   r   r  r  )r  r=   r  rm  r   r   r   r   r   r   flattenkronr   r   )r[   r  r  r   r   r  r  r  r  r  entropy1vecXvecMr   r  r  entropy2s                    rD   test_matches_multivariate*TestMatrixNormal.test_matches_multivariate>  s>    qA1QZGGQE3'"++a.(277A5#+>>"++a.(277A5#+>>&ABJJDJ1zz!} --*!>>+ss{{}ss{{}ggal*..tCH-44T#N.66DJ7u=(3)   rF   c           	         SnSn[         R                  " X4S5      nS[         R                  " U5      -  [         R                  " X4S5      -   nS[         R                  " U5      -  [         R                  " X"4S5      -   nSn[        X4US9nUR	                  USS	9nUR	                  US
S	9n	[         R
                  " U[         R                  S S 2S S 2S S 24   U	[         R                  S S 2S S 2S S 24   4SS9n
[        U
R                  SXaU45        UR                  U
5      n[        UR                  SU45        [        S5       H?  n[        U5       H-  n[        R                  " XU4   UXES9n[        XX4   S5        M/     MA     g )Nrl   rN   r   r  r  r  r  rs  r   i  r   r   rM   r  )r=   r  rm  r   r   r?  r-  r   r?   r   r  r   )r[   r  r  r   r   r  r'  r  X1X2r  array_logpdfr  r  separate_logpdfs                  rD   test_array_input!TestMatrixNormal.test_array_inputX  s[   GGX'-"++h''"''82F*LL"++h''"''82F*LLA:ZZQTZ2ZZQTZ2NNBrzz!Aa/0BJJq14D1EFQOQWWq!x89}}Q'\''!Q0qA1X"/"6"6q1vA>?#Kac1BEJ  rF   c                    SnSn[         R                  " X4S5      nS[         R                  " U5      -  [         R                  " X4S5      -   nS[         R                  " U5      -  [         R                  " X"4S5      -   nSn[        X4US9nUR	                  USS	9n[         R
                  " US
S9n	[        XSS9  [         R                  " UR                  Xa-  U5      R                  5      n
[        XSS9  [         R                  " [         R                  " USS5      R                  Xb-  U5      R                  5      n[        XSS9  g )Nrl   rN   r   r  r    r  rs  r   r   r   r   r  r   rM   )r=   r  rm  r   r   r   r   r   reshaper   swapaxes)r[   r  r  r   r   r  r'  r  r  sample_meansample_colcovsample_rowcovs               rD   test_momentsTestMatrixNormal.test_momentso  s   GGX'-"++h''"''82F*LL"++h''"''82F*LLA:JJADJ1ggaQ'S1qyyH=??@s3r{{1Qq19989
8 MMNQPs3rF   c           	      h   [         R                  " [        R                  " SS/SS//5      [        R                  " SS/SS//5      [        R                  " SS/SS//5      [        R                  R                  S5      SS	9n[        R                  " S
S/SS//SS/SS///5      n[        X5        g )Nr   rM   rN   rl   rn   rj   r  r   )r   r  r  r   r   g6?gǀgcϿ@g"'@gI2͖@g^jy%@gDn3@g|\3@)r   r   r=   r   r   r   r   )r[   r  expecteds      rD   test_samplesTestMatrixNormal.test_samples  s     ""Aq6Aq6*+88aWr1g./88aVaW-...q1
 88!23!124!23!1245
 	)rF   r   N)r   r   r   r   r  r  r  r  r  r  r  r  r   r   rF   rD   r  r    s.    M4%@N,/044K.4,*rF   r  c                       \ rS rSrS rS rS rS rS rS r	S r
S	 rS
 rS rS rS rS rS rS rS rS rS rS rSrg)TestDirichleti  c           	      b   [         R                  R                  S5        [         R                  R                  SS5      n[         R                  R	                  SSU5      n[        U5      n[        UR                  5       [
        R                  " U5      5        [        UR                  5       [
        R                  " U5      5        [        UR                  5       [
        R                  " U5      5        Sn[        U5       H  n[         R                  R	                  SSU5      nU[         R                  " U5      -  n[        UR                  US S 5      [
        R                  " US S U5      5        [        UR                  US S 5      [
        R                  " US S U5      5        M     g Nr+  r       &.>r  r  rn   )r=   r   r   randintr   r   r   varr   r   r  r   r   r   r[   r   r8  r'  	num_testsr  rb   s          rD   test_frozen_dirichlet#TestDirichlet.test_frozen_dirichlet  s)   
		tIIa$		!!&#q1eQUUWimmE23QVVXy~~e45QYY[)"3"3E":;	y!A		!!&#q1ANAq"v	afe(DE!CR&)9+;+;AcrFE+JK	 "rF   c                 j   [         R                  R                  S5        [         R                  " / SQ5      n[         R                  R	                  USS9n[        UR                  S5        [        [        [        R                  X!5        [        [        [        R                  X!5        [        R                  " UR                  U5        [        R                  " UR                  S S U5        [        R                  " UR                  U5        [        R                  " UR                  S S U5        g )Nr+  r          @      @rm   r   )rm   rN   rn   )r=   r   r   r   r   r   r?   rn  rS   r   r   r   r[   r8  rb   s      rD   "test_numpy_rvs_shape_compatibility0TestDirichlet.test_numpy_rvs_shape_compatibility  s    
		t)IIA.QWWf%j)--:j)"2"2A=acc5!acc#2h&e$Sb5)rF   c                 @   [         R                  R                  S5        / SQn[         R                  R                  [         R                  " SU5      SS9R
                  n[        [        [        R                  X!5        [        [        [        R                  X!5        g )Nr+  )r   r   r  r  rm   r   
r=   r   r   r   maximumr   rn  rS   r   r   r	  s      rD   test_alpha_with_zeros#TestDirichlet.test_alpha_with_zeros  sc    
		tII

4 7a@BBj)--:j)"2"2A=rF   c                 @   [         R                  R                  S5        / SQn[         R                  R                  [         R                  " SU5      SS9R
                  n[        [        [        R                  X!5        [        [        [        R                  X!5        g )Nr+  )r   g       r  r  rm   r   r  r	  s      rD    test_alpha_with_negative_entries.TestDirichlet.test_alpha_with_negative_entries  sc    
		t II

4 7a@BBj)--:j)"2"2A=rF   c                    [         R                  " / SQ5      n[         R                  " / SQ5      n[        R                  " X!5        [        R                  " X!5        [         R                  " / SQ5      n[        [        R                  " X!5      S5        [        [        R                  " X!5      [         R                  " S5      5        g )Nr   r  r        @r   r   r   r  )r   r   r   r   rk   )r=   r   r   r   r   r   r{  r	  s      rD   test_data_with_zeros"TestDirichlet.test_data_with_zeros  sy    -.HH)*a"-.IMM!3Q7I,,Q6q	BrF   c                     [         R                  " / SQ5      n[         R                  " / SQ5      n[        [        [        R
                  X!5        [        [        [        R                  X!5        g )N)r   r  r  r  r  r=   r   rn  rS   r   r   r   r	  s      rD   $test_data_with_zeros_and_small_alpha2TestDirichlet.test_data_with_zeros_and_small_alpha  B    -.HH)*j)--:j)"2"2A=rF   c                     [         R                  " / SQ5      n[         R                  " / SQ5      n[        [        [        R
                  X!5        [        [        [        R                  X!5        g )Nr  )r   rc  r   r  r  r	  s      rD   test_data_with_negative_entries-TestDirichlet.test_data_with_negative_entries  sB    -.HH*+j)--:j)"2"2A=rF   c                     [         R                  " / SQ5      n[         R                  " / SQ5      n[        [        [        R
                  X!5        [        [        [        R                  X!5        g )Nr  )r   rd  r   r  r  r	  s      rD    test_data_with_too_large_entries.TestDirichlet.test_data_with_too_large_entries  r  rF   c                     [         R                  " / SQ5      n[         R                  " SS5      n[        [        [
        R                  X!5        [        [        [
        R                  X!5        g )Nr  )rM   rm   rm   g$I$I?r=   r   r  rn  rS   r   r   r   r	  s      rD   test_data_too_deep_c"TestDirichlet.test_data_too_deep_c  sB    )GGIv&j)--:j)"2"2A=rF   c                     [         R                  " SS/SS//5      n[         R                  " SS5      n[        [        [
        R                  X!5        [        [        [
        R                  X!5        g )Nr   r  r  r  )rM   rM   rm         ?r&  r	  s      rD   test_alpha_too_deep!TestDirichlet.test_alpha_too_deep  sO    3*sCj12GGIu%j)--:j)"2"2A=rF   c                     [         R                  " / SQ5      n[         R                  " SS5      n[        R                  " X!5        [        R
                  " X!5        g )Nr  rN   rm   UUUUUU?)r=   r   r  r   r   r   r	  s      rD   test_alpha_correct_depth&TestDirichlet.test_alpha_correct_depth  s:    )GGFE"a"rF   c                     [         R                  " / SQ5      n[         R                  " SS5      n[        [        [
        R                  X!5        [        [        [
        R                  X!5        g )Nr  r.  r  r&  r	  s      rD   test_non_simplex_data#TestDirichlet.test_non_simplex_data  sB    )GGFE"j)--:j)"2"2A=rF   c                     [         R                  " / SQ5      n[         R                  " SS5      n[        [        [
        R                  X!5        [        [        [
        R                  X!5        g )Nr  )rM   rm   r  r&  r	  s      rD   test_data_vector_too_short(TestDirichlet.test_data_vector_too_short  C    -.GGFE"j)--:j)"2"2A=rF   c                     [         R                  " / SQ5      n[         R                  " SS5      n[        [        [
        R                  X!5        [        [        [
        R                  X!5        g )Nr  )rj   rm   r   r&  r	  s      rD   test_data_vector_too_long'TestDirichlet.test_data_vector_too_long  r8  rF   c                    [         R                  " / SQ5      n[        U5      n/ SQn/ SQn/ SQ/ SQ/ SQ/n[        UR	                  5       U5        [        UR                  5       U5        [        UR                  5       U5        g )N)r   皙?r   r  皙?r   )UUUUUU?{Gz?Q?)r@  )rC  rA  O贁N)rD  rE  rB  )r=   r   r   r   r   r   r   )r[   r8  r'  expected_meanexpected_varexpected_covs         rD   test_mean_var_covTestDirichlet.test_mean_var_cov  sh     (e'-../
 	"!&&(M:!!%%'<8!!%%'<8rF   c                 p   [         R                  " S/5      n[        U5      n[        UR	                  5       R
                  S5        [        UR                  5       R
                  S5        [        UR                  S/5      R
                  S5        [        UR                  S/5      R
                  S5        g )Nr   r   r   )	r=   r   r   r   r   r   r   r   r   )r[   r8  r'  s      rD   rw   TestDirichlet.test_scalar_values  sy    #e 	QVVX]]A&QUUW\\1%QUUB4[%%q)QXXrd^((!,rF   c                    [         R                  R                  S5        [         R                  R                  SS5      n[         R                  R	                  SSU5      n[        U5      nSn[        U5       Hj  n[         R                  R	                  SSU5      nU[         R                  " U5      -  n[        UR                  US S 5      UR                  U5      5        Ml     g r  )
r=   r   r   r  r   r   r  r   r   r   r  s          rD    test_K_and_K_minus_1_calls_equal.TestDirichlet.test_K_and_K_minus_1_calls_equal$  s     			tIIa$		!!&#q1e	y!A		!!&#q1ANAafquuQx8 "rF   c                    [         R                  R                  S5        [         R                  R                  SS5      n[         R                  R	                  SSU5      n[        U5      nSnSnS n[        U5       H  n[        U5       H[  n[         R                  R	                  SSU5      n	U	[         R                  " U	5      -  n	Ub  [         R                  " Xi45      nMY  U	nM]     UR                  UR                  5      n
S nU H1  nUR                  U5      nUb  [         R                  " X5      nM/  UnM3     [        X5        M     g )Nr+  r   r  r  r  r  rj   )r=   r   r   r  r   r   r  r   vstackr   r   appendr   )r[   r   r8  r'  r  num_multiplexmr  r]  rb   rmrsxsr  s                 rD   test_multiple_entry_calls'TestDirichlet.test_multiple_entry_calls3  s   
		tIIa$		!!&#q1e	y!A<(II%%fc15RVVAY>B7+BB ) rttBBEE"I>2)BB  &b-! "rF   c                 \   [         R                  R                  S5        [         R                  R                  SSS5      n[	        U5      n[        US   US   5      nSn[        U5       Hh  n[         R                  R                  SSS5      nU[         R                  " U5      -  n[        UR                  U5      UR                  U/5      5        Mj     [        UR                  5       UR                  5       S   5        [        UR                  5       UR                  5       S   5        g )Nr+  r  r  rM   r   r   r  )r=   r   r   r   r   r   r  r   r   r   r   r   )r[   r8  r'  r   r  r  rb   s          rD   test_2D_dirichlet_is_beta'TestDirichlet.test_2D_dirichlet_is_betaP  s    
		t		!!&#q1eq58$	y!A		!!&#q1ANAa!%%*5 "
 	AFFHaffhqk2AEEGQUUWQZ0rF   r   N)r   r   r   r   r  r
  r  r  r  r  r   r#  r'  r+  r0  r3  r6  r:  rI  rw  rN  rX  r[  r   r   rF   rD   r  r    sc    L$
*>>C>>>>>#>>>9$	-9.:1rF   r  c                     [         R                  " SS/5      n [         R                  " S//5      n[        [        [        X5         [	        X5        g ! [         a-  nSn[        [        U5      S [        U5       U5         S nAg S nAff = f)Nr   r   zDimension mismatch)r=   r   rn  rS   r   r   strr   )ro  r  r  r  s       rD   ,test_multivariate_normal_dimensions_mismatchr_  a  ss     
3*	BHHseWE*12=
-B& -"SVISX&,,-s   A 
B
#BB
c                   8    \ rS rSrS rS rS rS rS rS r	Sr
g	)
TestWishartit  c           	         [         R                  " SSS9nSS/[         R                  " S5      [         R                  S   [         R                  " SSS9/nU HO  n[        SU5      n[	        UR
                  U5        [	        UR
                  R                  UR                  5        MQ     [         R                  " SS/SS//5      nSS/[         R                  S   [         R                  " SS/SS//5      /nU HO  n[        SU5      n[	        UR
                  U5        [	        UR
                  R                  UR                  5        MQ     [        [        [        S[         R                  " S5      5        [        S[         R                  " S5      5        [         R                  " SSS9n[        [        [        SU5        g )Nr   rM   ndminr   r   rM   rd  rN   )
r=   r   r_r   r   r  r?   rn  rS   rV   )r[   
true_scalescalesr  ws        rD   test_scale_dimensions!TestWishart.test_scale_dimensionsu  sj    XXaq)
CHHQKEE!HHHQa 
 E5!A*-
(8(89  XX!u !!u& '
 qEEE#JHHqee 
 E5!A*-
(8(89  	j'1bffQi8 	RVVAY !$j'1e4rF   c           
      `   SS/[         R                  " S5      [         R                  S   [         R                  " SSS9[         R                  " S/SS9/n[        SS5      nUR	                  [         R                  " SSS95      nU H  n[        UR	                  U5      U5        M      / SQ[         R                  S   [         R                  " / SQSS9/n[        SS5      nUR	                  [         R                  " / SQSS95      nU H  n[        UR	                  U5      U5        M      SSS/[         R                  " S5      [         R                  S   [         R                  " SS/SS//5      [         R                  " SS/SS//5      S S 2S S 2[         R                  4   /n[        S[         R                  " S5      5      nUR	                  [         R                  " SS/SS//5      S S 2S S 2[         R                  4   5      nU H  n[        UR	                  U5      U5        M      g )Nr   rM   rc  rN   rQ   r!  r   )r=   r   rf  r   r   r   r-  rV   )r[   r  ri  densityrb   s        rD   test_quantile_dimensions$TestWishart.test_quantile_dimensions  s   
 CHHQKEE!HHHQa HHaS"
 AaL%%!,-Aq7+ 
 EE%LHHWA&
 AaL%%23Aq7+  qEHHQKEE#JHHqee HHqee "**n.	
 AbffQi %%1Q%#$Q%") **+Abjj.: ;Aq7+ rF   c           	         Sn[         R                  " [         R                  " U5      S-   5      n[         R                  " XS-
  -  S-  5      U[         R                  " USS9'   [         R                  " UR
                  U5      n/ n[        S5       H  n[         R                  " [         R                  " U5      US-   S-  -   5      n[         R                  " XS-
  -  S-  5      U[         R                  " USS9'   [         R                  " UR
                  U5      nUR                  U5        M     [         R                  " U5      R
                  nSS[         R                  " SSS5      4SX#4/nU H  u  prn[        Xr5      n[        UR                  5       [        R                  " Xr5      5        [        UR                  5       [        R                  " Xr5      5        [        UR                  5       [        R                  " Xr5      5        [        UR                  5       [        R                  " Xr5      5        [        UR!                  U5      [        R                   " XWU5      5        M     g 	Nrl   r   rM   rn   r  rj   r  r   )r=   rw   rl  tril_indicesr  r   r  rR  r   rB  r   r   r   r   moder   r   )	r[   r   r  r  r  rb   
parametersdfri  s	            rD   r  TestWishart.test_frozen  s    		#q(),.IIcUmq6H,IboocR()uww& qA		#!ax/0A,.IIcUmq6H,IAboocR()qssAAHHQK	 
 HHQKMM BKKR+,N


