
    UgV                    .   d Z ddlZddlmZmZmZmZmZmZ ddl	Z	ddl	m
Z ddlmZ ddlZddlZddlmZmZmZ ddlmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2 dd	lm3Z3m4Z4 dd
lm5Z5 ddl6m7Z7m8Z8m9Z9 ddl:m;Z; ddl<m=Z= ddl>m?Z? ddl@mAZA d ZB G d d          ZCd9dZDd ZE G d d          ZF G d d          ZG G d d          ZHd ZI G d d          ZJ G d d           ZK G d! d"          ZL G d# d$          ZM G d% d&          ZN G d' d(          ZO G d) d*          ZP G d+ d,          ZQ G d- d.          ZR G d/ d0          ZS G d1 d2          ZTd3 ZUd4 ZV G d5 d6          ZW G d7 d8          ZXdS ):z8
Test functions for multivariate normal distributions.

    N)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)stats)rombqmc_quadtplquad)multigammaln)check_random_state_property)_qsimvtv)patchc                     t          j        |           t          j        |          }} t          | |g|R i | t          | j        |j                   d S N)npasarrayr   r   shape)resrefargskwargss       b/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/stats/tests/test_multivariate.pyassert_closer?   *   sU    z#
3CC.t...v...CI&&&&&    c                   (   e Zd Zd Zej        ej        j        ej        j        ej        j	        d dZ
 ej         ee
                    Z ej        g d          g dg dg dg ej        g d          g d	g d
g dgdZeedd         eg d         edd         dZej                            dedd                   d             Zej                            d ee                    ej                            de          d                         Zej                            dd e            ddg          ej                            d ee                    ej                            de          d                                     Zej                            d e            dg          ej                            de          d                         Zd Zej                            d          d             Zd ZdS )TestCovariancec                    d}t          j        t          |          5  t          j        t          j        d                     d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j        t          j        d          t          j        d                     d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j        d           d d d            n# 1 swxY w Y   d	}t          j        t          |          5  t          j	        t          j        d                     d d d            n# 1 swxY w Y   d
}t          j        t          |          5  t          j
        dt          j        d          f           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j
        t          j        d          df           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j
        g dt          j        d          f           d d d            d S # 1 swxY w Y   d S )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
   rF   rG   )pytestr	   
ValueErrorr+   CovViaPrecisionr7   oneseyeCovViaDiagonalCovViaCholeskyCovViaEigendecompositionselfmessages     r>   test_input_validationz$TestCovariance.test_input_validation2   s:   N]:W555 	4 	4'

333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 E]:W555 	I 	I'q		bfQiiHHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I L]:W555 	1 	1&x000	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 N]:W555 	3 	3&rwqzz222	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 I]:W555 	H 	H0(BF1II1FGGG	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H A]:W555 	I 	I0"'!**h1GHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I N]:W555 	I 	I0)))RVAYY1GHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	Is}   'AAA9;C  CC(D		DD1'E$$E(+E()GGG))HH"%H"+I>>JJc                 $    t          | d          S )NTallow_singular)r   )xs    r>   <lambda>zTestCovariance.<lambda>T   s    %)!D%A%A%A r@   )Diagonal	PrecisionCholeskyEigendecompositionPSDrJ   )   r
   rG   )r
         )rG   rc      )r
   r   rG   )ra   r   )re   ra   r   r   r   r   )diagonal full rankzgeneral full rankzdiagonal singularzgeneral singularr
   N)r   re   rh   cov_type_namere   c                    t          j        g d          }g d}t          t          d|           }| j        |         }t          t
          d|                                           } | ||                    } | ||                    }t          |          t          |          k    sJ t          |	                    |          |	                    |                     d S )NrJ   )rF   ra   CovViafrom_)
r7   diaggetattrr+   _covariance_preprocessingr,   lowertyper   whiten)	rT   ri   ArZ   cov_typepreprocessingfactoryr:   r;   s	            r>   test_factorieszTestCovariance.test_factories`   s    GIIIJJ;(@(@(@AA6}E*&Em.A.A.C.C&E&EFFgmmA&&''h}}Q''((CyyDII%%%%

1szz!}}55555r@   matrix_typec                 l   d| d| d}|| j         |         vrt          j        |           | j        |         }t	          t
          d|           }| j        |         }t          |d          } | ||                    }t          |j	        |j	                   t          |j        |j                   t          |j        t          j        |          j                   t          |j        t          j        |                     t          j                            d          }	|	                    d          }
|                    |
          }|
|j        z  }t          ||z  ||z             t)          |d	          r'd
|vr#t          |                    |          |
           |	                    d          }
|                    |
          }|
|j        z  }t          |dz                      d          |dz                      d                     t)          |d	          r'd
|vr#t          |                    |          |
           t)          |d	          rN|                    t          j        t1          |                              }t          |j        |z  |           d S d S )Nrl    does not support 	 matricesTrX      VGiVK rG   size	_colorizesingularrF   rc   rG   rF   re   axis)
_cov_typesrK   skip	_matricesro   r+   rp   r   r?   log_pdetr   rankr9   r7   r8   rH   randomdefault_rngrs   UhasattrcolorizesumrO   lenT)rT   ry   ri   rU   rt   ru   rv   psd
cov_objectrngrZ   r:   r;   s                r>   test_covariancezTestCovariance.test_covariancen   s   M  [    <<<K   N;';(@(@(@AA6}E1T*** XmmA..//
Z(#,777Z_ch///Z%rz!}}':;;;Z*BJqMM::: i##$788JJAJ""#%iS3Yc	***:{++ 	6
+0M0M,,S111555 JJIJ&&""#%ic1f\\r\**S!VLLbL,A,ABBB:{++ 	6
+0M0M,,S111555 :{++ 	)%%bfSVVnn55Ca(((((	) 	)r@   r   r   c                 z   d| d| d}|| j         |         vrt          j        |           | j        |         }t	          t
          d|           }| j        |         }g d} | ||                    }	t          }
t          ||d          }t          ||	d          }t          j	        
                    d          }|                    |||          }t          j	        
                    d          }|
                    ||	||	          }t          j	        
                    d          } |
||	|
                              |          }t          |	t
          j                  rEt          |t          j        |                     t          |t          j        |                     nDt!          |j        |j                   t!          |j        |j                   t          ||           t          |
                    |||	          |                    |                     t          |                    |          |                    |                     t          |
                    |||	          |                    |                     t          |                    |          |                    |                     t          |
                    ||	          |                                           t          |                                |                                           d S )Nrl   r{   r|   皙?皙?333333?TrX   r}   r~   r   random_stateseed)r   rK   r   r   ro   r+   rp   r   r7   r   r   rvs
isinstance	CovViaPSDr?   squeezer   r9   pdflogpdfentropy)rT   r   ry   ri   rU   rt   ru   rv   meanr   mvndist0dist1r   rZ   x1x2s                    r>   test_mvn_with_covariancez'TestCovariance.test_mvn_with_covariance   s   M  [    <<<K   N;';(@(@(@AA6}EXmmA..//
!#D!DAAA#D*TJJJi##$788##D!$#77i##$788WWT:DsWCCi##$788Sz,,,00d0;;j+"788 	!RZ]]+++RZ]]++++17+++17+++R   SWWQj11599Q<<@@@UYYq\\599Q<<000SZZ444ell1ooFFFU\\!__ell1oo666S[[z22EMMOODDDU]]__emmoo66666r@   c                    d}| j         |         }t          t          d|           }| j        |         }g d} | ||                    }t          }	t	          ||d          }
t	          ||d          }t
          j                            d          }|                    |||          }t          |		                    |||          |
	                    |                     t          |	                    |          |
	                    |                     t          |	
                    |||          |

                    |                     t          |
                    |          |

                    |                     d S )Nrg   rl   r   TrX   r}   r~   )r   ro   r+   rp   r   r7   r   r   r?   cdflogcdf)rT   r   ri   ry   rt   ru   rv   r   r   r   r   r   r   rZ   s                 r>   test_mvn_with_covariance_cdfz+TestCovariance.test_mvn_with_covariance_cdf   s[    +N;';(@(@(@AA6}EXmmA..//
!#D!DAAA#D*TJJJi##$788##D!$#77SWWQj11599Q<<@@@UYYq\\599Q<<000SZZ444ell1ooFFFU\\!__ell1oo66666r@   c                     d}t          j        t          |          5  t                       d d d            d S # 1 swxY w Y   d S )Nz7The `Covariance` class cannot be instantiated directly.rD   )rK   r	   NotImplementedErrorr,   rS   s     r>   test_covariance_instantiationz,TestCovariance.test_covariance_instantiation   s    K].g>>> 	 	LLL	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s   :>>zignore::RuntimeWarningc                    t          j        g d          }|j        d         }t          j        |          }t	          j        t          d          5  t          ||                                           d d d            n# 1 swxY w Y   d}t           j	        
                    |          }t           j	        
                    |          }t          j        t           j                            |                    }t          ||          }|                    |          }	t          j        |||          }
t          |	|
           d S )N)r
   rF   g:0yEr   zThe input matrix must be...rD   l   .ypGw r   )r7   rn   r9   zerosrK   r	   rL   r   r   r   r   r,   from_eigendecompositionlinalgeighr   )rT   rt   nr   r   rng1rng2covrvr:   r;   s              r>   test_gh9942zTestCovariance.test_gh9942   sV   
 GMMM""GAJx{{ ]:-JKKK 	/ 	/a((,,...	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ #y$$T**y$$T**01B1BCC s++ff$f''!%dCdCCCS#s   #BB	Bc                    t          j        d          }t          j        t          j        d          t          j        d          f          }t          j                            ||          }|	                    d           }t          ||           t          j        j                            t          j        ddg          t          j        ddgddgg          f          }t          j                            ||          }|	                    d           }|d         |d         k    sJ |d         |d         k    sJ d S )	NrF   r   r   r~         ?        g      y@r   r
   )r7   rN   r,   r   r   rO   scipyr-   r   r   r   array)rT   r   r   distr   s        r>   test_gh19197zTestCovariance.test_gh19197   s!   
 wqzz0"(1++rvayy1IJJ{..Dc.BBhhDh!!S$k$<<Xr2hB8b$Z*@!A!ABD D{..Dc.BBhhDh!!1va    1va      r@   )__name__
__module____qualname__rV   r7   rn   r   invcholeskyr   rp   r   list_all_covariance_typesr   r   rK   markparametrizerx   r   tupler   r   r   filterwarningsr   r    r@   r>   rB   rB   0   s       I I I< .0W.0im-/Y-?79y~)B )B	!C !C %BHTT*C%D%DEE'.rwyyy'9'9'0yy)))YYY&G&-bgiii&8&8&0jj***iii%HJ JI )>'<QRR'@'<[[['I&;BCC&@B BJ
 [_.CCRC.HII6 6 JI6 []DDOO<<[_.CDD-) -) ED =<-)^ [VdEEGGQ	%BCC[]DDOO<<[_.CDD#7 #7 ED =< DC#7J [Veeggy%9::[_.CDD7 7 ED ;:70  
 [ 899  :9,! ! ! ! !r@   rB   Fc                    |                     | | f          }||j        z  }t          j                            |          \  }}|r|                    |           dk    }d||<   |t          j        |          z  |j        z  }|S )Nr~   r   )r   r   r7   r   r   normalrn   )	dimevalsr   r   rt   _v	zero_eigsr   s	            r>   _random_covariancer     s     	

