
    S_fV                       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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dlBmCZC d ZD G d d      ZEd9dZFd ZG G d d      ZH G d d      ZI G d d      ZJd 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+ d,      ZS G d- d.      ZT G d/ d0      ZU G d1 d2      ZVd3 ZWd4 ZX G d5 d6      ZY G d7 d8      ZZy):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)Version)check_random_state_property)_qsimvtv)patchc                     t        j                  |       t        j                  |      }} t        | |g|i | t        | j                  |j                         y N)npasarrayr   r   shape)resrefargskwargss       Clib/python3.12/site-packages/scipy/stats/tests/test_multivariate.pyassert_closer@   ,   sA    zz#

3CC.t.v.CII&    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"                  j%                  dedd       d        Zej"                  j%                  d ee            ej"                  j%                  de      d               Zej"                  j%                  dd e       ddg      ej"                  j%                  d ee            ej"                  j%                  de      d                      Zej"                  j%                  d e       dg      ej"                  j%                  de      d               Zd Zej"                  j3                  d      d        Zd Zy)TestCovariancec                    d}t        j                  t        |      5  t        j                  t        j                  d             d d d        d}t        j                  t        |      5  t        j                  t        j                  d      t        j                  d             d d d        d}t        j                  t        |      5  t        j                  d       d d d        d	}t        j                  t        |      5  t        j                  t        j                  d             d d d        d
}t        j                  t        |      5  t        j                  dt        j                  d      f       d d d        d}t        j                  t        |      5  t        j                  t        j                  d      df       d d d        d}t        j                  t        |      5  t        j                  g dt        j                  d      f       d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   exY w# 1 sw Y   $xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   y xY w)Nz:The input `precision` must be a square, two-dimensional...match   z0`precision.shape` must equal `covariance.shape`.   )
covariancez7The input `diagonal` must be a one-dimensional array...alpacaz9The input `cholesky` must be a square, two-dimensional...z4The input `eigenvalues` must be a one-dimensional...z,The input `eigenvectors` must be a square...z9The shapes of `eigenvalues` and `eigenvectors` must be...r
   rG   rH   )pytestr	   
ValueErrorr+   CovViaPrecisionr8   oneseyeCovViaDiagonalCovViaCholeskyCovViaEigendecompositionselfmessages     r?   test_input_validationz$TestCovariance.test_input_validation4   s   N]]:W5 	4''
3	4 E]]:W5 	I''q	bffQiH	I L]]:W5 	1&&x0	1 N]]:W5 	3&&rwwqz2	3 I]]:W5 	H00(BFF1I1FG	H A]]:W5 	I00"''!*h1GH	I N]]:W5 	I00)RVVAY1GH	I 	I1	4 	4	I 	I	1 	1	3 	3	H 	H	I 	I	I 	IsS   )H.,>H;I
)I+I"(+I.8-I:.H8;III"I+.I7:Jc                     t        | d      S )NTallow_singular)r   )xs    r?   <lambda>zTestCovariance.<lambda>V   s    %)!D%A rA   )Diagonal	PrecisionCholeskyEigendecompositionPSDrK   )   r
   rH   )r
         )rH   rd      )r
   r   rH   )rb   r   )rf   rb   r   r   r   r   )diagonal full rankzgeneral full rankzdiagonal singularzgeneral singularr
   N)r   rf   ri   cov_type_namerf   c                 ~   t        j                  g d      }g d}t        t        d|       }| j                  |   }t        t
        d|j                                } | ||            } | ||            }t        |      t        |      k(  sJ t        |j                  |      |j                  |             y )NrK   )rG   rb   CovViafrom_)
r8   diaggetattrr+   _covariance_preprocessingr,   lowertyper   whiten)	rU   rj   Ar[   cov_typepreprocessingfactoryr;   r<   s	            r?   test_factorieszTestCovariance.test_factoriesb   s    GGI;&(@A66}E*m.A.A.C-D&EFmA&'}Q'(CyDI%%%

1szz!}5rA   matrix_typec                    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                   j#                  d      }	|	j!                  d      }
|j%                  |
      }|
|j&                  z  }t        ||z  ||z         t)        |d	      rd
|vrt        |j+                  |      |
       |	j!                  d      }
|j%                  |
      }|
|j&                  z  }t        |dz  j-                  d      |dz  j-                  d             t)        |d	      rd
|vrt        |j+                  |      |
       t)        |d	      rG|j+                  t        j.                  t1        |                  }t        |j2                  |z  |       y y )Nrm    does not support 	 matricesTrY      VGiVK rH   size	_colorizesingularrG   rd   rH   rG   rf   axis)
_cov_typesrL   skip	_matricesrp   r+   rq   r   r@   log_pdetr   rankr:   r8   r9   rI   randomdefault_rngrt   UhasattrcolorizesumrP   lenT)rU   rz   rj   rV   ru   rv   rw   psd
cov_objectrngr[   r;   r<   s                r?   test_covariancezTestCovariance.test_covariancep   s    M?*<[M J  <<KK NN;';&(@A66}E1T* mA./
Z((#,,7Z__chh/Z%%rzz!}':':;Z**BJJqM: ii##$78JJAJ"#%%iS3Yc	*:{+
+0M,,S115 JJIJ&"#%%ic1f\\r\*S!VLLbL,AB:{+
+0M,,S115 :{+%%bffSVn5Ca( ,rA   r   r   c                    d| d| d}|| j                   |   vrt        j                  |       | j                  |   }t	        t
        d|       }| j                  |   }g d} | ||            }	t        }
t        ||d      }t        ||	d      }t        j                  j                  d      }|j                  |||      }t        j                  j                  d      }|
j                  ||	||	      }t        j                  j                  d      } |
||	|
      j                  |      }t        |	t
        j                        r?t        |t        j                  |             t        |t        j                  |             nLt!        |j"                  |j"                         t!        |j"                  |j"                         t        ||       t        |
j%                  |||	      |j%                  |             t        |j%                  |      |j%                  |             t        |
j'                  |||	      |j'                  |             t        |j'                  |      |j'                  |             t        |