 )NR"A'++b"897<<#:;7<<#:;goob&@Aq7;;qe#<= )rF   c                 @   SnSn[         R                  " U5      nSUS'   SUS'   [        X#5      n[         R                  R	                  S5      n[        R
                  " X#US9n[         R                  R	                  S5      nUR                  US9n[         R                  R	                  S5      nUR                  SS9n[         R                  UR                  U5      UR                  US	-
  5      UR                  US
-
  5      4   S-  n	[         R                  " U	5      n
X[         R                  " USS9'   [         R                  R                  U5      nUR                  U
5      n[         R                  " XR                  5      n[        Xm5        [        X}5        g )NrN   r  r  rj  r   r   i r   r   r   rM   rn   rr  )r=   rV   r   r   r  r   r   rf  	chisquarerw   rs  r   r   r  r   r   )r[   r   rv  r  ri  r   w_rvsfrozen_w_rvscovariances	variancesr}   DDAmanual_w_rvss                 rD   test_wishart_2D_rvsTestWishart.test_wishart_2D_rvs  s\    sc
c
 B ii##F+BC8ii##F+uu#u. ii##F+jjaj(EEMM"MM"Q$MM"Q$!
 		 GGI(3"//#
$% IIu%UU1Xvvb$$' 	,3rF   c                    [         R                  R                  S5      nSnSn[         R                  " U5      n[         R                  " SSS[
        S9n[         R                  " SSSS9nU H  n[        Xt5      n[        U5      n	[        UR                  5       U	R                  5       5        [        UR                  5       U	R                  5       5        [        UR                  5       U	R                  5       5        [        UR                  U5      U	R                  U5      5        UR                  X!S	9n
U4nS
n[        SXU
5        M     g )N^   r   r  rM   r  r   numr   r  r   )r=   r   r   rV   rl  rM  rB  r   r   r   r   r   r   r   r   r   )r[   r   snr   r  df_ranger  rv  ri  cr   rB   r8  s                rD   test_1D_is_chisquared!TestWishart.test_1D_is_chisquared  s    
 ii##F+s99QAU3KKB2&B"ARA AEEGQUUW-AFFHaffh/AIIK5 AEE!HaeeAh/ %%R%2C5DE"64<! rF   c                    [         R                  R                  S5      nSnSnSn[         R                  " [         R                  " S5      S-   5      n[         R                  " S5      U[         R
                  " SSS9'   [         R                  " UR                  U5      n[         R                  " US45      nUR                  R                  U5      R                  U5      R                  5       n[        X75      n[        X7S	9n	[        UR                  5       U	R                  5       5        [        UR                  5       U	R                  5       5        [        UR                  5       U	R                  5       5        [         R                   " S
SSS9n
[        UR#                  U
5      U	R#                  U
5      5        UR%                  X!S9nUSU4nSn['        SXU5        g )Nr  r  r  rl   r   rk   rn   rr  r  r   r  r   r   r  r   )r=   r   r   rw   rl  rs  r  r   rU   r   r   r   r   r   r   r   rB  r   r   r   )r[   r   r  rv  r   r  lamdasigma_lamdari  r  r  r   rB   r8  s                 rD   test_is_scaled_chisquared%TestWishart.test_is_scaled_chisquared<  s_   
 ii##F+		!Q'*,))A,booa2&'uww&Q ggkk%(,,U3;;=B$' 	)!&&(+		QYY[1 KKB2&a!%%(+ eee.1[!vtC8rF   r   N)r   r   r   r   rj  rn  r  r  r  r  r   r   rF   rD   ra  ra  t  s$    )5V/,b>@*4X=>!9rF   ra  c                      \ rS rSrS rS rS r\R                  R                  SSS/5      S 5       r
S	 rS
 r\R                  R                  SSS/5      S 5       rS r\R                  R                  SSS/5      S 5       rS r\R                  R                  SSS/5      S 5       rS rS rS r\R                  R                  S\R,                  \R.                  /5      S 5       rSrg)TestMultinomiali_  c                 b   [         R                  " SSS5      n[        USSS9  [         R                  " SS/S	S
S/5      nU[        R                  * :X  d   e[         R                  " S	S	/S	S
S/5      nUS	:X  d   e[         R                  " SS/S	SS/5      n[        U[        R
                  SS9  g )NrN   rl   rm   r   r  g&Mtyr  r  rN   rl   r   r   r  rq   )r   logpmfr   r=   r  r  )r[   vals1vals2vals3vals4s        rD   test_logpmfTestMultinomial.test_logpmf`  s    ""5!Z81=""Aq61r2h7""Aq61r2h7zz""Aq61r1g6rvvD1rF   c                     [         R                  " SSS5      n[        R                  " SSS5      n[        XSS9  [         R                  " SS	S
5      n[        R                  " SS	S5      n[        XSS9  g )Nr  rm   r  rN   r   r  r  )rk         r   r  rk   r   )r   r  r"   r   pmfr[   val1val2s      rD   test_reduces_binomial%TestMultinomial.test_reduces_binomialm  sb     !!&!Z8||Aq#&.vr:6yyB$.rF   c                 ~    S/ SQp!SSSSSSS	SS
SS.
nU H%  n[        [        R                  " XAU5      X4   SS9  M'     g )NrN   )g      ?r*  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rN   )r   r   rM   )rM   r   r   )rN   r   r   rk  r7  rM   r   r   )r   rM   r   r  )r   rN   r   +=r  )r   r   r  )r[   r   rV  r_valsrb   s        rD   test_RTestMultinomial.test_Rx  sR     $1([([([([([	B
 AKOOA!4fieL rF   r   r   rN   c                 <   Sn[         R                  " [        US9   [        R                  R                  S5      n[        R                  " US/S-  SSS9nUR                  US/S-  SS9n[        XE5        S S S 5        [         R                  " [        US9   [        R                  R                  S5      n[        R                  " US/S	-  SSS9nUR                  US/S	-  SS9n[        XE5        S S S 5        g ! , (       d  f       N= f! , (       d  f       g = f)
Nz,Some rows of `p` do not sum to 1.0 within...rK   rZ  r*  rN   rm   r   r   rj   )	rR   warnsFutureWarningr=   r   r  r   r   r   )r[   r   r\   rndmsc_rvsnp_rvss         rD   test_rvs_npTestMultinomial.test_rvs_np  s     A\\-w799((-D __QqqsKF%%a$%:F(	 8
 \\-w799((-D __QqqsKF%%a$%:F(	 87 87
 87s   AC<AD<
D

Dc                    [         R                  " SSS5      n[        USSS9  [         R                  " SSS	5      n[        US
SS9  [         R                  " SS/SS//SS/SS///SS5      n[        USS/SS//SS9  [        R                  " S[        R
                  S9n[         R                  " USS	5      n[        U[        R                  " / [        R
                  S95        [         R                  " SS/SS	5      n[        USSS9  [         R                  " / SQS/ SQ5      n[        USSS9  [         R                  " / SQS/ SQ5      nUS:X  d   e[         R                  " / SQS/ SQ5      nUS:X  d   eg )N)rj   rj   r   r   r  r  r  rm   r  g5
?rN   r   r  rn   	   r  g*7?g<Wƌ?r   rM   r  rl   rM   rN   rN   r   rk   )gUUUUUU?r/  r   gߦ?ro   r  )r   r  r   r=   r  float64r   )	r[   vals0r  r  rb   r  r  vals5vals6s	            rD   test_pmfTestMultinomial.test_pmf  sJ   a.qt,q(31=1Q%1"a1a&0A BA (*I 6A?dKHHU"**-1h/UBHHRrzz:;1q(3qt,	1.?@~D9	1.?@zz	1.?@zzrF   c                    [         R                  " SS/SSS/SS//5      n[        USS	/S
S9  [         R                  " SS/SS/SS/5      n[        USS/S
S9  [         R                  " SS/SS///SSS/5      n[        USS//S
S9  [         R                  " SS/S/S///SS/5      n[        US/S///S
S9  [         R                  " SS/SS//S////SS/5      n[        USS////S
S9  g )Nr   rM   rN   r   r  r   r=  gv?g~jt?r  r  rl   r   )r   r  r   )r[   r  r  r  r  r  s         rD   test_pmf_broadcasting%TestMultinomial.test_pmf_broadcasting  s   ARHr2h+?@d|$7AAR9ayt41a&1a&!1 2ABx@q	{6A1#sr2h?$!T:!Q!AQC5'RHE4)T:rF   rj   c                     [         R                  " US5      nUS-  S-  U* S-  S-  U* S-  S-  /U* S-  S-  US-  S-  U* S-  S-  /U* S-  S-  U* S-  S-  US-  S-  //n[        X#SS9  g )	N)r   r   r  r   r=  r   r  r  r  r  r   r   r   )r[   r   cov1r  s       rD   test_covTestMultinomial.test_cov  s    q,/2b1"R%(QBrE"H-Br1R47QBrE"H-BrA2b58QrT"W-/ 	.rF   c                 N   [         R                  " SSS/SS//5      nSS/SS//SS/SS///n[        XS	S
9  [         R                  " SS/SS/5      nSS/SS//SS/SS///n[        X4S	S
9  [         R                  " SS/SS/SS//5      nSS/SS//SS/SS///n[        XVS	S
9  g )Nrj   r   r  r   r=  g?gܿgr  r  rl   g
ףp=
?g
ףp=
׿r   r  r?  r  gzG?gzGr  g333333r  r[   r  r  cov3cov4cov5cov6s          rD   test_cov_broadcasting%TestMultinomial.test_cov_broadcasting  s    qB8b"X"67tdC[)RIRy+AB.1vBx0ttSk*c4[4+,FG.1vR2r(';<8$x&9:8$x&9:<.rF   rM   c                 v    [         R                  " USS/5      n[        U[        R                  " US5      SS9  g Nr   r=  r  r  r   r   r   r"   )r[   r   ent0s      rD   r4  TestMultinomial.test_entropy  s1     ""1r2h/emmAr2>rF   c           	      `   [         R                  " SS/SS/5      n[        U[        R                  " SS5      [        R                  " SS5      /SS9  [         R                  " SS/S	S
/SS//5      n[        U[        R                  " SS	5      [        R                  " SS5      /SS9  [         R                  " S/S//S	S
/SS//5      n[        U[        R                  " SS	5      [        R                  " SS5      /[        R                  " SS	5      [        R                  " SS5      //SS9  g )NrM   rN   r   r=  r  r  rm   r  r   r  r?  r  r  )r[   r  ent1ent2s       rD   test_entropy_broadcasting)TestMultinomial.test_entropy_broadcasting  s   ""Aq6B84u}}Q3U]]1b5IJ!	# ""Aq6RHr2h+?@u}}Q3U]]1b5IJ!	# ""QC!:R2r(/CD--2.a0DE--2.a0DEG!	#rF   c                 Z    [         R                  " USS/5      n[        X!S-  US-  /SS9  g r  r   r   r   )r[   r   mean1s      rD   	test_meanTestMultinomial.test_mean  s.      RH-"ad|$7rF   c                 \    [         R                  " SS/SS/5      n[        USS/SS//S	S
9  g )Nrj   rk   r   r=  r   r  g433333?g433333@r  r  r  )r[   r  s     rD   test_mean_broadcasting&TestMultinomial.test_mean_broadcasting  s5      !Q"b2ttTl;$GrF   c                    [         R                  R                  S5        SnSn/ SQ/ SQ/ SQ/ SQ/ SQ/n[         R                  " U[         R                  S	9n[        X5      n[        UR                  U5      [
        R                  " X1U5      5        [        UR                  U5      [
        R                  " X1U5      5        [        UR                  5       [
        R                  " X5      5        g )
Nrs  rc  )r   r   r   r?  r   r   r   rc  r   r   r   rp  r   r   r   r  r   r   r   r  r   r   rM   r  r  )
r=   r   r   r>   r  r   r   r  r  r   )r[   r   pvalsrb   	mn_frozens        rD   r  TestMultinomial.test_frozen  s    
		t 
:i	BJJq

+)		a(+//!*FG	((+[-?-?e-LM	))+[-@-@-JKrF   c                 8   Sn[         R                  R                  S5      nUR                  U5      nSUS'   U[         R                  " U5      -  n[         R                  " U5      n[
        R                  " XAU5      n[         R                  " U5      (       d   eg )NX   l   iRZY gKH9rn   )r=   r   r   r   rU   r   r  isfinite)r[   r   r   rV  rb   r  s         rD   test_gh_11860TestMultinomial.test_gh_11860  sy    
 ii##$78JJqM"	RVVAYGGAJ##A!,{{6""""rF   r  c                     Sn[         R                  " / SQUS9n[        R                  " / SQX#S9n[        R                  " / SQX#S9n[         R                  R                  XESS9  g )	N   )r   r   r   r   r   r  )r   rM   rj   rm   rl   )rb   r   rV  )r   rM   rl   rj   rm   r  r  )r=   r>   r   r  testingr   )r[   r  r   rV  res1res2s         rD   test_gh_22565TestMultinomial.test_gh_22565  sQ     JJ0>A;A;


""4E":rF   r   N)r   r   r   r   r  r  r  rR   r   r   r  r  r  r  r  r4  r  r  r  r  r  r=   float32r  r  r   r   rF   rD   r  r  _  s   2	/M" [[S1a&)) *)6;  [[S1a&)/ *// [[S1a&)? *?# [[S1a&)8 *8H
L# [[Wrzz2::&>?; @;rF   r  c                   2    \ rS rSrS rS rS rS rS rSr	g)	TestInvwisharti  c           	         Sn[         R                  " [         R                  " U5      S-   5      n[         R                  " XS-
  -  S-  5      U[         R                  " USS9'   [         R                  " UR
                  U5      n/ n[        S5       H  n[         R                  " [         R                  " U5      US-   S-  -   5      n[         R                  " XS-
  -  S-  5      U[         R                  " USS9'   [         R                  " UR
                  U5      nUR                  U5        M     [         R                  " U5      R
                  nSS[         R                  " SSS5      4SX#4/nU H  u  prn[        Xr5      n[        UR                  5       [        R                  " Xr5      5        [        UR                  5       [        R                  " Xr5      5        [        UR                  5       [        R                  " Xr5      5        [        UR!                  U5      [        R                   " XWU5      5        M     g rq  )r=   rw   rl  rs  r  r   r  rR  r   rB  r   r   r   r   rt  r   r   )	r[   r   r  r  r  rb   ru  rv  iws	            rD   r  TestInvwishart.test_frozen  s   
 		#q(),.IIcq5k!m,DboocR()uww& qA		#!ax/0A,.IIcq5k!m,DAboocR()qssAAHHQK	 
 HHQKMM BKKR+,N