C:A	ACA9>>!DAq JJCJ((1,	i
bgenn
qs
"CJr@   c                     t           j                            | |           }t          j                            |          \  }}}|S r6   )r7   r   randnr   r   svd)r   Musr   s        r>   _sample_orthonormal_matrixr     s7    
	1Alq!!GAq!Hr@   c                      e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zej                            d ej        d           ej        ddg          g          d             Zd Zd Zd Zd Zd Zd Zd Zd Z d Z!d Z"d Z#d Z$d Z%d  Z&d! Z'd" Z(ej                            d#d$          d%             Z)d& Z*ej                            d' ej+        d(           ej+        d)          g          d*             Z,ej                            d+ ej+        d,           ej+        d-           ej+        d.          g          d/             Z-d0 Z.d1 Z/d2 Z0d3S )4TestMultivariateNormalc                 f   t          j        d          }t          j        d          }t          t          t
          j        d||           t          t          t
          j        d||           t          t          t
          j        d||           t          t          t
          j        d||           d S )NrG   rF   r   r
   r   r
   rF   )r7   arangeidentityassert_raisesrL   r   r   r   )rT   mur   s      r>   test_input_shapez'TestMultivariateNormal.test_input_shape%  s    Yq\\k!nnj"5"962sKKKj"5"99b#NNNj"5"962sKKKj"5"99b#NNNNNr@   c                 p   t           j                            d           d\  }}}t          j        |||          }t          |j        d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          |j        d           d\  }}}t          j	        |||          }t          |j        d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j	        |||          }t          |j        d           d S )N  )      ?g333333?      @r   ra   )
r7   r   r   r   r   r   ndimr   absr   )rT   rZ   r   r   r   r   s         r>   test_scalar_valuesz)TestMultivariateNormal.test_scalar_values-  sX   
	t %4!%as33SXq!!! IOOAyq!!fRY__Q''((!%as33SXq!!! %4!%as33SXq!!! IOOAyq!!fRY__Q''((!%as33SXq!!!!!r@   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          j        |||          }t          |t          j	        |                     d S Nr   ra   )
r7   r   r   r   r   r   r   r   r   logrT   rZ   r   r   d1d2s         r>   test_logpdfz"TestMultivariateNormal.test_logpdfH      
	tIOOAyq!!fRY__Q''(( '455 $Qc22BF2JJ'''''r@   c                    t           j                            d           t           j                            d          }t	          j        |          }t	          j        |          }t	          j        |d d          }t	          j        |d d          }t          |t          j        |                     t          |t          j        |                     d S Nr   ra   r
   )	r7   r   r   r   r   r   r   r   r   rT   rZ   r   r   d3d4s         r>   test_logpdf_default_valuesz1TestMultivariateNormal.test_logpdf_default_valuesR       		tIOOA '** $Q'' '433 $Qa00BF2JJ'''BF2JJ'''''r@   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          j        |||          }t          |t          j	        |                     d S r   )
r7   r   r   r   r   r   r   r   r   r   r   s         r>   test_logcdfz"TestMultivariateNormal.test_logcdf_  r   r@   c                    t           j                            d           t           j                            d          }t	          j        |          }t	          j        |          }t	          j        |d d          }t	          j        |d d          }t          |t          j        |                     t          |t          j        |                     d S r   )	r7   r   r   r   r   r   r   r   r   r   s         r>   test_logcdf_default_valuesz1TestMultivariateNormal.test_logcdf_default_valuesi  r  r@   c                 ~   t           j                            d           d}t           j                            |          }t	          d|dz             D ]h}t           j                            ||          }t          j        ||j                  }t          ||d          }t          |j	        j
        |           id S )Nr   rc   r
   TrX   )r7   r   r   r   rangedotr   r   r   r   r   )rT   r   r   expected_rankr   r   distns          r>   	test_rankz TestMultivariateNormal.test_rankv  s    
	tyq!!"1a!e__ 	? 	?M	=11A&AC..C'c$GGGE).>>>>		? 	?r@   c           	         t          dd          D ]}t          j                            |          }t          d|          D ]}t          j                            ||          }t          j        ||j                  }t          j        ||f          }||d |d |f<   t          j        |          }|d |         |d |<   t          |          }t          j        |t          j        ||j                            }	t          j        ||          }
t          t          j        |          |d          }t          t          j        |          |d          }t          t          j        |          |	d          }t          |j
        j        |           t          |j
        j        |           t          |j
        j        |           |                    |d |                   }|                    |          }|                    |
          }t          ||           t          ||           |                    |d |                   }|                    |          }|                    |
          }t          ||           t          ||           |
|d d df         z   }|                    |          }|                    |          }t          |d           t          |t          j                    d S )Nr
   ra   TrX   re   r   )r  r7   r   r   r	  r   r   r   r   r   r   r   r   r   r   inf)rT   r   zkr   cov_kkcov_nnrZ   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                          r>   test_degenerate_distributionsz4TestMultivariateNormal.test_degenerate_distributions  s   q! 0	6 0	6A	""A1a[[ .6 .6IOOAq))13 1a&))!'rr2A2v HQKK"1""1" /q1126&!##6#677F1aLL /rx{{F>BD D D.rx{{F>BD D D.rx{{F>BD D DX05q999X05q999X05q999!ae,,!a!a//////$OOAbqbE22	$OOA..	$OOA..		9555	9555 Qqqq"uX&ll622!)!8!8 [#...^bfW5555].60	6 0	6r@   c                 L   d}t          dd          D ]}t          d|          D ]}t          j        |          }t          |          d d d |f         }t          j        ||j                  }t          j        |||          }t          j        |||d          }t          |j
        |           t          j        |dk              sJ t          j        |||d          }	t          |	j
        |           t          j        |	t          j         k              sJ d S )	N
   rF   rb   r
   r   r   r   T)r   r   rY   r   )r  r7   r   r   r	  r   r   r   r   r   r   allr   r  )
rT   r  r   rmnr   vrXr   r   s
             r>   test_degenerate_arrayz,TestMultivariateNormal.test_degenerate_array  s?    q! 	0 	0A1a[[ 0 0Xa[[.q11!!!RaR%8VAqs^^'+!DDD)-abb=AC C CSXq)))vcCi(((((,3ABBCGI I IV[!,,,vfw.//////0	0 	0r@   c                 f   d}d}d}t          j        ||z            }||z   }t          j        ||ft                    }t          j        ||           d|| d | d f<   t          t          j                            |          d           t          t          j                            |d |d |f                   t           j	                   t          t           j                            |d |d |f                   d|f           t          |          }t          |j        |           d S )Ng     @@d   rF   dtyper   r
   )r7   expr   floatfill_diagonalr   r   r   detr  r   slogdetr   r   )rT   large_total_lognposnzerolarge_entryr   r   r   s           r>   test_large_pseudo_determinantz4TestMultivariateNormal.test_large_pseudo_determinant  s-   
 !f_t3445Lh1vU+++
k*** !UFGGeVWW 	U\%%c**A...U\%%c%4%$,&788"&AAA	))#eteUdUl*;<<O,	. 	. 	. 3iio66666r@   c                    t           j                            d           d}t           j                            ||          }t          j        ||j                  }t           j                            |          }t           j                            dd|          }t          j        |||          }t          j        |||          }t          d          D ]}t          d          D ]p}	t          j        |||	f         ||          }
t          |
|||	f                    t          j        |||	f         ||          }
t          |
|||	f         d           qd S )Nr   rc   rF   rG   MbP?rtol)r7   r   r   r   r	  r   r   r   r   r  r   )rT   r   datar   r   r)  desired_pdfdesired_cdfijactuals              r>   test_broadcastingz(TestMultivariateNormal.test_broadcasting  sM   
	t yq!$$fT46""yq!! IOOAq!$$ *-as;;)-as;;q 	E 	EA1XX E E,01a4$DDAaC(8999,01a4$DDAaC(8tDDDDDE	E 	Er@   c                 6   t          j        ddd          }d\  }}|dz  }t          j        |||          }t	          j        |||          }t          ||           t          j        |||          }t	          j        |||          }t          ||           d S )Nr   rF   r#  )333333??      ?)r7   linspacer   r   r   r   r   )rT   rZ   r   r   scaler   r   s          r>   test_normal_1Dz%TestMultivariateNormal.test_normal_1D  s     K1b!!	cSXau%% $Qc22BXau%% $Qc22Br@   c                    t          j        ddg          }t          j        ddgddgg          }d}d|dz
  z  }t          j        d	d|          }t          j        ||          \  }}t          j        ||d
f          }||d d d d d	f<   ||d d d d df<   t          j        |||          }	t          |	|d	          }
t          |	|d          }t          j        ||d	         |d         dz            }t          j        ||d         |d         dz            }t          |
|dd           t          ||dd           d S )Nr   g      @rG  r   333333?i  rb   r
   r   rF   r   r   r   )locrI  )r
   r
   {Gz?r<  atol)
r7   r   rH  meshgridemptyr   r   r.   r   r   )rT   r   r   r   deltar   xvyvposr   margin_xmargin_ygauss_xgauss_ys                 r>   test_marginalizationz+TestMultivariateNormal.test_marginalization	  sj    xc
##hS	C9-..QUK1a  Q""Bh1ay!!AAAqqq!GAAAqqq!G!%c455 U+++U+++ (1$q'Tc1ABBB(1$q'Tc1ABBB'4@@@@'4@@@@@@r@   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                    |          t          j	        |||                     t          |
                    |          t          j
        |||                     d S r   )r7   r   r   r   r   r   r   r   r   r   r   )rT   rZ   r   r   norm_frozens        r>   test_frozenz"TestMultivariateNormal.test_frozen"  s:   
	tIOOAyq!!fRY__Q''(()$44**,?,CAtS,Q,QRRR**1--+21dC@@	B 	B 	B**,?,CAtS,Q,QRRR**1--+21dC@@	B 	B 	B 	B 	Br@   rH   rF   r
   c                     t          j        d          }t          j        d          }t          ||          }t          j        |j        |          sJ t          j        |j        |          sJ d S )NrF   rF   )r7   rN   rO   r   allcloser   r   )rT   rH   r   cov_should_ber^  s        r>   2test_frozen_multivariate_normal_exposes_attributeszITestMultivariateNormal.test_frozen_multivariate_normal_exposes_attributes0  sh     wt}}q		)$
;;{;+T22222{;?M:::::::r@   c           
         t           j                            d           d}t           j                            ||          }t          j        ||j                  }t          j                            |          \  }}t          j	        |d          }d|d<   d|d<   t          j        |t          j        t          j
        |          |j                            }d}t          ||	          }t          |j        |	          }t          |j        t          j        t          j        |d d                                        t          |j         |j                   d S )
Nr   rd   rG  r   r   Hz>re   h㈵>)cond)r7   r   r   r   r	  r   r   r   r   fullrn   r   pinvr   r   r   r   )	rT   r   rZ   r   r   r   rh  r   psd_pinvs	            r>   test_pseudodet_pinvz*TestMultivariateNormal.test_pseudodet_pinv>  s    		tIOOAq!!fQnn|  %%1GAsOO!"fQrwqzz13//00 3T"""t,,, 	bfRVAcrcF^^&<&<=== 	x'899999r@   c                 L    g dg dg}t          t          t          |           d S )NrJ   rc   ra   rb   r   rL   r   rT   r   s     r>   test_exception_nonsquare_covz3TestMultivariateNormal.test_exception_nonsquare_covX  s,    yy)))$j$,,,,,r@   c                     ddgdt           j        gg}t          t          t          |           ddgdt           j        gg}t          t          t          |           d S )Nr
   r   )r7   nanr   rL   r   r  )rT   cov_nancov_infs      r>   test_exception_nonfinite_covz3TestMultivariateNormal.test_exception_nonfinite_cov\  sT    q6Arv;'j$000q6Arv;'j$00000r@   c                 L    ddgddgg}t          t          t          |           d S )Nr
   r   re   ro  rp  s     r>   test_exception_non_psd_covz1TestMultivariateNormal.test_exception_non_psd_covb  s,    1v2wj$,,,,,r@   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        d          }t           j        j        }t          |t          ||           t          |t          j	        |||           t          |t          j
        |||           t          |t          j        |||           t          |t          j        |||           ddgddgg}d}t          j        t           j        j        |          5  t          |           d d d            d S # 1 swxY w Y   d S )	Nr   ra   )ra   ra   r   r   z0When `allow_singular is False`, the input matrixrD   r   )r7   r   r   r   rN   r   LinAlgErrorr   r   r   r   r   r   rK   r	   )rT   rZ   r   r   emsgs         r>   test_exception_singular_covz2TestMultivariateNormal.test_exception_singular_covf  sx   
	tIOOAyq!!gfooI!a,dC888a,0!T3???a,3QcBBBa,0!T3???a,3QcBBB Bx"b"@]290<<< 	) 	)C((((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)s   =EE"Ec                     t          j        g d          }t          j        ddd          }d|z  dz
  }|t          j        |          z   }t          j        |||g          j        }t          j        g dd          }t          j        g dg d	g d
gd          }t          j        |||          }t          ||d           t          j        g d          }	t          j        |||          }
t          |
|	d           t          j        g d          }t          j        ||g          j        }t          j        ddgd          }t          j        ddgddggd          }t          j        |||          }t          ||d           d S )N)g0Q-?gox'V?g[S, t?gDB?gc_.?r   rF   ra   rG   )r
   rG   rF   dr
   rF   r   )rF   ra   rG  )r   rG  rG   绽|=rQ  )gwk:E]?g̙Z?g0?gL8?gAG*?gh㈵>)gIى?gG?gƏ)?gėh?gEE?r
   rg  )	r7   r   rH  cosr   r   r   r   r   )rT   r_pdfrZ   r  r  r&  r   r   r   r_cdfr   r_cdf2r2mean2cov2cdf2s                   r>   test_R_valuesz$TestMultivariateNormal.test_R_valuesy  s     6 6 6 7 7 K1a  EAIq		MHaAY!x			3''h			:::zzz:C@@!%as33U////  6 6 6 7 7 "%as33U....  3 3 3 4 4 Xq!f!Q%%x!Q!Q(#.."&r5$77f4000000r@   c                     t          j        d          }t          j        d          }t          ||d          }|                                }t	          |ddg           d S )NrF   rF   rF   TrX   r   )r7   r   r   r   r   )rT   r   rH   modelsamples        r>   ,test_multivariate_normal_rvs_zero_covariancezCTestMultivariateNormal.test_multivariate_normal_rvs_zero_covariance  sY    x{{Xf%%
#D*TJJJVaV$$$$$r@   c                    d}d}t          j        t          j        |          d|          }t	          |j        ||f           t          j        d t          j        ddgddgg          |          }t	          |j        |df           t          dd          }|                    |          }t	          |j        |f           d S )	Ni,  rc   r
   r$  rF   r   r   r   )r   r   r7   r   r   r9   r   )rT   Nr  r  r   s        r>   test_rvs_shapez%TestMultivariateNormal.test_rvs_shape  s     $(bhqkkqqIIIV\Aq6***$(d-/X2wQ6H-I-I./1 1 1 	V\Aq6***QA...qV\A5)))))r@   c                    t           j                            d           d}t           j                            |          }t           j                            ||          }t          j        ||j                  }d}t          j        |||          }t          t          j	        |j                  |d           t          |
                    d          |d           d S )N  rG     r   r;  r   )r7   r   r   r   r	  r   r   r   r   r   r   )rT   r   r   r   r   r   r  s          r>   test_large_samplez(TestMultivariateNormal.test_large_sample  s     		tyq!!IOOAq!!fQnn$(sD99vx((#D9999A4888888r@   c                    t           j                            d           d}t           j                            |          }t           j                            ||          }t          j        ||j                  }t          ||          }t          |                                t          j        ||                     t           j	        
                    |          d         }d|t          j        dt           j        z            dz   z  t          j        t          j        |                    z   z  }t          ||                                           d S )Nr  rG   r   rG  rF   r
   )r7   r   r   r   r	  r   r   r   r   r   eigr   pir   )rT   r   r   r   r   r   eigsdesireds           r>   test_entropyz#TestMultivariateNormal.test_entropy  s    
	tyq!!IOOAq!!fQnn s++ 	BJJLL*=*EdC*P*PQQQ y}}S!!!$1q25y 1 1A 56t9M9MMNGRZZ\\22222r@   c                     t          j        g d          }d}t          t          j        t	          |                    |           d S )Nr
   r
   r
   rG  )r7   r   r   r/  r   )rT   alphar  s      r>   test_lnBzTestMultivariateNormal.test_lnB  s@    ##BF4;;//99999r@   c                    t           j                            d          }ddg}t          j        d          }|                    d          dz  dz
  }|                    d          dz  dz
  }t	          j        ||||          }t	          j        |||          }t	          j        |||          }t          j        |ddd	f         |dd	df         fd
          }	t          j        |dd	df         |ddd	f         fd
          }
t	          j        |	||          }t	          j        |
||          }||z   |z
  |z
  }t          ||           d S )N   FYc@Y r   rF   )rc   rG   rF   rb   rG   lower_limit.r
   re   r   )r7   r   r   rO   r   r   concatenater   )rT   r   r   r   abcdf1cdf2acdf2bab1ab2cdf2ab1cdf2ab2r  s                 r>    test_cdf_with_lower_limit_arraysz7TestMultivariateNormal.test_cdf_with_lower_limit_arrays  sX   i##$7881vfQiiJJy!!!#a'JJy!!!#a'"&q$CCC#'455#'455naQqSk1S!A#X;7bAAAnaQqSk1S!A#X;7bAAA%)#tS99%)#tS99u}w&0d#####r@   c                    t           j                            d          }|                    d          }|                    d          }||j        z  }|                    d          dz  dz
  }|                    d          dz  dz
  }t	          j        ||||          }t	          ||                              ||          }t          j        t	          j        ||||                    }t          j        t	          ||                              ||                    }	t          ||d           t          ||d           t          |	|d           d S )	Nr  rG   rG   rG   rF   rG   rb   r  -C6?r;  )	r7   r   r   r   r   r   r/  r   r   )
rT   r   r   r   r  r  r  r  cdf3cdf4s
             r>   %test_cdf_with_lower_limit_consistencyz<TestMultivariateNormal.test_cdf_with_lower_limit_consistency  sJ   i##$788zz!}}jj  CEkJJvq 1$JJvq 1$"&q$CCC"4--11!1CCv)0D#1MMMNNv)$44;;A1;MMNNd....d....d......r@   c                    t          j        d          }t          j        d          }g dg dg dg dg}g dg dg dg dg}t          j        g d          }t	          j        ||||          }t          ||d         |z             d S )	NrG   r  rf   r
   r   r
   r   r
   r   r
   re   re   r
   r  r   r7   r   rO   r   r   r   r   )rT   r   r   r  r  expected_signsr   s          r>   test_cdf_signsz%TestMultivariateNormal.test_cdf_signs   s    x{{fQiiYY			999iii8YY			999iii8...11!%asBBBSVN233333r@   c                    t          j        dt          j        g d          z            }t          j        |          }d}t          j        t          |          5  t          j	        ddg|           d d d            n# 1 swxY w Y   t          j        t          |          5  t          ddg|           d d d            n# 1 swxY w Y   g d}t          j
        |g d|          }t          t          j
        ||          |           t          j
        |g d	|          }t          t          j
        |d|          |           d S )
Nr
   rJ   z7`cov` represents a covariance matrix in 3 dimensions...rD   r   )rG  rG  rG  rf   rz  r  )r7   rn   r   r+   rM   rK   r	   rL   r   r   r   r   )rT   Pr   rU   rZ   r;   s         r>   test_mean_covz$TestMultivariateNormal.test_mean_cov+  s   GA+++,, 033
K]:W555 	< 	<'A
;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< ]:W555 	4 	4A
333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 OO!%aJ??(,QJ???EEE!%aJ??(,QzBBBCHHHHHs$   BBB'CC
C
c                     ddg}d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )Nr
   rG   z`x` must be two-dimensional.rD   )rK   r	   rL   r   fit)rT   r=  	error_msgs      r>   test_fit_wrong_fit_data_shapez4TestMultivariateNormal.test_fit_wrong_fit_data_shape>  s    1v2	]:Y777 	* 	*#D)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	*s   AAAr   )rG   ra   c                 J   t           j                            d          }|                    d|f          }t          j        |          \  }}t          j        |d          t          j        |j        d          }}t          ||d           t          ||d           d S )	N   @,Q| r,  r   r   )ddofV瞯<r  r;  )	r7   r   r   r   r  r   r   r   r   )rT   r   r   rZ   mean_estcov_estmean_refcov_refs           r>   test_fit_correctnessz+TestMultivariateNormal.test_fit_correctnessD  s    i##$455JJSz""/3A66'GAA...qs0C0C0C'(7777u555555r@   c                     t          j        dd          }d}t          j        d          }t          j        |||          \  }}t          ||           t          ||           d S )N)rF   r
   rG   r   )fix_meanfix_cov)r7   ri  
atleast_2dr   r  r   )rT   r=  
mean_fixed	cov_fixedr   r   s         r>   test_fit_both_parameters_fixedz5TestMultivariateNormal.test_fit_both_parameters_fixedM  so    wvq!!
M"%%	'+D:4=? ? ?	cT:&&&S)$$$$$r@   r  r  rG   c                     d}t          j        t          |          5  t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nzd`fix_mean` must be a one-dimensional array the same length as the dimensionality of the vectors `x`.rD   rF   r  rK   r	   rL   r   r  r7   rO   )rT   r  r}  s      r>   "test_fit_fix_mean_input_validationz9TestMultivariateNormal.test_fit_fix_mean_input_validationV  s    C]:S111 	B 	B#BF1IIAAAA	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B   )AAAr  ra  )rG   rF   )rc   rc   c                     d}t          j        t          |          5  t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nzn`fix_cov` must be a two-dimensional square array of same side length as the dimensionality of the vectors `x`.rD   rG   r  r  )rT   r  r}  s      r>   +test_fit_fix_cov_input_validation_dimensionzBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimension^  s     ]:S111 	@ 	@#BF1IIw????	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@r  c                     d}t          j        t          |          5  t          j        ddgddgg          }t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nz2`fix_cov` must be symmetric positive semidefinite.rD   r   r   g      rF   r  )rK   r	   rL   r7   r   r   r  rO   )rT   r  r  s      r>   *test_fit_fix_cov_not_positive_semidefinitezATestMultivariateNormal.test_fit_fix_cov_not_positive_semidefiniteh  s    H	]:Y777 	@ 	@hR2s)455G#BF1IIw????	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@s   AA..A25A2c                     t           j                            d          }|                    d          }|                    d          }t          j        ||j                  }t          j        ||d|          }t          j        |          \  }}t          j        |||          	                                }t          j        ||          \  }	}
t          |	|           t          j        ||	|
          	                                }||k     sJ |                    d          }dt          j        ||j                  z  }|
|z   }t          j        ||	|          	                                }||k     sJ d S )	Nr  rG   r  r,  r   r   r   r   r   r  :0yE>)r7   r   r   r	  r   r   r   r  r   r   r   )rT   r   rN  rt   r   samples	mean_freecov_free	logp_freemean_fixcov_fixlogp_fixmcov_perturbedlogp_perturbeds                  r>   test_fit_fix_meanz(TestMultivariateNormal.test_fit_fix_meann  s   i##$455jjmmJJvfQnn%)s#7:< < <15g>>	8'.wY3;= = ==@SUU 	/3GcJJJ'Xs###&-gH29; ; ;;>355 	 )#### JJv26!QS>>!!-4W:B9FH H H 8;suu 	 ((((((r@   c                    t           j                            d          }|                    d          }|                    d          }t          j        ||j                  }t          j        ||d|          }t          j        |          \  }}t          j        |||          	                                }t          j        ||          \  }	}
t          |	t          j        |d	                     t          |
|           t          j        ||	|
          	                                }||k     sJ |	d
|                    d          z  z   }t          j        |||
          	                                }||k     sJ d S )Nr  rG   r  r,  r  r   r  r   r   r  )r7   r   r   r	  r   r   r   r  r   r   r   r   )rT   r   rN  rt   r   r  r  r  r  r  r  r  mean_perturbedr  s                 r>   test_fit_fix_covz'TestMultivariateNormal.test_fit_fix_cov  s   i##$455jjmmJJvfQnn%)s/2F F F15g>>	8'.wY3;= = ==@SUU 	/3GSIII'XrwwQ777888Wc"""&-gH29; ; ;;>355 	 )#### "D3::a==$88-4W:H9@B B B 8;suu 	 ((((((r@   N)1r   r   r   r   r   r   r  r  r  r  r!  r*  r8  rC  rJ  r\  r_  rK   r   r   r7   rO   r,   from_diagonalrd  rl  rq  rv  rx  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r   r@   r>   r   r   $  sf       O O O" " "6( ( (( ( (( ( (( ( (	? 	? 	?26 26 26h0 0 0,7 7 70E E E0     A A A2B B B [BF1II$J$aV,,	
 ; ; ;: : :4- - -1 1 1- - -) ) )&>1 >1 >1@% % %* * *"9 9 9"3 3 3$: : :$ $ $(/ / /$	4 	4 	4I I I&* * * [UF++6 6 ,+6% % % [Z("(6*:*:*2"(5//*; < <B B< <B [Y%)1&)9)9)1&)9)9); < <@ @< <@@ @ @) ) ):) ) ) ) )r@   r   c                   >    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	S )
TestMatrixNormalc           
      \   d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t          t          t
          t          j        d                     t          t          t
          |t          j        d          |           t          t          t
          ||t          j        d                     t          t          t
          |||           t          t          t
          |||           t          t          t
          |j        ||           t           j        j	        }t          |t
          j
        ||t          j        ||f                     t          |t
          j
        |t          j        ||f          |           t          |t
          ||t          j        ||f                     t          |t
          |t          j        ||f          |           d S )Nrc   rG   r   rG  ffffff?)ra   rc   rG   r#  )r7   ri  r   r   rL   r   r   r   r   r{  r   rN   )rT   num_rowsnum_colsr   r   Vr|  s          r>   test_bad_inputzTestMatrixNormal.test_bad_input  s   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LL 	j-'1B1BCCCj-BHRLL!DDDj-Arx||DDDj-Aq999j-Aq999j-a;;;I!a*BGXx$899	; 	; 	;a*(H!566	; 	; 	; 	a1bgx6J.K.KLLLa27Hh3G+H+H!LLLLLr@   c                    d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t          j        ||f          }t          j        |df          }t          j        d|f          }t          j        |          }	t          j        |          }
t          j        d          }t	          t          j        |||          j        ||f           t	          t          j        |          j        ||f           t	          t          j        |	          j        |df           t	          t          j        |
          j        d|f           t	          t          j        ||          j        ||f           t	          t          j        ||          j        ||f           t	          t          j        ||          j        ||f           t	          t          |          j        |	           t	          t          |          j	        |
           t	          t          |	          j
        |           t	          t          |	          j	        |           t	          t          |
          j
        |           t	          t          |
          j        |           t	          t          ||          j	        |
           t	          t          ||          j        |	           t	          t          ||          j
        |           d S )Nrc   rG   r   rG  r  r
   r   rowcovcolcov)r   )r  )r  )r   r  )r   r  )r  r  )r7   ri  r   r   r   r   r   r9   r  r  r   )rT   r  r  r   r   r  ZZrZcIrIcI1s               r>   test_default_inputsz$TestMatrixNormal.test_default_inputs  s:   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLHh)**Xxm$$Xq(m$$[""[""[^^]&AaBBBH)	+ 	+ 	+]&A...4)	+ 	+ 	+]&a0006]	$ 	$ 	$]&a0006]	$ 	$ 	$]&Aa888>)	+ 	+ 	+]&Aa888>)	+ 	+ 	+]&a:::@)	+ 	+ 	+ 	]***12666]***12666]!,,,12666]!,,,3R888]!,,,12666]!,,,3R888]!444;R@@@]!444;R@@@]!A666;Q?????r@   c                 (   d}d}t          j        ||fd          }t          j        |d          }d}t          j        |d          }d}t          j        |          }t          j        |          }	t          t	          |||          j        d|z             t          t	          |||          j        d|	z             t          t	          |||          j        d|z             t          t	          |||          j        d|	z             d S )Nrc   rG   r   r   r   r  )r7   ri  r   r   r   r  r  )
rT   r  r  r   UvUsVvVsr  r  s
             r>   test_covariance_expansionz*TestMatrixNormal.test_covariance_expansion  s*   GXx(#..WXs##WXs##[""[""]"R@@@GV	 	 	]"R@@@GV	 	 	]"R@@@GV	 	 	]"R@@@GV	 	 	 	 	r@   c                    t          dd          D ]m}t          dd          D ]X}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t	          |||          }|                    d          }t	          j        |||d	          }t          ||           |                    d          }	|                    |	          }
t	          j        |	|||          }t          |
|           |                    |	          }t	          j        |	|||          }t          ||           Zod S )
Nr
   ra   r   rG  r  r  r   r   )r   r  r  r   )	r  r7   ri  r   r   r   r   r   r   )rT   r@  rA  r   r   r  frozenrvs1rvs2r)  pdf1pdf2logpdf1logpdf2s                 r>   test_frozen_matrix_normalz*TestMatrixNormal.test_frozen_matrix_normal   s   q 	/ 	/A1QZZ / /GQqE3''"+a..(27Aa5#+>+>>"+a..(27Aa5#+>+>>&AaBBBzztz44$(a!6:< < <T4(((JJDJ11zz!}}$(1QGGGT4((( --**'.qq1MMMWg....)/	/ 	/r@   c                    t          dd          D ]}t          dd          D ]}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t	          |||          }|                    d          }|                    |          }|                    |          }	|                                }
|j	        
                                }|j	        
                                }t          j        ||          }t          j        |||	          }t          j        |||	          }t          j        ||	          }t          ||d
           t          |	|d
           t          |
|           d S )Nr
   ra   r   rG  r  r  r   r   r   r  r;  )r  r7   ri  r   r   r   r   r   r   r   flattenkronr   r   )rT   r@  rA  r   r   r  r  r)  r  r  entropy1vecXvecMr   r  r  entropy2s                    r>   test_matches_multivariatez*TestMatrixNormal.test_matches_multivariate  s    q 	4 	4A1QZZ 4 4GQqE3''"+a..(27Aa5#+>+>>"+a..(27Aa5#+>+>>&AaBBBJJDJ11zz!}} --**!>>++s{{}}s{{}}gall*.t$CHHH-4T#NNN.6DcJJJd7777u====(3333)4	4 	4r@   c           	      X   d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }d}t          |||          }|                    |d	          }|                    |d
	          }	t          j        |t           j        d d d d d d f         |	t           j        d d d d d d f         fd          }
t          |
j        d|||f           |	                    |
          }t          |j        d|f           t          d          D ]M}t          |          D ];}t          j	        |
||f         |||          }t          ||||f         d           <Nd S )Nrc   rG   r   rG  r  r#  r  r   r   i  r   r   rF   r  )r7   ri  r   r   r   r  newaxisr   r9   r   r  r   )rT   r  r  r   r   r  r  r  X1X2r)  array_logpdfr@  rA  separate_logpdfs                  r>   test_array_inputz!TestMatrixNormal.test_array_input2  s   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLAa:::ZZQTZ22ZZQTZ22NBrz!!!AAAaaa/0BJqqq1114D1EFQOOOQWq!Xx8999}}Q''\'!Q000q 	K 	KA1XX K K"/"6q1vA>?#K #K #Kac1BEJJJJK	K 	Kr@   c                    d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }d}t          |||          }|                    |d	          }t          j        |d
          }	t          |	|d           t          j        |                    ||z  |          j	                  }
t          |
|d           t          j        t          j
        |dd                              ||z  |          j	                  }t          ||d           d S )Nrc   rG   r   rG  r    r  r   r   r   r   r   r  r
   rF   )r7   ri  r   r   r   r   r   r   reshaper   swapaxes)rT   r  r  r   r   r  r  r  r)  sample_meansample_colcovsample_rowcovs               r>   test_momentszTestMatrixNormal.test_momentsI  sb   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLAa:::JJADJ11gaQ'''QS1111qyy8H==?@@qs3333r{1Qq119989(
8 M  MMNP Pqs333333r@   c           	      f   t          j        t          j        ddgddgg          t          j        ddgddgg          t          j        ddgddgg          t          j                            d          d	          }t          j        d
dgddggddgddggg          }t          ||           d S )Nr
   rF   rG   rc   re   ra   r#  r   )r   r  r  r   r   g6?gǀgcϿ@g"'@gI2͖@g^jy%@gDn3@g|\3@)r   r   r7   r   r   r   r   )rT   rB  expecteds      r>   test_sampleszTestMatrixNormal.test_samples_  s     "Aq6Aq6*++8aWr1g.//8aVaW-....q11
 