j)                  ||	      |j)                                t        |j)                         |j)                                y )Nrm   r|   r}   皙?皙?333333?TrY   r~   r   r   random_stateseed)r   rL   r   r   rp   r+   rq   r   r8   r   r   rvs
isinstance	CovViaPSDr@   squeezer   r:   pdflogpdfentropy)rU   r   rz   rj   rV   ru   rv   rw   meanr   mvndist0dist1r   r[   x1x2s                    r?   test_mvn_with_covariancez'TestCovariance.test_mvn_with_covariance   s/    M?*<[M J  <<KK NN;';&(@A66}EmA./
!#D!DA#D*TJii##$78##D!$#7ii##$78WWT:DsWCii##$78z,00d0;j+"7"78RZZ]+RZZ]+177+177+R SWWQj1599Q<@UYYq\599Q<0SZZ44ell1oFU\\!_ell1o6S[[z2EMMODU]]_emmo6rA   c                    d}| j                   |   }t        t        d|       }| j                  |   }g d} | ||            }t        }	t	        ||d      }
t	        ||d      }t
        j                  j                  d      }|j	                  |||      }t        |	j                  |||      |
j                  |             t        |j                  |      |
j                  |             t        |	j                  |||      |
j                  |             t        |j                  |      |
j                  |             y )Nrh   rm   r   TrY   r~   r   )r   rp   r+   rq   r   r8   r   r   r@   cdflogcdf)rU   r   rj   rz   ru   rv   rw   r   r   r   r   r   r   r[   s                 r?   test_mvn_with_covariance_cdfz+TestCovariance.test_mvn_with_covariance_cdf   s    +NN;';&(@A66}EmA./
!#D!DA#D*TJii##$78##D!$#7SWWQj1599Q<@UYYq\599Q<0SZZ44ell1oFU\\!_ell1o6rA   c                 |    d}t        j                  t        |      5  t                d d d        y # 1 sw Y   y xY w)Nz7The `Covariance` class cannot be instantiated directly.rE   )rL   r	   NotImplementedErrorr,   rT   s     r?   test_covariance_instantiationz,TestCovariance.test_covariance_instantiation   s0    K]].g> 	L	 	 	s   2;zignore::RuntimeWarningc                 v   t        j                  g d      }|j                  d   }t        j                  |      }t	        j
                  t        d      5  t        ||      j                          d d d        d}t         j                  j                  |      }t         j                  j                  |      }t        j                  t         j                  j                  |            }t        ||      }|j                  |      }	t        j                  |||      }
t        |	|
       y # 1 sw Y   xY w)N)r
   rG   g:0yEr   zThe input matrix must be...rE   l   .ypGw r   )r8   ro   r:   zerosrL   r	   rM   r   r   r   r   r,   from_eigendecompositionlinalgeighr   )rU   ru   nr   r   rng1rng2covrvr;   r<   s              r?   test_gh9942zTestCovariance.test_gh9942   s    
 GGM"GGAJxx{ ]]:-JK 	/a(,,.	/ #yy$$T*yy$$T*001BC s+ff$f'!%%dCdCS#	/ 	/s   D//D8c                 r   t        j                  d      }t        j                  t        j                  d      t        j
                  d      f      }t        j                  j                  ||      }|j                  d       }t        ||       t        j                  j                  j                  t        j                  ddg      t        j                  ddgddgg      f      }t        j                  j                  ||      }|j                  d       }|d   |d   k7  sJ |d   |d   k(  sJ y )	NrG   r   r   r         ?        g      y@r   r
   )r8   rO   r,   r   r   rP   scipyr-   r   r   r   array)rU   r   r   distr   s        r?   test_gh19197zTestCovariance.test_gh19197   s   
 wwqz00"((1+rvvay1IJ{{..Dc.BhhDh!S$kk$$<<XXr2hB8b$Z*@!ABD{{..Dc.BhhDh!1va   1va   rA   )__name__
__module____qualname__rW   r8   ro   r   invcholeskyr   rq   r   list_all_covariance_typesr   r   rL   markparametrizery   r   tupler   r   r   filterwarningsr   r    rA   r?   rC   rC   2   s   I< .0WW.0iimm-/YY-?-?79yy~~)B	!C %BHHT*C%DE'.rwwy'9'0)Y&G&-bggi&8&0*i%HJI )>'<QR'@'<['I&;BC&@BJ
 [[_.CCR.HI6 J6 [[]DO<[[_.CD-) E =-)^ [[VdEGQ	%BC[[]DO<[[_.CD#7 E = D#7J [[Vegy%9:[[_.CD7 E ;70
 [[ 89 :,!rA   rC   c                    |j                  | | f      }||j                  z  }t        j                  j	                  |      \  }}|r|j                  |       dkD  }d||<   |t        j                  |      z  |j                  z  }|S )Nr   r   )r   r   r8   r   r   normalro   )	dimevalsr   r   ru   _v	zero_eigsr   s	            r?   _random_covariancer     s{     	

C:A	ACCA99>>!DAqJJCJ(1,	i
bggen
qss
"CJrA   c                     t         j                  j                  | |       }t        j                  j                  |      \  }}}|S r7   )r8   r   randnr   r   svd)r   Musr   s        r?   _sample_orthonormal_matrixr      s5    
		1Allq!GAq!HrA   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$                  j'                  d ej*                  d       ej.                  ddg      g      d        Zd Zd Zd Zd Zd Zd Zd Zd Z d Z!d Z"d Z#d Z$d Z%d  Z&d! Z'd" Z(ej$                  j'                  d#d$      d%        Z)d& Z*ej$                  j'                  d' ejV                  d(       ejV                  d)      g      d*        Z,ej$                  j'                  d+ ejV                  d,       ejV                  d-       ejV                  d.      g      d/        Z-d0 Z.d1 Z/d2 Z0y3)4TestMultivariateNormalc                 `   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||       y )NrH   rG   r   r
   r   r
   rG   )r8   arangeidentityassert_raisesrM   r   r   r   )rU   mur   s      r?   test_input_shapez'TestMultivariateNormal.test_input_shape'  sx    YYq\kk!nj"5"9"962sKj"5"9"99b#Nj"5"9"962sKj"5"9"99b#NrA   c                    t         j                  j                  d       d\  }}}t        j                  |||      }t        |j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        j                  |||      }t        |j                  d       d\  }}}t        j                  |||      }t        |j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        j                  |||      }t        |j                  d       y )N  )      ?g333333?      @r   rb   )
r8   r   r   r   r   r   ndimr   absr   )rU   r[   r   r   r   r   s         r?   test_scalar_valuesz)TestMultivariateNormal.test_scalar_values/  s6   
		t %4!%%as3SXXq! IIOOAyyq!ffRYY__Q'(!%%as3SXXq! %4!%%as3SXXq! IIOOAyyq!ffRYY__Q'(!%%as3SXXq!rA   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        j                  |||      }t        j                  |||      }t        |t        j                  |             y Nr   rb   )