 )NRB&B:>>"#<=JOOB$>?JOOB$>?BFF1Iz~~aU'CD )rF   c                    [         R                  R                  S5      nSnSn[         R                  " U5      n[         R                  " SSS[
        S9n[         R                  " SS	S	S
9nU H  n[        Xt5      n[        US-  SS9n	[        UR                  5       U	R                  5       5        [        UR                  5       U	R                  5       5        [        UR                  U5      U	R                  U5      5        UR                  X!S9n
US-  SS4nSn[        SXU
5        [        UR                  5       U	R                  5       5        M     g )Nr  r  r   rj      rM   r  r   r  r  r  r  r   r   r  r   )r=   r   r  rV   rl  rM  rB  r   r   r   r   r   r   r   r   r   )r[   r   r  r   r  r  r  rv  r  igr   rB   r8  s                rD   test_1D_is_invgamma"TestInvwishart.test_1D_is_invgamma>  s   
 ii##F+s99QAU3KKB2&BB&B"Q$d+B BFFHbffh/BGGIrwwy1 BFF1Irvvay1 &&b&3CqD!T?DE":tC@ BJJL"**,7% rF   c                    SnSn[         R                  " U5      nSUS'   SUS'   [        X#5      n[         R                  R	                  S5      n[        R
                  " X#US9n[         R                  R	                  S5      nUR                  US9n[         R                  R	                  S5      nUR                  SS9n[         R                  UR                  US	-
  5      UR                  US
-
  5      UR                  U5      4   S-  n	[         R                  " U	5      n
X[         R                  " USS9'   [         R                  R                  U5      n[         R                  R                  U
R                  UR                  5      R                  n[         R                  " XR                  5      n[!        Xm5        [!        X}5        g )NrN   r  r  rj  ry  iHG	 r   r   rM   r   rn   rr  )r=   rV   r   r   r  r   r   rf  rz  rw   rs  r   r   solver   r  r   )r[   r   rv  r  r  r   iw_rvsfrozen_iw_rvsr}  r~  r}   r  Lmanual_iw_rvss                 rD   test_invwishart_2D_rvs%TestInvwishart.test_invwishart_2D_rvs_  sp    sc
c
 " ii##F+<ii##F+C0 ii##F+jjaj(EEMM"Q$MM"Q$MM"
 		 GGI(3"//#
$% IIu%IIOOACC%''q## 	.5rF   c                 b   SnSnS GH$  n[         R                  " [         R                  " U5      S-   5      n[         R                  " X3S-
  -  S-  5      U[         R                  " USS9'   [         R                  " UR
                  U5      n[        X5      nUR                  5       nUR                  5       nXr-  S-  nUR                  US	S
9n	U	R                  SS9n
X3S-   -  S-  nSU-  n[        R                  " SUS-  -
  5      n[         R                  " X-
  U-  SUS9(       a  GM%   e   g)z1Test that sample mean consistent with known mean.r   N  r   rj   r   rM   rn   rr  r  rs  r   r   r   r  r  N)r=   rw   rl  rs  r  r   r   r   r   r   r   ppfr  )r[   rv  sample_sizer   r  r   	Xmean_expXvar_exp	Xmean_stdr  	Xmean_estntests	fail_ratemax_diffs                 rD   test_sample_meanTestInvwishart.test_sample_mean  s    CGGBIIcNQ./E02		#q/A:M0NE"//#,-FF577E*Eb(D		IxxzH!/#5Ik=AAI']A%FvIxxIM 12H;;&)3   ! rF   c                 f   [         R                  " / SQ/ SQ/ SQ/ SQ/5      n[         R                  " / SQ/ SQ/ SQ/ SQ/5      nS	n[        R                  " XU5      nUR                  S
   n[         R
                  R                  U5      u  pg[         R
                  R                  U5      u  ph[         R
                  R                  X5      n	US-  U-  X5-  S-  [         R                  " S5      -  -
  [        US-  U5      -
  X5-   S-   S-  U-  -
  SU	R                  5       -  -
  n
[        XJ5        g)zRegression test for gh-8844.)rM   r   r   r  )r   rM   r  r  )r   r  rN   r   )r  r  r   rM   )r  rm   rN   r   )rm   r  rj   r   )rN   rj   r  rM   )r   r   rM   r  rk   r   rM   r   r  N)r=   r   r   r   r?   r   r  r  r{  r7   tracer   )r[   r  PsinuprobrV  siglogdetX	logdetPsir   r  s              rD   test_logpdf_4x4TestInvwishart.test_logpdf_4x4  s   HHn&$&( ) hh$$$& '   ,GGAJyy((+**3/IIOOA#T9$tAvrvvay()"2a4+, vz1nW,- !'')m	$
 	'rF   r   N)
r   r   r   r   r  r  r  r  r#  r   r   rF   rD   r  r    s    E@8B,6\6(rF   r  c                   >    \ rS rSrS rS rS rS rS rS r	S r
S	rg
)TestSpecialOrthoGroupi  c                     [         R                  " S[        R                  R	                  S5      S9n[        R
                  " / SQ/ SQ/ SQ/5      n[        X5        g )NrN     r   )gDbgMPFh?g,׿)g7?g++?guC))g?gg]Qg^ɿ)r   r   r=   r   r   r   r   )r[   rb   r  s      rD   test_reproducibility*TestSpecialOrthoGroup.test_reproducibility  sK    ##ABII4I4I#4NO88CBCE F 	"!.rF   c                     [        [        [        R                  S 5        [        [        [        R                  S5        [        [        [        R                  S5        [        [        [        R                  S5        g Nr!  rn   ru  )rn  rS   r   r   r[   s    rD   test_invalid_dim&TestSpecialOrthoGroup.test_invalid_dim  sN    j"5"9"94@j"5"9"96Bj"5"9"92>j"5"9"93?rF   c                 |    Sn[        U5      nUR                  SS9n[         R                  " USS9n[        X45        g )Nrm   rs  r   )r   r   r   )r[   r   r  r  r  s        rD   test_frozen_matrix(TestSpecialOrthoGroup.test_frozen_matrix  s;    $S)zztz,"&&s>T rF   c                    [        SS5       VVs/ s H,  n[        S5        H  n[        R                  " U5      PM     M.     nnnU Vs/ s H"  n[        R                  R                  U5      PM$     nn[        US/S-  SS9  U HN  n[        [        R                  " XDR                  5      [        R                  " UR                  S   5      5        MP     g s  snnf s  snf )	NrM   rc  rN   r      vIh%<=r  r   )r  r   r   r=   r   r  r   r   r  r   rV   r?   )r[   r   r  rW  rb   detss         rD   test_det_and_ortho(TestSpecialOrthoGroup.test_det_and_ortho  s    q!$#Qx! "%%c* +$ 	 !
 +--"Q		a "-rd2gE2 A%bffQn&(ffQWWQZ&8: !
 .s   3C
)Cc                    SnSnSn[         R                  " X[        R                  R	                  S5      S9nSnU VVVs0 s H(  u  pgXg4[        U Vs/ s H
  oU   U   PM     sn5      _M*     n	nnnU V
Vs/ s H  o  H  oU:  d  M
  X4PM     M     nn
nU VVs/ s H  u  p[        X   X   5      S   PM     nnn[        U/[        U5      -  U5        g s  snf s  snnnf s  snn
f s  snnf )Nrj   r  皙?i  r   r  r  )r   rl   rK  r   )	r   r   r=   r   r   sortedr    r   r   )r[   r   r  ks_probrW  elserecrb   proje0e1pairsp0p1ks_testss                   rD   	test_haarTestSpecialOrthoGroup.test_haar  s      $$BII,A,A#,F
 +HKLfb&R!8RB%)R!899L$'ACb#Bb"#CADIJEHTXtx03EJ7)CJ.9 "9LAJs*   CC%C9C&C&C,Cc                 @    [        [        R                  " SSS9SSS9  g )Nr   r  r   r5  r  )r   r   r   r-  s    rD   test_one_by_one%TestSpecialOrthoGroup.test_one_by_one	  s     	+//=quMrF   c                 V    [        [        R                  " SSS9R                  S5        g Nr   rl   r   )rl   r   r   r   r   r   r?   r-  s    rD   test_zero_by_zero'TestSpecialOrthoGroup.test_zero_by_zero	       (,,QQ7==yIrF   r   N)r   r   r   r   r)  r.  r1  r7  rH  rK  rP  r   r   rF   rD   r&  r&    s(    /@!::8N
JrF   r&  c                       \ rS rSrS rS rS rS r\R                  R                  S/ SQ5      S 5       rS	 rS
 rS r\R                  R                  S 5       rSrg)TestOrthoGroupi	  c                 V   Sn[         R                  R                  U5      n[        R                  " SUS9n[        R                  " SUS9n[        [         R                  R                  U5      S5        [         R                  " / SQ/ SQ/ SQ/5      n[        X55        [        XE5        g )Nr(  rN   r   rn   )gm?gӠh"gEo?)g~7ݲC?g>Ŀg0J_ٿ)gݱ&ǿg 6qrg`X|[)
r=   r   r  r   r   r   r   r  r   r   )r[   r   r   rb   r   r  s         rD   r)  #TestOrthoGroup.test_reproducibility	  s    ii##D)OOAC0__QT2BIIMM!,b188<==? @ 	"!.!"/rF   c                     [        [        [        R                  S 5        [        [        [        R                  S5        [        [        [        R                  S5        [        [        [        R                  S5        g r,  )rn  rS   r   r   r-  s    rD   r.  TestOrthoGroup.test_invalid_dim	  sB    j+//48j+//6:j+//26j+//37rF   c                     Sn[        U5      n[        USS9nUR                  SS9n[         R                  " USS9nUR                  SS9n[        XE5        [        XF5        g )Nrm   rs  r   r   r   r   )r   r   r   r[   r   r  frozen_seedr  r  rvs3s          rD   r1  !TestOrthoGroup.test_frozen_matrix	  s]    S!!#D1zztz,s6A&T T rF   c                    [        SS5       VVs/ s H3  n[        S5       Vs/ s H  n[        R                  " U5      PM     snPM5     nnn[        R                  " U VVs/ s H2  oD Vs/ s H"  n[        R
                  R                  U5      PM$     snPM4     snn5      n[        [        R                  " U5      [        R                  " UR                  5      SS9  U HW  nU HN  n[        [        R                  " XUR                  5      [        R                  " UR                  S   5      5        MP     MY     g s  snf s  snnf s  snf s  snnf )NrM   rc  r  r5  r  r   )r  r   r   r=   r   r   r  r   fabsrU   r?   r   r  r   rV   )r[   r   r  rW  xxrb   r6  s          rD   r7  !TestOrthoGroup.test_det_and_ortho+	  s     q&$# b	#!1 s#!#$ 	 &
 xx"E"BB7Bq"))--*B7"EFrwwtzz':G B)"&&CC.*,&&*<>  # &
 8Es.   E D>E"	E
+)E	E
>E	E
r   )rM   rj   r  r  c                 l   [         R                  R                  S5      n[        US9nUR	                  SUS9n[
        R                  R                  U5      n[         R                  " US:  5      n[        U5      n[        R                  " Xg5      nUR                  SS9u  pU	Ss=:  a  U
:  d   e   eg )	Nl   <`Lr )r   r,  r   r   ffffff?confidence_levelr  )r=   r   r   r   r   r   r   r  r   r   r/   	binomtestproportion_ci)r[   r   r   r   r   r6  r  r   r@   r   r   s              rD   test_det_distribution_gh18272,TestOrthoGroup.test_det_distribution_gh18272:	  s     ii##$78s#hhDsh3||$FF4!8Iooa#%%t%<	S4rF   c                    SnSnSn[         R                  R                  S5      n[        R                  " XUS9nSnU VVV	s0 s H(  u  pxXx4[        U V	s/ s H
  oU   U   PM     sn	5      _M*     n
nnn	U VVs/ s H  o  H  oU:  d  M
  X4PM     M     nnnU VVs/ s H  u  p[        X   X   5      S   PM     nnn[        U/[        U5      -  U5        g s  sn	f s  sn	nnf s  snnf s  snnf )Nrj   r  r:  i  r   r;  r   )	r=   r   r  r   r   r<  r    r   r   )r[   r   r  r=  r   rW  r>  r?  r@  rb   rA  rB  rC  rD  rE  rF  rG  s                    rD   rH  TestOrthoGroup.test_haarG	  s     ii##C(__SSA +HKLfb&R!8RB%)R!899L$'ACb#Bb"#CADIJEHTXtx03EJ7)CJ.9 "9LAJs*   C!C'C!;C(C( C.C!c                 f   Sn[         R                  " US[        R                  R	                  S5      S9n[        [        R                  " U5      SSS9  [        R                  " US:  5      n[        U5      n[        R                  " X45      nUR                  SS	9u  pgUS
s=:  a  U:  d   e   eg )Nr   r,  r(  r   r5  r  r   rc  rd  r  )r   r   r=   r   r   r   rv  r   r   r/   rf  rg  )r[   r   rW  r  r   r@   r   r   s           rD   rK  TestOrthoGroup.test_one_by_oneb	  s    __St")):O:OPS:TUr
AE2FF26NGooa#%%t%<	S4rF   c                 V    [        [        R                  " SSS9R                  S5        g rN  rO  r-  s    rD   rP   TestOrthoGroup.test_zero_by_zerom	  rR  rF   c                 L  ^^ [         R                  R                  S5      mSU4S jjn[        SS5       Hk  mSUU4S jjnU" U5      nU" [        R
                  R                  R                  5      n[        R
                  R                  X45      u  pV[        SU5        Mm     g )	Nr(  c                    > [         R                  R                  TR                  X 4S95      u  p#n[         R                  " X$5      $ Nr   )r=   r   r   r   r  )r   r   r   _sr   r   s        rD   random_ortho<TestOrthoGroup.test_pairwise_distances.<locals>.random_orthou	  s4    yy}}SZZcZZ%@AHA166!<rF   rM   rk   c                   > [         R                  " [        U5       Vs/ s H)  n[         R                  " U " TTS9U " TTS9-
  S-  5      PM+     sn5      nU[         R                  R                  U* X$R                  S9-  nU$ s  snf )N)r   r   rM   r   )r=   r   r  r   r   r   r?   )r   r'  epsr   r/   r   r   s        rD   generate_test_statisticsHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statisticsz	  s     #1X" & FFCCc:Cc:;=>? @%"  **C4;;*GG"s   0Br:  r<   )r  r  )
r=   r   r  r  r   r/   r   r   r    r   )	r[   rt  rx  r  r  _DrV  r   r   s	          @@rD   test_pairwise_distances&TestOrthoGroup.test_pairwise_distancesp	  s     ii##C(	  A;C  0=H-ekk.E.E.I.IJFKK((:EBc1%! rF   r   N)r   r   r   r   r)  r.  r1  r7  rR   r   r   rh  rH  rK  rP  r  r{  r   r   rF   rD   rT  rT  	  si    08
!> [[UN3
  4
 :6	 J [[& &rF   rT  c                   2    \ rS rSrS rS rS rS rS rSr	g)	TestRandomCorrelationi	  c                    [         R                  R                  S5      nSn[        R                  " X!S9n[        R                  " USS9n[         R
                  " / SQ/ SQ/ SQ/ SQ/5      n[        X55        [        XE5        g )Nr(  r  r=  r  rt  r   )r   ѓ2ǿA?Ϳ)r  r   4($?R}%?)r  r  r   qTnƿ)r  r  r  r   )r=   r   r  r   r   r   r   )r[   r   r2  rb   r   r  s         rD   r)  *TestRandomCorrelation.test_reproducibility	  sp    ii##C(!""4:##Ds;88A@@AC D 	"!.!"/rF   c                    [        [        [        R                  S 5        [        [        [        R                  S5        [        [        [        R                  S5        [        [        [        R                  S/5        [        [        [        R                  SS/SS//5        [        [        [        R                  SS/5        [        [        [        R                  / SQ5        g )	Ntestru  r   rM   rN   rl   g      )r   rM   r   )rn  rS   r   r   r-  s    rD   test_invalid_eigs'TestRandomCorrelation.test_invalid_eigs	  s    j"4"8"8$?j"4"8"8&Aj"4"8"8#>j"4"8"83%@j"4"8"8Aa5!A-Hj"4"8"83*Ej"4"8"8*ErF   c                     Sn[        U5      n[        USS9n[         R                  " USS9nUR                  SS9nUR                  5       n[        XE5        [        XF5        g )Nr  r(  r   r   )r   r   r   )r[   r2  r  r[  r  r  r\  s          rD   r1  (TestRandomCorrelation.test_frozen_matrix	  s[    !#D)(C8!%%d=zzsz+ T T rF   c           
      6   S n[         R                  R                  S5      n[        SS5       Vs/ s H  o1" X2R	                  US95      PM     nnUR                  / SQ5        U Vs/ s H  nS/[        U5      -  PM     nnU Vs/ s H  n[        R                  " XRS9PM     nnU Vs/ s H6  n[         R                  " [         R                  R                  U5      5      PM8     n	nU Vs/ s H  n[         R                  " U5      PM     n
n[        XS	S	S
9  U Vs/ s H  n[         R                  " U5      PM     nn[        X5       H  u  p[        XS	S9  M     U H  n[        XR                   S	S9  M     g s  snf s  snf s  snf s  snf s  snf s  snf )Nc                 "    X-  [        U5      -  $ r<   )r   )r  r  s     rD   r   3TestRandomCorrelation.test_definition.<locals>.norm	  s    3s1v:rF   rZ  rM   rk   r   )rl   r   r   r   r   r   r5  r  r  )r=   r   r  r  r   rR  r   r   r   r_  r   r  r*  r   rw   zipr   )r[   r   r   r  r2  r  rU   rW  rb   r6  
dets_knowndiagsr  r   s                 rD   test_definition%TestRandomCorrelation.test_definition	  sS   	 ii##C(6;AqkBkQ+,kBI%)*TSVT*CGH4a $$Q94H 4662a		a()26*./$Qbggaj$
/u5A &((RR($DAAu- % AAss/ ) C +H 7/ )s#   E=(FF+=F. F Fc           	         [         R                  " SS/SS//[        S9n[        R                  " U5      n[        U[         R                  " SS/SS//5      5        [         R                  " SS9   [         R                  " SS/SS//5      n[         R                  " SS/S[         R                  " SS5      //[        S9n[        R                  " UR                  5       5      n[        XR                  R                  U5      R                  U5      5        [         R                  " S	S/SS
//[        S9n[        R                  " UR                  5       5      n[        XR                  R                  U5      R                  U5      5        S S S 5        [         R                  " SS/SS//[        S9n[        R                  " UR                  5       5      n[        US   S5        [         R                  " SS/SS//[        S9n[        R                  " UR                  5       5      n[        US   S5        g ! , (       d  f       N= f)Nr   r   r   r  ignore)overrn   gu <7~r  rd  rM   r  gMk   @)r=   r   rM  r   _to_corrr   errstate	nextaftercopyr   r  )r[   r]  gm0s       rD   test_to_corr"TestRandomCorrelation.test_to_corr	  s    HHsAhA'u5''*288aVaX$678
 [[h'1a&2q'*+AE1:2<<1+='>?uMB"++BGGI6AAsswwr{q12C<%6eDB"++BGGI6AAsswwr{q12 ( XX1v1v&e4''	2#" XX!}q!f-U;''	2#"' ('s   0DH;;
I	r   N)
r   r   r   r   r)  r  r1  r  r  r   r   rF   rD   r~  r~  	  s    
0F
!"0H#rF   r~  c                   4   \ rS rSr\R
                  R                  SSS/5      \R
                  R                  S/ SQ5      S 5       5       r\R
                  R                  S/ SQ5      S	 5       rS
 r	\R
                  R                  S/ SQ5      S 5       r
Srg)TestUniformDirectioni	  r   r   rN   r   Nr   rj   )rj   rl   c                 x   [         R                  R                  S5      n[        XS9nUR	                  U5      n[         R
                  " U5      [         R                  " U5      pvUR                  XgUS9R                  nUR                  U:X  d   e[         R                  R                  USS9n	[        U	S5        g )N   Sid)_i4 r   r   rn   r   r   )r=   r   r   r(   r   r   rV   r   r?   r   r   r   )
r[   r   r   r   uniform_direction_distr  r   r   expected_shapenormss
             rD   r  !TestUniformDirection.test_samples	  s     ii##$78!23!A(,,T2HHSM266#;c000FLL}}...		wR0r"rF   )Nr   r!  ru  c                     Sn[         R                  " [        US9   [        R                  " U5        S S S 5        g ! , (       d  f       g = f)NzMDimension of vector must be specified, and must be an integer greater than 0.rK   )rR   r
   rS   r(   r   )r[   r   r\   s      rD   r.  %TestUniformDirection.test_invalid_dim
  s1    <]]:W5!!#& 655s	   <
A
c                     Sn[        U5      n[        USS9nUR                  SS9n[         R                  " USS9nUR                  5       n[        XE5        [        XF5        g )Nrj   r(  r   r   )r(   r   r   rZ  s          rD   test_frozen_distribution-TestUniformDirection.test_frozen_distribution
  s[    "3''#6zzsz+ $$Ss; T T rF   )rM   rj   r  c                    [         R                  R                  S5      n[        XS9nUR	                  SS9u  pEXTU-  U-  -  nU[         R
                  R                  U5      -  n[        XE-  SSS9  UR	                  SS9nXd-  nXe-  n[         R                  " Xx5      n	U	[         R                  -  n	U	S[         R                  -  -  n	[        5       n
[        XR                  5      nUR                  S	:  d   eg )
Nl   @9Y sr   rM   r   r   r  r  ru  r:  )r=   r   r   r(   r   r   r   r   arctan2r1  r   r!   r   pvalue)r[   r   r   spherical_distv1v2r  s1s2anglesuniform_distkstest_results               rD   test_uniform!TestUniformDirection.test_uniform
  s    ii##$78*39###+
2gl
biinnR  / $$%$0\\B# 	"%%!BEE'yv'7'78##d***rF   r   N)r   r   r   r   rR   r   r   r  r.  r  r  r   r   rF   rD   r  r  	  s    [[UQF+[[V%9:	# ; ,	# [[U$:;' <'
! [[UI.+ /+rF   r  c                   8    \ rS rSrS rS rS rS rS rS r	Sr
g	)
TestUnitaryGroupi,
  c                     [         R                  R                  S5      n[        R                  " SUS9n[        R                  " SSS9n[         R
                  " / SQ/ SQ/ SQ/5      n[        X$5        [        X45        g )Nr(  rN   r   )y~p?yZ?y뉦?ĭ?y8Z?&4?)yEHξr?8i?ye??+ݓݿyu=ٿB۽'?)yqXQÿ?yN6ҿzܷy! 8l?2W'?)r=   r   r  r   r   r   r   )r[   r   rb   r   r  s        rD   r)  %TestUnitaryGroup.test_reproducibility-
  si    ii##C(ac2qs388IHKM
 	"!.!"/rF   c                     [        [        [        R                  S 5        [        [        [        R                  S5        [        [        [        R                  S5        [        [        [        R                  S5        g r,  )rn  rS   r   r   r-  s    rD   r.  !TestUnitaryGroup.test_invalid_dim;
  sJ    j-"3"3T:j-"3"3V<j-"3"3R8j-"3"3S9rF   c                     Sn[        U5      n[        USS9nUR                  SS9n[         R                  " USS9nUR                  SS9n[        XE5        [        XF5        g )Nrm   r(  r   r   r   r   )r   r   r   rZ  s          rD   r1  #TestUnitaryGroup.test_frozen_matrixA
  s_    s##Cc2zzsz+  37A&T T rF   c                 \   [        SS5       VVs/ s H,  n[        S5        H  n[        R                  " U5      PM     M.     nnnU H[  n[        [        R
                  " XDR                  5       R                  5      [        R                  " UR                  S   5      SS9  M]     g s  snnf )NrM   rc  rN   r   r  r  )
r  r   r   r   r=   r  conjr   rV   r?   )r[   r   r  rW  rb   s        rD   test_unitarityTestUnitaryGroup.test_unitarityM
  s    q!$#Qx! $ %$ 	 !
 ABFF1ffhjj1266!''!*3EER !s   3B(c           	      6   S GH  nSn[         R                  " X[        R                  R	                  S5      S9n[        R
                  " U Vs/ s H"  n[        R                  R                  U5      PM$     sn5      n[        R                  " UR                  UR                  5      n[        UR                  5       [        [        R                  * S[        R                  -  5      R                   5      n[#        UR$                  S:  5        GM     g s  snf )Nr  r  r(  r   rM   r:  )r   r   r=   r   r   rQ  r   r   eigvalsr  imagr\  r!   ravelr   r1  r   r	   r  )r[   r   r  rW  rb   r2  r@   s          rD   rH  TestUnitaryGroup.test_haarV
  s    
 CG""		0E0Ec0JB 99rBr!ell2215rBCD