 
 8!23!124!23!1245
 
 	)))))r@   N)r   r   r   r  r  r  r  r  r$  r,  r/  r   r@   r>   r  r    s        M M M4%@ %@ %@N  ,/ / /04 4 44K K K.4 4 4,* * * * *r@   r  c                       e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	 Zd
 Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdS )TestDirichletc           	         t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }t          |                                t          j        |                     t          |                                t          j        |                     t          |	                                t          j	        |                     d}t          |          D ]}t           j                            dd|          }|t          j        |          z  }t          |                    |d d                   t          j        |d d         |                     t          |                    |d d                   t          j        |d d         |                     d S Nr  r
       &.>r,  r#  re   )r7   r   r   randintr   r   r   varr   r   r  r   r   r   rT   r   r  r  	num_testsr@  rZ   s          r>   test_frozen_dirichletz#TestDirichlet.test_frozen_dirichlett  s   
	tIa$$	!!&#q11eQUUWWimE22333QVVXXy~e44555QYY[[)"3E":":;;;	y!! 	L 	LA	!!&#q11ANAq"v	afe(D(DEEE!CRC&))9+;AcrcFE+J+JKKKK		L 	Lr@   c                 P   t           j                            d           t          j        g d          }t           j                            |d          }t          |j        d           t          t          t          j	        ||           t          t          t          j
        ||           t	          j	        |j        |           t	          j	        |j        d d         |           t	          j
        |j        |           t	          j
        |j        d d         |           d S )Nr  r          @      @rd   r~   )rd   rG   re   )r7   r   r   r   r   r   r9   r   rL   r   r   r   rT   r  rZ   s      r>   "test_numpy_rvs_shape_compatibilityz0TestDirichlet.test_numpy_rvs_shape_compatibility  s    
	t))IA..QWf%%%j)-E:::j)"2Au===ac5!!!ac#2#h&&&e$$$SbS5)))))r@   c                 B   t           j                            d           g d}t           j                            t          j        d|          d          j        }t          t          t          j        ||           t          t          t          j	        ||           d S )Nr  )r   r   r>  r5  rd   r~   
r7   r   r   r   maximumr   r   rL   r   r   r?  s      r>   test_alpha_with_zerosz#TestDirichlet.test_alpha_with_zeros  s{    
	tI
4 7 7a@@Bj)-E:::j)"2Au=====r@   c                 B   t           j                            d           g d}t           j                            t          j        d|          d          j        }t          t          t          j        ||           t          t          t          j	        ||           d S )Nr  )r   g       r>  r5  rd   r~   rB  r?  s      r>    test_alpha_with_negative_entriesz.TestDirichlet.test_alpha_with_negative_entries  s}    
	t   I
4 7 7a@@Bj)-E:::j)"2Au=====r@   c                    t          j        g d          }t          j        g d          }t          j        ||           t          j        ||           t          j        g d          }t          t          j        ||          d           t          t          j        ||          t          j        d                     d S )Nr   r=  r>        @r   r   r   r  )r   r   r   r   rb   )r7   r   r   r   r   r   r   r?  s      r>   test_data_with_zerosz"TestDirichlet.test_data_with_zeros  s    ---..H)))**aE"""---..IM!U33Q777I,Q66q		BBBBBr@   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )N)r   rG  r>  rI  rJ  r7   r   r   rL   r   r   r   r?  s      r>   $test_data_with_zeros_and_small_alphaz2TestDirichlet.test_data_with_zeros_and_small_alpha  a    ---..H)))**j)-E:::j)"2Au=====r@   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )NrH  )r   皙r   r  rM  r?  s      r>   test_data_with_negative_entriesz-TestDirichlet.test_data_with_negative_entries  sa    ---..H***++j)-E:::j)"2Au=====r@   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )NrH  )r   皙?r   r  rM  r?  s      r>    test_data_with_too_large_entriesz.TestDirichlet.test_data_with_too_large_entries  rO  r@   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr<  )rF   rd   rd   g$I$I?r7   r   ri  r   rL   r   r   r   r?  s      r>   test_data_too_deep_cz"TestDirichlet.test_data_too_deep_c  sY    ))GIv&&j)-E:::j)"2Au=====r@   c                     t          j        ddgddgg          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr   r=  r>  rI  )rF   rF   rd         ?rW  r?  s      r>   test_alpha_too_deepz!TestDirichlet.test_alpha_too_deep  sb    3*sCj122GIu%%j)-E:::j)"2Au=====r@   c                     t          j        g d          }t          j        dd          }t          j        ||           t          j        ||           d S )Nr<  rG   rd   UUUUUU?)r7   r   ri  r   r   r   r?  s      r>   test_alpha_correct_depthz&TestDirichlet.test_alpha_correct_depth  sQ    ))GFE""aE"""""r@   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr<  r]  rG  rW  r?  s      r>   test_non_simplex_dataz#TestDirichlet.test_non_simplex_data  sY    ))GFE""j)-E:::j)"2Au=====r@   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )NrH  )rF   rd   rG  rW  r?  s      r>   test_data_vector_too_shortz(TestDirichlet.test_data_vector_too_short  \    ---..GFE""j)-E:::j)"2Au=====r@   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )NrH  )ra   rd   r   rW  r?  s      r>   test_data_vector_too_longz'TestDirichlet.test_data_vector_too_long  rd  r@   c                 B   t          j        g d          }t          |          }g d}g d}g dg dg dg}t          |                                |           t          |                                |           t          |                                |           d S )N)r   皙?r   rG  皙?r   )UUUUUU?{Gz?Q?)rk  )rn  rl  O贁N)ro  rp  rm  )r7   r   r   r   r   r7  r   )rT   r  r  expected_meanexpected_varexpected_covs         r>   test_mean_var_covzTestDirichlet.test_mean_var_cov  s     ((e'---......///
 	"!&&((M:::!!%%''<888!!%%''<88888r@   c                    t          j        dg          }t          |          }t          |                                j        d           t          |                                j        d           t          |                    dg          j        d           t          |                    dg          j        d           d S )Nr   r   r   )	r7   r   r   r   r   r   r7  r   r   )rT   r  r  s      r>   r   z TestDirichlet.test_scalar_values  s    #e 	QVVXX]A&&&QUUWW\1%%%QUUB4[[%q)))QXXrd^^(!,,,,,r@   c                    t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }d}t          |          D ]x}t           j                            dd|          }|t          j        |          z  }t          |	                    |d d                   |	                    |                     yd S r3  )
r7   r   r   r6  r   r   r  r   r   r   r8  s          r>    test_K_and_K_minus_1_calls_equalz.TestDirichlet.test_K_and_K_minus_1_calls_equal  s     		tIa$$	!!&#q11e	y!! 	9 	9A	!!&#q11ANAafquuQxx8888	9 	9r@   c                    t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }d}d}d }t          |          D ]}t          |          D ]U}t           j                            dd|          }	|	t          j        |	          z  }	|t          j        ||	f          }S|	}V|	                    |j
                  }
d }|D ]1}|	                    |          }|t          j        ||          }/|}2t          |
|           d S )Nr  r
   r4  r5  r,  r#  ra   )r7   r   r   r6  r   r   r  r   vstackr   r   appendr   )rT   r   r  r  r9  num_multiplexmr@  r  rZ   rmrsxsr&  s                 r>   test_multiple_entry_callsz'TestDirichlet.test_multiple_entry_calls  sK   
	tIa$$	!!&#q11e	y!! 	. 	.A<((  I%%fc155RVAYY>B7++BBBBrtBB  EE"II>2q))BBBB%b"----!	. 	.r@   c                    t           j                            d           t           j                            ddd          }t	          |          }t          |d         |d                   }d}t          |          D ]q}t           j                            ddd          }|t          j        |          z  }t          |	                    |          |	                    |g                     rt          |
                                |
                                d                    t          |                                |                                d                    d S )Nr  r5  r,  rF   r   r
   r#  )r7   r   r   r   r   r   r  r   r   r   r   r7  )rT   r  r  r  r9  r@  rZ   s          r>   test_2D_dirichlet_is_betaz'TestDirichlet.test_2D_dirichlet_is_beta*  s   
	t	!!&#q11eq58$$	y!! 	6 	6A	!!&#q11ANAa!%%**5555AFFHHaffhhqk222AEEGGQUUWWQZ00000r@   N)r   r   r   r:  r@  rD  rF  rK  rN  rR  rU  rX  r[  r_  ra  rc  rf  rt  r   rw  r  r  r   r@   r>   r1  r1  r  s7       L L L$
* 
* 
*> > >> > >C C C> > >> > >> > >> > >> > ># # #> > >> > >> > >9 9 9$	- 	- 	-9 9 9. . .:1 1 1 1 1r@   r1  c                  P   t          j        ddg          } t          j        dgg          }t          t          t          | |           	 t	          | |           d S # t          $ r?}d}t          t          |          d t          |                   |           Y d }~d S d }~ww xY w)Nr   r   zDimension mismatch)r7   r   r   rL   r   r   strr   )r   sigmar|  r}  s       r>   ,test_multivariate_normal_dimensions_mismatchr  ;  s     
3*		BHseWE*12u===
-B&&&&& - - -"SVVISXXI&,,,,,,,,,-s   
A 
B%&4B  B%c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestWishartc                 h   t          j        dd          }ddgt          j        d          t           j        d         t          j        dd          g}|D ]F}t          d|          }t	          |j        |           t	          |j        j        |j                   Gt          j        ddgddgg          }ddgt           j        d         t          j        ddgddgg          g}|D ]F}t          d|          }t	          |j        |           t	          |j        j        |j                   Gt          t          t          dt          j	        d                     t          dt          j	        d                     t          j        dd          }t          t          t          d|           d S )Nr
   rF   ndminr   r
   rF   rT  rG   )
r7   r   r_r   r   rI  r9   r   rL   rO   )rT   
true_scalescalesrI  ws        r>   test_scale_dimensionsz!TestWishart.test_scale_dimensionsO  s    Xaq)))
CHQKKE!HHQa   
  	: 	:E5!!A*---
(89999 X!u !!u& ' '
 qEE#JHqee  
  	: 	:E5!!A*---
(89999 	j'1bfQii888 	RVAYY !$$$j'1e44444r@   c           
         ddgt          j        d          t           j        d         t          j        dd          t          j        dgd          g}t          dd          }|                    t          j        dd                    }|D ]%}t          |                    |          |           &g dt           j        d         t          j        g dd          g}t          dd          }|                    t          j        g dd                    }|D ]%}t          |                    |          |           &dddgt          j        d          t           j        d         t          j        ddgddgg          t          j        ddgddgg          d d d d t           j        f         g}t          dt          j        d                    }|                    t          j        ddgddgg          d d d d t           j        f                   }|D ]%}t          |                    |          |           &d S )Nr
   rF   r  rG   rJ   r  r   )r7   r   r  r   r   r   r  rO   )rT   r)  r  densityrZ   s        r>   test_quantile_dimensionsz$TestWishart.test_quantile_dimensionsz  sQ   
 CHQKKE!HHQa   HaS"""
 AaLL%%!,,,-- 	, 	,Aq7++++ GGE%LHWWWA&&&
 AaLL%%22233 	, 	,Aq7++++
 qEHQKKE#JHqee  Hqee  aa"*n.	
 AbfQii  %%1Q%#$Q%") * **+!!AAAbj.: ; ; 	, 	,Aq7++++	, 	,r@   c           	         d}t          j        t          j        |          dz             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }g }t          d          D ]}t          j        t          j        |          |dz   dz  z             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }|                    |           t          j        |          j        }ddt          j	        ddd          fd||fg}|D ]"\  }}}t          ||          }t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                    |          t          j        |||                     $d S 	Nrc   r
   rF   re   r  ra   r#  r   )r7   rn   r   tril_indicesr	  r   r  rz  r   rH  r   r   r7  r   moder   r   )	rT   r   rI  r)  r@  rZ   
parametersdfr  s	            r>   r_  zTestWishart.test_frozen  s    	#q()),.IcSUmq6H,I,IbocR((()uw&& q 	 	A	#!ax/00A,.IcSUmq6H,I,IAbocR((()qsAAHHQKKKKHQKKM BKR++,N