r8   r   r   r   r   r   r   r   r   logrU   r[   r   r   d1d2s         r?   test_logpdfz"TestMultivariateNormal.test_logpdfJ      
		tIIOOAyyq!ffRYY__Q'( ''45 $$Qc2BFF2J'rA   c                    t         j                  j                  d       t         j                  j                  d      }t	        j
                  |      }t	        j                  |      }t	        j
                  |d d      }t	        j                  |d d      }t        |t        j                  |             t        |t        j                  |             y Nr   rb   r
   )	r8   r   r   r   r   r   r   r   r   rU   r[   r   r   d3d4s         r?   test_logpdf_default_valuesz1TestMultivariateNormal.test_logpdf_default_valuesT       			tIIOOA ''* $$Q' ''43 $$Qa0BFF2J'BFF2J'rA   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        j                  |||      }t        j                  |||      }t        |t        j                  |             y r   )
r8   r   r   r   r   r   r   r   r   r   r   s         r?   test_logcdfz"TestMultivariateNormal.test_logcdfa  r   rA   c                    t         j                  j                  d       t         j                  j                  d      }t	        j
                  |      }t	        j                  |      }t	        j
                  |d d      }t	        j                  |d d      }t        |t        j                  |             t        |t        j                  |             y r   )	r8   r   r   r   r   r   r   r   r   r   s         r?   test_logcdf_default_valuesz1TestMultivariateNormal.test_logcdf_default_valuesk  r  rA   c                    t         j                  j                  d       d}t         j                  j                  |      }t	        d|dz         D ]p  }t         j                  j                  ||      }t        j
                  ||j                        }t        ||d      }t        |j                  j                  |       r y )Nr   rd   r
   TrY   )r8   r   r   r   rangedotr   r   r   r   r   )rU   r   r   expected_rankr   r   distns          r?   	test_rankz TestMultivariateNormal.test_rankx  s    
		tyyq!"1a!e_ 	?M		=1A&&ACC.C'c$GE))..>		?rA   c           	         t        dd      D ]  }t        j                  j                  |      }t        d|      D ]  }t        j                  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                  |       |j                  |d |       }|j                  |      }|j                  |
      }t        ||       t        ||       |j                  |d |       }|j                  |      }|j                  |
      }t        ||       t        ||       |
|d d df   z   }|j                  |      }|j                  |      }t        |d       t        |t        j                            y )Nr
   rb   TrY   rf   r   )r	  r8   r   r   r
  r   r   r   r   r   r   r   r   r   r   inf)rU   r   zkr   cov_kkcov_nnr[   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  sL   q! 0	6A		"A1a[ .6IIOOAq)133 1a&)!'rr2A2v HHQK"1"1 /q1266&!###67FF1aL /rxx{F>BD.rxx{F>BD.rxx{F>BDX0055q9X0055q9X0055q9!ae,!a!a//$OOAbqE2	$OOA.	$OOA.		95	95 Qq"uX&ll62!)!8 [#.^bffW5].60	6rA   c                 X   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kD        sJ t        j                  |||d      }	t        |	j                  |       t        j                  |	t        j                   kD        rJ   y )	N
   rG   rc   r
   r   r   r   T)r   r   rZ   r   )r	  r8   r   r   r
  r   r   r   r   r   r   allr   r  )
rU   r  r   rmnr   vrXr   r   s
             r?   test_degenerate_arrayz,TestMultivariateNormal.test_degenerate_array  s    q! 	0A1a[ 0XXa[.q1!RaR%8VVAqss^'++!D)--abb=ACSXXq)vvcCi(((,33ABBCGIV[[!,vvfw.///0	0rA   c                 F   d}d}d}t        j                  ||z        }||z   }t        j                  ||ft              }t        j                  ||       d|| d | d f<   t        t        j                  j                  |      d       t        t        j                  j                  |d |d |f         t         j                         t        t         j                  j                  |d |d |f         d|f       t        |      }t        |j                  |       y )Ng     @@d   rG   dtyper   r
   )r8   expr   floatfill_diagonalr   r   r   detr  r   slogdetr   r   )rU   large_total_lognposnzerolarge_entryr   r   r   s           r?   test_large_pseudo_determinantz4TestMultivariateNormal.test_large_pseudo_determinant  s    
 !ff_t345Lhh1vU+
k* !UFGeVW 	U\\%%c*A.U\\%%c%4%$,&78"&&A		))#eteUdUl*;<O,	. 3io6rA   c                    t         j                  j                  d       d}t         j                  j                  ||      }t        j                  ||j
                        }t         j                  j                  |      }t         j                  j                  dd|      }t        j                  |||      }t        j                  |||      }t        d      D ]n  }t        d      D ]^  }	t        j                  |||	f   ||      }
t        |
|||	f          t        j                  |||	f   ||      }
t        |
|||	f   d       ` p y )Nr   rd   rG   rH   MbP?rtol)r8   r   r   r   r
  r   r   r   r   r	  r   )rU   r   datar   r   r*  desired_pdfdesired_cdfijactuals              r?   test_broadcastingz(TestMultivariateNormal.test_broadcasting  s   
		t yyq!$ffT466"yyq! IIOOAq!$ *--as;)--as;q 	EA1X E,001a4$DAaC(89,001a4$DAaC(8tDE	ErA   c                 .   t        j                  ddd      }d\  }}|dz  }t        j                  |||      }t	        j                  |||      }t        ||       t        j                  |||      }t	        j                  |||      }t        ||       y )Nr   rG   r$  )333333??      ?)r8   linspacer   r   r   r   r   )rU   r[   r   r   scaler   r   s          r?   test_normal_1Dz%TestMultivariateNormal.test_normal_1D  s     KK1b!	cSXXau% $$Qc2BXXau% $$Qc2BrA   c                 b   t        j                  ddg      }t        j                  ddgddgg      }d}d|dz
  z  }t        j                  d	d|      }t        j                  ||      \  }}t        j                  ||d
f      }||d d d d d	f<   ||d d d d df<   t        j                  |||      }	t        |	|d	      }
t        |	|d      }t        j                  ||d	   |d   dz        }t        j                  ||d   |d   dz        }t        |
|dd       t        ||dd       y )Nr   g      @rH  r   333333?i  rc   r
   r   rG   r   r   r   )locrJ  )r
   r
   {Gz?r=  atol)
r8   r   rI  meshgridemptyr   r   r.   r   r   )rU   r   r   r   deltar   xvyvposr   margin_xmargin_ygauss_xgauss_ys                 r?   test_marginalizationz+TestMultivariateNormal.test_marginalization  s)    xxc