499dii0AGRUUFAbeeG$<$@$@ACCJJ%&  Cs   )D
c                 V    [        [        R                  " SSS9R                  S5        g rN  )r   r   r   r?   r-  s    rD   rP  "TestUnitaryGroup.test_zero_by_zeroi
  s    ]&&qq177CrF   r   N)r   r   r   r   r)  r.  r1  r  rH  rP  r   r   rF   rD   r  r  ,
  s"    0:
!S'&DrF   r  c                      \ rS rSrSS/SS/SS/SS/SS/SS/SS/SS/SS/SS//
SS/SS/SS//S/ SQ4/ S	Q/ S
Q/ SQ/ SQ/ SQ// SQ/ SQ/ SQ/ SQ/S/ SQ4/r\R                  R                  S\5      S 5       r\R                  R                  S\5      S 5       r	S r
S r\R                  R                  \" S5      S 5       5       rS rS rSSSS S/SS //SSS/S S/SS //S4SS S/SS //S SS/S S/SS //S 4S S /SSS S /SS/SS//S4S S /SS S S /SS/SS//S 4S S /S S/SS //SS S /S S/SS //S4S S /S S/SS //S S S /S S/SS //S 4/r\R                  R                  S!\5      S" 5       rS#SSS#/S//S4S#/S/SS#/S//S4\R(                  " S#/5      \R(                  " S/5      SS#/S//S4/r\R                  R                  S!\5      S$ 5       rS% rS& rS' r\R                  R                  S(S)S*/5      \R                  R                  S+/ S,Q5      \R                  R                  S-S.S/\R4                  /5      S0 5       5       5       rS1 r\R                  R                  S+/ S2Q5      S3 5       r\R                  R                  S+/ S4Q5      S5 5       rSVS7 jrS8 r \R                  R                  S+/ S9Q5      \R                  R                  S:/ S;Q5      \R                  R                  S<S6S=/5      S> 5       5       5       r!\R                  RD                  S? 5       r#S@ r$SA r%SB r&\R                  R                  S+SC5      SD 5       r'SE r(\R                  R                  S-/ SFQ5      SG 5       r)\R                  R                  SHSI\RT                  " SS5      SJSK4SL\R(                  " SMS/SSI//5      SNSO4/5      SP 5       r+\R                  R                  SQ/ SRQ5      SS 5       r,ST r-SUr.g)WTestMultivariateTim
  r   rM   rl   rN   rj   r   )
|	ߌ?v
2R?r  g0$H?r  r  gO`?gՒXO?g	ߌ,?g8N8?)gHP?gQI?go_?)g9m4?g=U?gˡE?)g$C?ghs?gǺ?)g!uq?g%C?gS㥛?)gOec?gz,C?g	h"l?)rn   r   2   )r   r  r*  )r  r   rc  )r*  rc  r   r  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 R    [        X#USS9nUR                  U5      n[        Xu5        g Nr   r   )r$   r   r   )r[   rb   r  r?   rv  ansr   vals           rD   test_pdf_correctness&TestMultivariateT.test_pdf_correctness
  s%    c"15hhqk!#+rF   c                     [        X#USS9nUR                  U5      nUR                  U5      n[        [        R
                  " U5      U5        g r  )r$   r   r   r   r=   r{  )	r[   rb   r  r?   rv  r  r   r  r  s	            rD   test_logpdf_correct%TestMultivariateT.test_logpdf_correct
  s<    c"15xx{{{1~!"&&,5rF   c                 x    / SQn[         R                  " USS9n[        R                  " U5      n[        X#5        g )N)
r  rm   rl   r   r[  r  r   r[  rn   rN   r   rv  )r$   r   r%   r   )r[   rb   r  r  s       rD   test_mvt_with_df_one_is_cauchy0TestMultivariateT.test_mvt_with_df_one_is_cauchy
  s.    -  q)jjm!#+rF   c                     Sn[        SSSSS9nUR                  SS9n[        U5      u  pEXQ:  d   e[        SS/S	S
/S
S	//SSS9nUR                  SS9n[        U5      u  pEXQ:  R                  5       (       d   eg )Nr   r   r   順 rv  r   r   rq   rN   r  rn   *   )r$   r   r&   r  )r[   	P_VAL_MINr   r  r   rV  s         rD   &test_mvt_with_high_df_is_approx_normal8TestMultivariateT.test_mvt_with_high_df_is_approx_normal
  s    
 	avA6(((''"r1gR2r(';#%'(((''"##%%&%rF   z'scipy.stats.multivariate_normal._logpdfc                 :   [        SS[        R                  SS9n[        U[        5      (       d   e[         R
                  " S[        R                  S9  UR                  S:X  d   e[         R                  " S[        R                  S9  UR                  S:X  d   eg )Nr   r   rm   r  r  rM   )r$   r=   r  r   r   r   
call_countr   )r[   mockr   s      rD   !test_mvt_with_inf_df_calls_normal3TestMultivariateT.test_mvt_with_inf_df_calls_normal
  sx     arvvA6$ :;;;;1(!###aBFF+!###rF   c                    Sn[         R                  " U5      n[         R                  " U5      nSn[         R                  " U5      n[        X#U5      R	                  U5      n[         R
                  " U5      (       d   e[        X#U5      R                  U5      n[         R
                  " U5      (       d   eSn[         R                  R                  Xq45      n[        X#U5      R	                  U5      nUR                  U4:X  d   e[        X#U5      R                  U5      nUR                  U4:X  d   e[        [         R                  " S5      [         R                  " S5      S5      R                  5       n[         R
                  " U5      (       d   eSn[        [         R                  " S5      [         R                  " S5      S5      R                  US9nUR                  U4:X  d   eg )Nrl         @rm   r   r   )
r=   r   rV   r$   r   isscalarr   r   r?   r   )	r[   r   r  r?   rv  rb   r@   	n_samplesr   s	            rD   test_shape_correctness(TestMultivariateT.test_shape_correctness
  s    hhsmsHHSMS,003{{3S,33A6{{3 	IIi-.S,003		i\)*)S,33A6		i\)*) RXXa["&&)Q7;;={{3 RXXa["&&)Q7;;;F		dW$%$rF   c                     [        5       n[        UR                  S/5        [        UR                  S//5        UR                  S:X  d   eg )Nr   r   r$   r   r  r?   rv  )r[   r   s     rD   test_default_arguments(TestMultivariateT.test_default_arguments  s<    TXXs#TZZ1#'1rF   )NNNr   r   r   )NNrm   r   r   rm   Nrm   z*loc, shape, df, loc_ans, shape_ans, df_ansc                     [        XUS9n[        UR                  U5        [        UR                  U5        UR                  U:X  d   eg )Nr  r?   rv  r  r[   r  r?   rv  loc_ans	shape_ansdf_ansr   s           rD   test_default_args#TestMultivariateT.test_default_args  s>     #r:TXXw'TZZ+6!"!rF   rn   c                     [        XU5      n[        UR                  U5        [        UR                  U5        [        UR                  U5        g r<   r  r  s           rD   &test_scalar_list_and_ndarray_arguments8TestMultivariateT.test_scalar_list_and_ndarray_arguments%  s:     c"-TXXw'TZZ+TWWf%rF   c           
      h   SS//n[        [        [        40 [        US9D6  SS/SS/SS//n[        [        [        40 [        XS9D6  [        R
                  " S5      n[        R                  " S5      nSn[        [        [        40 [        XUS9D6  Sn[        [        [        40 [        XUS9D6  g )	Nr   )r  rM   rN   )r  r?   rn   r  r   )rn  rS   r$   r"  r=   r   rV   )r[   r  r?   rv  s       rD   test_argument_error_handling.TestMultivariateT.test_argument_error_handling.  s    1vhj$	'	'
 Q!Q!Q(j$	42	4
 hhqkq	j$	;b9	; j$	;b9	;rF   c                 
   [         R                  R                  S5      nUR                  SS9n[         R                  " S5      n[        X#SSS9n[        X#SSS9nUR                  SS9nUR                  SS9n[        Xg5        g )Nrl   rN   r   rM   r  r  )r=   r   r  r   rV   r$   r   r   )r[   r   r  r?   r   dist2samples1samples2s           rD   r)  &TestMultivariateT.test_reproducibilityG  sw    ii##A&kkqk!q	saa8saa899"9%99"9%X(rF   c                 ~    [        SS/SS/SS//SSS9n[        [        R                  R                  [
        40 UD6  g )Nr   r   F)r  r?   rv  ra   )r"  rn  r=   r   r  r$   )r[   rB   s     rD   test_allow_singular%TestMultivariateT.test_allow_singularQ  s;    1qeQqE]qObii++^DtDrF   r   )r  rN   )rj   rk   rl   rN   r   )rM   rN   rl   rj   rv  r   r  c                     [        [        R                  " U5      [        R                  " U5      U5      nUR	                  US9nUR
                  X4-   :X  d   eg rr  )r$   r=   r   rV   r   r?   )r[   r   r   rv  r   r   s         rD   test_rvsTestMultivariateT.test_rvsV  sH     bhhsmRVVC["=hhDh!yyD7N***rF   c                    [         R                  " S5      n[         R                  " S5      nSn/ SQ/ SQ/ SQ/ SQ/n/ SQ/ SQ/ SQ/ SQ/n[         R                  " / SQ5      n[        R
                  " XAX#US9n[        XwS	   U-  5        g )
NrN   r  r7  ro   rR  rS  rT  r=  r   rU  )r[   r   r   rv  r   r  rV  r   s           rD   rW   TestMultivariateT.test_cdf_signs^  sp    xx{ffQi	9i8	9i8.1!%%asAFVN23rF   )r   rM   rj   c                 &    U R                  U5        g r<   cdf_against_mvn_testr[   r   s     rD   $test_cdf_against_multivariate_normal6TestMultivariateT.test_cdf_against_multivariate_normalj  s     	!!#&rF   )rN   rk   r  c                 (    U R                  SS5        g )NrN   Tr  r  s     rD   -test_cdf_against_multivariate_normal_singular?TestMultivariateT.test_cdf_against_multivariate_normal_singularo  s     	!!!T*rF   Fc           
         [         R                  R                  S5      nSnSUR                  SSUS9-  n[	        XX25      nSUR                  SSUS9-  [         R
                  " UR                  US95      -  nSUR                  SSXA4S9-  * U-   nSUR                  SSXA4S9-  U-   n	[        R                  R                  XUS	US
US9n
[        R                  R                  XUS
US9n[        XSS9  g )N   ]J>?a rN   r  rq   r   r   rn   rM   ru  T)rv  r>  ra   r   )ra   r>  Mb@?r  )r=   r   r   r   r   signr   r/   r$   r   r   r   )r[   r   r   r   r   ri  r   r   r  r   r@   rA   s               rD   r  &TestMultivariateT.cdf_against_mvn_testt  s   ii##O4B,, 73;;r13;//"''#**#*:N2OOR!222T9B11D8""&&q16: ' N''++AS89 , ;t,rF   c           	      F   [         R                  R                  S5      nSnSnUR                  S[         R                  " U5      S9nSn[
        R                  R                  XCX%[         R                  * US9n[
        R                  R                  XEU[         R                  " U5      5      n[
        R                  R                  XC[         R                  " U5      5      n[        XgSS	9  [         R                  " [         R                  " Xh-
  5      S
:  5      (       d   eg )Nr  rM   r   r  )r   r  rN   )r>  r   r  r  r  )r=   r   r   r   r  r/   r$   r   r  r.  r   r   r  rv  )	r[   r   r   r   rb   rv  r@   rA   	incorrects	            rD   test_cdf_against_univariate_t/TestMultivariateT.test_cdf_against_univariate_t  s    ii##O4JJBbggclJ3""&&qbffW47 ' 9ggkk!rwws|4JJNN1BGGCL9	t,vvbffS_-45555rF   )rM   rN   rj   r  r   )   no l   m, l   sO l   U iOfYl   O_ r   Tc           
      4   U(       a  US:w  a  [         R                  " S5        [        R                  R	                  U5      nSUR                  SSUS9-  n[        XXC5      nUR                  U5      nUR                  U5      * nUR                  U5      n	UR                  5       S-  n
[        R                  R                  XXjUSS	9n[        R                  " S
S9   [        SX[        R                  U-  X-
  U5      S   nS S S 5        [        UWSSS9  [        R                  R                  XXjUUSS9n[        R                  " S
S9   [        SXX-
  X-
  U5      S   nS S S 5        [        XSSS9  g ! , (       d  f       Nz= f! , (       d  f       N+= f)Nr$  z4Agreement with qsimvtv is not great in singular caser  rq   rM   r   rj   T)r   ra   r  )invalidr  r   g-C6*?r  r  r  )r>  r   ra   rL  )rR   r   r=   r   r   r   r   r/   r$   r   r  r9   r  r   )r[   r   r   r   r   ri  r   r   r  r   rv  r@   rA   s                rD   test_cdf_against_qsimvtv*TestMultivariateT.test_cdf_against_qsimvtv  sg   
 