 ) 	> 	>NRE""A'+b%"8"89997<E#:#:;;;7<E#:#:;;;gob%&@&@AAAq7;q"e#<#<====	> 	>r@   c                    d}d}t          j        |          }d|d<   d|d<   t          ||          }t           j                            d           t          j        ||          }t           j                            d           |                                }t           j                            d           t           j                            d          }t           j        t           j                            |          t           j                            |dz
            t           j                            |d	z
            f         dz  }t          j	        |          }	||	t          j
        |d
          <   t           j                            |          }
|
                    |	          }t          j        ||j                  }t          ||           t          ||           d S )NrG   r#  rG  r   r
   r   i r~   r
   rF   re   r  )r7   rO   r   r   r   r   r   r  	chisquarern   r  r   r   r	  r   r   )rT   r   r  rI  r  w_rvsfrozen_w_rvscovariances	variancesrt   DDAmanual_w_rvss                r>   test_wishart_2D_rvszTestWishart.test_wishart_2D_rvs  s    sc
c
 B 		vB&&
	vuuww 		vi&&A&..EI##I1%%I1%%'
 		 GI(3"/#
$
$
$% Iu%%UU1XXvb"$'' 	|,,,l33333r@   c                 &   t           j                            d           d}d}t          j        |          }t          j        dddt
                    }t          j        ddd          }|D ]!}t          ||          }t          |          }t          |
                                |
                                           t          |                                |                                           t          |                                |                                           t          |                    |          |                    |                     |                    |	          }	|f}
d
}t          d|
||	           #d S )N^   r
   r#  rF   r-  r   numr~   rO  r   )r7   r   r   rO   r   r0  rH  r   r   r   r7  r   r   r   r   r   )rT   snr   rI  df_ranger)  r  r  cr   r<   r  s               r>   test_1D_is_chisquaredz!TestWishart.test_1D_is_chisquared  sN   
 		vs9QAU333KB2&&& 	= 	=BE""ARA AEEGGQUUWW---AFFHHaffhh///AIIKK555 AEE!HHaeeAhh/// %%R%..C5DE"64<<<<!	= 	=r@   c                 H   t           j                            d           d}d}d}t          j        t          j        d          dz             }t          j        d          |t          j        dd          <   t          j        |j        |          }t          j        |df          }|j                            |                              |          	                                }t          ||          }t          ||	          }t          |                                |                                           t          |                                |                                           t          |                                |                                           t          j        d
dd          }	t          |                    |	          |                    |	                     |                    |          }
|d|f}d}t'          d|||
           d S )Nr  r  r#  rc   r
   rb   re   r  rI  r   r  r~   r   rO  r   )r7   r   r   rn   r   r  r	  r   rN   r   r   r   r   r7  r   r   rH  r   r   r   )rT   r  r  r   rI  lamdasigma_lamdar  r  r)  r   r<   r  s                r>   test_is_scaled_chisquaredz%TestWishart.test_is_scaled_chisquared  s   
 		v	!Q''*,)A,,boa2&&&'uw&&Q  gkk%((,,U33;;==B$$;''' 	)))!&&((+++		QYY[[111 KB2&&&a!%%((+++ eeenn1[!vtUC88888r@   N)	r   r   r   r  r  r_  r  r  r  r   r@   r>   r  r  N  sr        )5 )5 )5V/, /, /,b> > >@*4 *4 *4X= = =>!9 !9 !9 !9 !9r@   r  c                   z   e Zd Zd Zd Zd Zej                            dddg          d             Z	d Z
d	 Zej                            ddd
g          d             Zd Zej                            dddg          d             Zd Zej                            ddd
g          d             Zd Zd Zd ZdS )TestMultinomialc                 `   t          j        ddd          }t          |dd           t          j        ddgd	d
dg          }|t          j         k    sJ t          j        d	d	gd	d
dg          }|d	k    sJ t          j        ddgd	ddg          }t          |t          j        d           d S )NrG   rc   rd   r   r  g&Mtyr  r;  rG   rc   r   r   r  rh   )r   logpmfr   r7   r  rs  )rT   vals1vals2vals3vals4s        r>   test_logpmfzTestMultinomial.test_logpmf:  s    "5!Z881===="Aq61r2h77"Aq61r2h77zzzz"Aq61r1g66rvD111111r@   c                     t          j        ddd          }t          j        ddd          }t          ||d           t          j        dd	d
          }t          j        dd	d          }t          ||d           d S )Nr  rd   r  rG   r   r  r;  )rb         r   rF  rb   r   )r   r  r!   r   pmfrT   val1val2s      r>   test_reduces_binomialz%TestMultinomial.test_reduces_binomialG  s     !&!Z88|Aq#&&d....vr:66yB$$d......r@   c                     dg d}}ddddddd	dd
dd
}|D ].}t          t          j        |||          ||         d           /d S )NrG   )g      ?rZ  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rG   )r
   r   rF   )rF   r   r
   )rG   r   r   r   r  rF   r
   r   )r   rF   r
   r  )r   rG   r   +=r  )r   r   r  )rT   r   pr_valsrZ   s        r>   test_RzTestMultinomial.test_RR  s     $$$1([([([([([	B B
  	M 	MAKOAq!44fQieLLLLL	M 	Mr@   r   r   rG   c                     t          j        |dgdz  dd          }t          j                            d          }|                     |dgdz  d          }t          ||           d S )NrZ  rG   rd   {   r   r~   )r   r   r7   r   RandomStater   )rT   r   sc_rvsrndmnp_rvss        r>   test_rvs_npzTestMultinomial.test_rvs_npc  sm     TF1H13GGGy$$S))!!!dVAXA!66VV$$$$$r@   c                    t          j        ddd          }t          |dd           t          j        ddd	          }t          |d
d           t          j        ddgddggddgddgggdd          }t          |ddgddggd           t          j        dt          j                  }t          j        |dd	          }t          |t          j        g t          j                             t          j        ddgdd	          }t          |dd           t          j        g ddg d          }t          |dd           t          j        g ddg d          }|dk    sJ t          j        g ddg d          }|dk    sJ d S )N)ra   ra   r
   r
   r  r;  r  rd   r  g5
?rG   r   r  re   	   r  g*7?g<Wƌ?r   rF   r-  rc   rF   rG   rG   r   rb   )gUUUUUU?r^  r   gߦ?rf   r  )r   r  r   r7   rS  float64r   )	rT   vals0r  r  rZ   r  r  vals5vals6s	            r>   test_pmfzTestMultinomial.test_pmfk  s   a..qt,,,,q(331====1Q%1"a1a&0A BA (* *I 6A?dKKKKHU"*---1h//UBHRrz:::;;;1q(33qt,,,,			1.?.?.?@@~D9999			1.?.?.?@@zzzz			1.?.?.?@@zzzzzzr@   c                    t          j        ddgdddgddgg          }t          |dd	gd
           t          j        ddgddgddg          }t          |ddgd
           t          j        ddgddgggdddg          }t          |ddggd
           t          j        ddgdgdgggddg          }t          |dgdgggd
           t          j        ddgddggdggggddg          }t          |ddggggd
           d S )Nr
   rF   rG   r   rF  r   rh  gv?g~jt?r  r;  rc   r   )r   r  r   )rT   r  r  r  r  r  s         r>   test_pmf_broadcastingz%TestMultinomial.test_pmf_broadcasting  sM   ARHr2h+?@@d|$7777AAR99ayt44441a&1a&!1 2ABx@@q	{6666A1#sr2h??$!T::::!Q!AQC5'RHEE4)T::::::r@   ra   c                     t          j        |d          }|dz  dz  | dz  dz  | dz  dz  g| dz  dz  |dz  dz  | dz  dz  g| dz  dz  | dz  dz  |dz  dz  gg}t          ||d           d S )	N)r   r   rG  r   rh  r   rG  r  r  r;  r   r   r   )rT   r   cov1r  s       r>   test_covzTestMultinomial.test_cov  s    q,//2b1"R%(QBrE"H-Br1R47QBrE"H-BrA2b58QrT"W-/ 	d......r@   c                 t   t          j        dddgddgg          }ddgddggddgddggg}t          ||d	
           t          j        ddgddg          }ddgddggddgddggg}t          ||d	
           t          j        ddgddgddgg          }ddgddggddgddggg}t          ||d	
           d S )Nra   r   rF  r   rh  g?gܿgr  r;  rc   g
ףp=
?g
ףp=
׿r   r  rj  rL  gzG?gzGrE  g333333r  rT   r  r  cov3cov4cov5cov6s          r>   test_cov_broadcastingz%TestMultinomial.test_cov_broadcasting  s   qB8b"X"677tdC[)RIRy+ABd....1vBx00ttSk*c4[4+,FGd....1vR2r(';<<8$x&9:8$x&9:<d......r@   rF   c                 ~    t          j        |ddg          }t          |t          j        |d          d           d S Nr   rh  r  r;  r   r   r   r!   )rT   r   ent0s      r>   r  zTestMultinomial.test_entropy  sA     "1r2h//emAr22>>>>>>r@   c           	      `   t          j        ddgddg          }t          |t          j        dd          t          j        dd          gd           t          j        ddgdd	gd
dgg          }t          |t          j        dd          t          j        dd
          gd           t          j        dgdggdd	gd
dgg          }t          |t          j        dd          t          j        dd
          gt          j        dd          t          j        dd
          ggd           d S )NrF   rG   r   r   r  r;  rd   r  r  rj  rL  r  )rT   r  ent1ent2s       r>   test_entropy_broadcastingz)TestMultinomial.test_entropy_broadcasting  sL   "Aq6B844u}Q33U]1b5I5IJ!	# 	# 	# 	# "Aq6RHr2h+?@@u}Q33U]1b5I5IJ!	# 	# 	# 	# "QC!:R2r(/CDD-2..a0D0DE-2..a0D0DEG!	# 	# 	# 	# 	# 	#r@   c                 h    t          j        |ddg          }t          ||dz  |dz  gd           d S r  r   r   r   )rT   r   mean1s      r>   	test_meanzTestMultinomial.test_mean  s?     RH--"ad|$777777r@   c                 h    t          j        ddgddg          }t          |ddgddggd	
           d S )Nra   rb   r   rh  r   rI  g433333?g433333@r  r;  r  )rT   r  s     r>   test_mean_broadcastingz&TestMultinomial.test_mean_broadcasting  sD     !Q"b22ttTl;$GGGGGGr@   c                    t           j                            d           d}d}g dg dg dg dg dg}t          j        |t           j        	          }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                                t          j	        ||                     d S )
Nr      )r   r   r   rj  r   r   r   r  r   r   r
      r   r
   r
   r#  r
   r
   r
   r  r
   r
   rF   r  r-  )
r7   r   r   r8   r  r   r   r  r  r   )rT   r   pvalsrZ   	mn_frozens        r>   r_  zTestMultinomial.test_frozen  s    
	t ZZ


:::iii			BJq
+++5))		a((+/!Q*F*FGGG	((++[-?1e-L-LMMM	))++[-@E-J-JKKKKKr@   c                 *   d}t           j                            d          }|                    |          }d|d<   |t          j        |          z  }t          j        |          }t          j        |||          }t          j        |          sJ d S )NX   l   iRZY gKH9re   )r7   r   r   r   rN   r   r  isfinite)rT   r   r   r  rZ   r  s         r>   test_gh_11860zTestMultinomial.test_gh_11860  s    
 i##$788JJqMM"	RVAYYGAJJ#Aq!,,{6"""""""r@   N)r   r   r   r  r  r  rK   r   r   r  r  r  r  r  r  r  r  r  r_  r  r   r@   r>   r  r  9  s{       2 2 2	/ 	/ 	/M M M" [S1a&))% % *)%  6; ; ;  [S1a&))/ / *)// / / [S1a&))? ? *)?# # # [S1a&))8 8 *)8H H H
L 
L 
L# # # # #r@   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestInvwishartc           	         d}t          j        t          j        |          dz             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }g }t          d          D ]}t          j        t          j        |          |dz   dz  z             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }|                    |           t          j        |          j        }ddt          j	        ddd          fd||fg}|D ]\  }}}t          ||          }t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                    |          t          j        |||                     d S r  )r7   rn   r   r  r	  r   r  rz  r   rH  r   r   r7  r   r  r   r   )	rT   r   rI  r)  r@  rZ   r  r  iws	            r>   r_  zTestInvwishart.test_frozen  s   
 	#q()),.Ic3q5k!m,D,DbocR((()uw&& q 	 	A	#!ax/00A,.Ic3q5k!m,D,DAbocR((()qsAAHHQKKKKHQKKM BKR++,N


 ) 	E 	ENRB&&B:>"e#<#<===JOB$>$>???JOB$>$>???BFF1IIz~aU'C'CDDDD	E 	Er@   c                 :   t           j                            d           d}d}t          j        |          }t          j        dddt
                    }t          j        dd	d	
          }|D ]+}t          ||          }t          |dz  d          }t          |
                                |
                                           t          |                                |                                           t          |                    |          |                    |                     |                    |          }	|dz  ddf}
d}t          d|
||	           t          |                                |                                           -d S )Nr  r  r
   ra      rF   r-  r   r#  r  rG  r  r~   r   rO  r   )r7   r   r   rO   r   r0  rH  r   r   r   r7  r   r   r   r   r   )rT   r  r   rI  r  r)  r  r  igr   r<   r  s               r>   test_1D_is_invgammaz"TestInvwishart.test_1D_is_invgamma  sc   
 		vs9QAU333KB2&&& 	8 	8BB&&B"Q$d+++B BFFHHbffhh///BGGIIrwwyy111 BFF1IIrvvayy111 &&b&//CqD!T?DE":tUC@@@ BJJLL"**,,7777%	8 	8r@   c                 
   d}d}t          j        |          }d|d<   d|d<   t          ||          }t           j                            d           t          j        ||          }t           j                            d           |                                }t           j                            d           t           j                            d          }t           j        t           j                            |dz
            t           j                            |d	z
            t           j                            |          f         dz  }t          j	        |          }	||	t          j
        |d
          <   t           j                            |          }
t           j                            |	j        |
j                  j        }t          j        ||j                  }t!          ||           t!          ||           d S )NrG   r#  rG  r   r  iHG	 r~   rF   r
   re   r  )r7   rO   r   r   r   r   r   r  r  rn   r  r   r   solver   r	  r   )rT   r   r  rI  r  iw_rvsfrozen_iw_rvsr  r  rt   r  Lmanual_iw_rvss                r>   test_invwishart_2D_rvsz%TestInvwishart.test_invwishart_2D_rvs'  s    sc
c
 E"" 		vE**
	v 		vi&&A&..EI1%%I1%%I##%
 		 GI(3"/#
$
$
$% Iu%%IOOAC%%'q!# 	...}55555r@   c                 v   d}d}dD ]0}t          j        t          j        |          dz             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }t          ||          }|                                }|                                }||z  dz  }|	                    |d	
          }	|	                    d          }
||dz   z  dz  }d|z  }t          j        d|dz  z
            }t          j        |
|z
  |z  d|          sJ 2dS )z1Test that sample mean consistent with known mean.r#   N  )r
   ra   r
   rF   re   r  rG  r   r   r   r   rO  r  N)r7   rn   r   r  r	  r   r   r   r7  r   r   ppfrb  )rT   r  sample_sizer   rI  r   	Xmean_expXvar_exp	Xmean_stdr)  	Xmean_estntests	fail_ratemax_diffs                 r>   test_sample_meanzTestInvwishart.test_sample_meanU  sR     	 	CGBIcNNQ.//E02	#q/A:M0N0NE"/#,,,-F57E**Eb%((D		IxxzzH!K/#5Ik==AAI#']A%FvIxIM 122H;Y&)3      !	 	r@   c                 z   t          j        g dg dg dg dg          }t          j        g dg dg dg dg          }d	}t          j        |||          }|j        d
         }t           j                            |          \  }}t           j                            |          \  }}t           j                            ||          }	|dz  |z  ||z  dz  t          j        d          z  z
  t          |dz  |          z
  ||z   dz   dz  |z  z
  d|	
                                z  z
  }
t          ||
           dS )zRegression test for gh-8844.)rF   r
   r   rG  )r
   rF   rG  rG  )r   rG  rG   r
   )rG  rG  r
   rF   )r  rd   rG   r
   )rd   r  ra   r
   )rG   ra   r  rF   )r
   r
   rF   r  rb   r   rF   r
   rG  N)r7   r   r   r   r9   r   r3  r  r   r1   tracer   )rT   r)  Psinuprobr  siglogdetX	logdetPsir   r.  s              r>   test_logpdf_4x4zTestInvwishart.test_logpdf_4x4p  sa   Hnnn&&&$nn&&&( ) ) h$$$& ' '  B,,GAJy((++W**3//YIOOAs##T9$!tAvrvayy()"2a4++, Avz1nW,- !''))m	$
 	h'''''r@   N)r   r   r   r_  r  r  r#  r,  r   r@   r>   r
  r
    se        E E E@8 8 8B,6 ,6 ,6\  6( ( ( ( (r@   r
  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestSpecialOrthoGroupc                 R   t           j                            d           t          j        d          }t          j        g dg dg dg          }t          ||           t           j                            d          }t          j        d|          }t          ||           d S )N  rG   )g(fg^A.g*B?)g:d?g2ugi}?)gR#xlF?g^`D?g?r   r   )r7   r   r   r   r   r   r   r  )rT   rZ   r.  r   s       r>   test_reproducibilityz*TestSpecialOrthoGroup.test_reproducibility  s    
	s#A&&8CCCBBBAAAC D D 	"!X...y,,#,66#ALAAA!!X.....r@   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        d           d S Nr  r
   r   )r   rL   r   r   rT   s    r>   test_invalid_dimz&TestSpecialOrthoGroup.test_invalid_dim  s`    j"5"94@@@j"5"96BBBj"5"91===j"5"93?????r@   c                     d}t          |          }|                    d          }t          j        |d          }t          ||           d S )Nrd   r   r   )r   r   r   )rT   r   r  r  r  s        r>   test_frozen_matrixz(TestSpecialOrthoGroup.test_frozen_matrix  sR    $S))zztz,,"&s>>>T4     r@   c                    d t          dd          D             }d |D             }t          |dgdz  d           |D ]G}t          t          j        ||j                  t          j        |j        d	                              Hd S )
Nc                 Z    g | ](}t          d           D ]}t          j        |          )S r  )r  r   r   .0r   r@  s      r>   
<listcomp>z<TestSpecialOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  sN     ! ! !Qxx! ! "%c** ! ! ! !r@   rF   r  c                 L    g | ]!}t           j                            |          "S r   r7   r   r2  r;  rZ   s     r>   r<  z<TestSpecialOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  s&    ---Q	a  ---r@   r      vIh%<=r;  r   )r  r   r   r7   r	  r   rO   r9   )rT   r  detsrZ   s       r>   test_det_and_orthoz(TestSpecialOrthoGroup.test_det_and_ortho  s    ! !q! ! !
 .-"---rd2gE2222  	: 	:A%bfQnn&(fQWQZ&8&8: : : :	: 	:r@   c                    d}d}d}t           j                            d           t          j        ||          dfdD             fdD             }fd	|D             }t          |gt          |          z  |           d S )
Nra   r&  皙?r0  r~   rM  r  )r
   rc   r  c                 X    i | ]$\  ft          fd D                       %S )c                 ,    g | ]}|                  S r   r   r;  rZ   ecers     r>   r<  z>TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>  !    !8!8!8!B%)!8!8!8r@   sortedr;  rJ  rK  r  s    @@r>   
<dictcomp>z3TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>  E    LLLfb"R&!8!8!8!8!8R!8!8!899LLLr@   c                 .    g | ]}D ]}||k    ||fS r   r   r;  e0e1elss      r>   r<  z3TestSpecialOrthoGroup.test_haar.<locals>.<listcomp>  .    AAAb#AABb"br@   c                 Z    g | ]'\  }}t          |         |                   d          (S r  r   r;  p0p1projs      r>   r<  z3TestSpecialOrthoGroup.test_haar.<locals>.<listcomp>  4    JJJRHT"XtBx003JJJr@   )r7   r   r   r   r   r   r   	rT   r   r  ks_probpairsks_testsrV  r]  r  s	         @@@r>   	test_haarzTestSpecialOrthoGroup.test_haar  s     
	s $Sw777 +LLLLLLLAAAACAAAJJJJEJJJ7)CJJ.99999r@   N)r   r   r   r1  r5  r7  rC  rc  r   r@   r>   r.  r.    sb        
/ 
/ 
/@ @ @! ! !: : :: : : : :r@   r.  c                       e Zd Zd Zd Zd Zd Zej        	                    dg d          d             Z
d Zej        j        d	             Zd
S )TestOrthoGroupc                 p   d}t           j                            |           t          j        d          }t          j        d|          }t          t           j                            |          d           t          j        g dg dg dg          }t          ||           t          ||           d S )Nr0  rG   r   re   )gm?gӠh"gEo?)g~7ݲC?g>Ŀg0J_ٿ)gݱ&ǿg 6qrg`X|[)
r7   r   r   r   r   r   r   r2  r   r   )rT   r   rZ   r   r.  s        r>   r1  z#TestOrthoGroup.test_reproducibility  s    
	tOA_QT222BIMM!,,b1118<<<======? @ @ 	"!X...!"h/////r@   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        d           d S r3  )r   rL   r   r   r4  s    r>   r5  zTestOrthoGroup.test_invalid_dim  sX    j+/4888j+/6:::j+/1555j+/377777r@   c                    d}t          |          }t          |d          }|                    d          }t          j        |d          }|                    d          }t          ||           t          ||           d S )Nrd   r   r   r   r
   r~   )r   r   r   rT   r   r  frozen_seedr  r  rvs3s          r>   r7  z!TestOrthoGroup.test_frozen_matrix  s    S!!!#D111zztz,,s666A&&T4   T4     r@   c           	         d t          dd          D             }t          j        d |D                       }t          t          j        |          t          j        |j                  d           |D ]L}|D ]G}t          t          j        ||j	                  t          j
        |j        d                              HMd S )Nc                 F    g | ]fd t          d          D             S )c                 8    g | ]}t          j                  S r   )r   r   )r;  r@  r   s     r>   r<  z@TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>.<listcomp>  s3     # # # s## # # #r@   r#  )r  )r;  r   s    @r>   r<  z5TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  sP     & & &# # # #b		# # # & & &r@   rF   r  c                 &    g | ]}d  |D             S )c                 L    g | ]!}t           j                            |          "S r   r>  r?  s     r>   r<  z@TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>.<listcomp>  s&    777q")--**777r@   r   )r;  xxs     r>   r<  z5TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  s'    EEEB77B777EEEr@   rA  r;  r   )r  r7   r   r   fabsrN   r9   r   r	  r   rO   )rT   r  rB  rq  rZ   s        r>   rC  z!TestOrthoGroup.test_det_and_ortho  s    & &q& & &
 xEE"EEEFFrwtz':':GGGG  	> 	>B > >)"&AC..*,&*<*<> > > >>	> 	>r@   r   )rF   ra   r#  r  c                    t           j                            d          }t          |          }|                    d|          }t
          j                            |          }t          j        |dk              }t          |          }t          j        ||          }|                    d          \  }	}
|	dcxk     r|
k     sn J d S )	Nl   <`Lr r   r  r   r   gffffff?)confidence_levelrG  )r7   r   r   r   r   r   r   r2  r   r   r-   	binomtestproportion_ci)rT   r   r   r   r   rB  r  r   r:   lowhighs              r>   test_det_distribution_gh18272z,TestOrthoGroup.test_det_distribution_gh18272  s     i##$788s###hhDsh33|$$F4!8IIoa##%%t%<<	TS4r@   c                    d}d}d}t           j                            d           t          j        ||          dfdD             fdD             }fd	|D             }t          |gt          |          z  |           d S )
Nra   r&  rE  i  r~   rF  c                 X    i | ]$\  ft          fd D                       %S )c                 ,    g | ]}|                  S r   r   rI  s     r>   r<  z7TestOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>!  rL  r@   rM  rO  s    @@r>   rP  z,TestOrthoGroup.test_haar.<locals>.<dictcomp>!  rQ  r@   c                 .    g | ]}D ]}||k    ||fS r   r   rS  s      r>   r<  z,TestOrthoGroup.test_haar.<locals>.<listcomp>"  rW  r@   c                 Z    g | ]'\  }}t          |         |                   d          (S r  rY  rZ  s      r>   r<  z,TestOrthoGroup.test_haar.<locals>.<listcomp>#  r^  r@   )r7   r   r   r   r   r   r   r_  s	         @@@r>   rc  zTestOrthoGroup.test_haar  s     
	s_Sw/// +LLLLLLLAAAACAAAJJJJEJJJ7)CJJ.99999r@   c                 8   t           j                            d           d }t          dd          D ]ed	fd	} ||          } |t          j        j        j                  }t          j                            ||          \  }}t          d|           fd S )
Nr0  c                     t           j                            t           j                            | | f                    \  }}}t          j        ||          S Nr~   )r7   r   r   r   r   r	  )r   r   _sr   s       r>   random_orthoz<TestOrthoGroup.test_pairwise_distances.<locals>.random_ortho+  sB    y}}RY%5%5C:%5%F%FGGHAr16!Q<<r@   rF   rb   r&  r  c                      t          j         fdt          |          D                       }|t           j                            | ||j                  z  }|S )Nc                 l    g | ]0}t          j                                z
  dz            1S )rt  rF   )r7   r   )r;  r   r   r   s     r>   r<  z\TestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statistics.<locals>.<listcomp>1  sQ     " " " FCCCLLL333<<<7!;<<" " "r@   r~   )r7   r   r  r   r   r9   )r   r  epsr-   r   s   `   r>   generate_test_statisticszHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statistics0  sr     " " " " ""1XX" " "  
 **C45;*GGGr@   rE  )r&  r  )
r7   r   r   r  r   r-   r   r   r   r   )rT   r  r  r.  rB  _Dr  r   s          @r>   test_pairwise_distancesz&TestOrthoGroup.test_pairwise_distances&  s     		s	  	  	  A;; 	& 	&C      0/==H--ek.E.IJJFK((6::EBc1%%%%	& 	&r@   N)r   r   r   r1  r5  r7  rC  rK   r   r   rz  rc  slowr  r   r@   r>   re  re    s        0 0 08 8 8
! 
! 
!> > > [UNNN33
  