#hhS	C9-.QUKK1a Q"Bhh1ay!Aq!GAq!G!%%c45 U+U+ ((1$q'Tc1AB((1$q'Tc1AB'4@'4@rA   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             y r   )r8   r   r   r   r   r   r   r   r   r   r   )rU   r[   r   r   norm_frozens        r?   test_frozenz"TestMultivariateNormal.test_frozen$  s    
		tIIOOAyyq!ffRYY__Q'()$4*,?,C,CAtS,QR**1-+221dC@	B*,?,C,CAtS,QR**1-+221dC@	BrA   rI   rG   r
   c                     t        j                  d      }t        j                  d      }t        ||      }t        j                  |j
                  |      sJ t        j                  |j                  |      sJ y )NrG   rG   )r8   rO   rP   r   allcloser   r   )rU   rI   r   cov_should_ber_  s        r?   2test_frozen_multivariate_normal_exposes_attributeszITestMultivariateNormal.test_frozen_multivariate_normal_exposes_attributes2  s\     wwt}q	)$
;{{;++T222{{;??M:::rA   c           
         t         j                  j                  d       d}t         j                  j                  ||      }t        j                  ||j
                        }t        j                  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                         y )
Nr   re   rH  r   r   Hz>rf   h㈵>)cond)r8   r   r   r   r
  r   r   r   r   fullro   r   pinvr   r   r   r   )	rU   r   r[   r   r   r   ri  r   psd_pinvs	            r?   test_pseudodet_pinvz*TestMultivariateNormal.test_pseudodet_pinv@  s    			tIIOOAq!ffQn||  %1GGAsO!"ffQrwwqz133/0 3T"t, 	bffRVVAcrF^&<= 	x'8'89rA   c                 >    g dg dg}t        t        t        |       y )NrK   rd   rb   rc   r   rM   r   rU   r   s     r?   test_exception_nonsquare_covz3TestMultivariateNormal.test_exception_nonsquare_covZ  s    )$j$,rA   c                     ddgdt         j                  gg}t        t        t        |       ddgdt         j
                  gg}t        t        t        |       y )Nr
   r   )r8   nanr   rM   r   r  )rU   cov_nancov_infs      r?   test_exception_nonfinite_covz3TestMultivariateNormal.test_exception_nonfinite_cov^  sF    q6Arvv;'j$0q6Arvv;'j$0rA   c                 >    ddgddgg}t        t        t        |       y )Nr
   r   rf   rp  rq  s     r?   test_exception_non_psd_covz1TestMultivariateNormal.test_exception_non_psd_covd  s     1v2wj$,rA   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  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        y # 1 sw Y   y xY w)	Nr   rb   )rb   rb   r   r   z0When `allow_singular is False`, the input matrixrE   r   )r8   r   r   r   rO   r   LinAlgErrorr   r   r   r   r   r   rL   r	   )rU   r[   r   r   emsgs         r?   test_exception_singular_covz2TestMultivariateNormal.test_exception_singular_covh  s   
		tIIOOAyyq!ggfoII!!a,dC8a,00!T3?a,33QcBa,00!T3?a,33QcB Bx"b"@]]29900< 	)C(	) 	) 	)s   E""E+c                 6   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       y )N)g0Q-?gox'V?g[S, t?gDB?gc_.?r   rG   rb   rH   )r
   rH   rG   dr
   rG   r   )rG   rb   rH  )r   rH  rH   绽|=rR  )gwk:E]?g̙Z?g0?gL8?gAG*?gh㈵>)gIى?gG?gƏ)?gėh?gEE?r
   rh  )	r8   r   rI  cosr   r   r   r   r   )rU   r_pdfr[   r  r  r'  r   r   r   r_cdfr   r_cdf2r2mean2cov2cdf2s                   r?   test_R_valuesz$TestMultivariateNormal.test_R_values{  sa     6 7 KK1a EAIq	MHHaAY!!xx	3'hh	:z:C@!%%as3U/  6 7 "%%as3U.  3 4 XXq!f!Q%xx!Q!Q(#."&&r5$7f40rA   c                     t        j                  d      }t        j                  d      }t        ||d      }|j                         }t	        |ddg       y )NrG   rG   rG   TrY   r   )r8   r   r   r   r   )rU   r   rI   modelsamples        r?   ,test_multivariate_normal_rvs_zero_covariancezCTestMultivariateNormal.test_multivariate_normal_rvs_zero_covariance  sD    xx{XXf%
#D*TJVaV$rA   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      }|j                  |      }t	        |j
                  |f       y )	Ni,  rd   r
   r%  rG   r   r   r   )r   r   r8   r   r   r:   r   )rU   Nr  r  r   s        r?   test_rvs_shapez%TestMultivariateNormal.test_rvs_shape  s     $((bhhqkqqIV\\Aq6*$((d-/XX2wQ6H-I./1 	V\\Aq6*QA.qV\\A5)rA   c                    t         j                  j                  d       d}t         j                  j                  |      }t         j                  j                  ||      }t        j                  ||j
                        }d}t        j                  |||      }t        t        j                  |j
                        |d       t        |j                  d      |d       y )N  rH     r   r<  r   )r8   r   r   r   r
  r   r   r   r   numpyr   r   )rU   r   r   r   r   r   r  s          r?   test_large_samplez(TestMultivariateNormal.test_large_sample  s     			tyyq!IIOOAq!ffQn$((sD9		&((+St<A48rA   c                    t         j                  j                  d       d}t         j                  j                  |      }t         j                  j                  ||      }t        j                  ||j
                        }t        ||      }t        |j                         t        j                  ||             t         j                  j                  |      d   }d|t        j                  dt         j                  z        dz   z  t        j                  t        j                  |            z   z  }t        ||j                                y )Nr  rH   r   rH  rG   r
   )r8   r   r   r   r
  r   r   r   r   r   eigr   pir   )rU   r   r   r   r   r   eigsdesireds           r?   test_entropyz#TestMultivariateNormal.test_entropy  s    
		tyyq!IIOOAq!ffQn s+ 	BJJL*=*E*EdC*PQ yy}}S!!$1q255y 1A 56t9MMNGRZZ\2rA   c                     t        j                  g d      }d}t        t        j                  t	        |            |       y )Nr
   r
   r
   rH  )r8   r   r   r0  r   )rU   alphar  s      r?   test_lnBzTestMultivariateNormal.test_lnB  s,    #BFF4;/9rA   c                    t         j                  j                  d      }ddg}t        j                  d      }|j                  d      dz  dz
  }|j                  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        ||       y )N   FYc@Y r   rG   )rd   rH   rG   rc   rH   lower_limit.r
   rf   r   )r8   r   r   rP   r   r   concatenater   )rU   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  s:   ii##$781vffQiJJy!!#a'JJy!!#a'"&&q$C#''45#''45nnaQqSk1S!A#X;7bAnnaQqSk1S!A#X;7bA%))#tS9%))#tS9u}w&0d#rA   c                 x   t         j                  j                  d      }|j                  d      }|j                  d      }||j                  z  }|j                  d      dz  dz
  }|j                  d      dz  dz