*KKNOii##D)B,, 7zz#ZZ_JJsOZZ\A ""&&qc6: ' <[[*5"266!8QXsCAFC +St$7 ""&&qQ47 ' N[[*5"18QXsCAFC +t$7 +* +*s   &E8F	8
F	
Fc           
      N  ^	^
^ Sn[         R                  R                  S5      nSUR                  SSUS9-  n[	        XUSS9m	UR                  U5      mUR                  U5      * nUR                  U5      nUR                  5       S	-  m
[
        R                  R                  UTT	T
UUS
9nU	U
U4S jn[        XtU[
        R                  R                  XS9S9n[        XhR                  SS9  U	U
U4S jn[        XtS   US   US   US   US   US   5      n[        XhS   SS9  g )NrN   l   	!y r  rn   r   r   T)r   rj   )r   r>  c                 \   > [         R                  R                  U R                  TTT5      $ r<   )r/   r$   r   r   )rb   r   rv  r   s    rD   	integrandITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand  s$    ''++ACCsB??rF   )r'  r   )qrngr  r  c                  T   > [         R                  R                  U S S S2   TTT5      $ )Nrn   )r/   r$   r   )zyxr   rv  r   s    rD   r,  r-    s(    ''++C"ItS"EErF   r   rM   )r=   r   r   r   r   r/   r$   r   r4   qmcHaltonr   integralr6   )r[   r   r   ri  r  r   r@   r,  rA   r   rv  r   s            @@@rD   $test_cdf_against_generic_integrators6TestMultivariateT.test_cdf_against_generic_integrators  s    ii##N3#++b!#+.. t<zz#ZZ_JJsOZZ\A""&&q$Rc34 ' 6	@ yQUYY-=-=-=-NO\\5	F i1qtQqT1Q41qtDV$/rF   c                     [         R                  R                  S5      n[         R                  " / SQ/ SQ/ SQ/5      nSn[        R
                  " X#S9nUR                  / SQUS9nS	n[        XVS
S9  g )Nl   Ja )go!@S<?^Ss@)r7  gRP=@jT0@)r8  r9  gk`-3@gWK?r?   rv  ro   r   g1%?r  r  )r=   r   r   r   r/   r$   r   r   )r[   r   r   rv  r   r@   rA   s          rD   test_against_matlab%TestMultivariateT.test_against_matlab  sn     ii##J/hh???A B  ###5hhysh3t,rF   c                    Sn[         R                  R                  U5      nUR                  SS9nUR                  SS9U-   n[         R                  " S5      nUR                  5       nX5U4n[         R                  R                  U5      n[         R                  R                  U5      n	[
        R                  " USU06n
[        U
R                  U5      [        R                  " U/UQ7SU	065        g )Nl   2m rN   r   r   r   )	r=   r   r   r   rV   r/   r$   r   r   )r[   r   r   r  rb   r?   rv  rB   
rng_frozenrng_unfrozenr   s              rD   r  TestMultivariateT.test_frozen  s    ii##D)kkqk!KKQK#%q	ZZ\BYY**40
yy,,T2##T;
;TXXa[#''LDL|L	NrF   c                   ^^	^
^ SnSn[         R                  R                  S5      mTR                  X4S9nX3R                  -  mTR                  U5      m
TR                  X!4-   5      nTR                  5       S-  m	[        R
                  R                  UT
TT	TS9nUU	U
U4S jn[         R                  " USU5      n[        XWS	S
S9  g )Nrl   rK  r  r   rj   r   c                 T   > [        STT[        R                  * U -  U T-
  T5      S   $ )Nru  r   )r9   r=   r  )rb   r   rv  r   r   s    rD   _cdf_1d2TestMultivariateT.test_vectorized.<locals>._cdf_1d  s+    E2sRVVGAIqvsCAFFrF   rn   rL  r  r'  )	r=   r   r   r   r/   r$   r   apply_along_axisr   )r[   r   r   r}   rb   r@   rC  rA   r   rv  r   r   s           @@@@rD   test_vectorized!TestMultivariateT.test_vectorized  s    ii##O4JJSJJ'##gzz#JJq6z"ZZ\A""&&q$Rc&J	G 	G !!'2q1t$7rF   r.  c                    [         R                  R                  S5      n[        R                  R                  S/S/US-
  -  -   S9n[        R                  " US9R                  S/U-  US9nSUS-   -  n[        XESS	9  g )
Nr  r   r  )r  )r?   r   r   rd  r  )
r=   r   r   r   r   toeplitzr/   r$   r   r   )r[   r   r   r}   r@   rA   s         rD   test_against_analytical)TestMultivariateT.test_against_analytical  s|    ii##O4LL!!QC3%37*;$;!<""+//c	/L37mt,rF   c                     [         R                  " SS5      n[         R                  n[        R                  R                  XS9n[        R                  R                  S U5      nX4:X  d   eg )NrN   r:  )r=   rV   r  r/   r$   r   r   )r[   r   rv  mvt_entropymvn_entropys        rD   test_entropy_inf_df%TestMultivariateT.test_entropy_inf_df  sW    ffQlVV**222D//77cB)))rF   )r   r  r  c                     [         R                  R                  SUS9n[         R                  R                  US9n[	        X#SS9  g )Nr   r:  r  r5  r  )r/   r$   r   r.  r   )r[   rv  rM  	t_entropys       rD   test_entropy_1d!TestMultivariateT.test_entropy_1d  s;    **222CGGOOrO*	U;rF   zdf, cov, ref, tolr  g}M@r  r  r  gNfh@r  c                     [         R                  " S5      n[        R                  " XRU5      n[	        UR                  5       X4S9  g )Nr  r  )r=   r   r/   r$   r   r   )r[   rv  r   rA   tolr  mvts          rD   %test_entropy_vs_numerical_integration7TestMultivariateT.test_entropy_vs_numerical_integration"  s3    
 hhuo""3R0s5rF   zdf, dim, ref, tol))r  r   gDdVW?r  )r  r   gU?r5  )r  r   g/+?r  )@xDr   Z_2?r  )}Ô%ITr   r[  r  )r  r  gzg#.@r  )r  r  gD:f,@r5  )rZ  r  1>`,@r  )r\  r  r]  r  )r  r  g8d?b@r  )r  r  g-YҺa@r  )rZ  r  ZGra@r  )r\  r  r^  r  c                     [         R                  " [        R                  " U5      US9n[	        UR                  5       X4S9  g )Nr:  r  )r/   r$   r=   rV   r   r   )r[   rv  r   rA   rV  rW  s         rD   test_extreme_entropy&TestMultivariateT.test_extreme_entropy+  s/    F ""<s5rF   c                 |   [         R                  " / SQ/ SQ/ SQ/ SQ/ SQ/5      nXR                  -  nSn[        R                  R                  X#S9n[        S US9R                  5       n[        XES	S
9  SnSn[        R                  R                  X&S9n[        R                  R                  X'S9n	[        XSS
9  g )N)gQ?g
ףp=
?g\(\߿(\?gGz?)gGzg{GzgQ?r?  gQ)gQ?g)\(?gQѿg)\(ܿg(\?)g      gGzgq=
ףpg\(\?g)rc  g{Gzg\(\?g{GzԿg(\?rZ  r:  r  r  r  i  i   r  )r=   r   r   r/   r$   r   r   r   )
r[   _Ar   rv  mul_t_entropymul_norm_entropydf1df2	_entropy1	_entropy2s
             rD   test_entropy_with_covariance.TestMultivariateT.test_entropy_with_covarianceQ  s     XX+-,,,
  44i ,,4434F.t=EEGeD ((00s0C	((00s0C		48rF   r   F)/r   r   r   r   	PDF_TESTSrR   r   r   r  r  r  r  thread_unsafer:   r  r  r  DEFAULT_ARGS_TESTSr  r=   r   ARGS_SHAPES_TESTSr   r  r)  r  r  r  rW  r  r  r  r"  r(  r  r4  r;  r  rF  rJ  rO  rS  rV   rX  r`  rk  r   r   rF   rD   r  r  m
  sg    FFFFFFFFFF	
 
A FF	

 	
	
1%P %$$$$	
 	 %%%	
 	
	
)K@ID [[5yA, B,
 [[5yA6 B6,'$ [[
45$ 6 $&@ 	$ 	AA1vAA/?C	AAQFaVaV,<a@
QtaVq!fq!f%5q9
Qq1a&Aq6Aq6"2A6
Q1a&1a&!4!Q1a&1a&1A1E
Q1a&1a&!1q!f1v1v.>B	 [[I/1#1# 
QB41#"
sAtqcUA&	2$1#B41#: [[I.0&0&;2)E
 [[Vg|%<=[[UL1[[TBBFF#34+ 5 2 >+

4 [[UI.' /' [[UI.+ /+-$6 [[UM2[[V &J K[[Z%78 8K 382 [[0 04-"N8$ [[UF+- ,-* [[T<0< 1<& [[0!266!Q<1CUK"BHHsAhB-@$A/7896	96
 [[	
$6%$6(9rF   r  c                      \ rS rSr\R
                  R                  SSS/SS/SS4SS/SS/S	\R                  * 4S
S/SS/S\R                  * 4SS/SS/S\R                  4SS/SS//SS/SS//SS/\R                  \R                  /4S
S/SS/S\R                  4SS/SS/S\R                  4SS/SS/S\R                  4SS/SS/S\R                  4SS/SS/S\R                  * 4/
5      S 5       r
S rS rS r\R
                  R                  S/ SQS4/ SQS	4S	S	/S	4S	/S	445      S 5       r\R
                  R                  SS/S/SS4SS/SS/SS4SS/S	S//SS/SS///SS/SS/SS//S S!/S	S"//4\R                  " / \S#9\R                  " / \S#9S	/ 4SS/SS/SS	4/ S$Q/ S%QS&S'4/5      S( 5       r\R
                  R                  SSS/SS/SS)//SSS*/4S/S//S/S//SS/S+S,/4S/S///S/S//SS/S+S,//4S/S//S////SS/S+S,///4/5      S- 5       rS. rS/ rS0 rS1 rS2 rS3 rS4 rS5 rS6 rS7 rS8 rS9rg:);TestMultivariateHypergeomip  zx, m, n, expectedrN   rl   rj   r  rm   gr   r[  r   rM   rt   iirp  rc  rn   ic                 F    [         R                  " XU5      n[        XTSS9  g )Nư>r  )r   r  r   r[   rb   r]  r   r  valss         rD   r  %TestMultivariateHypergeom.test_logpmfq  s     6 &,,Q15T2rF   c                     [         R                  " SS/SS/SS9n[        R                  " SSSSS9n[        XS	S
9  [         R                  " SS/SS/SS9n[        R                  " SSSSS9n[        XS	S
9  g )NrN   r   r  rj   rl   )rb   r]  r      )r  r   r   r'  r  r  rm      )r   r  r#   r   r  s      rD   test_reduces_hypergeom0TestMultivariateHypergeom.test_reduces_hypergeom  sx     &))QFr1gC}}qB!r2.%))QFr2h"E}}qB"3.rF   c                     [        SS/SS9nUR                  SSS9n[        UR                  S5      UR                  5       S	S
9  g )NrN   rj   rl   r]  r   r  rZ  r   r   r  r  r   r   r   r   r[   r   r   s      rD   r  "TestMultivariateHypergeom.test_rvs  s@     $q!f2ff$Sf1RWWYT:rF   c                     [        SS/SS//SS/S9nUR                  SSS	9n[        UR                  S
5      UR                  5       SS9  g )NrN   rj   r  rl   r  r  r  rM   rZ  r   r   r  r  r  r  s      rD   test_rvs_broadcasting/TestMultivariateHypergeom.test_rvs_broadcasting  sK    #1v2w&7Aq6Bff)#f6RWWYT:rF   zm, n)r   r   r  r   r   )r   r   r   r   r   c                     [         R                  " X5      n[        R                  " U5      nUR	                  5       nX$US:g  '   [        X45        g )Nr   )r   r   r=   r>   r  r   )r[   r]  r   r@   res_exs        rD   test_rvs_gh16171*TestMultivariateHypergeom.test_rvs_gh16171  s?    
 %((.JJqMqAvS!rF   g zl?r  r  gQ?gE|?g
y?r  r  )rj   rk   rm   rk   gzp?c                 F    [         R                  " XU5      n[        XTSS9  g Nr  r  r   r  r   rw  s         rD   r  "TestMultivariateHypergeom.test_pmf  s     " &))!2T2rF   r{  g ?r   r   c                 F    [         R                  " XU5      n[        XTSS9  g r  r  rw  s         rD   r  /TestMultivariateHypergeom.test_pmf_broadcasting  s      &))!2T2rF   c                 \    [         R                  " / SQSS9n/ SQ/ SQ/ SQ/n[        XSS9  g )	N)rN   rm   r  rc  r  )gf_?&BUп疈Cx@ؿ)r  ggs>d?ZsK)r  r  g35?r  r  r   r   r   )r[   r  r  s      rD   r  "TestMultivariateHypergeom.test_cov  s0    %))J"=6668 	.rF   c                 2   [         R                  " SS/SS//SS/S9nSS	/S	S//S
S/SS
///n[        XSS9  [         R                  " S/S//SS/S9nS//S///n[        X4SS9  [         R                  " SS/SS/S9nSS	/S	S//SS/SS///n[        XVSS9  g )Nrm   r  r  r{  r  rc  r  g?gg(\?g(\r  r  rl   rj   r   g333333?g333333r  r  s          rD   r  /TestMultivariateHypergeom.test_cov_broadcasting  s    %))aVb"X,>1b'J..0.%))aS1#J1a&A".%))QFq"g>.'"Wf$568.rF   c                 r    [         R                  " SS/SS9n[        R                  " SSSS9n[        XSS9  g )	Nr  rj   rl   r  r{  r   r   r'  r  r  )r   r   r#   r   )r[   var0var1s      rD   test_var"TestMultivariateHypergeom.test_var  s4    %))RGq9}}rQ"-.rF   c                 ~   [         R                  " SS/SS/S9n[         R                  " SS/SS9n[         R                  " SS/SS9n[        US   USS9  [        US	   USS9  [         R                  " SS/SS
//SS/S9nSS/SS//n[        XESS9  [         R                  " S/S//SS/S9nS/S//n[        XgSS9  g )Nr  rj   rl   r  r  r   r  r  r   r  g̍3eY?gI{?r   )r   r   r   )r[   r  r  var2var3var4var5var6s           rD   test_var_broadcasting/TestMultivariateHypergeom.test_var_broadcasting  s    %))RG1v>%))RGq9%))RGq9QD1QD1%))b!Wr2h,?Aq6JI&8(<=.%))aS2$KAr7Crd|.rF   c                     [         R                  " SS/SS9n[        R                  " SSSS9n[        US   USS	9  [         R                  " S
S/SS9nSS/n[        X4SS	9  g )Nr  rj   rl   r  r{  r  r   r  r  rc  r  g      @r  )r   r   r#   r   r[   mean0r  r  mean3s        rD   r  #TestMultivariateHypergeom.test_mean  sd    &++r1g;qB/a%d3&++r1g<j)40rF   c                 b    [         R                  " SS/SS//SS/S9nSS/S	S
//n[        XSS9  g )NrN   rj   r  rl   r  r  rt  ru  gUUUUUU@gUUUUUU@r  r  )r   r   r   )r[   r  r  s      rD   r  0TestMultivariateHypergeom.test_mean_broadcasting  sC    &++1vAw.?Aq6JH%
I'>?40rF   c                 <   [         R                  " / SQSS9n[        U/ SQ5        [         R                  " / SQSS9n[        U[        R                  [        R                  [        R                  /5        [         R                  " / SQ/ SQ/SS9n[        U[        R                  [        R                  [        R                  // SQ/S	S
9  [         R                  " [        R                  " / [        S9SS9n[        U/ 5        [        UR                  S:H  5        g )Nro   r   r  r   r   r   r   r   r   rM   rR  )r   r   r   FFg<r  r  r   )
r   r   r   r=   r  r   r   rJ  r	   r?   r  s        rD   test_mean_edge_cases.TestMultivariateHypergeom.test_mean_edge_cases  s    &++i1=UL)&++i1=URVVRVVRVV45&++y).DJ 8,G"	$ '++bhhr.EKUBu$%rF   c                 :   [         R                  " / SQSS9n[        U/ SQSS9  [         R                  " / SQSS9n[        U[        R
                  [        R
                  [        R
                  /5        [         R                  " / SQ/ S	Q/SS9n[        U[        R
                  [        R
                  [        R
                  // SQ/S
S9  [         R                  " [        R                  " / [        S9SS9n[        U/ 5        [        UR                  S:H  5        g )Nro   r   r  r  gؗҜ<r  r  rM   rR  r  r  r  )
r   r   r   r   r=   r  r   rJ  r	   r?   )r[   r  r  r  r  s        rD   test_var_edge_cases-TestMultivariateHypergeom.test_var_edge_cases  s    %))I;l7%))I;TBFFBFFBFF34%))Y	,BaH7F"	$ &))BHHRs,CqIT2