  43
 : : :6 [& & & & &r@   re  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestRandomCorrelationc                    t           j                            d           d}t          j        |          }t          j        |d          }t          j        g dg dg dg dg          }t          ||           t          ||           d S )Nr0  rG  rh  rE  r   r   )r   ѓ2ǿA?Ϳ)r  r   4($?R}%?)r  r  r   qTnƿ)r  r  r  r   )r7   r   r   r   r   r   r   )rT   r  rZ   r   r.  s        r>   r1  z*TestRandomCorrelation.test_reproducibilityB  s    
	s!"4((#Ds;;;8AAA@@@@@@AAAC D D 	"!X...!"h/////r@   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        dg           t          t          t          j        ddgddgg           t          t          t          j        ddg           t          t          t          j        g d           d S )	Ntestr   r
   rF   rG   rc   g      )r
   rF   r   )r   rL   r   r   r4  s    r>   test_invalid_eigsz'TestRandomCorrelation.test_invalid_eigsN  s    j"4"8$???j"4"8&AAAj"4"8#>>>j"4"83%@@@j"4"8Aa5!A-HHHj"4"83*EEEj"4"8***EEEEEr@   c                 
   d}t          |          }t          |d          }t          j        |d          }|                    d          }|                                }t          ||           t          ||           d S )Nr  r0  r   r   )r   r   r   )rT   r  r  rj  r  r  rk  s          r>   r7  z(TestRandomCorrelation.test_frozen_matrixW  s    !#D))(C888!%d===zzsz++  T4   T4     r@   c                   
 d 
t           j                            d           
fdt          dd          D             }|                    g d           d |D             }d |D             }d	 |D             }d
 |D             }t          ||dd           d |D             }t          ||          D ]\  }}t          ||d           |D ]}	t          |	|	j        d           d S )Nc                 ,    | |z  t          |          z  S r6   )r   )r@  r|  s     r>   r   z3TestRandomCorrelation.test_definition.<locals>.normk  s    Q3s1vv:r@   r  c                 d    g | ],} |t           j                            |                     -S )r~   )r7   r   r   )r;  r@  r   s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>p  s8    HHHqQ	))q)1122HHHr@   rF   rb   )rc   r   r   r   c                 4    g | ]}d gt          |          z  S )r   )r   r;  r|  s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>s  s$    ***SVV***r@   c                 6    g | ]}t          j        |          S r   )r   r   r  s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>t  s$    666A $Q''666r@   c                 p    g | ]3}t          j        t           j                            |                    4S r   )r7   rr  r   r2  r?  s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>z  s0    666a	a(())666r@   c                 6    g | ]}t          j        |          S r   )r7   prodr  s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>{  s     ///Qbgajj///r@   rA  rP  c                 6    g | ]}t          j        |          S r   )r7   rn   r?  s     r>   r<  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>  s     ((((((r@   r;  )r7   r   r   r  rz  r   zipr   )rT   r  rN   r  rB  
dets_knowndiagsr  r  rZ   r   s             @r>   test_definitionz%TestRandomCorrelation.test_definitionc  sC   	 	 	 		sHHHHE!QKKHHHIII**T***66666 762666//$///
ju5AAAA )(R(((t$$ 	. 	.DAqAqu-----  	0 	0AAqs/////	0 	0r@   c           	         t          j        ddgddggt                    }t          j        |          }t          |t          j        ddgddgg                     t          j        d          5  t          j        ddgddgg          }t          j        ddgdt          j        dd          ggt                    }t          j        |                                          }t          ||j	        
                    |          
                    |                     t          j        d	dgdd
ggt                    }t          j        |                                          }t          ||j	        
                    |          
                    |                     d d d            n# 1 swxY w Y   t          j        ddgddggt                    }t          j        |                                          }t          |d         d           t          j        ddgddggt                    }t          j        |                                          }t          |d         d           d S )Nr   r   r
   r-  ignore)overre   gu <7~rF  rT  rF   rM  gMk   @)r7   r   r0  r   _to_corrr   errstate	nextaftercopyr   r	  )rT   r  gm0s       r>   test_to_corrz"TestRandomCorrelation.test_to_corr  sU    HsAhA'u555'**28aVaX$677888
 [h''' 		3 		31a&2q'*++AE1:2<1+=+='>?uMMMB"+BGGII66AAqswwr{{q11222C<%6eDDDB"+BGGII66AAqswwr{{q11222		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 X1v1v&e444'		22#""" X!}q!f-U;;;'		22#"""""s   3D2F11F58F5N)r   r   r   r1  r  r7  r  r  r   r@   r>   r  r  A  sc        
0 
0 
0F F F
! 
! 
!"0 "0 "0H# # # # #r@   r  c                   >   e Zd Zej                            dddg          ej                            dg d          d                         Zej                            dg d          d             Zd	 Zej                            dg d
          d             Z	dS )TestUniformDirectionr   r
   rG   r   Nr
   ra   )ra   rc   c                    t           j                            d          }t          ||          }|                    |          }t          j        |          t          j        |          }}|                    |||          j        }|j        |k    sJ t           j	        
                    |d          }	t          |	d           d S )N   Sid)_i4 r   r~   re   r   r   )r7   r   r   r'   r   r   rO   r   r9   r   r   r   )
rT   r   r   r   uniform_direction_distr  r   r   expected_shapenormss
             r>   r/  z!TestUniformDirection.test_samples  s     i##$788!23S!A!A!A(,,T22HSMM26#;;c00s0FFL}....	wR00r"""""r@   )Nr   r  r   c                     d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )NzMDimension of vector must be specified, and must be an integer greater than 0.rD   )rK   r	   rL   r'   r   )rT   r   rU   s      r>   r5  z%TestUniformDirection.test_invalid_dim  s    <]:W555 	' 	'!#&&&	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	's   A  AAc                 
   d}t          |          }t          |d          }|                    d          }t          j        |d          }|                                }t          ||           t          ||           d S )Nra   r0  r   r   )r'   r   r   ri  s          r>   test_frozen_distributionz-TestUniformDirection.test_frozen_distribution  s    "3'''#666zzsz++ $Ss;;;  T4   T4     r@   )rF   ra   r  c                 (   t           j                            d          }t          ||          }|                    d          \  }}|||z  |z  z  }|t           j                            |          z  }t          ||z  dd           |                    d          }||z  }||z  }t          j        ||          }	|	t           j	        z  }	|	dt           j	        z  z  }	t                      }
t          |	|
j                  }|j        d	k    sJ d S )
Nl   @9Y sr   rF   r~   r   r  r  '  rE  )r7   r   r   r'   r   r   r   r   arctan2r  r   r    r   pvalue)rT   r   r   spherical_distv1v2r  s1s2anglesuniform_distkstest_results               r>   test_uniformz!TestUniformDirection.test_uniform  s   i##$788*3S999###++B
b2gl
binnR   R//// $$%$00r\r\B## 	"%!BE'yyv|'788#d******r@   N)
r   r   r   rK   r   r   r/  r5  r  r  r   r@   r>   r  r    s        [UQF++[V%9%9%9::	# 	# ;: ,+	# [U$:$:$:;;' ' <;'
! 
! 
! [UIII..+ + /.+ + +r@   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestUnitaryGroupc                    t           j                            d           t          j        d          }t          j        dd          }t          j        g dg dg dg          }t          ||           t          ||           d S )Nr0  rG   r   )y~p?yZ?y뉦?ĭ?y8Z?&4?)yEHξr?8i?ye??+ݓݿyu=ٿB۽'?)yqXQÿ?yN6ҿzܷy! 8l?2W'?)r7   r   r   r   r   r   r   )rT   rZ   r   r.  s       r>   r1  z%TestUnitaryGroup.test_reproducibility  s    
	sa  qs3338IIIHHHKKKM
 
 	"!X...!"h/////r@   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        d           d S r3  )r   rL   r   r   r4  s    r>   r5  z!TestUnitaryGroup.test_invalid_dim  s\    j-"3T:::j-"3V<<<j-"3Q777j-"3S99999r@   c                    d}t          |          }t          |d          }|                    d          }t          j        |d          }|                    d          }t          ||           t          ||           d S )Nrd   r0  r   r   r
   r~   )r   r   r   ri  s          r>   r7  z#TestUnitaryGroup.test_frozen_matrix  s    s###Cc222zzsz++ 3777A&&T4   T4     r@   c                     d t          dd          D             }|D ][}t          t          j        ||                                j                  t          j        |j        d                   d           \d S )Nc                 Z    g | ](}t          d           D ]}t          j        |          )S r  )r  r   r   r:  s      r>   r<  z3TestUnitaryGroup.test_unitarity.<locals>.<listcomp>	  sN     ! ! !Qxx! ! $$ ! ! ! !r@   rF   r  r   r  r  )r  r   r7   r	  conjr   rO   r9   )rT   r  rZ   s      r>   test_unitarityzTestUnitaryGroup.test_unitarity	  s    ! !q! ! !
  	S 	SABF1affhhj1126!'!*3E3EERRRRR	S 	Sr@   c                    d}d}t           j                            d           t          j        ||          }t          j        d |D                       }t          j        |j        |j                  }t          |
                                t          t           j         dt           j        z            j                  }t          |j        dk               d S )Nra   r&  r0  r~   c                 L    g | ]!}t           j                            |          "S r   )r   r   eigvalsr?  s     r>   r<  z.TestUnitaryGroup.test_haar.<locals>.<listcomp>	  s(    >>>a%,..q11>>>r@   rF   rE  )r7   r   r   r   r   ry  r  imagrealr    ravelr   r  r   r   r  )rT   r   r  r  r  rZ   r:   s          r>   rc  zTestUnitaryGroup.test_haar	  s    
 
	ss111 y>>2>>>??Jty$),,QWWYY"% 8 8 <==
T!"""""r@   N)r   r   r   r1  r5  r7  r  rc  r   r@   r>   r  r    sb        0 0 0: : :
! 
! 
!S S S# # # # #r@   r  c                      e Zd Zddgddgddgddgddgddgddgddgddgddgg
ddgddgddggdg dfg dg d	g d
g dg dgg dg dg dg dgdg dfgZej                            de          d             Zej                            de          d             Zd Z	d Z
 ed          d             Zd Zd ZdddddgddggdddgddgddggdfdddgddggdddgddgddggdfddgddddgddgddggdfddgddddgddgddggdfddgddgddggdddgddgddggdfddgddgddggdddgddgddggdfgZej                            d e          d!             Zd"ddd"gdggdfd"gdgdd"gdggdf ej        d"g           ej        dg          dd"gdggdfgZej                            d e          d#             Zd$ Zd% Zd& Zej                            d'd(d)g          ej                            d*g d+          ej                            d,d-d.ej        g          d/                                     Zd0 Zej                            d*g d1          d2             Zej                            d*g d3          d4             ZdTd6Zd7 Zej                            d*g d8          ej                            d9g d:          ej                            d;d5d<g          d=                                     Zej        j         d>             Z!d? Z"d@ Z#dA Z$ej                            d*dB          dC             Z%dD Z&ej                            d,g dE          dF             Z'ej                            dGdH ej(        dd          dIdJfdK ej        dLdgddHgg          dMdNfg          dO             Z)ej                            dPg dQ          dR             Z*dS Z+dS )UTestMultivariateTr
   rF   rc   rG   ra   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?)re   r
   2   )r   rG  rZ  )rG  r   rQ  )rZ  rQ  r   r  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 v    t          |||d          }|                    |          }t          ||           d S Nr   r   )r#   r   r   )rT   rZ   rN  r9   r  ansr   vals           r>   test_pdf_correctnessz&TestMultivariateT.test_pdf_correctnessf	  s=    c5"1555hhqkk!#s+++++r@   c                     t          |||d          }|                    |          }|                    |          }t          t	          j        |          |           d S r  )r#   r   r   r   r7   r   )	rT   rZ   rN  r9   r  r  r   r  r  s	            r>   test_logpdf_correctz%TestMultivariateT.test_logpdf_correctl	  sT    c5"1555xx{{{{1~~!"&,,55555r@   c                     g d}t          j        |d          }t          j        |          }t          ||           d S )N)
r  rd   rc   r
   r  r   r  re   rG   r
   r  )r#   r   r$   r   )rT   rZ   r  r  s       r>   test_mvt_with_df_one_is_cauchyz0TestMultivariateT.test_mvt_with_df_one_is_cauchyt	  sE    --- q)))jmm!#s+++++r@   c                 J   d}t          dddd          }|                    d          }t          |          \  }}||k    sJ t          ddgd	d
gd
d	ggdd          }|                    d          }t          |          \  }}||k                                    sJ d S )Nr   r   r
   順 r  r   r~   rh   rG   r#  re   *   )r#   r   r%   r%  )rT   	P_VAL_MINr   r  r   r  s         r>   &test_mvt_with_high_df_is_approx_normalz8TestMultivariateT.test_mvt_with_high_df_is_approx_normalz	  s    
 	avA666((('''""1Ir1gR2r(';#%' ' '((('''""1Y##%%&&&&&r@   z'scipy.stats.multivariate_normal._logpdfc                 "   t          ddt          j        d          }t          |t                    sJ t          j        dt          j                   |j        dk    sJ t          j        dt          j                   |j        dk    sJ d S )Nr   r
   rd   r  r  rF   )r#   r7   r  r   r   r   
call_countr   )rT   mockr   s      r>   !test_mvt_with_inf_df_calls_normalz3TestMultivariateT.test_mvt_with_inf_df_calls_normal	  s    arvA666$ :;;;;;1((((!####aBF++++!######r@   c                    d}t          j        |          }t          j        |          }d}t          j        |          }t          |||                              |          }t          j        |          sJ t          |||                              |          }t          j        |          sJ d}t           j                            ||f          }t          |||                              |          }|j        |fk    sJ t          |||                              |          }|j        |fk    sJ t          t          j        d          t          j        d          d          	                                }t          j        |          sJ d}t          t          j        d          t          j        d          d          	                    |          }|j        |fk    sJ d S )Nrc         @rd   r
   r~   )
r7   r   rO   r#   r   isscalarr   r   r9   r   )	rT   r   rN  r9   r  rZ   r:   	n_samplesr   s	            r>   test_shape_correctnessz(TestMultivariateT.test_shape_correctness	  s    hsmmsHSMMS%,,0033{3S%,,33A66{3 	Ii-..S%,,0033	i\))))S%,,33A66	i\)))) RXa[["&))Q77;;=={3 RXa[["&))Q77;;;FF	dW$$$$$$r@   c                     t                      }t          |j        dg           t          |j        dgg           |j        dk    sJ d S )Nr   r
   r#   r   rN  r9   r  )rT   r   s     r>   test_default_argumentsz(TestMultivariateT.test_default_arguments	  sJ    TXs###TZ1#'''1r@   )NNNr   r
   r
   )NNrd   r   r
   rd   Nrd   z*loc, shape, df, loc_ans, shape_ans, df_ansc                     t          |||          }t          |j        |           t          |j        |           |j        |k    sJ d S )NrN  r9   r  r  rT   rN  r9   r  loc_ans	shape_ansdf_ansr   s           r>   test_default_argsz#TestMultivariateT.test_default_args	  sU     #Ur:::TXw'''TZ+++6!!!!!!r@   re   c                     t          |||          }t          |j        |           t          |j        |           t          |j        |           d S r6   r  r  s           r>   &test_scalar_list_and_ndarray_argumentsz8TestMultivariateT.test_scalar_list_and_ndarray_arguments	  sQ     c5"--TXw'''TZ+++TWf%%%%%r@   c           	         ddgg}t          t          t          fi t          |           ddgddgddgg}t          t          t          fi t          ||           t	          j        d          }t	          j        d          }d}t          t          t          fi t          |||           d}t          t          t          fi t          |||           d S )	Nr
   )rN  rF   rG   )rN  r9   re   r  r   )r   rL   r#   dictr7   r   rO   )rT   rN  r9   r  s       r>   test_argument_error_handlingz.TestMultivariateT.test_argument_error_handling	  s   1vhj$	' 	'	' 	' 	'
 Q!Q!Q(j$	4 	4E222	4 	4 	4
 hqkkq		j$	; 	;Eb999	; 	; 	; j$	; 	;Eb999	; 	; 	; 	; 	;r@   c                 \   t           j                            d          }|                    d          }t          j        d          }t          ||dd          }t          ||dd          }|                    d          }|                    d          }t          ||           d S )Nrc   rG   r~   rF   r  r#  )r7   r   r  r   rO   r#   r   r   )rT   r   rN  r9   r   dist2samples1samples2s           r>   r1  z&TestMultivariateT.test_reproducibility	  s    i##A&&kkqk!!q		sEaa888sEaa88899"9%%99"9%%Xx(((((r@   c                     t          ddgddgddggdd          }t          t          j        j        t
          fi | d S )Nr   r
   F)rN  r9   r  rY   )r  r   r7   r   r{  r#   )rT   r<   s     r>   test_allow_singularz%TestMultivariateT.test_allow_singular 
  sK    1qeQqE]qOOObi+^DDtDDDDDr@   r   )r#  rG   )ra   rb   rc   rG   r   )rF   rG   rc   ra   r  r   r=  c                     t          t          j        |          t          j        |          |          }|                    |          }|j        ||fz   k    sJ d S r  )r#   r7   r   rO   r   r9   )rT   r   r   r  r   r   s         r>   test_rvszTestMultivariateT.test_rvs
  sW     bhsmmRVC[["==hhDh!!yDC7N******r@   c                 "   t          j        d          }t          j        d          }d}g dg dg dg dg}g dg dg dg dg}t          j        g d          }t	          j        |||||          }t          ||d	         |z             d S )
NrG   r#  r  rf   r  r  r  r  r   r  )rT   r   r   r  r  r  r  r   s           r>   r  z TestMultivariateT.test_cdf_signs
  s    x{{fQiiYY			999iii8YY			999iii8...11!%asBAFFFSVN233333r@   )r
   rF   ra   c                 0    |                      |           d S r6   cdf_against_mvn_testrT   r   s     r>   $test_cdf_against_multivariate_normalz6TestMultivariateT.test_cdf_against_multivariate_normal
  s     	!!#&&&&&r@   )rG   rb   r  c                 2    |                      dd           d S )NrG   Tr  r  s     r>   -test_cdf_against_multivariate_normal_singularz?TestMultivariateT.test_cdf_against_multivariate_normal_singular
  s      	!!!T*****r@   Fc           	      d   t           j                            d          }d}d|                    dd|          z  }t	          ||||          }d|                    dd|          z  t          j        |                    |                    z  }d|                    dd||f          z   |z   }d|                    dd||f          z  |z   }	t          j        	                    |	||d	|d
|          }
t          j
        	                    |	||d
|          }t          |
|d           d S )N   ]J>?a rG   r#  rh   r
   r~   re   rF   r  T)r  r  rY   r   )rY   r  Mb@?r  )r7   r   r   r   r   signr   r-   r#   r   r   r   )rT   r   r   r   r   r  r   r   r  r  r:   r;   s               r>   r  z&TestMultivariateT.cdf_against_mvn_test#
  sB   i##O44B,,, ah773;;r13;///"'#**#*:N:N2O2OOR!S2222T9BC111D8"&&q$16: ' N N'++AtS89 , ; ;St,,,,,,r@   c                 R   t           j                            d          }d}d}|                    dt          j        |                    }d}t
          j                            ||||t           j         |          }t
          j	                            |||t          j        |                    }t
          j
                            ||t          j        |                    }t          ||d	           t          j        t          j        ||z
            d
k              sJ d S )Nr  rF   r   r#  )r   rI  rG   )r  r   r  r  r:  )r7   r   r   r   sqrtr-   r#   r   r  tr   r   r%  r   )	rT   r   r   r   rZ   r  r:   r;   	incorrects	            r>   test_cdf_against_univariate_tz/TestMultivariateT.test_cdf_against_univariate_t5
  s    i##O44JJBbgcllJ33"&&q$RbfW47 ' 9 9gkk!Rrws||44JNN1dBGCLL99	St,,,,vbfS9_--45555555r@   )rF   rG   ra   r#  r   )   no l   m, l   sO l   U iOfYl   O_ r   Tc           	         |r|dk    rt          j        d           t          j                            |          }d|                    dd|          z  }t          ||||          }|                    |          }|                    |           }|                    |          }	|                                dz  }
t          j        	                    |	|||
|d	          }t          j
        d
          5  t          d|
|t          j        |z  |	|z
  |          d         }d d d            n# 1 swxY w Y   t          ||dd           t          j        	                    |	|||
||d          }t          j
        d
          5  t          d|
|||z
  |	|z
  |          d         }d d d            n# 1 swxY w Y   t          ||dd           d S )Nr   z4Agreement with qsimvtv is not great in singular caser#  rh   rF   r~   ra   T)r   rY   r  )invalidr  r   g-C6*?r:  rQ  r<  )r  r   rY   r  )rK   r   r7   r   r   r   r   r-   r#   r   r  r3   r  r   )rT   r   r   r   r   r  r   r   r  r  r  r:   r;   s                r>   test_cdf_against_qsimvtvz*TestMultivariateT.test_cdf_against_qsimvtvD
  sz   
  	P
**KNOOOi##D))B,,, ah77zz#ZZ__JJsOOZZ\\A "&&q$Rc6: ' < <[*** 	G 	G5"c26!8QXsCCAFC	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	GSt$7777 "&&q$RQ47 ' N N[*** 	G 	G5"c1t8QXsCCAFC	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	GSt$777777s$   :+D11D58D5
!F77F;>F;c           
        	