  }t	        j
                  ||||      }t	        ||      j                  ||      }t        j                  t	        j                  ||||            }t        j                  t	        ||      j                  ||            }	t        ||d       t        ||d       t        |	|d       y )	Nr  rH   rH   rH   rG   rH   rc   r  -C6?r<  )	r8   r   r   r   r   r   r0  r   r   )
rU   r   r   r   r  r  r  r  cdf3cdf4s
             r?   %test_cdf_with_lower_limit_consistencyz<TestMultivariateNormal.test_cdf_with_lower_limit_consistency  s   ii##$78zz!}jj CEEkJJvq 1$JJvq 1$"&&q$C"4-11!1Cvv)00D#1MNvv)$4;;A1;MNd.d.d.rA   c                    t        j                  d      }t        j                  d      }g dg dg dg dg}g dg dg dg dg}t        j                  g d      }t	        j
                  ||||      }t        ||d   |z         y )	NrH   r  rg   r
   r   r
   r   r
   r   r
   rf   rf   r
   r  r   r8   r   rP   r   r   r   r   )rU   r   r   r  r  expected_signsr   s          r?   test_cdf_signsz%TestMultivariateNormal.test_cdf_signs"  so    xx{ffQi	9i8	9i8.1!%%asBSVN23rA   c                    t        j                  dt        j                  g d      z        }t        j                  |      }d}t        j                  t        |      5  t        j                  ddg|       d d d        t        j                  t        |      5  t        ddg|       d d d        g d}t        j                  |g d|      }t        t        j                  ||      |       t        j                  |g d	|      }t        t        j                  |d|      |       y # 1 sw Y   xY w# 1 sw Y   xY w)
Nr
   rK   z7`cov` represents a covariance matrix in 3 dimensions...rE   r   )rH  rH  rH  rg   r{  r  )r8   ro   r   r+   rN   rL   r	   rM   r   r   r   r   )rU   Pr   rV   r[   r<   s         r?   test_mean_covz$TestMultivariateNormal.test_mean_cov-  s    GGA++, 003
K]]:W5 	<''A
;	< ]]:W5 	4A
3	4 !%%aJ?(,,QJ?E!%%aJ?(,,QzBCH	< 	<	4 	4s    D-D9-D69Ec                     ddg}d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)Nr
   rH   z`x` must be two-dimensional.rE   )rL   r	   rM   r   fit)rU   r>  	error_msgs      r?   test_fit_wrong_fit_data_shapez4TestMultivariateNormal.test_fit_wrong_fit_data_shape@  sA    1v2	]]:Y7 	*##D)	* 	* 	*s   AA
r   )rH   rb   c                 @   t         j                  j                  d      }|j                  d|f      }t        j                  |      \  }}t        j
                  |d      t        j                  |j                  d      }}t        ||d       t        ||d       y )	N   @,Q| r-  r   r   )ddofV瞯<r  r<  )	r8   r   r   r   r  r   r   r   r   )rU   r   r   r[   mean_estcov_estmean_refcov_refs           r?   test_fit_correctnessz+TestMultivariateNormal.test_fit_correctnessF  sy    ii##$45JJSz"/33A6'GGAA.qss0C'(7u5rA   c                     t        j                  dd      }d}t        j                  d      }t        j                  |||      \  }}t        ||       t        ||       y )N)rG   r
   rH   r   )fix_meanfix_cov)r8   rj  
atleast_2dr   r  r   )rU   r>  
mean_fixed	cov_fixedr   r   s         r?   test_fit_both_parameters_fixedz5TestMultivariateNormal.test_fit_both_parameters_fixedO  sT    wwvq!
MM"%	'++D:4=?	cT:&S)$rA   r  r  rH   c                     d}t        j                  t        |      5  t        j                  t        j                  d      |       d d d        y # 1 sw Y   y xY w)Nzd`fix_mean` must be a one-dimensional array the same length as the dimensionality of the vectors `x`.rE   rG   r  rL   r	   rM   r   r  r8   rP   )rU   r  r~  s      r?   "test_fit_fix_mean_input_validationz9TestMultivariateNormal.test_fit_fix_mean_input_validationX  sI    C]]:S1 	B##BFF1IA	B 	B 	B   +AAr  rb  )rH   rG   )rd   rd   c                     d}t        j                  t        |      5  t        j                  t        j                  d      |       d d d        y # 1 sw Y   y xY w)Nzn`fix_cov` must be a two-dimensional square array of same side length as the dimensionality of the vectors `x`.rE   rH   r  r  )rU   r  r~  s      r?   +test_fit_fix_cov_input_validation_dimensionzBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimension`  sJ     ]]:S1 	@##BFF1Iw?	@ 	@ 	@r  c                     d}t        j                  t        |      5  t        j                  ddgddgg      }t        j                  t        j                  d      |       d d d        y # 1 sw Y   y xY w)Nz2`fix_cov` must be symmetric positive semidefinite.rE   r   r   g      rG   r  )rL   r	   rM   r8   r   r   r  rP   )rU   r  r  s      r?   *test_fit_fix_cov_not_positive_semidefinitezATestMultivariateNormal.test_fit_fix_cov_not_positive_semidefinitej  sa    H	]]:Y7 	@hhR2s)45G##BFF1Iw?	@ 	@ 	@s   AA--A6c                    t         j                  j                  d      }|j                  d      }|j                  d      }t        j                  ||j                        }t        j                  ||d|      }t        j                  |      \  }}t        j                  |||      j                         }t        j                  ||      \  }	}
t        |	|       t        j                  ||	|
      j                         }||k  sJ |j                  d      }dt        j                  ||j                        z  }|
|z   }t        j                  ||	|      j                         }||k  sJ y )	Nr  rH   r  r-  r   r   r   r   r   r  :0yE>)r8   r   r   r
  r   r   r   r  r   r   r   )rU   r   rO  ru   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_meanp  sL   ii##$45jjmJJvffQn%))s#7:<155g>	8'..wY3;==@SU 	/33GcJ'Xs#&--gH29;;>35 	 )### JJv266!QSS>!!-44W:B9FH 8;su 	 (((rA   c                    t         j                  j                  d      }|j                  d      }|j                  d      }t        j                  ||j                        }t        j                  ||d|      }t        j                  |      \  }}t        j                  |||      j                         }t        j                  ||      \  }	}
t        |	t        j                  |d	             t        |
|       t        j                  ||	|
      j                         }||k  sJ |	d
|j                  d      z  z   }t        j                  |||
      j                         }||k  sJ y )Nr  rH   r  r-  r  r   r  r   r   r  )r8   r   r   r
  r   r   r   r  r   r   r   r   )rU   r   rO  ru   r   r  r  r  r  r  r  r  mean_perturbedr  s                 r?   test_fit_fix_covz'TestMultivariateNormal.test_fit_fix_cov  sJ   ii##$45jjmJJvffQn%))s/2F155g>	8'..wY3;==@SU 	/33GSI'XrwwwQ78Wc"&--gH29;;>35 	 )### "D3::a=$88-44W:H9@B 8;su 	 (((rA   N)1r   r   r   r   r   r   r  r  r  r  r"  r+  r9  rD  rK  r]  r`  rL   r   r   r8   rP   r,   from_diagonalre  rm  rr  rw  ry  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r   rA   r?   r   r   &  s   O"6((((	?26h0,70E0 A2B [[BFF1I$J$$aV,	