e#$rF   c                    [         R                  " / SQSS9n/ SQ/ SQ/ SQ/n[        XSS9  [         R                  " / SQSS9n/ SQ/ SQ/ SQ/n[        X45        [         R                  " [        R
                  " / [        S	9SS9n[        R
                  " / [        R                  S	9R                  SS5      n[        XVSS9  [        UR                  S
:H  5        g )Nr  r   r  r  r  r  ro   r   r  r  )r   r   r   r   r=   r   rJ  r  r  r	   r?   )r[   cov0r  r  r  r  r  s          rD   test_cov_edge_cases-TestMultivariateHypergeom.test_cov_edge_cases*  s    %))I;lL9/%))I;lL9T %))BHHRs,CqIxx"**-55a;/

f$%rF   c                 0   [         R                  R                  S5        Sn/ SQn/ SQ/ SQ/ SQ/ SQ/ SQ/n[         R                  " U[        S	9n[        X!5      n[        UR                  U5      [
        R                  " X2U5      5        [        UR                  U5      [
        R                  " X2U5      5        [        UR                  5       [
        R                  " X!5      5        [        UR                  5       [
        R                  " X!5      5        g )
Nrs  rc  )rm   r  rp     r  r  r  r  r  r  )r=   r   r   r>   rJ  r   r   r  r  r   r   )r[   r   r]  rb   
mhg_frozens        rD   r  %TestMultivariateHypergeom.test_frozen8  s    
		tM=<)JJq$+A1

q).221;	=
))!,.55aA>	@
(*@*D*DQ*JK
(*@*D*DQ*JKrF   c                    [        [        [        R                  SSS5        [        [        [        R                  SS/S5        [        [        [        R                  SS/S/S5        [        [        [        R                  SS/SS/S5        [        [        [        R                  SS/SS/S5        [        [        [        R                  SS/SS/S5        g )	Nrj   r  rl   g      @r  r{  g      %@g      /@)rn  rS   r   r  	TypeErrorr-  s    rD   test_invalid_params-TestMultivariateHypergeom.test_invalid_paramsH  s    j"8"<"<aQGj"8"<"<a"qIj"8"<"<q!frdANi!7!;!;c3Z2h	#i!7!;!;aVTlA	'i!7!;!;aV2h	%rF   r   N)r   r   r   r   rR   r   r   r=   r  r  r  r}  r  r  r  r   rJ  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   rF   rD   rs  rs  p  sx   [[ VaWa+VaWa"&&)!Wq"gq266'*Vb"Xq"&&)!fq!fR2s)4Vbffbff%' !Wr2h266*Wr1gr266*Wr2hBFF+VaWb"&&)VaWa"&&)+	
43543	/;;
 [[V	13
Qqc1X& "	" [[S1#q!VaWa+1v1v"a1a& 12W1v1v&+&I79 XXb$bhhr&=q"EVaVQ"	1j1	
 3! 3 [[Vq"gBx(!i-CDcA3Z1#saVb"X6sQCj\QC!:1vRz:cA3ZQC5'QFr2hZL9		
33////11
&%&L 	%rF   rs  c                   \   \ rS rSrS rS r\R                  R                  SS5      S 5       r	S r
\R                  R                  SS	5      \R                  R                  S
S	5      S 5       5       r\R                  R                  SS5      S 5       rS r\R                  R                  SS5      S 5       r\R                  R                  SS5      S 5       r\R                  R                  SS5      S 5       r\R                  R                  SS5      \R                  R                  S/ S/45      \R                  R                  S/ S/45      S 5       5       5       r\R                  R                  SS5      S 5       rS r\R                  R                  SS5      S 5       rSrg)TestRandomTableiT  c                 @    [         R                  R                  S5      $ )Nl   OfE)r=   r   r   r-  s    rD   get_rngTestRandomTable.get_rngU  s    yy$$%788rF   c                    Sn[         R                  " [        US9   [        SS//SS/5        S S S 5        Sn[         R                  " [        US9   [        SS/SS//5        S S S 5        Sn[         R                  " [        US9   [        SS/SS/5        S S S 5        Sn[         R                  " [        US9   [        SS/SS	/5        S S S 5        S
n[         R                  " [        US9   [        SS/SS/5        S S S 5        Sn[         R                  " [        US9   [        SS// SQ5        S S S 5        Sn[         R                  " [        US9   [        SS// SQ5        S S S 5        SS/n/ SQn[        R                  " SS// SQ5      u  pEn[        X$5        [        X55        U[        R                  " U5      :X  d   eg ! , (       d  f       GN= f! , (       d  f       GN~= f! , (       d  f       GN\= f! , (       d  f       GN:= f! , (       d  f       GN= f! , (       d  f       N= f! , (       d  f       N= f)Nz`row` must be one-dimensionalrK   r   rM   z`col` must be one-dimensionalz*each element of `row` must be non-negativern   z*each element of `col` must be non-negativerq   z'sums over `row` and `col` must be equalr   z(each element of `row` must be an integer @)r   r   rM   z(each element of `col` must be an integer)rd  rd  r   rN   rM   r   r   )rR   r
   rS   r'   _process_parametersr   r=   r   )r[   r\   rowcolr  r  r   s          rD   test_process_parameters'TestRandomTable.test_process_parametersX  s   1]]:W51a&Aq6* 6 2]]:W5!Q1a&* 6 ?]]:W5!R1a&) 6 ?]]:W5!Q!R) 6 <]]:W5!Q!Q( 6 =]]:W5#sY/ 6 =]]:W5!Q/ 6 !f22Aq69EaSSBFF3KA 65 65 65 65 65 65 65sS   GGG,:G>.H"H"H3
G
G),
G;>
H
H"
H03
Izscale,method))r   boyett)r  	patefieldc                     [         R                  " SS/5      U-  n[         R                  " / SQ5      U-  n[        nUR                  X4USS9nUR                  X4S SS9n[	        Xg5        g )Nr   rN   r  methodr   )r=   r   r'   r   r   )r[   r  r  r  r  ctr  gots           rD   test_process_rvs_method_on_None/TestRandomTable.test_process_rvs_method_on_None|  sc     hh1v&hhy!E)66#66BffSdf;X#rF   c                     SS/n/ SQnSn[         R                  " [        US9   [        R                  " XSS9  S S S 5        g ! , (       d  f       g = f)Nr   rN   r  z$'foo' not recognized, must be one ofrK   foo)r  )rR   r
   rS   r'   r   )r[   r  r  r\   s       rD   $test_process_rvs_method_bad_argument4TestRandomTable.test_process_rvs_method_bad_argument  sA    !f 9]]:W5Se4 655s   A
Ar  )TFr{  c                   ^^^^ U R                  5       nSS/m/ SQm[        R                  " TTSSUS9nU(       a  [        TT5      O[        n[        XR(       a  SOS5      mU(       d
  TmUUU4S	 jmU(       a  U4S
 jOTn[        R
                  " USSS9u  pxU" U5      n	[        U	[        U5      -  USS9  U" [        US   5      5      n
[        XS   5        UR                  SUR                  SS  -   5      nU" U5      n	U	R                  S:X  d   e[        U	R                  S   5       HB  n[        U	R                  S   5       H#  nXU4   nXU4   nU" U5      n[        UU5        M%     MD     / SQ/ SQ/n[        [        R                  " USS9T5        U" U5      n	U	S:X  d   e/ SQ/ SQ/n[        [        R                  " USS9T5        U" U5      n	U	S:X  d   eSn[        R                  " [         US9   U" S/5        S S S 5        Sn[        R                  " [         US9   U" S//5        S S S 5        Sn[        R                  " [         US9   U" [        R"                  //5        S S S 5        Sn[        R                  " [         US9   U" S//5        S S S 5        Sn[        R                  " [         US9   U" / SQ/5        S S S 5        S n[        R                  " [         US9   U" SS/S!S"//5        S S S 5        g ! , (       d  f       GN	= f! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       g = f)#NrM   rk   r   rN   rl   r  r  r   r  r   r  r  c                    > T" U TT5      $ r<   r   )rb   r  original_methodr  s    rD   r  /TestRandomTable.test_pmf_logpmf.<locals>.method  s    &q#s33rF   c                 <   > [         R                  " T" U 5      5      $ r<   )r=   r  )rb   r  s    rD   rc   1TestRandomTable.test_pmf_logpmf.<locals>.<lambda>  s    q	*rF   r   Tr   return_countsr   r  )r  r  r   )r   r   r   )rM   r   rN   rn   r   rk  )r   rM   rM   rq   z$`x` must be at least two-dimensionalrK   z%`x` must contain only integral valuesrd  z)`x` must contain only non-negative valuesz"shape of `x` must agree with `row`rQ   z"shape of `x` must agree with `col`rN   rl   )r  r'   r   rx   r=   uniquer   r   r   r   r  r?   r  r   rR   r
   rS   r  )r[   r  r{  r   r   objr  
unique_rvscountsrV  p2rvs_ndr  r  pijrvijqijrb   r\   r  r  r  r  s                      @@@@rD   test_pmf_logpmfTestRandomTable.test_pmf_logpmf  s    lln!fsCd&.SB )/l3$L#h59$O4/2*YYs$G
 
OCHf37 jm$%R1 Y1267Kww)###qwwqz"A1771:&1gd|$iS#&	 ' # 	"RVVAB'-FAvv 	"RVVAB'-FAvv 9]]:W5H 6 :]]:W5#L 6 :]]:W5"&&
O 6 >]]:W5"K 6 7]]:W5 6 7]]:W5!QQ  65) 65 65 65 65 65 65sH   =
L	*LL,L=M1M	
L
L),
L:=
M
M
M-r  )r  r  c                    U R                  5       nSS/n/ SQn[        R                  " X4SUUS9n[        R                  " X45      n[	        [
        R                  " U5      [
        R                  " U5      5        [        UR                  S5      USS9  [	        UR                  S	S
9[
        R                  " US5      5        [	        UR                  SS
9[
        R                  " US5      5        g )NrM   rk   r  r  r  r   r:  r  rn   r   r  rq   )r  rN   )	r  r'   r   r   r   r=   r   r   broadcast_to)r[   r  r   r  r  r   r   s          rD   test_rvs_meanTestRandomTable.test_rvs_mean  s     lln!fsd6,/1  *RVVD\266#;/T5SWW"W%rsI'FGSWW"W%rsI'FGrF   c                     U R                  5       nSS/n/ SQn[        R                  " X#SSUS9n[        R                  " X#SSUS9n[        R                  " USS	9n[        R                  " USS	9n[        XgS
S9  g )NrM   rk   r  ru  r  r  r  r   r   {Gz?r  )r  r'   r   r=   r   r   )r[   r   r  r  r  r  r  r  s           rD   test_rvs_covTestRandomTable.test_rvs_cov  sy     lln!fuX-02u[-02vvd#vvd#.rF   c           	         SS/n/ SQn[         R                  " X#UU R                  5       S9nUR                  S:X  d   e[         R                  " X#SUU R                  5       S9nUR                  S:X  d   e[	        XES	   5        [         R                  " X#S	UU R                  5       S9nUR                  S
:X  d   e[         R                  " X#SUU R                  5       S9nUR                  S:X  d   e[         R                  " X#SUU R                  5       S9nUR                  S:X  d   e[        UR                  SSS5      USS9  Sn	[        R                  " [        U	S9   [         R                  " X#SUU R                  5       S9  S S S 5        [        R                  " [        U	S9   [         R                  " X#[        R                  UU R                  5       S9  S S S 5        g ! , (       d  f       Nd= f! , (       d  f       g = f)NrM   rk   r  r  rK  r   r  rQ   r   )r   rM   rN   r  )r  rM   rN   )rl   rj   )rl   rj   rM   rN   rN   r  r  z/`size` must be a non-negative integer or `None`rK   rn   )r'   r   r  r?   r   r   r  rR   r
   rS   r=   r  )
r[   r  r  r  r   rv2rv3rv4rv5r\   s
             rD   test_rvs_sizeTestRandomTable.test_rvs_size  s   !f cv+/<<>;xx6!!! sa,0LLN<yyI%%%RQ  sa,0LLN<yyI%%% sb,0LLN<yyJ&&&sfV,0LLN<yyL(((B1-s? D]]:W5SBv*.,,.: 6 ]]:W5SBFF6*.,,.: 65	 65 65s    &G$'4G5$
G25
Hc                     SS/n/ SQn[         nUR                  X#SUU R                  5       S9n[        R                  " USSS9u  pgUR                  XbU5      n[        U[        U5      -  US	S
9  g )NrM   rk   r  r  r  r   Tr  r  r  )r'   r   r  r=   r  r  r   r   )	r[   r  r  r  r  r   r  r  rV  s	            rD   test_rvs_methodTestRandomTable.test_rvs_method(  sv     !fffSF6"&,,.  2  YYs$G
 FF:C(CHf48rF   c                     / SQn/ SQn[        X#5      nUR                  SXR                  5       S9n[        R                  " S[        U5      [        U5      45      n/ SQ/ SQ/ SQ/US'   [        XV5        g )NrS  )r   r   r   r   r  r  )r   r   r   r   .r'   r   r  r=   r   r   r   r[   r  r  r  r'  r   r  s          rD   test_rvs_with_zeros_in_col_row.TestRandomTable.test_rvs_with_zeros_in_col_row=  si    "UU4\\^UD88T3s8SX67%%%' 	R"rF   )Nr  r  r  r   r  c                     [        X#5      nUR                  SXR                  5       S9n[        R                  " S[        U5      [        U5      45      n[        XV5        g )Nr  r  r  r  s          rD   test_rvs_with_edge_cases(TestRandomTable.test_rvs_with_edge_casesI  sK     "UU2f<<>UB88RS3s845R"rF   r   re  c                    SS K Js  Jn  [        R                  " SS/[        R
                  S9n[        R                  " / SQ[        R
                  S9n[        USU 35      n[        R                  " U5      nU" X4USU R                  5       5      nUR                  S[        U5      [        U5      4:X  d   e[        R                  " U5      U:X  d   eg )Nr   r   rN   r  r  	rvs_rcont)scipy.stats._rcontr/   _rcontr=   r   int64rx   r   r  r?   r   )r[   r   r  r  r  r   ntotresults           rD   test_rvs_rcontTestRandomTable.test_rvs_rcontR  s     	,+hh1vRXX.hhy1f	!o.vvc{StQ7||3s8SX6666vvf~%%%rF   c                    SS/n/ SQn[        XU R                  5       S9nUR                  5       n[         R                  " X5      n[	        XSR                  5       5        [         R
                  " XAU5      n[	        XSR                  U5      5        [         R                  " XAU5      n[	        XSR                  U5      5        g )NrM   rk   r  r   )r'   r  r   r   r   r  r  )r[   r  r  r'  r#  r  s         rD   r  TestRandomTable.test_frozenc  s    !f7$$S.Xvvx(##F5XuuV}-&&vC8Xxx/0rF   c                     SS/n/ SQn[        X#U R                  5       S9n[         R                  " X#SUU R                  5       S9nUR                  SUS9n[        XV5        g )NrM   rk   r  r   r  r  )r   r  )r'   r  r   r   )r[   r  r  r  r'  r  r  s          rD   test_rvs_frozenTestRandomTable.test_rvs_frozens  s\    !f7##C2f15AeeFe+X#rF   r   N)r   r   r   r   r  r  rR   r   r   r  r  r  r  r  r  r  r	  r  r  r  r  r   r   rF   rD   r  r  T  s   9" H [[^@B$B$5 [[X}5[[UM2L 3 6L\ [[X'>?H @H/ [[X'>?': @':R [[X'>?9 @9( [[X'>?	# @	# [[X'DE[[UR!I.[[UR!I.# / / F# [[S&)& *& 1  [[X'>?$ @$rF   r  c                    U R                   nSU l         U R                  " USS06  [        R                  " U 5      nU R                  " USS06n[        R                  " U5      nUR                  " USS06n[        XF5        X l         g )Nrs  r   r  )r   r   pickledumpsloadsr   )distfnrB   r  r   r0	unpickledr1s          rD   check_picklingr$    sy    
 DF
JJ1VA	T	"	"BQI		%1	%B rF   c                 (   [         R                  " S5      nSUS'   SUS'   [        S/[        [         R                  " S/5      4/[
        SU4/[        SU4/[        S/ S	Q4/[        S
/[        S
//nU H  u  p4[        X45        [        X45        M     g )NrN   r  rj  ry  r   r   r  rj   r>  r  )r=   rV   r   r   r   r   r   r   r   r   r8   r$  )num_parallel_threadsr  distsr   rB   s        rD   test_random_state_propertyr(    s    FF1IEE$KE$K	b!	RXXrd^&'	2u+	b%[!	q/*+	d	d#E #F1v$ rF   c                      \ rS rSr\R
                  R                  S/ SQ5      \R
                  R                  S/ SQ5      S 5       5       r\R
                  R                  SSS/5      \R
                  R                  S	/ S
Q5      S 5       5       rS r	S r
S r\R
                  R                  S	SS/5      S 5       r\R
                  R                  S	SS/5      S 5       r\R
                  R                  S\R                  \R                   /5      S 5       r\R
                  R                  S\R                  \R                   /5      S 5       r\R
                  R                  S\R(                  " / SQ5      \R(                  " / SQ5      SS4\R(                  " / SQ5      \R(                  " / SQ5      SS4\R(                  " / SQ5      \R(                  " / SQ5      SS 4\R(                  " / SQ5      \R(                  " / SQ5      SS!4\R(                  " / SQ5      \R(                  " \R*                  " S"5      \R*                  " S#5      S/5      S$S%4\R(                  " / SQ5      \R(                  " / SQ5      S$S&4\R(                  " / S'Q5      \R(                  " / S'Q5      S$S(4\R(                  " / S'Q5      \R(                  " \R*                  " S"5      \R*                  " S#5      SSS/5      S$S)4\R(                  " / S'Q5      \R(                  " \R*                  " S*5      \R*                  " S+5      SSS/5      S$S,4/	5      S- 5       r\R
                  R                  S\R(                  " / SQ5      \R(                  " / SQ5      SS.4\R(                  " / SQ5      \R(                  " / SQ5      SS/4\R(                  " / SQ5      \R(                  " / SQ5      SS04\R(                  " / SQ5      \R(                  " / SQ5      SS14\R(                  " / SQ5      \R(                  " \R*                  " S"5      \R*                  " S#5      S/5      S$S24\R(                  " / SQ5      \R(                  " / SQ5      S$S34\R(                  " / S'Q5      \R(                  " / S'Q5      S$S44\R(                  " / S'Q5      \R(                  " \R*                  " S"5      \R*                  " S#5      SSS/5      S$S54\R(                  " / S'Q5      \R(                  " \R*                  " S*5      \R*                  " S+5      SSS/5      S$S64/	5      S7 5       r\R
                  R                  S8/ S9Q5      S: 5       r\R
                  R                  S\R                  \R                   /5      S; 5       rS< r\R
                  R                  S/ S=Q5      \R
                  R                  S>/ S?Q5      S@ 5       5       rSA rSB rSC rSDrgE)FTestVonMises_Fisheri  r   )rM   rN   rl   rk   r   r  c                    [         R                  R                  S5      n[         R                  " U4S[         R                  " U5      -  5      n[        USUS9nUR                  U5      n[         R                  " U5      [         R                  " U5      pUR                  XxUS9R                  n	UR                  U	:X  d   e[         R                  R                  USS9n
[        U
S5        g )Nr  r   r   r   rn   r   r   )r=   r   r   r  r  r)   r   r   rV   r   r?   r   r   r   )r[   r   r   r   ro  vmf_distr  r   r   r  r  s              rD   r   TestVonMises_Fisher.test_samples  s     ii##$78WWcWan-"2qs3,,t$HHSM266#;c000FLL}}...		wR0r"rF   rj   r  kappa)g  4&kCrZ  gꌠ9Y>)Fc                     [         R                  R                  S5      n[         R                  " U4S[         R                  " U5      -  5      n[        XBUS9nUR                  S5        g )Nr  r   r   r  )r=   r   r   r  r  r)   r   )r[   r   r.  r   ro  r,  s         rD    test_sampling_high_concentration4TestVonMises_Fisher.test_sampling_high_concentration  sO     ii##$78WWcWan-"237RrF   c                     [         R                  " S5      nSn[        R                  " [        US9   [        US5        S S S 5        g ! , (       d  f       g = f)Nr!  z%'mu' must have one-dimensional shape.rK   r   r=   rU   rR   r
   rS   r)   r[   ro  r  s      rD   test_two_dimensional_mu+TestVonMises_Fisher.test_two_dimensional_mu  s8    WWV_5]]:S1B" 211   A
Ac                     [         R                  " S5      nSn[        R                  " [        US9   [        US5        S S S 5        g ! , (       d  f       g = f)Nr  z%'mu' must be a unit vector of norm 1.rK   r   r3  r4  s      rD   test_wrong_norm_mu&TestVonMises_Fisher.test_wrong_norm_mu  s8    WWU^5]]:S1B" 211r7  c                     [         R                  " S5      nSn[        R                  " [        US9   [        US5        S S S 5        g ! , (       d  f       g = f)Nr  z$'mu' must have at least two entries.rK   r   r3  r4  s      rD   test_one_entry_mu%TestVonMises_Fisher.test_one_entry_mu  s8    WWU^4]]:S1B" 211r7  rn   )rj   rN   c                     Sn[         R                  " [        US9   [        SS/U5        S S S 5        g ! , (       d  f       g = f)Nz"'kappa' must be a positive scalar.rK   r   r   rR   r
   rS   r)   r[   r.  r  s      rD   test_kappa_validation)TestVonMises_Fisher.test_kappa_validation  s/    2]]:S1QFE* 211	   4
Ar   r   c                     Sn[         R                  " [        US9   [        SS/U5        S S S 5        g ! , (       d  f       g = f)NzFor 'kappa=0' the von Mises-Fisher distribution becomes the uniform distribution on the sphere surface. Consider using 'scipy.stats.uniform_direction' instead.rK   r   r   r?  r@  s      rD   test_kappa_zero#TestVonMises_Fisher.test_kappa_zero  s3     ]]:S1QFE* 211rC  r  c                     [         R                  " / SQ5      nSn[        R                  " [        US9   U" USS/S5        S S S 5        g ! , (       d  f       g = f)Nr   r   r   znThe dimensionality of the last axis of 'x' must match the dimensionality of the von Mises Fisher distribution.rK   r   r   r=   r   rR   r
   rS   r[   r  rb   r  s       rD   test_invalid_shapes_pdf_logpdf2TestVonMises_Fisher.test_invalid_shapes_pdf_logpdf  sE     HH[! ]]:S11q!fa  211   A