 d}t           j                            d          }d|                    dd|          z  }t	          |||d          	|                    |          |                    |           }|                    |          }|                                d	z  
t
          j                            |	
||
          }	
fd}t          |||t
          j	        
                    ||                    }t          ||j        d           	
fd}t          ||d         |d         |d         |d         |d         |d                   }t          ||d         d           d S )NrG   l   	!y r#  re   r
   r~   T)r   ra   )r   r  c                 R    t           j                            | j                  S r6   )r-   r#   r   r   )rZ   r   r  r   s    r>   	integrandzITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrandp
  s"    '++ACsB???r@   )r  r   )qrngr:  r;  c                  Z    t           j                            | d d d                   S )Nre   )r-   r#   r   )zyxr   r  r   s    r>   r'  zITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrandv
  s*    '++C"ItS"EEEr@   r   rF   )r7   r   r   r   r   r-   r#   r   r/   qmcHaltonr   integralr0   )rT   r   r   r  r  r  r:   r'  r;   r   r  r   s            @@@r>   $test_cdf_against_generic_integratorsz6TestMultivariateT.test_cdf_against_generic_integratorsa
  s    i##N33#++b!#+... at<<<zz#ZZ__JJsOOZZ\\A"&&q$Rc34 ' 6 6	@ 	@ 	@ 	@ 	@ 	@ 	@ y!QUY-=-=#-=-N-NOOOS\5555	F 	F 	F 	F 	F 	F 	F i1qtQqT1Q41qtDDSV$//////r@   c                    t           j                            d          }t          j        g dg dg dg          }d}t	          j        ||          }|                    g d|          }d	}t          ||d
           d S )Nl   Ja )go!@S<?^Ss@)r0  gRP=@jT0@)r1  r2  gk`-3@gWK?r9   r  rf   r   g1%?r:  r;  )r7   r   r   r   r-   r#   r   r   )rT   r   r   r  r   r:   r;   s          r>   test_against_matlabz%TestMultivariateT.test_against_matlab|
  s     i##J//h?????????A B B  ##"555hhyyysh33St,,,,,,r@   c                 
   d}t           j                            |          }|                    d          }|                    d          |z   }t          j        d          }|                                }|||f}t           j                            |          }t           j                            |          }	t          j        |d|i}
t          |
                    |          t          j        |g|R d|	i           d S )Nl   2m rG   r~   r   r   )	r7   r   r   r   rO   r-   r#   r   r   )rT   r   r   rN  rZ   r9   r  r<   
rng_frozenrng_unfrozenr   s              r>   r_  zTestMultivariateT.test_frozen
  s    i##D))kkqk!!KKQK#%q		ZZ\\UBY**400
y,,T22#T;
;;TXXa[[#'LDLLL|LL	N 	N 	N 	N 	Nr@   c                   	
 d}d}t           j                            d                              ||f          }||j        z                      |          
                    ||fz             }                                dz  	t          j                            |
	          }	
fd}t          j        |d|          }t          ||d	d
           d S )Nrc   r  r  r~   ra   r   c                 Z    t          dt          j         | z  | z
            d         S )Nr  r   )r3   r7   r  )rZ   r   r  r   r   s    r>   _cdf_1dz2TestMultivariateT.test_vectorized.<locals>._cdf_1d
  s,    E2sRVGAIqvsCCAFFr@   re   r  r:  r#  )	r7   r   r   r   r-   r#   r   apply_along_axisr   )rT   r   r   rt   rZ   r:   r:  r;   r   r  r   r   s           @@@@r>   test_vectorizedz!TestMultivariateT.test_vectorized
  s   i##O44JJS#JJ''!#gzz#JJqC6z""ZZ\\A"&&q$Rc&JJ	G 	G 	G 	G 	G 	G 	G 	G !'2q11St$777777r@   r]  c                 *   t           j                            d          }t          j                            dgdg|dz
  z  z             }t          j        |                              dg|z  |          }d|dz   z  }t          ||d	           d S )
Nr  r
   rG  )r  )r9   r   r   g-C6
?r;  )
r7   r   r   r   r   toeplitzr-   r#   r   r   )rT   r   r   rt   r:   r;   s         r>   test_against_analyticalz)TestMultivariateT.test_against_analytical
  s    i##O44L!!QC3%37*;$;!<<"+++//c	/LL37mSt,,,,,,r@   c                     t          j        dd          }t           j        }t          j                            ||          }t          j                            d |          }||k    sJ d S )NrG   r3  )r7   rO   r  r-   r#   r   r   )rT   r   r  mvt_entropymvn_entropys        r>   test_entropy_inf_dfz%TestMultivariateT.test_entropy_inf_df
  sb    fQllV*222DD/77cBBk))))))r@   )r
   r#  r,  c                     t           j                            d|          }t           j                            |          }t	          ||d           d S )Nr   r3  r  rA  r;  )r-   r#   r   r  r   )rT   r  rA  	t_entropys       r>   test_entropy_1dz!TestMultivariateT.test_entropy_1d
  sM    *222CCGOOrO**	YU;;;;;;r@   zdf, cov, ref, tolr#  g}M@r  r,  rG  gNfh@r  c                     t          j        d          }t          j        |||          }t	          |                                ||           d S )Nra  r;  )r7   r   r-   r#   r   r   )rT   r  r   r;   tolrN  mvts          r>   %test_entropy_vs_numerical_integrationz7TestMultivariateT.test_entropy_vs_numerical_integration
  sH    
 huoo"3R00s555555r@   zdf, dim, ref, tol))r#  r
   gDdVW?r  )r,  r
   gU?rA  )r  r
   g/+?r  )@xDr
   Z_2?r  )}Ô%ITr
   rL  r  )r#  r#  gzg#.@r  )r&  r#  gD:f,@rA  )rK  r#  1>`,@r  )rM  r#  rN  r  )r#  r,  g8d?b@r  )r&  r,  g-YҺa@r  )rK  r,  ZGra@r  )rM  r,  rO  r  c                     t          j        t          j        |          |          }t	          |                                ||           d S )Nr3  r;  )r-   r#   r7   rO   r   r   )rT   r  r   r;   rH  rI  s         r>   test_extreme_entropyz&TestMultivariateT.test_extreme_entropy
  sE    F "<<<s555555r@   c                    t          j        g dg dg dg dg dg          }||j        z  }d}t          j                            ||          }t          d |                                          }t          ||d	
           d}d}t          j                            ||          }t          j                            ||          }	t          ||	d
           d S )N)gQ?g
ףp=
?g\(\߿(\?gGz?)gGzg{GzgQ?rj  gQ)gQ?g)\(?gQѿg)\(ܿg(\?)g      gGzgq=
ףpg\(\?g)rS  g{Gzg\(\?g{GzԿg(\?rK  r3  rz  r  r;  i  i   rg  )r7   r   r   r-   r#   r   r   r   )
rT   _Ar   r  mul_t_entropymul_norm_entropydf1df2	_entropy1	_entropy2s
             r>   test_entropy_with_covariancez.TestMultivariateT.test_entropy_with_covariance   s    X+++---,,,,,,,,,
   24i ,44324FF.t===EEGG'7eDDDD (00ss0CC	(00ss0CC		94888888r@   F),r   r   r   	PDF_TESTSrK   r   r   r  r  r  r  r4   r  r  r  DEFAULT_ARGS_TESTSr  r7   r   ARGS_SHAPES_TESTSr  r  r1  r  r  r  r  r  r  r  r  r$  r  r.  r4  r_  r<  r?  rC  rF  rO   rJ  rQ  r[  r   r@   r>   r  r  	  s!        FFFFFFFFFF	
 
A FF	

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

4 
4 
4 [UIII..' ' /.' [UIII..+ + /.+- - - -$6 6 6 [UMMM22[V &J &J &J K K[Z%778 8 87K K 3282 [0 0 04- - -"N N N8 8 8$ [UF++- - ,+-* * * [T<<<00< < 10<& [0!626!Q<<1CUK"HBHsAhB-@$A$A/789 96 6	9 96
 [	
 	
 	
 $6 6% $6(9 9 9 9 9r@   r  c                   :   e Zd Zej                            dddgddgddfddgddgdej         fd	dgddgdej         fddgd
dgdej        fddgddggddgd
dggddgej        ej        gfd	dgd
dgdej        fddgddgdej        fddgddgdej        fddgddgdej        fddgddgdej         fg
          d             Z	d Z
d Zd Zej                            dg ddfg ddfddgdfdgdff          d             Zej                            ddgdgddfddgddgddfddgddggddgddgggddgddgddggdd gdd!ggf ej        g e"           ej        g e"          dg fddgddgddfg d#g d$d%d&fg          d'             Zej                            dddgddgdd(ggddd)gfdgdggdgdggddgd*d+gfdgdgggdgdggddgd*d+ggfdgdggdggggddgd*d+gggfg          d,             Zd- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8S )9TestMultivariateHypergeomzx, m, n, expectedrG   rc   ra   r#  rd   gr   r  r
   rF   rk   iir  r  re   ic                 V    t          j        |||          }t          ||d           d S )Ngư>r;  )r   r  r   rT   rZ   r  r   r.  valss         r>   r  z%TestMultivariateHypergeom.test_logpmf   s3    6 &,Q155hT222222r@   c                    t          j        ddgddgd          }t          j        dddd          }t          ||d	
           t          j        ddgddgd          }t          j        dddd          }t          ||d	
           d S )NrG   r
   r#  ra   rc   )rZ   r  r      )r  r   r   r  r  r;  rd      )r   r  r"   r   r  s      r>   test_reduces_hypergeomz0TestMultivariateHypergeom.test_reduces_hypergeom>  s     &)QFr1gCCC}qB!r222d....%)QFr2h"EEE}qB"333d......r@   c                     t          ddgd          }|                    dd          }t          |                    d          |                                d	
           d S )NrG   ra   rc   r  r   r&  r  r   r   rO  r;  r   r   r   r   rT   r   r   s      r>   r  z"TestMultivariateHypergeom.test_rvsI  s\     $q!f222ff$Sf11RWWYYT::::::r@   c                     t          ddgddggddg          }|                    dd	          }t          |                    d
          |                                d           d S )NrG   ra   r#  rc   r  rk  r&  rF   r  r   r   rO  r;  rl  rm  s      r>   test_rvs_broadcastingz/TestMultivariateHypergeom.test_rvs_broadcastingP  sg    #1v2w&7Aq6BBBff)#f66RWWYYT::::::r@   zm, n)r   r   r  r   r   )r   r   r   r   r   c                     t          j        ||          }t          j        |          }|                                }|||dk    <   t          ||           d S )Nr   )r   r   r7   r8   r  r   )rT   r  r   r:   res_exs        r>   test_rvs_gh16171z*TestMultivariateHypergeom.test_rvs_gh16171U  sS    
 %(A..JqMMqAvS&!!!!!r@   g zl?r  r  gQ?gE|?g
y?r-  r  )ra   rb   rd   rb   gzp?c                 V    t          j        |||          }t          ||d           d S Nrf  r;  r   r  r   rd  s         r>   r  z"TestMultivariateHypergeom.test_pmf`  s3    " &)!Q22hT222222r@   rg  g ?r   r   c                 V    t          j        |||          }t          ||d           d S ru  rv  rd  s         r>   r  z/TestMultivariateHypergeom.test_pmf_broadcastingt  s3     &)!Q22hT222222r@   c                 p    t          j        g dd          }g dg dg dg}t          ||d           d S )	N)rG   rd   r#  r  rk  )gf_?&BUп疈Cx@ؿ)ry  ggs>d?ZsK)rz  r{  g35?r  r;  r   r   r   )rT   r  r  s      r>   r  z"TestMultivariateHypergeom.test_cov  sZ    %)JJJ"===6666666668 	d......r@   c                 j   t          j        ddgddggddg          }dd	gd	dggd
dgdd
ggg}t          ||d           t          j        dgdggddg          }dggdggg}t          ||d           t          j        ddgddg          }dd	gd	dggddgddggg}t          ||d           d S )Nrd   r  r#  rg  r  r  rk  g?gg(\?g(\r  r;  rc   ra   r   g333333?g333333r|  r  s          r>   r  z/TestMultivariateHypergeom.test_cov_broadcasting  s   %)aVb"X,>1b'JJJ..0d....%)aS1#J1a&AAA"d....%)QFq"g>>>.'"Wf$568d......r@   c                     t          j        ddgd          }t          j        ddd          }t          ||d           d S )	Nr#  ra   rc   rk  rg  r   r   r  r  r;  )r   r7  r"   r   )rT   var0var1s      r>   test_varz"TestMultivariateHypergeom.test_var  sL    %)RGq999}rQ"---d......r@   c                    t          j        ddgddg          }t          j        ddgd          }t          j        ddgd          }t          |d         |d           t          |d	         |d           t          j        ddgdd
ggddg          }ddgddgg}t          ||d           t          j        dgdggddg          }dgdgg}t          ||d           d S )Nr#  ra   rc   r  rk  r   r  r;  r
   r  g̍3eY?gI{?r   )r   r7  r   )rT   r  r  var2var3var4var5var6s           r>   test_var_broadcastingz/TestMultivariateHypergeom.test_var_broadcasting  s   %)RG1v>>>%)RGq999%)RGq999QD1111QD1111%)b!Wr2h,?Aq6JJJI&8(<=d....%)aS2$KAr7CCCrd|d......r@   c                     t          j        ddgd          }t          j        ddd          }t          |d         |d	           t          j        d
dgd          }ddg}t          ||d	           d S )Nr#  ra   rc   rk  rg  r  r   r  r;  r  r  g      @rI  )r   r   r"   r   rT   mean0r  r  mean3s        r>   r  z#TestMultivariateHypergeom.test_mean  s    &+r1g;;;qB///a%d3333&+r1g<<<j)u4000000r@   c                 v    t          j        ddgddggddg          }ddgd	d
gg}t          ||d           d S )NrG   ra   r#  rc   r  rk  r   r   gUUUUUU@gUUUUUU@r  r;  )r   r   r   )rT   r  r  s      r>   r  z0TestMultivariateHypergeom.test_mean_broadcasting  sW    &+1vAw.?Aq6JJJH%
I'>?u4000000r@   c                 @   t          j        g dd          }t          |g d           t          j        g dd          }t          |t          j        t          j        t          j        g           t          j        g dg dgd          }t          |t          j        t          j        t          j        gg dgd	
           t          j        t          j        g t                    d          }t          |g            t          |j	        dk               d S )Nrf   r   rk  r   r   r   r
   r   r   rF   r  )r   r   r   FFg<r;  r-  r   )
r   r   r   r7   rs  r   r   intr   r9   r  s        r>   test_mean_edge_casesz.TestMultivariateHypergeom.test_mean_edge_cases  s   &+iii1===ULLL)))&+iii1===URVRVRV4555&+yyy))).DJJJ 8,,,G"	$ 	$ 	$ 	$ '+bhr.E.E.EKKKUBu$%%%%%r@   c                 D   t          j        g dd          }t          |g dd           t          j        g dd          }t          |t          j        t          j        t          j        g           t          j        g dg d	gd          }t          |t          j        t          j        t          j        gg dgd
           t          j        t	          j        g t                    d          }t          |g            t          |j	        dk               d S )Nrf   r   rk  r  gؗҜ<r;  r  rF   r  r  r-  r  )
r   r7  r   r   r7   rs  r   r  r   r9   )rT   r  r  r  r  s        r>   test_var_edge_casesz-TestMultivariateHypergeom.test_var_edge_cases  s   %)III;;;lll7777%)III;;;TBFBFBF3444%)YYY			,BaHHH7F"	$ 	$ 	$ 	$ &)BHRs,C,C,CqIIIT2
e#$$$$$r@   c                    t          j        g dd          }g dg dg dg}t          ||d           t          j        g dd          }g dg dg dg}t          ||           t          j        t	          j        g t          	          d          }t	          j        g t          j        	                              dd          }t          ||d           t          |j
        d
k               d S )Nr  r
   rk  r  r  r;  rf   r   r-  rM  )r   r   r   r   r7   r   r  r  r'  r   r9   )rT   cov0r  r  r  r  r  s          r>   test_cov_edge_casesz-TestMultivariateHypergeom.test_cov_edge_cases  s   %)III;;;lllLLL9d////%)III;;;lllLLL9T4   %)BHRs,C,C,CqIIIx"*---55a;;d////
f$%%%%%r@   c                 x   t           j                            d           d}g d}g dg dg dg dg dg}t          j        |t          	          }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                                t          j	        ||                     t          |
                                t          j
        ||                     d S )
Nr   r  )rd   r  r     r  r  r   r  r  r-  )r7   r   r   r8   r  r   r   r  r  r7  r   )rT   r   r  rZ   
mhg_frozens        r>   r_  z%TestMultivariateHypergeom.test_frozen  s-   
	tNN]]MMM===\\<<<)Jq$$$+Aq11