;;:4-1-)&>1@%*"9"3$:$(/$	4I&* [[UF+6 ,6% [[Z("((6*:*2"((5/*; <B<B [[Y%)1&)9)1&)9); <@<@@):)rA   r   c                   <    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
y	)
TestMatrixNormalc           
      2   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      |       y )Nrd   rH   r   rH  ffffff?)rb   rd   rH   r$  )r8   rj  r   r   rM   r   r   r   r   r|  r   rO   )rU   num_rowsnum_colsr   r   Vr}  s          r?   test_bad_inputzTestMatrixNormal.test_bad_input  s   GGXh'-"++h''"''8X2F*LL"++h''"''8X2F*LL 	j-'1BCj-BHHRL!Dj-Arxx|Dj-Aq9j-Aq9j-a;II!!a**BGGXx$89	;a**(H!56	; 	a1bggx6J.KLa277Hh3G+H!LrA   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                  |       y )Nrd   rH   r   rH  r  r
   r   rowcovcolcov)r   )r   )r  )r   r  )r   r   )r   r  )r8   rj  r   r   r   r   r   r:   r   r  r   )rU   r  r  r   r   r  ZZrZcIrIcI1s               r?   test_default_inputsz$TestMatrixNormal.test_default_inputs  s   GGXh'-"++h''"''8X2F*LL"++h''"''8X2F*LLHHh)*XXxm$XXq(m$[["[["[[^]&&AaBHH)	+]&&A.44)	+]&&a066]	$]&&a066]	$]&&Aa8>>)	+]&&Aa8>>)	+]&&a:@@)	+ 	]*1126]*1126]!,1126]!,33R8]!,1126]!,33R8]!4;;R@]!4;;R@]!A6;;Q?rA   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         y )Nrd   rH   r   r   r   r  )r8   rj  r   r   r   r   r  )
rU   r  r  r   UvUsVvVsr  r  s
             r?   test_covariance_expansionz*TestMatrixNormal.test_covariance_expansion  s    GGXx(#.WWXs#WWXs#[["[["]"R@GGV	]"R@GGV	]"R@GGV	]"R@GGV	rA   c                    t        dd      D ]S  }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	        |||      }|j                  d      }t	        j
                  |||d	      }t        ||       |j                  d      }	|j                  |	      }
t	        j                  |	|||      }t        |
|       |j                  |	      }t	        j                  |	|||      }t        ||       C V y )
Nr
   rb   r   rH  r  r  r   r   )r   r   r  r   )	r	  r8   rj  r   r   r   r   r   r   )rU   rA  rB  r   r   r  frozenrvs1rvs2r*  pdf1pdf2logpdf1logpdf2s                 r?   test_frozen_matrix_normalz*TestMatrixNormal.test_frozen_matrix_normal  s8   q 	/A1QZ /GGQqE3'"++a.(277Aa5#+>>"++a.(277Aa5#+>>&AaBzztz4$((a!6:<T4(JJDJ1zz!}$((1QGT4( --*'..qq1MWg.)/	/rA   c                 Z   t        dd      D ]  }t        dd      D ]  }t        j                  ||fd      }dt        j                  |      z  t        j                  ||fd      z   }dt        j                  |      z  t        j                  ||fd      z   }t	        |||      }|j                  d      }|j                  |      }|j                  |      }	|j                         }
|j                  j                         }|j                  j                         }t        j                  ||      }t        j                  |||	      }t        j                  |||	      }t        j                  ||	      }t        ||d
       t        |	|d
       t        |
|         y )Nr
   rb   r   rH  r  r  r   r   r   r  r<  )r	  r8   rj  r   r   r   r   r   r   r   flattenkronr   r   )rU   rA  rB  r   r   r  r  r*  r  r  entropy1vecXvecMr   r  r  entropy2s                    r?   test_matches_multivariatez*TestMatrixNormal.test_matches_multivariate  s\    q 	4A1QZ 4GGQqE3'"++a.(277Aa5#+>>"++a.(277Aa5#+>>&AaBJJDJ1zz!} --*!>>+ss{{}ss{{}ggal*..t$CH-44T#N.66DcJd7u=(3)4	4rA   c           	      0   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        |||      }|j	                  |d	      }|j	                  |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       |j                  |
      }t        |j                  d|f       t        d      D ]B  }t        |      D ]2  }t        j                  |
||f   |||      }t        ||||f   d       4 D y )Nrd   rH   r   rH  r  r$  r  r   r   i  r   r   rG   r  )r8   rj  r   r   r   r  newaxisr   r:   r   r	  r   )rU   r  r  r   r   r  r  r  X1X2r*  array_logpdfrA  rB  separate_logpdfs                  r?   test_array_inputz!TestMatrixNormal.test_array_input4  s{   GGXh'-"++h''"''8X2F*LL"++h''"''8X2F*LLAa:ZZQTZ2ZZQTZ2NNBrzz!Aa/0BJJq14D1EFQOQWWq!Xx89}}Q'\''!Q0q 	KA1X K"/"6"6q1vA>?#Kac1BEJK	KrA   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        |||      }|j	                  |d	      }t        j
                  |d
      }	t        |	|d       t        j                  |j                  ||z  |      j                        }
t        |
|d       t        j                  t        j                  |dd      j                  ||z  |      j                        }t        ||d       y )Nrd   rH   r   rH  r    r  r   r   r   r   r   r  r
   rG   )r8   rj  r   r   r   r   r   r   reshaper   swapaxes)rU   r  r  r   r   r  r  r  r*  sample_meansample_colcovsample_rowcovs               r?   test_momentszTestMatrixNormal.test_momentsK  s%   GGXh'-"++h''"''8X2F*LL"++h''"''8X2F*LLAa:JJADJ1ggaQ'QS1qyy8H=??@qs3r{{1Qq19989(
8 MMNQPqs3rA   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                  j                  d      d	      }t        j                  d
dgddggddgddggg      }t        ||       y )Nr
   rG   rH   rd   rf   rb   r$  r   )r   r   r  r   r   g6?gǀgcϿ@g"'@gI2͖@g^jy%@gDn3@g|\3@)r   r   r8   r   r   r   r   )rU   rC  expecteds      r?   test_sampleszTestMatrixNormal.test_samplesa  s     ""Aq6Aq6*+88aWr1g./88aVaW-...q1
 88!23!124!23!1245
 	)rA   N)r   r   r   r  r  r  r  r  r&  r.  r1  r   rA   r?   r  r    s.    M4%@N,/044K.4,*rA   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y)TestDirichletc           	      R   t         j                  j                  d       t         j                  j                  dd      }t         j                  j	                  dd|      }t        |      }t        |j                         t        j                  |             t        |j                         t        j                  |             t        |j                         t        j                  |             d}t        |      D ]  }t         j                  j	                  dd|      }|t        j                  |      z  }t        |j                  |d d       t        j                  |d d |             t        |j                  |d d       t        j                  |d d |              y Nr  r
       &.>r-  r$  rf   )r8   r   r   randintr   r   r   varr   r   r	  r   r   r   rU   r   r  r  	num_testsrA  r[   s          r?   test_frozen_dirichletz#TestDirichlet.test_frozen_dirichletv  s0   