Ac                     [         R                  " SS/5      nSn[        R                  " [        US9   U" USS/S5        S S S 5        g ! , (       d  f       g = f)Nr  r   8'x' must be unit vectors of norm 1 along last dimension.rK   r   r   rI  rJ  s       rD   test_unnormalized_input+TestVonMises_Fisher.test_unnormalized_input  sE     HHc2YH]]:S11q!fa  211rM  zx, mu, kappa, reference)r   r   r   rL  g0_?rH  )r   r   r   g7m0_?r  gLI/@gFK:h*7g\(\?r  i  g3pB>g7Ks@)r   r   r   r   r   go齿@gW+x\(?r=  r   gS-c                 L    [        X#5      R                  U5      n[        XTSS9  g )Nr5  r  )r)   r   r   )r[   rb   ro  r.  	referencer   s         rD   test_pdf_accuracy%TestVonMises_Fisher.test_pdf_accuracy  s#    4 b(,,Q/U3rF   g[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 L    [        X#5      R                  U5      n[        XTSS9  g )Nr  r  )r)   r   r   )r[   rb   ro  r.  rS  r   s         rD   test_logpdf_accuracy(TestVonMises_Fisher.test_logpdf_accuracy(  s#    4 !+22156rF   zdim, kappa, reference))rN   rL  g?@)rN   r  gp&F)rj   r,  gT;ӷ&)r  r   goZ@c                     [         R                  " U4S[         R                  " U5      -  5      n[        XB5      R	                  5       n[        XSSS9  g )Nr   g+=r  )r=   r  r  r)   r   r   )r[   r   r.  rS  ro  r   s         rD   test_entropy_accuracy)TestVonMises_Fisher.test_entropy_accuracyS  s?     WWcWan-!",4467rF   c           	         Sn[         R                  R                  S5      n[        S5      R	                  X#S9n[         R
                  " SS[         R                  " S5      -  5      nSnU" XEU5      nUR                  U:X  d   e[        US   5       H6  n[        US   5       H!  n	U" XHU	S S 24   XV5      n
[        XX4   S	S
9  M#     M8     g )Nr!  r  rN   r   r  r   rj   r   r  r  )
r=   r   r   r(   r   r  r  r?   r  r   )r[   r  	testshaper   rb   ro  r.  
result_allr  r  current_vals              rD   r  %TestVonMises_Fisher.test_broadcasting]  s     	ii##$78a $$Y$AWWUAbggajL)A5)
9,,,y|$A9Q<($Q!QwZ;-=EJ ) %rF   c                 L   [         R                  R                  S5      n[         R                  " SS/5      n[         R                  " US   US   5      nSn[        X$5      n[        X4S9n[        S5      R                  SUS9n[         R                  " US S 2S4   US S 2S4   5      n[        UR                  5       UR                  5       5        [        UR                  U5      UR                  U5      5        [        UR                  U5      UR                  U5      5        g )	Nr  r   r   r  )r  r.  rM   r  r   )r=   r   r   r   r  r)   r+   r(   r   r   r   r   r   )	r[   r   ro  mu_angler.  vmfvonmises_distvectorsr  s	            rD   test_vs_vonmises_2d'TestVonMises_Fisher.test_vs_vonmises_2dm  s     ii##$78XXq!f::beRU+b( X;#A&**2C*@GAqDM71a4=9--/?))&137773CD,,V4cjj6IJrF   )rM   rN   rk   zkappa, mu_tol, kappa_tol))r   r:  r:  )r  r  r  )r  {Gzt?r  )r  r  r  c                 ~   [         R                  " U4S[         R                  " U5      -  5      n[        XR5      n[         R                  R                  S5      nSnUR                  XS9n	[        R                  " U	5      u  p[         R                  " UR                  U
5      5      n[        USUSS9  [        X+US9  g )	Nr   r  ru  r   r   r   r'  r  )r=   r  r  r)   r   r   r   r~  arccosr  r   )r[   r   r.  mu_tol	kappa_tolro  r,  r   r  r  mu_fit	kappa_fitangular_errors                rD   test_fit_accuracy%TestVonMises_Fisher.test_fit_accuracy|  s     WWcWan-"2-ii##$78	,,y,;+//8		"&&.1rQ?y9rF   c                     [         R                  " S5      nSn[        R                  " [        US9   [
        R                  " U5        S S S 5        g ! , (       d  f       g = f)Nr  z'x' must be two dimensional.rK   )r=   r   rR   r
   rS   r)   r~  r[   rb   r  s      rD   #test_fit_error_one_dimensional_data7TestVonMises_Fisher.test_fit_error_one_dimensional_data  s<    HHUO,]]:S1" 211   A
A c                     [         R                  " S5      nSn[        R                  " [        US9   [
        R                  " U5        S S S 5        g ! , (       d  f       g = f)NrJ  rO  rK   )r=   rU   rR   r
   rS   r)   r~  rs  s      rD    test_fit_error_unnormalized_data4TestVonMises_Fisher.test_fit_error_unnormalized_data  s<    GGFOH]]:S1" 211rv  c                     [         R                  " / SQ5      nSn[        X5      n[        XSS9nUR                  SS9n[        R                  " XSS9nUR                  5       n[	        XV5        [	        XW5        g )N)r   r   r   rj   r(  r   r   )r=   r   r)   r   r   )r[   ro  r.  r  r[  r  r  r\  s           rD   r  ,TestVonMises_Fisher.test_frozen_distribution  si    XXi  +%bc:zzsz+""23? T T rF   r   N) r   r   r   r   rR   r   r   r  r0  r5  r9  r<  rA  rE  r)   r   r   rK  rP  r=   r   r  rT  rW  rZ  r  rf  rp  rt  rx  r  r   r   rF   rD   r*  r*    s   [[UL1[[V%9:
# ; 2
# [[UQF+[[W&89 : ,### [[Wr6l3+ 4+
 [[Wq"g.+ /+ [[X(;(;(7(>(>(@ A!A! [[X(;(;(7(>(>(@ A!A!$ [[6!xx5rxx7M#%79!xx4bhh|6L#%8:!xx5rxx7M"$68!xx4bhh|6L"$9;!xx5!xxr(JK#%:<  "xx4bhh|6L#%68!xx(<=!xx(<=#%79  "xx(<=!xxr)*B)0  1#%;=  "xx(<=!xxrwws|R)*B)0  1#%;=)>?243?24" [[6!xx5rxx7M#%8:!xx4bhh|6L#%8:!xx5rxx7M"$57!xx4bhh|6L"$68!xx5!xxr(JK#%8:  "xx4bhh|6L#%68!xx(<=!xx(<=#%79  "xx(<=!xxr)*B)0  1#%79  "xx(<=!xxrwws|R)*B)0  1#%8:);<273<27$ [[4:;
8;
8
 [[X(;(;(7(>(>(@ AKAKK [[UI.[[723
	:3 /	:##!rF   r*  c                   n   \ rS rSr\S 5       rS rS rS rS r	S r
\R                  R                  SS	S
/5      S 5       r\R                  R                  SSS/5      S 5       rS rS r\R                  R                  SS	S
/5      S 5       r\R                  R                  S/ SQ5      S 5       rSrg)TestDirichletMultinomiali  c                     [         R                  R                  S5      nUR                  SSSS9nUR	                  SSUS4S9nUR                  SS	9nX!X5U4$ )
N   t7)r   r  rM   r   r   r  rn   r   )r=   r   r   r   integersr   )r[   r]  r   r8  rb   r   s         rD   
get_params#TestDirichletMultinomial.get_params  s_    ii##$56As+LLBaVL,EErENu""rF   c                    [         R                  R                  S5      nUR                  SSS5      nUR	                  SSS5      n[         R
                  " USS9n[        X$5      n[        UR                  U5      [        R                  " X2U5      5        [        UR                  U5      [        R                  " X2U5      5        [        UR                  5       [        R                  " X$5      5        [        UR                  5       [        R                  " X$5      5        [        UR                  5       [        R                  " X$5      5        g )Nr  r   r  r  rn   r   )r=   r   r   r   r  r   r*   r   r  r  r   r   r   )r[   r   r8  rb   r   r'  s         rD   r  $TestDirichletMultinomial.test_frozen  s    ii##$56AsB'LLB#FF12!%+QXXa["7">">q"KLQUU1X4881EFQVVX499%CDQUUW377ABQUUW377ABrF   c                    [         R                  " / SQ5      n[         R                  " U5      n[         R                  " / SQ5      n[        R                  " XU5      n[        R
                  " XU5      nSn[        XF5        [        U[         R                  " U5      5        UR                  UR                  s=:X  a  S:X  d   e   e[         R                  R                  S5      nUR                  SSS5      nUR                  SSS5      n[         R                  " US	S
9n[        X25      R	                  U5      n[        R
                  " XU5      nSn[        XF5        [        U[         R                  " U5      5        g )NrQ   rN   rl   rj   gp.U.?r   r  r   r  r  rn   r   g+T<)r=   r   r   r*   r  r  r   r{  r?   r   r   r   r  )r[   rb   r   r8  r@   logresrA   r   s           rD   test_pmf_logpmf_against_R2TestDirichletMultinomial.test_pmf_logpmf_against_R  s"   
 HHYFF1I##''!4&--a:!!s,yyFLL.B..... ii##$56AsB'LLB#FF12#E-11!4&--a:"!s,rF   c                 6   U R                  S5      u  pp4nUS-  n[        [        X45      R                  U5      S5        [        [        X45      R	                  U5      [
        R                  * 5        U R                  S5      u  pp4nUR                  SS9S:  n[
        R                  " XV   S-  5      XV'   [        [        X45      R                  U5      U   S5        [        [        X45      R	                  U5      U   [
        R                  * 5        [
        R                  " [        X45      R                  U5      U)    S:  5      (       d   e[
        R                  " [        X45      R	                  U5      U)    [
        R                  * :  5      (       d   eg )Nr   r   r  r   r  rM   )
r  r   r*   r  r  r=   r  r   roundr  )r[   r   r]  r8  r   rb   r  s          rD   test_pmf_logpmf_support0TestDirichletMultinomial.test_pmf_logpmf_support  sN    #ooa0!	Q*5488;Q?*54;;A>H"oob1!JJBJ#%xxq!*5488;A>B*54;;A>qABFF7Kvv+E599!<aR@1DEEEEvv+E5<<Q?CrvvgMNNNNrF   c                    SnS/n[         R                  " U/5      n[        X!5      n[        UR	                  U5      S5        [        UR	                  US-   5      S5        [        UR                  U5      S5        [        UR                  US-   5      [         R                  * 5        [        UR                  5       U5        [        UR                  5       S5        [        UR                  5       S5        g )Nrk   r  r   r   
r=   r>   r*   r   r  r  r  r   r   r   r[   r   r8  rb   r   s        rD   test_dimensionality_one0TestDirichletMultinomial.test_dimensionality_one  s    JJsO$U.TXXa[!$TXXac]A&T[[^Q'T[[1%w/TYY[!$TXXZ#TXXZ#rF   c                 0   Sn[         R                  " SS/5      n[         R                  " SS/5      n[        X!5      n[        UR	                  U5      S5        [        UR	                  US-   5      S5        [        UR                  U5      S5        [        UR                  US-   5      [         R                  * 5        [        UR                  5       SS/5        [        UR                  5       SS/5        [        UR                  5       SS/SS//5        g )Nr   r   r   r  r  s        rD   test_n_is_zero'TestDirichletMultinomial.test_n_is_zero  s    