q)).21a;;	= 	= 	=
))!,,.5aA>>	@ 	@ 	@
((*@*DQ*J*JKKK
((*@*DQ*J*JKKKKKr@   c                    t          t          t          j        ddd           t          t          t          j        ddgd           t          t          t          j        ddgdgd           t          t          t          j        ddgddgd           t          t          t          j        ddgddgd           t          t          t          j        ddgddgd           d S )	Nra   r#  rc   g      @r  rg  g      %@g      /@)r   rL   r   r  	TypeErrorr4  s    r>   test_invalid_paramsz-TestMultivariateHypergeom.test_invalid_params  s    j"8"<aQGGGj"8"<a"qIIIj"8"<q!frdANNNi!7!;c3Z2h	# 	# 	#i!7!;aVTlA	' 	' 	'i!7!;aV2h	% 	% 	% 	% 	%r@   N)r   r   r   rK   r   r   r7   r  rs  r  ri  r  rp  rs  r   r  r  r  r  r  r  r  r  r  r  r  r  r_  r  r   r@   r>   ra  ra    sV       [ VaWa+VaWa"&)!Wq"gq26'*Vb"Xq"&)!fq!fR2s)4Vbfbf%' !Wr2h26*Wr1gr26*Wr2hBF+VaWb"&)VaWa"&)+	
 43 35 43	/ 	/ 	/; ; ;; ; ;
 [V			13
Qqc1X&  " "	 " [S1#q!VaWa+1v1v"a1a& 12W1v1v&+&I79 RXb$$$hbhr&=&=&=q"EVaVQ"YY			1j1	
  3 3!  3 [Vq"gBx(!i-CDcA3Z1#saVb"X6sQCj\QC!:1vRz:cA3ZQC5'QFr2hZL9		
 3 3 3/ / // / // / // / /1 1 11 1 1
& & &% % %& & &L L L 	% 	% 	% 	% 	%r@   ra  c                      e Zd Zd Zd Zej                            dd          d             Zd Z	ej                            dd          ej                            d	d          d
                         Z
ej                            dd          d             Zd Zej                            dd          d             Zej                            dd          d             Zej                            dd          d             Zej                            dd          ej                            dg dgf          ej                            dg dgf          d                                     Zej                            dd          d             Zd Zej                            dd          d             ZdS )TestRandomTablec                 @    t           j                            d          S )Nl   OfE)r7   r   r   r4  s    r>   get_rngzTestRandomTable.get_rng  s    y$$%7888r@   c                    d}t          j        t          |          5  t          ddggddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgddgg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgdd	g           d d d            n# 1 swxY w Y   d
}t          j        t          |          5  t          ddgddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgg d           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgg d           d d d            n# 1 swxY w Y   ddg}g d}t          j        ddgg d          \  }}}t          ||           t          ||           |t          j        |          k    sJ d S )Nz`row` must be one-dimensionalrD   r
   rF   z`col` must be one-dimensionalz*each element of `row` must be non-negativere   z*each element of `col` must be non-negativerh   z'sums over `row` and `col` must be equalr   z(each element of `row` must be an integer @)r
   r
   rF   z(each element of `col` must be an integer)rT  rT  r
   rG   rF   r
   r
   )rK   r	   rL   r&   _process_parametersr   r7   r   )rT   rU   rowcolr&  r  r   s          r>   test_process_parametersz'TestRandomTable.test_process_parameters  s6   1]:W555 	+ 	+1a&Aq6***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 2]:W555 	+ 	+!Q1a&***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ ?]:W555 	* 	*!R1a&)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* ?]:W555 	* 	*!Q!R)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* <]:W555 	) 	)!Q!Q(((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) =]:W555 	0 	0#sYYY///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 =]:W555 	0 	0!Q///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 !fii2Aq6999EE1aS!S!BF3KKs}   A  AA(B