		tIIa$		!!&#q1eQUUWimmE23QVVXy~~e45QYY[)"3"3E":;	y! 	LA		!!&#q1ANAq"v	afe(DE!CR&)9+;+;AcrFE+JK		LrA   c                 j   t         j                  j                  d       t        j                  g d      }t         j                  j	                  |d      }t        |j                  d       t        t        t        j                  ||       t        t        t        j                  ||       t	        j                  |j                  |       t	        j                  |j                  d d |       t	        j                  |j                  |       t	        j                  |j                  d d |       y )Nr  r          @      @re   r   )re   rH   rf   )r8   r   r   r   r   r   r:   r   rM   r   r   r   rU   r  r[   s      r?   "test_numpy_rvs_shape_compatibilityz0TestDirichlet.test_numpy_rvs_shape_compatibility  s    
		t)IIA.QWWf%j)--E:j)"2"2Au=acc5!acc#2h&e$Sb5)rA   c                 H   t         j                  j                  d       g d}t         j                  j                  t        j                  d|      d      j
                  }t        t        t        j                  ||       t        t        t        j                  ||       y )Nr  )r   r   r@  r7  re   r   
r8   r   r   r   maximumr   r   rM   r   r   rA  s      r?   test_alpha_with_zerosz#TestDirichlet.test_alpha_with_zeros  sg    
		tII

4 7a@BBj)--E:j)"2"2Au=rA   c                 H   t         j                  j                  d       g d}t         j                  j                  t        j                  d|      d      j
                  }t        t        t        j                  ||       t        t        t        j                  ||       y )Nr  )r   g       r@  r7  re   r   rD  rA  s      r?    test_alpha_with_negative_entriesz.TestDirichlet.test_alpha_with_negative_entries  sg    
		t II

4 7a@BBj)--E:j)"2"2Au=rA   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             y )Nr   r?  r@        @r   r   r   r  )r   r   r   r   rc   )r8   r   r   r   r   r   r   rA  s      r?   test_data_with_zerosz"TestDirichlet.test_data_with_zeros  s    -.HH)*aE"-.IMM!U3Q7I,,Q6q	BrA   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )N)r   rH  r@  rK  rL  r8   r   r   rM   r   r   r   rA  s      r?   $test_data_with_zeros_and_small_alphaz2TestDirichlet.test_data_with_zeros_and_small_alpha  F    -.HH)*j)--E:j)"2"2Au=rA   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )NrJ  )r   皙r   r  rO  rA  s      r?   test_data_with_negative_entriesz-TestDirichlet.test_data_with_negative_entries  sF    -.HH*+j)--E:j)"2"2Au=rA   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )NrJ  )r   皙?r   r  rO  rA  s      r?    test_data_with_too_large_entriesz.TestDirichlet.test_data_with_too_large_entries  rQ  rA   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr>  )rG   re   re   g$I$I?r8   r   rj  r   rM   r   r   r   rA  s      r?   test_data_too_deep_cz"TestDirichlet.test_data_too_deep_c  sF    )GGIv&j)--E:j)"2"2Au=rA   c                     t        j                  ddgddgg      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr   r?  r@  rK  )rG   rG   re         ?rY  rA  s      r?   test_alpha_too_deepz!TestDirichlet.test_alpha_too_deep  sS    3*sCj12GGIu%j)--E:j)"2"2Au=rA   c                     t        j                  g d      }t        j                  dd      }t        j                  ||       t        j
                  ||       y )Nr>  rH   re   UUUUUU?)r8   r   rj  r   r   r   rA  s      r?   test_alpha_correct_depthz&TestDirichlet.test_alpha_correct_depth  s>    )GGFE"aE"rA   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr>  r_  rH  rY  rA  s      r?   test_non_simplex_dataz#TestDirichlet.test_non_simplex_data  sF    )GGFE"j)--E:j)"2"2Au=rA   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )NrJ  )rG   re   rH  rY  rA  s      r?   test_data_vector_too_shortz(TestDirichlet.test_data_vector_too_short  G    -.GGFE"j)--E:j)"2"2Au=rA   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )NrJ  )rb   re   r   rY  rA  s      r?   test_data_vector_too_longz'TestDirichlet.test_data_vector_too_long  rf  rA   c                 
   t        j                  g d      }t        |      }g d}g d}g dg dg dg}t        |j	                         |       t        |j                         |       t        |j                         |       y )N)r   皙?r   rH  皙?r   )UUUUUU?{Gz?Q?)rm  )rp  rn  O贁N)rq  rr  ro  )r8   r   r   r   r   r9  r   )rU   r  r  expected_meanexpected_varexpected_covs         r?   test_mean_var_covzTestDirichlet.test_mean_var_cov  sh     (e'-../
 	"!&&(M:!!%%'<8!!%%'<8rA   c                 n   t        j                  dg      }t        |      }t        |j	                         j
                  d       t        |j                         j
                  d       t        |j                  dg      j
                  d       t        |j                  dg      j
                  d       y )Nr   r   r   )	r8   r   r   r   r   r   r9  r   r   )rU   r  r  s      r?   r   z TestDirichlet.test_scalar_values  sy    #e 	QVVX]]A&QUUW\\1%QUUB4[%%q)QXXrd^((!,rA   c                    t         j                  j                  d       t         j                  j                  dd      }t         j                  j	                  dd|      }t        |      }d}t        |      D ]h  }t         j                  j	                  dd|      }|t        j                  |      z  }t        |j                  |d d       |j                  |             j y r5  )
r8   r   r   r8  r   r   r	  r   r   r   r:  s          r?    test_K_and_K_minus_1_calls_equalz.TestDirichlet.test_K_and_K_minus_1_calls_equal   s     			tIIa$		!!&#q1e	y! 	9A		!!&#q1ANAafquuQx8	9rA   c                    t         j                  j                  d       t         j                  j                  dd      }t         j                  j	                  dd|      }t        |      }d}d}d }t        |      D ]  }t        |      D ]W  }t         j                  j	                  dd|      }	|	t        j                  |	      z  }	|t        j                  ||	f      }V|	}Y |j                  |j                        }
d }|D ].  }|j                  |      }|t        j                  ||      }-|}0 t        |
|        y )Nr  r
   r6  r7  r-  r$  rb   )r8   r   r   r8  r   r   r	  r   vstackr   r   appendr   )rU   r   r  r  r;  num_multiplexmrA  r  r[   rmrsxsr'  s                 r?   test_multiple_entry_callsz'TestDirichlet.test_multiple_entry_calls  s    