B8$JJ1v$U.TXXa[!$TXXac]A&T[[^Q'T[[1%w/TYY[1a&)TXXZ!Q(TXXZ1a&1a&!12rF   method_namer  r  c                     U R                  S5      u  p#pEn[        [        XE5      U5      n[        [        R                  " U/UR
                  Q76 U5      nU" U5      n	U" UR
                  S   5      n
[        X5        g Nr  r   r  rx   r*   r/   	betabinomr   r   r[   r  r   r]  r8  r   rb   r  
ref_methodr@   rA   s              rD   test_against_betabinom_pmf3TestDirichletMultinomial.test_against_betabinom_pmf  sj    "ooc2!.u8+FU__Q99;G
QiQ !rF   r   r   c                     U R                  S5      u  p#pEn[        [        XE5      U5      n[        [        R                  " U/UR
                  Q76 U5      nU" 5       S S 2S4   n	U" 5       n
[        X5        g r  r  r  s              rD   test_against_betabinom_moments7TestDirichletMultinomial.test_against_betabinom_moments  se    "ooc2!.u8+FU__Q99;G
hq!tnl!rF   c                    [         R                  R                  S5      nSnUR                  SS5      nUR                  US9S-  n[	        XC5      nSnUR                  XFS9nUR                  X7US9n[        UR                  5       [         R                  " USS	9S
S9  [        UR                  5       [         R                  " USS	9SS9  UR                  5       R                  UR                  5       R                  s=:X  a  U4:X  d   e   eUR                  5       n	U	R                  X"4:X  d   e[        U	[         R                  " UR                  5      SS9  [        [         R                  " U	5      UR                  5       5        [         R                  " [         R"                  R%                  U	5      S   S:  5      (       d   eg )Nr  rj   r   r  r   r  r  r   r   rh  r  r  r  )r=   r   r   r  r*   r   r   r   r   r   r?   r   r   r   rw   r  r   r   r   )
r[   r   r   r   r8  r   r]  rV  rb   r   s
             rD   r  %TestDirichletMultinomial.test_moments!  s^   ii##$56LLC 


$r)$U. MM%M(OOAqO)		RWWQQ%7dC
BFF11$5DAyy{  DHHJ$4$4>>>>>>hhjyySJ&&&RVVACC[t4RWWS\488:.vvell'',Q/!34444rF   c                    [         R                  " / SQ5      n[         R                  " U5      n[         R                  " / SQ5      nSn[        [        US9   [
        R                  " / SQX25        S S S 5        [        [        US9   [
        R                  " / SQX25        S S S 5        Sn[        [        US9   [
        R                  " U/ SQU5        S S S 5        [        [        US9   [
        R                  " U/ S	QU5        S S S 5        S
n[        [        US9   [
        R                  " XS5        S S S 5        [        [        US9   [
        R                  " XS5        S S S 5        [         R                  " / SQ5      n[         R                  " / SQ5      nSn[        [        US9   [
        R                  " XVUR                  5       5        S S S 5        g ! , (       d  f       GNp= f! , (       d  f       GNR= f! , (       d  f       GN1= f! , (       d  f       GN= f! , (       d  f       N= f! , (       d  f       N= f! , (       d  f       g = f)NrQ   r  z,`x` must contain only non-negative integers.rK   )r   rn   rN   )r   r  rN   z*`alpha` must contain only positive values.)rN   r   rl   )rN   rn   rl   z#`n` must be a non-negative integer.ǧH@rn   )r   rM   rN   rl   z&`x` and `alpha` must be broadcastable.)r=   r   r   rn  rS   r*   r  )r[   x0n0alpha0textrb   r8  s          rD   r]   .TestDirichletMultinomial.test_input_validation7  s   XXi VVBZ)$=:T2!((V@ 3:T2!((fA 3 <:T2!((Y; 3:T2!((Z< 3 5:T2!((T: 3:T2!((R8 3 HH\"#7:T2!((1557; 32) 3222 3222 3222 32sT   GG,9G>*HH"H3+&I
G),
G;>
H
H"
H03
I
Ir  c           	      d   [         R                  " / SQ/ SQ/ SQ/ SQ/5      n[         R                  " S/S/S//5      n[         R                  " / SQ/ S	Q/5      R                  S
5      n[        [        U5      nU" XBU5      nUR
                  S:X  d   e[        [        U5      5       H  n[        [        U5      5       Hi  n[        [        U5      5       HN  nXVXx4   n	U" XF   R                  5       X(   R                  5       X7   R                  5       5      n
[        X5        MP     Mk     M     g )Nr  r  rj   rj   rm   r  r  r  rk   rm   r  rQ   )rM   rM   rN   )rM   r   r   rN   )rM   rN   rl   )
r=   r   r  rx   r*   r?   r  r   r   r   )r[   r  r8  r   rb   r@   r  r  r  res_ijkrA   s              rD   test_broadcasting_pmf.TestDirichletMultinomial.test_broadcasting_pmfU  s    )Y	:FGHHqcA3_%HHi+,44\B.7Qq!yyI%%%s1vA3q6]s5z*A!Q'lG 1A1A1CQT\\^TC#G1 + # rF   )r   r   r   c                    [         R                  " / SQ/ SQ/ SQ/ SQ/5      n[         R                  " S/S/S//5      n[        [        U5      nU" X#5      nUS:w  a  UR                  S	:X  d   e [        [        U5      5       HX  n[        [        U5      5       H=  nXVU4   nU" X'   R                  5       X6   R                  5       5      n	[        X5        M?     MZ     g )
Nr  r  r  r  rk   rm   r  r   )rN   rl   rN   )	r=   r   rx   r*   r?   r  r   r   r   )
r[   r  r8  r   r  r@   r  r  r  rA   s
             rD   test_broadcasting_moments2TestDirichletMultinomial.test_broadcasting_momentsd  s    )Y	:FGHHqcA3_%.<U)4)=syyI%OO<s1vA3u:&d)UX--/@- ' rF   r   N)r   r   r   r   rN  r  r  r  r  r  r  rR   r   r   r  r  r  r]   r  r  r   r   rF   rD   r}  r}    s    # #C->O $3 [[]UH,=>" ?" [[]VUO<" ="5,<< [[Xx'892 :2 [[],BC
. D
.rF   r}  c                   B   \ rS rSrS rS rS rS rS r\	R                  R                  \	R                  R                  S5      S 5       5       r\	R                  R                  S	\R                   \R"                  \R$                  \R&                  /5      S
 5       rSrg)TestNormalInverseGammair  c           	      <  ^ [         R                  R                  S5      nUR                  S5      u  p#pE[        R                  " X#XE5      m[        R
                  " SU-  US[         R                  " XC-  U-  5      -  S9n[         R                  " SSS5      n[        U4S	 jS
[         R                  U4S9nUR                  U5      n	[        UR                  U	5        TR                  SUS9n[        R                  " US
   UR                  5      u  pUS:  d   eg )N   &( rl   rM   r   r  rt  rj   rp  c                 &   > TR                  X5      $ r<   r   )r  rb   norm_inv_gammas     rD   rc   8TestNormalInverseGamma.test_marginal_x.<locals>.<lambda>      ^%7%7%>rF   r   rB   ru  r   r   )r=   r   r   r/   normal_inverse_gammar.  r  rB  r0   r  r   r   r3  r   ks_1sampr   )r[   r   ro  lmbdar  r   r.  rb   r@   rA   r   r  r  s               @rD   test_marginal_x&TestNormalInverseGamma.test_marginal_xt  s     ii##J/**Q-133BqDGGAaCRqQ)?'?@ KKAr">266QRPTUeeAhc*   e# >NN3q61551	||rF   c                   ^ [         R                  R                  S5      nUR                  S5      u  p#pE[        R                  " X#XE5      m[        R
                  " XES9n[         R                  " SSS5      n[        U4S j[         R                  * [         R                  U4S9nUR                  U5      n	[        UR                  U	5        TR                  SUS	9n[        R                  " US
   UR                  5      u  pUS:  d   eg )Nr  rl   r  r   r  c                 &   > TR                  X5      $ r<   r  )rb   r  r  s     rD   rc   9TestNormalInverseGamma.test_marginal_s2.<locals>.<lambda>  r  rF   r  ru  r   r   )r=   r   r   r/   r  r   rB  r0   r  r   r   r3  r   r  r   )r[   r   ro  r  r  r   	inv_gammar  r@   rA   r   r  r  s               @rD   test_marginal_s2'TestNormalInverseGamma.test_marginal_s2  s     ii##J/**Q-133BqDNN1.	 [[b"%>wbU4mmBc*   e# >NN3q69==9	||rF   c                 f   [         R                  R                  S5      nUR                  S5      S-
  u  p#pEUR                  SS9S-
  u  pg[        R                  " X#XE5      R                  Xg5      n[        R                  R                  XgX#XE5      n	[        U[         R                  " U	5      5        g )Nr  )rl   r  r*  )rM   r  r   )	r=   r   r   r/   r  r   r   r   r  )
r[   r   ro  r  r  r   rb   r  r@   rA   s
             rD   test_pdf_logpdf&TestNormalInverseGamma.test_pdf_logpdf  s    ii##J/**W-41


(4/((A9==aD((//r!GRVVC[)rF   c                    [         R                  R                  S5      nUR                  S5      u  p#pEUR                  S5      u  pg[        R                  " [         R
                  X4U5      R                  Xg5      n[        U[         R
                  5        [        R                  " USXE5      R                  Xg5      n[        U[         R
                  5        [        R                  " X#SU5      R                  Xg5      n[        U[         R
                  5        [        R                  " X#US5      R                  Xg5      n[        U[         R
                  5        [        R                  " X#XE5      R                  US5      n[        US5        [        R                  " US[         R
                  /XE5      R                  US5      n[        U[         R
                  5        [        R                  " USXE5      R                  5       n[        U[         R
                  [         R
                  45        [        R                  " X#SU5      R                  5       n[        U[         R
                  [         R
                  45        [        R                  " [        SS9   [        R                  " X#US5      R                  5         S S S 5        g ! , (       d  f       g = f)Nr  rl   rM   rn   r   zDomain error in arguments...rK   )r=   r   r   r/   r  r  r   r   r   r   rR   r
   rS   r   )	r[   r   ro  r  r  r   rb   r  r@   s	            rD   test_invalid_and_special_cases5TestNormalInverseGamma.test_invalid_and_special_cases  s   ii##J/**Q-1

1((1=AA!HS"&&!((R6::1AS"&&!((Aq9==aDS"&&!((Ar:>>qES"&&!((A9==aDS! ((b"&&\1@DDQKS"&&!((R6;;=S266266*+((B:>>@S266266*+]]:-KL&&r!R8<<> MLLs   'K
Kc                    [         R                  R                  S5      nUR                  S5      nUR                  S5      S-   nUR                  S5      nUR                  S5      nUR                  S5      nUR                  S5      n[        R                  " XTX25      n[         R
                  " XvXTX25      n	U	 V
s/ s H  n
[         R                  " U
5      PM     nn
UR                  Xv5      nUR                  U	S   R                  :X  d   e[        UR                  5       [        R                  R                  " U6 5        UR                  Xv5      nUR                  U	S   R                  :X  d   e[        UR                  5       [        R                  R                  " U6 5        [         R
                  " XTX25      n	U	 V
s/ s H  n
[         R                  " U
5      PM     nn
UR                  5       nUS   R                  U	S   R                  :X  d   e[        US   R                  5       US	   R                  5       4[        R                  R                  " U6 5        UR                  5       nUS   R                  U	S   R                  :X  d   e[        US   R                  5       US	   R                  5       4[        R                  R                  " U6 5        S
n[         R                  R                  S5      nUR                  XS9n[         R                  R                  S5      nSn[        R                  R                  " XUS.6n[        US   R                  U5      US	   R                  U5      4U5        g s  sn
f s  sn
f )Nr  rM   )rN   r   )rl   r   r   )rj   r   r   r   )rk   r   r   r   r   )rm   r   r   r   r   r   r   r   )rk   rj   rl   rN   rM   l   Mr   )rk   x   )r=   r   r   r/   r  broadcast_arraysr  r   r?   r   r   r   r   r   r  )r[   r   r   r  r  ro  r  rb   r   broadcastedarrbroadcasted_raveledr@   r   r?   rA   s                   rD   r  (TestNormalInverseGamma.test_broadcasting  s    ii##J/JJqMJJv"

9%ZZ%ZZ(JJ)*))"Q: ))!AA8CDrxx}DhhqoyyKN00000		22668KL	N kk! yyKN00000		2299;NO	Q ))"Q:8CDrxx}Diik1v||{1~33333QQ822779LM	O hhj1v||{1~33333QQ822668KL	N ii##M2hhDh3ii##M2((,,.A:=?Q.Au0EFLE E Es   < N Nr  c                    ^ [         R                  R                  S5      nUR                  S5      u  p#pEUS-  n[        R                  " X#XE5      mTR                  5       n[        U4S j[         R                  * [         R                  S[         R                  5      n[        US   US   SS9  [        U4S j[         R                  * [         R                  S[         R                  5      n[        US	   US   SS9  g )
Nr  rl   rM   c                 ,   > TR                  X5      U-  $ r<   r  r  rb   r   s     rD   rc   5TestNormalInverseGamma.test_moments.<locals>.<lambda>  s    DHHQOa$7rF   r   rv  r  c                 ,   > TR                  X5      U -  $ r<   r  r  s     rD   rc   r    s    DHHQOb$8rF   r   )	r=   r   r   r/   r  r   r5   r  r   )	r[   r   ro  r  r  r   r@   rA   r   s	           @rD   r  #TestNormalInverseGamma.test_moments  s     ii##J/**Q-1	Q))"Q:iik7"&&"&&!RVVTAAT28266'2661bffUAAT2rF   r  c                 b   [         R                  S:  a  [        R                  " S5        [         R                  R                  S5      nUR                  SSSS9R                  U5      u  p4pVpx[         R                  " SU5      n	[        R                  " XVXx5      n
U
R                  5       S	   R                  U	:X  d   eU
R                  5       S
   R                  U	:X  d   eU
R                  5       S	   R                  U	:X  d   eU
R                  5       S
   R                  U	:X  d   eU
R                  5       S	   R                  U	:X  d   eU
R                  5       S
   R                  U	:X  d   eU
R                  X45      R                  U	:X  d   eU
R!                  X45      R                  U	:X  d   eg )N2z*Scalar dtypes only respected after NEP 50.r  rN   r  rk   r   r   r   r   )r=   __version__rR   r   r   r   r   astyperesult_typer/   r  r   r  r   r   r   r   )r[   r  r   rb   r  ro  r  r  r   	dtype_outr   s              rD   
test_dtype!TestNormalInverseGamma.test_dtype  sd   >>CKKDEii##J/!$Q!;!B!B5!Ir!NN3.	))"Q:xxz!}""i///xxz!}""i///yy{1~##y000yy{1~##y000xxz!}""i///xxz!}""i///{{1!''9444xx$$	111rF   r   N)r   r   r   r   r  r  r  r  r  rR   r   r  	fail_slowr  r   r=   int32float16r  r  r  r   r   rF   rD   r  r  r  s    *,* ?D1Mf [[[[23  3 [[WrxxRZZ&TU2 V2rF   r  rm  )hrI  r  dataclassesr   numpy.testingr   r   r   r   r   r	   rR   r
   rn  test_continuous_basicr   numpyr=   scipy.linalgr   scipy.stats._multivariater   r   r   scipy.statsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   scipy.stats._continuous_distnsr.   r4  r/   scipy.integrater0   r1   r2   r3   r4   r5   r6   scipy.specialr7   r+  common_testsr8   	data._mvtr9   unittest.mockr:   rE   rH   r   r   r   rQ  rh  r  r  r_  ra  r  r  r&  rT  r~  r  r  r  rs  r  r$  r   ro  r(  r*  r}  r  r   rF   rD   <module>r     s    !7 7  * 9  C C: : : : : : : : 0 @  4 4 < < &  5  ']! ]!@ A A AH X X Xv@) @)FH* H*VF1 F1R-&i9 i9V{; {;|a( a(HGJ GJT~& ~&Bd# d#N6+ 6+r>D >DB@9 @9Fa% a%Hh$ h$V	( % %$~! ~!BH. H.Vk2 k2rF   