BB2CCC;DD #D E%%E),E)F..F25F2G77G;>G;zscale,method))r
   boyett)r,  	patefieldc                     t          j        ddg          |z  }t          j        g d          |z  }t          }|                    |||d          }|                    ||d d          }t	          ||           d S )Nr
   rG   r  methodr   )r7   r   r&   r   r   )rT   rI  r  r  r  ctr.  gots           r>   test_process_rvs_method_on_Nonez/TestRandomTable.test_process_rvs_method_on_None+  s     h1v&hyyy!!E)66#s66BBffS#df;;Xs#####r@   c                     ddg}g d}d}t          j        t          |          5  t          j        ||d           d d d            d S # 1 swxY w Y   d S )Nr
   rG   r  z$'foo' not recognized, must be one ofrD   foo)r  )rK   r	   rL   r&   r   )rT   r  r  rU   s       r>   $test_process_rvs_method_bad_argumentz4TestRandomTable.test_process_rvs_method_bad_argument7  s    !fii 9]:W555 	5 	5S#e4444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5s   AAAr  )TFr   c                 n   |                                  }ddgg dt          j        dd|          }|rt                    nt          }t          ||rdnd          |s	fd	|rfd
n}t	          j        |dd          \  }} ||          }	t          |	t          |          z  |d            |t          |d                             }
t          |
|	d                    |
                    d|j        dd          z             } ||          }	|	j        dk    sJ t          |	j        d                   D ]N}t          |	j        d                   D ]1}|	||f         }|||f         } ||          }t          ||           2Og dg dg}t          t	          j        |d                      ||          }	|	dk    sJ g dg dg}t          t	          j        |d                      ||          }	|	dk    sJ d}t          j        t           |          5   |dg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |dgg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |t          j        gg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |dgg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |g dg           d d d            n# 1 swxY w Y   d }t          j        t           |          5   |ddgd!d"gg           d d d            d S # 1 swxY w Y   d S )#NrF   rb   r
   rG   rc   r&  r  r   r  r   r  r  c                      |           S r6   r   )rZ   r  original_methodr  s    r>   r  z/TestRandomTable.test_pmf_logpmf.<locals>.methodQ  s    &q#s333r@   c                 >    t          j         |                     S r6   )r7   r/  )rZ   r  s    r>   r[   z1TestRandomTable.test_pmf_logpmf.<locals>.<lambda>S  s    q		** r@   r   Tr   return_countsr   r;  )r#  r,  r
   )r   r
   r
   )rF   r
   rG   re   r   r   )r
   rF   rF   rh   z$`x` must be at least two-dimensionalrD   z%`x` must contain only integral valuesrT  z)`x` must contain only non-negative valuesz"shape of `x` must agree with `row`rJ   z"shape of `x` must agree with `col`rG   rc   )r  r&   r   ro   r7   uniquer   r   r   r   r'  r9   r  r   rK   r	   rL   rs  )rT   r  r   r   r   objr  
unique_rvscountsr  p2rvs_ndr@  rA  pijrvijqijrZ   rU   r  r  r  r  s                      @@@@r>   test_pmf_logpmfzTestRandomTable.test_pmf_logpmf@  s    llnn!fiisCd&.SB B B )/@l3$$$L#8hh599 	4$O4 4 4 4 4 4 4/2>*****Ys$GGG
F C
OOCHHf37777 Sjm$$%%R1 Y122677CKKw)####qwqz"" 	' 	'A171:&& ' '1gad|c$iiS#&&&&	' YY			"RVAB'''---CFFAvvvv YY			"RVAB'''---CFFAvvvv 9]:W555 	 	CHHH	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 :]:W555 	 	C#LLL	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 :]:W555 	 	C"&
OOO	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 >]:W555 	 	C"KKK	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 7]:W555 	 	C	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 7]:W555 	 	C!QQ   	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	sl   7III8JJJ:KK"%K"L  L$'L$M##M'*M'N**N.1N.r  )r  r  c                 (   |                                  }ddg}g d}t          j        ||d||          }t          j        ||          }t	          t          j        |          t          j        |                     t          |                    d          |d           t	          |                    d	
          t          j        |d                     t	          |                    d
          t          j        |d                     d S )NrF   rb   r  r&  r  r   rE  r  re   r   ro  rh   )r&  rG   )	r  r&   r   r   r   r7   r   r   broadcast_to)rT   r  r   r  r  r   r   s          r>   test_rvs_meanzTestRandomTable.test_rvs_mean  s     llnn!fiisCd6,/1 1 1 c**RVD\\26#;;///T5555SWW"W%%rsI'F'FGGGSWW"W%%rsI'F'FGGGGGr@   c                    |                                  }ddg}g d}t          j        ||dd|          }t          j        ||dd|          }t          j        |d	          }t          j        |d	          }t          ||d
           d S )NrF   rb   r  r  r  r  r  r   r   {Gz?r  )r  r&   r   r7   r7  r   )rT   r   r  r  r  r  r  r  s           r>   test_rvs_covzTestRandomTable.test_rvs_cov  s     llnn!fiiSuX-02 2 2Su[-02 2 2vd###vd###d......r@   c           	      P   ddg}g d}t          j        ||||                                           }|j        dk    sJ t          j        ||d||                                           }|j        dk    sJ t	          ||d	                    t          j        ||d	||                                           }|j        d
k    sJ t          j        ||d||                                           }|j        dk    sJ t          j        ||d||                                           }|j        dk    sJ t          |                    ddd          |d           d}	t          j        t          |	          5  t          j        ||d||                                            d d d            n# 1 swxY w Y   t          j        t          |	          5  t          j        ||t          j        ||                                            d d d            d S # 1 swxY w Y   d S )NrF   rb   r  r  r  r
   r  rJ   r   )r   rF   rG   r  )r  rF   rG   )rc   ra   )rc   ra   rF   rG   rG   r  r;  z/`size` must be a non-negative integer or `None`rD   re   )r&   r   r  r9   r   r   r'  rK   r	   rL   r7   rs  )
rT   r  r  r  r   rv2rv3rv4rv5rU   s
             r>   test_rvs_sizezTestRandomTable.test_rvs_size  s   !fii c3v+/<<>>; ; ;x6!!!! sCa,0LLNN< < <yI%%%%RQ    sCa,0LLNN< < <yI%%%% sCb,0LLNN< < <yJ&&&&sCfV,0LLNN< < <yL((((B1--s???? D]:W555 	: 	:S#Bv*.,,..: : : :	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: ]:W555 	: 	:S#BF6*.,,..: : : :	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	:s$   :,F22F69F66HH"Hc                 "   ddg}g d}t           }|                    ||d||                                           }t          j        |dd          \  }}|                    |||          }t          |t          |          z  |d	
           d S )NrF   rb   r  r  r  r   Tr  r  r;  )r&   r   r  r7   r  r  r   r   )	rT   r  r  r  r  r   r  r  r  s	            r>   test_rvs_methodzTestRandomTable.test_rvs_method  s     !fiiffS#F6"&,,..  2 2  Ys$GGG
F FF:sC((CHHf4888888r@   c                 (   g d}g d}t          ||          }|                    d||                                           }t          j        dt          |          t          |          f          }g dg dg dg|d<   t          ||           d S )Nr  )r
   r   r   r   r&  r  )r   r   r   r   .r&   r   r  r7   r   r   r   rT   r  r  r  r  r   r.  s          r>   test_rvs_with_zeros_in_col_rowz.TestRandomTable.test_rvs_with_zeros_in_col_row  s    iillc""UU4T\\^^UDD8T3s88SXX677%%%' 	R"""""r@   )Nr  r  r  r   r  c                     t          ||          }|                    d||                                           }t          j        dt          |          t          |          f          }t          ||           d S )Nr#  r  r  r  s          r>   test_rvs_with_edge_casesz(TestRandomTable.test_rvs_with_edge_cases  sj     c""UU2f4<<>>UBB8RS3s88455R"""""r@   r   r  c                    dd l mc m} t          j        ddgt          j                  }t          j        g dt          j                  }t          |d|           }t          j        |          } ||||d|                                           }|j	        dt          |          t          |          fk    sJ t          j        |          |k    sJ d S )Nr   r
   rG   r-  r  	rvs_rcont)scipy.stats._rcontr-   _rcontr7   r   int64ro   r   r  r9   r   )rT   r   r  r  r  r   ntotresults           r>   test_rvs_rcontzTestRandomTable.test_rvs_rcont  s     	,++++++++h1vRX...hyyy111fo!oo..vc{{S#tQ77|3s88SXX66666vf~~%%%%%%r@   c                    ddg}g d}t          |||                                           }|                                }t          j        ||          }t	          ||                                           t          j        |||          }t	          ||                    |                     t          j        |||          }t	          ||                    |                     d S )NrF   rb   r  r   )r&   r  r   r   r   r  r  )rT   r  r  r  r  r.  s         r>   r_  zTestRandomTable.test_frozen  s    !fiic777$S#..Xqvvxx(((#FC55XquuV}}---&vsC88Xqxx//00000r@   c                    ddg}g d}t          |||                                           }t          j        ||d||                                           }|                    d|          }t          ||           d S )NrF   rb   r  r   r#  r  )r   r  )r&   r  r   r   )rT   r  r  r  r  r.  r  s          r>   test_rvs_frozenzTestRandomTable.test_rvs_frozen"  s    !fiic777#C2f15A A AeeFe++Xs#####r@   N)r   r   r   r  r  rK   r   r   r  r  r  r  r  r  r  r  r  r  r_  r  r   r@   r>   r  r    s       9 9 9"  "  " H [^@B B$ $B B$5 5 5 [X}55[UM22L L 32 65L\ [X'>??H H @?H/ / / [X'>??': ': @?':R [X'>??9 9 @?9( [X'>??	# 	# @?	# [X'DEE[UR!I..[UR!I..# # /. /. FE# [S&))& & *)& 1 1 1  [X'>??$ $ @?$ $ $r@   r  c                     | j         }d| _          | j        |ddi t          j        |           } | j        |ddi}t          j        |          } |j        |ddi}t          ||           || _         d S )Nr   r   r  )r   r   pickledumpsloadsr   )distfnr<   r  r   r0	unpickledr1s          r>   check_picklingr  .  s    
 DFFJ1VA	T	"	"	"BQI		%1	%	%BR Fr@   c                  >   t          j        d          } d| d<   d| d<   t          dgt          t          j        dg          fgt
          d| fgt          d| fgt          dg d	fgt          d
gt          d
gg}|D ]%\  }}t          ||           t          ||           &d S )NrG   rG  r   r  r   r   r#  ra   ri  ra  )r7   rO   r   r   r   r   r   r   r   r   r2   r  )rI  distsr  r<   s       r>   test_random_state_propertyr  B  s    F1IIEE$KE$K	b!	RXrd^^&'	2u+	b%[!	q///*+	d	d#E  % %#FD111vt$$$$% %r@   c                   "   e Zd Zej                            dg d          ej                            dg d          d                         Zej                            dddg          ej                            dg d	          d
                         Zd Zd Z	d Z
ej                            dddg          d             Zej                            dddg          d             Zej                            dej        ej        g          d             Zej                            dej        ej        g          d             Zej                            d ej        g d           ej        g d          ddf ej        g d           ej        g d          ddf ej        g d           ej        g d          ddf ej        g d           ej        g d          dd f ej        g d           ej         ej        d!           ej        d"          dg          d#d$f ej        g d           ej        g d          d#d%f ej        g d&           ej        g d&          d#d'f ej        g d&           ej         ej        d!           ej        d"          dddg          d#d(f ej        g d&           ej         ej        d)           ej        d*          dddg          d#d+fg	          d,             Zej                            d ej        g d           ej        g d          dd-f ej        g d           ej        g d          dd.f ej        g d           ej        g d          dd/f ej        g d           ej        g d          dd0f ej        g d           ej         ej        d!           ej        d"          dg          d#d1f ej        g d           ej        g d          d#d2f ej        g d&           ej        g d&          d#d3f ej        g d&           ej         ej        d!           ej        d"          dddg          d#d4f ej        g d&           ej         ej        d)           ej        d*          dddg          d#d5fg	          d6             Zej                            d7g d8          d9             Zej                            dej        ej        g          d:             Zd; Zej                            dg d<          ej                            d=g d>          d?                         Zd@ ZdA ZdB ZdCS )DTestVonMises_Fisherr   )rF   rG   rc   rb   r   r  c                    t           j                            d          }t          j        |fdt          j        |          z            }t          |d|          }|                    |          }t          j        |          t          j        |          }}|	                    |||          j
        }	|j
        |	k    sJ t           j                            |d          }
t          |
d           d S )Nr  r
   r   r~   re   r   r   )r7   r   r   ri  r  r(   r   r   rO   r   r9   r   r   r   )rT   r   r   r   r   vmf_distr  r   r   r  r  s              r>   r/  z TestVonMises_Fisher.test_samplesU  s     i##$788WcWan--"2qs333,,t$$HSMM26#;;c00s0FFL}....	wR00r"""""r@   ra   r  kappa)g  4&kCrK  gꌠ9Y>)Fc                     t           j                            d          }t          j        |fdt          j        |          z            }t          |||          }|                    d           d S )Nr  r
   r   r#  )r7   r   r   ri  r  r(   r   )rT   r   r  r   r   r  s         r>    test_sampling_high_concentrationz4TestVonMises_Fisher.test_sampling_high_concentrationc  se     i##$788WcWan--"2u3777Rr@   c                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )Nr  z%'mu' must have one-dimensional shape.rD   r
   r7   rN   rK   r	   rL   r(   rT   r   r}  s      r>   test_two_dimensional_muz+TestVonMises_Fisher.test_two_dimensional_mul  s    WV__5]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#   AAAc                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )Nra  z%'mu' must be a unit vector of norm 1.rD   r
   r  r  s      r>   test_wrong_norm_muz&TestVonMises_Fisher.test_wrong_norm_mur  s    WU^^5]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r  c                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )Nr  z$'mu' must have at least two entries.rD   r
   r  r  s      r>   test_one_entry_muz%TestVonMises_Fisher.test_one_entry_mux  s    WU^^4]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r  re   )ra   rG   c                     d}t          j        t          |          5  t          ddg|           d d d            d S # 1 swxY w Y   d S )Nz"'kappa' must be a positive scalar.rD   r
   r   rK   r	   rL   r(   rT   r  r}  s      r>   test_kappa_validationz)TestVonMises_Fisher.test_kappa_validation~  s    2]:S111 	+ 	+QFE***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+   >AAr   r   c                     d}t          j        t          |          5  t          ddg|           d d d            d S # 1 swxY w Y   d S )NzFor 'kappa=0' the von Mises-Fisher distribution becomes the uniform distribution on the sphere surface. Consider using 'scipy.stats.uniform_direction' instead.rD   r
   r   r  r  s      r>   test_kappa_zeroz#TestVonMises_Fisher.test_kappa_zero  s     ]:S111 	+ 	+QFE***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+r  r  c                     t          j        g d          }d}t          j        t          |          5   ||ddgd           d d d            d S # 1 swxY w Y   d S )Nr   r   r   znThe dimensionality of the last axis of 'x' must match the dimensionality of the von Mises Fisher distribution.rD   r
   r   r7   r   rK   r	   rL   rT   r  rZ   r}  s       r>   test_invalid_shapes_pdf_logpdfz2TestVonMises_Fisher.test_invalid_shapes_pdf_logpdf  s     H[[[!! ]:S111 	! 	!F1q!fa   	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	!   AAAc                     t          j        ddg          }d}t          j        t          |          5   ||ddgd           d d d            d S # 1 swxY w Y   d S )NrG  r   8'x' must be unit vectors of norm 1 along last dimension.rD   r
   r   r  r  s       r>   test_unnormalized_inputz+TestVonMises_Fisher.test_unnormalized_input  s     Hc2YH]:S111 	! 	!F1q!fa   	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	!r  zx, mu, kappa, reference)r   r   r   r  g0_?r  )r   r   r   g7m0_?r,  gLI/@gFK:h*7g\(\?r  i  g3pB>g7Ks@)r   r   r   r   r   go齿@gW+x\(?rh  r   gS-c                 p    t          ||                              |          }t          ||d           d S )NrA  r;  )r(   r   r   )rT   rZ   r   r  	referencer   s         r>   test_pdf_accuracyz%TestVonMises_Fisher.test_pdf_accuracy  s<    4 b%((,,Q//YU333333r@   g[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 p    t          ||                              |          }t          ||d           d S )Nr  r;  )r(   r   r   )rT   rZ   r   r  r  r   s         r>   test_logpdf_accuracyz(TestVonMises_Fisher.test_logpdf_accuracy  s<    4 !U++22155	666666r@   zdim, kappa, reference))rG   r  g?@)rG   r,  gp&F)ra   r  gT;ӷ&)r  r
   goZ@c                     t          j        |fdt          j        |          z            }t          ||                                          }t          ||d           d S )Nr
   g+=r;  )r7   ri  r  r(   r   r   )rT   r   r  r  r   r   s         r>   test_entropy_accuracyz)TestVonMises_Fisher.test_entropy_accuracy  sY     WcWan--!"e,,4466777777r@   c           	         d}t           j                            d          }t          d                              ||          }t          j        ddt          j        d          z            }d} ||||          }|j        |k    sJ t          |d                   D ]L}t          |d                   D ]4}	 ||||	d d f         ||          }
t          |
|||	f         d	
           5Md S )Nr  r  rG   r   r  r
   ra   r   r  r;  )
r7   r   r   r'   r   ri  r  r9   r  r   )rT   r  	testshaper   rZ   r   r  
result_allr@  rA  current_vals              r>   rC  z%TestVonMises_Fisher.test_broadcasting  s    	i##$788a  $$YS$AAWUAbgajjL))VAr5))
9,,,,y|$$ 	K 	KA9Q<(( K K$fQq!QQQwZU;;Z1-=EJJJJJK	K 	Kr@   c                    t           j                            d          }t          j        ddg          }t          j        |d         |d                   }d}t          ||          }t          ||          }t          d                              d|          }t          j        |d d df         |d d df                   }t          |
                                |
                                           t          |                    |          |                    |                     t          |                    |          |                    |                     d S )	Nr  r   r
   r  )rN  r  rF   r#  r   )r7   r   r   r   r  r(   r*   r'   r   r   r   r   r   )	rT   r   r   mu_angler  vmfvonmises_distvectorsr  s	            r>   test_vs_vonmises_2dz'TestVonMises_Fisher.test_vs_vonmises_2d  s3    i##$788Xq!f:beRU++b%(( XU;;;#A&&**2C*@@GAAAqDM7111a4=99--//???))&1137773C3CDDD,,V44cjj6I6IJJJJJr@   )rF   rG   rb   zkappa, mu_tol, kappa_tol))r
   rE  rE  )r#  rO  rO  )r,  {Gzt?r  )r&  r:  r  c                    t          j        |fdt          j        |          z            }t          ||          }t           j                            d          }d}|                    ||          }	t          j        |	          \  }
}t          j        |	                    |
                    }t          |d|d           t          |||           d S )	Nr
   r  r  r   r   r   r#  r;  )r7   ri  r  r(   r   r   r   r  arccosr	  r   )rT   r   r  mu_tol	kappa_tolr   r  r   r  r  mu_fit	kappa_fitangular_errors                r>   test_fit_accuracyz%TestVonMises_Fisher.test_fit_accuracy*  s     WcWan--"2u--i##$788	,,ys,;;+/88		"&&..11rQ????yy999999r@   c                     t          j        d          }d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )Nr  z'x' must be two dimensional.rD   )r7   r   rK   r	   rL   r(   r  rT   rZ   r}  s      r>   #test_fit_error_one_dimensional_dataz7TestVonMises_Fisher.test_fit_error_one_dimensional_data;  s    HUOO,]:S111 	# 	#"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#   AAAc                     t          j        d          }d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )Nr  r  rD   )r7   rN   rK   r	   rL   r(   r  r/  s      r>    test_fit_error_unnormalized_dataz4TestVonMises_Fisher.test_fit_error_unnormalized_dataA  s    GFOOH]:S111 	# 	#"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r1  c                 <   t          j        g d          }d}t          ||          }t          ||d          }|                    d          }t          j        ||d          }|                                }t	          ||           t	          ||           d S )N)r   r   r
   ra   r0  r   r   )r7   r   r(   r   r   )rT   r   r  r  rj  r  r  rk  s           r>   r  z,TestVonMises_Fisher.test_frozen_distributionG  s    Xiii   U++%b%c:::zzsz++"2u3???  T4   T4     r@   N)r   r   r   rK   r   r   r/  r  r  r  r  r  r
  r(   r   r   r  r  r7   r   r  r  r  r  rC  r$  r-  r0  r3  r  r   r@   r>   r  r  T  s       [ULLL11[V%9%9%9::
# 
# ;: 21
# [UQF++[W&8&8&899  :9 ,+# # ## # ## # # [Wr6l33+ + 43+
 [Wq"g..+ + /.+ [X(;(7(>(@ A A! !A A! [X(;(7(>(@ A A! !A A!$ [6'rx55xrx7M7M#%79'rx44hbh|||6L6L#%8:'rx55xrx7M7M"$68'rx44hbh|||6L6L"$9;'rx55'rxr(JKK#%:<  (rx44hbh|||6L6L#%68'rx(<(<(<=='rx(<(<(<==#%79  (rx(<(<(<=='rxr)*B)0  1  1#%;=  (rx(<(<(<=='rxwrws||R)*B)0  1  1#%;=)>? ?24 43? ?24" [6'rx55xrx7M7M#%8:'rx44hbh|||6L6L#%8:'rx55xrx7M7M"$57'rx44hbh|||6L6L"$68'rx55'rxr(JKK#%8:  (rx44hbh|||6L6L#%68'rx(<(<(<=='rx(<(<(<==#%79  (rx(<(<(<=='rxr)*B)0  1  1#%79  (rx(<(<(<=='rxwrws||R)*B)0  1  1#%8:);< <27 73< <27$ [4: : :; ;
8 8; ;
8
 [X(;(7(>(@ A AK KA AKK K K [UIII..[72 2 23 3
	: 	:3 3 /.	:# # ## # #! ! ! ! !r@   r  c                   x   e Zd Zed             Zd Zd Zd Zd Ze	j
                            dddg          d	             Ze	j
                            dd
dg          d             Zd Zd Ze	j
                            dddg          d             Ze	j
                            dg d          d             ZdS )TestDirichletMultinomialc                     t           j                            d          }|                    ddd          }|                    dd|df          }|                    d	          }|||||fS )
N   t7)r   r,  rF   r~   r
   r  re   r   )r7   r   r   r   integersr   )rT   r  r   r  rZ   r   s         r>   
get_paramsz#TestDirichletMultinomial.get_paramsV  sl    i##$566As++LLBaVL,,EErENNAua""r@   c                    t           j                            d          }|                    ddd          }|                    ddd          }t          j        |d          }t          ||          }t          |                    |          t          j        |||                     t          |	                    |          t          j	        |||                     t          |
                                t          j
        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     d S )Nr8  r   r,  r#  re   r   )r7   r   r   r   r9  r   r)   r   r  r  r   r7  r   )rT   r   r  rZ   r   r  s         r>   r_  z$TestDirichletMultinomial.test_frozen^  s1   i##$566AsB''LLB##F12!%++QXXa[["7">q%"K"KLLLQUU1XX48E1EEFFFQVVXX49%CCDDDQUUWW37qAABBBQUUWW37qAABBBBBr@   c                    t          j        g d          }t          j        |          }t          j        g d          }t          j        |||          }t          j        |||          }d}t          ||           t          |t          j        |                     |j        |j        cxk    rdk    sn J t           j	        
                    d          }|                    ddd          }|                    ddd          }t          j        |d	
          }t          ||                              |          }t          j        |||          }d}t          ||           t          |t          j        |                     d S )NrJ   rG   rc   ra   gp.U.?r   r8  r   r,  r#  re   r   g+T<)r7   r   r   r)   r  r  r   r   r9   r   r   r   r9  )rT   rZ   r   r  r:   logresr;   r   s           r>   test_pmf_logpmf_against_Rz2TestDirichletMultinomial.test_pmf_logpmf_against_Rl  so   
 HYYYF1II###'5!44&-a::!S!!!s,,,yFL....B...... i##$566AsB''LLB##F12#E1--11!44&-a::"S!!!s,,,,,r@   c                    |                      d          \  }}}}}|dz  }t          t          ||                              |          d           t          t          ||                              |          t
          j                    |                      d          \  }}}}}|                    d          dk    }t          j        ||         dz            ||<   t          t          ||                              |          |         d           t          t          ||                              |          |         t
          j                    t          j	        t          ||                              |          |          dk              sJ t          j	        t          ||                              |          |          t
          j         k              sJ d S )Nr
   r   r#  r~   rG  rF   )
r:  r   r)   r  r  r7   r  r   roundr%  )rT   r   r  r  r   rZ   r@  s          r>   test_pmf_logpmf_supportz0TestDirichletMultinomial.test_pmf_logpmf_support  s    #ooa00Qq!	Q*5!4488;;Q???*5!44;;A>>HHH"oob11Qq!JJBJ#%x!q!!!*5!4488;;A>BBB*5!44;;A>>qABF7KKKv+E15599!<<aR@1DEEEEEv+E155<<Q??CrvgMNNNNNNNr@   c                 `   d}dg}t          j        |g          }t          ||          }t          |                    |          d           t          |                    |dz             d           t          |                    |          d           t          |                    |dz             t           j                    t          |                                |           t          |                                d           t          |	                                d           d S )Nrb   r#  r
   r   )
r7   r8   r)   r   r  r  r  r   r7  r   )rT   r   r  rZ   r   s        r>   test_dimensionality_onez0TestDirichletMultinomial.test_dimensionality_one  s    JsOO$UA..TXXa[[!$$$TXXac]]A&&&T[[^^Q'''T[[1%%w///TYY[[!$$$TXXZZ###TXXZZ#####r@   method_namer  r  c                 $   |                      d          \  }}}}}t          t          ||          |          }t          t          j        |g|j        R  |          } ||          }	 ||j        d                   }
t          |	|
           d S Nr,  r   r:  ro   r)   r-   	betabinomr   r   rT   rE  r   r  r  r   rZ   r  
ref_methodr:   r;   s              r>   test_against_betabinom_pmfz3TestDirichletMultinomial.test_against_betabinom_pmf  s    "ooc22Qq!.ua88+FFU_Q9999;GG
fQiijQ  S!!!!!r@   r   r7  c                    |                      d          \  }}}}}t          t          ||          |          }t          t          j        |g|j        R  |          } |            d d df         }	 |            }
t          |	|
           d S rG  rH  rJ  s              r>   test_against_betabinom_momentsz7TestDirichletMultinomial.test_against_betabinom_moments  s    "ooc22Qq!.ua88+FFU_Q9999;GG
fhhqqq!tnjllS!!!!!r@   c                    t           j                            d          }d}|                    dd          }|                    |          dz  }t	          ||          }d}|                    ||          }|                    |||          }t          |                                t          j        |d	          d
           t          |	                                t          j	        |d	          d           |                                j
        |	                                j
        cxk    r|fk    sn J |                                }	|	j
        ||fk    sJ t          |	t          j        |j                  d           t          t          j        |	          |	                                           t          j        t           j                            |	          d         dk              sJ d S )Nr8  ra   r
   r,  r~   r#  r  r   r   r%  r;  rO  r  )r7   r   r   r9  r)   r   r   r   r   r7  r9   r   r   r   rn   r%  r   r   r   )
rT   r   r   r   r  r   r  r  rZ   r   s
             r>   r,  z%TestDirichletMultinomial.test_moments  s   i##$566LLC  


$$r)$UA.. MM%aM((OOAqqO))		RWQQ%7%7%7dCCCC

BF11$5$5$5DAAAAyy{{ DHHJJ$4>>>>>>>>>>hhjjyS#J&&&&RVAC[[t4444RWS\\488::...vel'',,Q/!34444444r@   c                    t          j        g d          }t          j        |          }t          j        g d          }d}t          t          |          5  t          j        g d||           d d d            n# 1 swxY w Y   t          t          |          5  t          j        g d||           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j        |g d|           d d d            n# 1 swxY w Y   t          t          |          5  t          j        |g d	|           d d d            n# 1 swxY w Y   d
}t          t          |          5  t          j        ||d           d d d            n# 1 swxY w Y   t          t          |          5  t          j        ||d           d d d            n# 1 swxY w Y   t          j        g d          }t          j        g d          }d}t          t          |          5  t          j        |||                                           d d d            d S # 1 swxY w Y   d S )NrJ   r=  z,`x` must contain only non-negative integers.rD   )r
   re   rG   )r
   r  rG   z*`alpha` must contain only positive values.)rG   r   rc   )rG   re   rc   z`n` must be a positive integer.ǧH@r   )r
   rF   rG   rc   z&`x` and `alpha` must be broadcastable.)r7   r   r   r   rL   r)   r  )rT   x0n0alpha0textrZ   r  s          r>   rV   z.TestDirichletMultinomial.test_input_validation  s)   Xiii  VBZZ)))$$=:T222 	A 	A!(VR@@@	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A:T222 	B 	B!(fbAAA	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B <:T222 	< 	<!(YYY;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	<:T222 	= 	=!(ZZZ<<<	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 1:T222 	; 	;!(VT:::	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	;:T222 	8 	8!(VQ777	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 	8 H\\\""##7:T222 	< 	<!(E15577;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	<s~   A>>BBCCC'DDD-EEE5FFF9GG #G +)I!!I%(I%r  c           	         t          j        g dg dg dg dg          }t          j        dgdgdgg          }t          j        g dg d	g                              d
          }t          t          |          } ||||          }|j        dk    sJ t          t          |                    D ]}t          t          |                    D ]}t          t          |                    D ]r}||||f         }	 |||                                         ||                                         ||                                                   }
t          |	|
           sd S )Nr=  rn  ra   ra   rd   r  r  r#  rb   rd   r  rJ   )rF   rF   rG   )rF   r
   r
   rG   )rF   rG   rc   )
r7   r   r'  ro   r)   r9   r  r   r   r   )rT   r  r  r   rZ   r:   r@  rA  r  res_ijkr;   s              r>   test_broadcasting_pmfz.TestDirichletMultinomial.test_broadcasting_pmf  si   )))YYY			:::FGGHqcA3_%%Hiii+,,44\BB.77fQq!!yI%%%%s1vv 	2 	2A3q66]] 2 2s5zz** 2 2A!!Q'lG &1q1A1A1C1CQqT\\^^TTC#GS111122	2 	2r@   )r   r7  r   c                    t          j        g dg dg dg dg          }t          j        dgdgdgg          }t          t          |          } |||          }|dk    r|j        d	k    snnJ t          t          |                    D ]w}t          t          |                    D ]X}|||f         } |||                                         ||                                                   }	t          ||	           Yxd S )
Nr=  rn  rV  rW  rb   rd   r  r   )rG   rc   rG   )	r7   r   ro   r)   r9   r  r   r   r   )
rT   rE  r  r   r  r:   rA  r  rX  r;   s
             r>   test_broadcasting_momentsz2TestDirichletMultinomial.test_broadcasting_moments  s   )))YYY			:::FGGHqcA3_%%.<<fUA)4)=)=syI%%%%%%s1vv 	. 	.A3u::&& . .ad)fU1X--//1@@----.	. 	.r@   N)r   r   r   classmethodr:  r_  r?  rB  rD  rK   r   r   rL  rN  r,  rV   rY  r[  r   r@   r>   r6  r6  U  s[       # # [#C C C- - ->O O O $ $ $ []UH,=>>" " ?>" []VUO<<" " =<"5 5 5,< < << [Xx'8992 2 :92 [],B,B,BCC
. 
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.r@   r6  r\  )Y__doc__r  numpy.testingr   r   r   r   r   r   rK   r	   r   test_continuous_basicr   numpyr7   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,   r-   scipy.integrater.   r/   r0   scipy.specialr1   common_testsr2   	data._mvtr3   unittest.mockr4   r?   rB   r   r   r   r  r1  r  r  r  r
  r.  re  r  r  r  r  ra  r  r  r  r  r6  r   r@   r>   <module>ri     sF    7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  * * * * * * 9 9 9 9 9 9        C C C C C C C C C C: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 0 / / / / / / /       3 3 3 3 3 3 3 3 3 3 & & & & & & 5 5 5 5 5 5            ' ' ']! ]! ]! ]! ]! ]! ]! ]!@     @
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