		tIIa$		!!&#q1e	y! 	.A<( II%%fc15RVVAY>B7+BB rttBB EE"I>2q)BB &b"-!	.rA   c                 V   t         j                  j                  d       t         j                  j                  ddd      }t	        |      }t        |d   |d         }d}t        |      D ]f  }t         j                  j                  ddd      }|t        j                  |      z  }t        |j                  |      |j                  |g             h t        |j                         |j                         d          t        |j                         |j                         d          y )Nr  r7  r-  rG   r   r
   r$  )r8   r   r   r   r   r   r	  r   r   r   r   r9  )rU   r  r  r  r;  rA  r[   s          r?   test_2D_dirichlet_is_betaz'TestDirichlet.test_2D_dirichlet_is_beta,  s    
		t		!!&#q1eq58$	y! 	6A		!!&#q1ANAa!%%*5	6
 	AFFHaffhqk2AEEGQUUWQZ0rA   N)r   r   r   r<  rB  rF  rH  rM  rP  rT  rW  rZ  r]  ra  rc  re  rh  rv  r   ry  r  r  r   rA   r?   r3  r3  t  sc    L$
*>>C>>>>>#>>>9$	-9.:1rA   r3  c                     t        j                  ddg      } t        j                  dgg      }t        t        t        | |       	 t	        | |       y # t        $ r-}d}t        t        |      d t        |       |       Y d }~y d }~ww xY w)Nr   r   zDimension mismatch)r8   r   r   rM   r   r   strr   )r   sigmar}  r~  s       r?   ,test_multivariate_normal_dimensions_mismatchr  =  sw     
3*	BHHseWE*12u=
-B& -"SVISX&,,-s   A 	B	#BB	c                   0    e Zd Zd Zd Zd Zd Zd Zd Zy)TestWishartc                    t        j                  dd      }ddgt        j                  d      t         j                  d   t        j                  dd      g}|D ]N  }t        d|      }t	        |j
                  |       t	        |j
                  j                  |j                         P t        j                  ddgddgg      }ddgt         j                  d   t        j                  ddgddgg      g}|D ]N  }t        d|      }t	        |j
                  |       t	        |j
                  j                  |j                         P t        t        t        dt        j                  d             t        dt        j                  d             t        j                  dd      }t        t        t        d|       y )Nr
   rG   ndminr   r
   rG   rV  rH   )
r8   r   r_r   r   rJ  r:   r   rM   rP   )rU   
true_scalescalesrJ  ws        r?   test_scale_dimensionsz!TestWishart.test_scale_dimensionsQ  st    XXaq)
CHHQKEE!HHHQa 
  	:E5!A*-
(8(89	: XX!u !!u& '
 qEEE#JHHqee 
  	:E5!A*-
(8(89	: 	j'1bffQi8 	RVVAY !$j'1e4rA   c           
      \   ddgt        j                  d      t         j                  d   t        j                  dd      t        j                  dgd      g}t        dd      }|j	                  t        j                  dd            }|D ]  }t        |j	                  |      |        g dt         j                  d   t        j                  g dd      g}t        dd      }|j	                  t        j                  g dd            }|D ]  }t        |j	                  |      |        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            }|j	                  t        j                  ddgddgg      d d d d t         j                  f         }|D ]  }t        |j	                  |      |        y )Nr
   rG   r  rH   rK   r  r   )r8   r   r  r   r   r   r!  rP   )rU   r*  r  densityr[   s        r?   test_quantile_dimensionsz$TestWishart.test_quantile_dimensions|  s   
 CHHQKEE!HHHQa HHaS"
 AaL%%!,- 	,Aq7+	,
 EE%LHHWA&
 AaL%%23 	,Aq7+	, qEHHQKEE#JHHqee HHqee "**n.	
 AbffQi %%1Q%#$Q%") **+Abjj.: ; 	,Aq7+	,rA   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
                  |      }|j                  |        t        j                  |      j
                  }ddt        j                  ddd      fd||fg}|D ]  \  }}}t        ||      }t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j!                  |      t        j                   |||              y 	Nrd   r
   rG   rf   r  rb   r$  r   )r8   ro   r   tril_indicesr
  r   r	  r|  r   rI  r   r   r9  r   moder   r   )	rU   r   rJ  r*  rA  r[   
parametersdfr  s	            r?   r`  zTestWishart.test_frozen  s    		#q(),.IIcSUmq6H,IboocR()uww& q 	A		#!ax/0A,.IIcSUmq6H,IAboocR()qssAAHHQK		
 HHQKMM BKKR+,N


 ) 	>NRE"A'++b%"897<<E#:;7<<E#:;goob%&@Aq7;;q"e#<=	>rA   c                    d}d}t        j                  |      }d|d<   d|d<   t        ||      }t         j                  j	                  d       t        j
                  ||      }t         j                  j	                  d       |j                         }t         j                  j	                  d       t         j                  j                  d      }t         j                  t         j                  j                  |      t         j                  j                  |dz
        t         j                  j                  |d	z
        f   dz  }t        j                  |      }	||	t        j                  |d
      <   t         j                  j                  |      }
|
j                  |	      }t        j                  ||j                        }t        ||       t        ||       y )NrH   r$  rH  r   r
   r   i r   r
   rG   rf   r  )r8   rP   r   r   r   r   r   r  	chisquarero   r  r   r   r
  r   r   )rU   r   r  rJ  r  w_rvsfrozen_w_rvscovariances	variancesru   DDAmanual_w_rvss                r?   test_wishart_2D_rvszTestWishart.test_wishart_2D_rvs  sn    sc
c
 B 			vB&
		vuuw 			vii&&A&.EEII#II1%II1%'
 		 GGI(3"//#
$% IIu%UU1Xvvb"$$' 	|,l3rA   c                    t         j                  j                  d       d}d}t        j                  |      }t        j                  dddt
              }t        j                  ddd      }|D ]  }t        ||      }t        |      }t        |j                         |j                                t        |j                         |j                                t        |j                         |j                                t        |j                  |      |j                  |             |j                  |	      }	|f}
d
}t        d|
||	        y )N^   r
   r$  rG   r.  r   numr   rP  r   )r8   r   r   rP   r   r1  rI  r   r   r   r9  r   r   r   r   r   )rU   snr   rJ  df_ranger*  r  r  cr   r=   r  s               r?   test_1D_is_chisquaredz!TestWishart.test_1D_is_chisquared  s    
 			vs99QAU3KKB2& 	=BE"ARA AEEGQUUW-AFFHaffh/AIIK5 AEE!HaeeAh/ %%R%.C5DE"64<!	=rA   c                    t         j                  j                  d       d}d}d}t        j                  t        j                  d      dz         }t        j                  d      |t        j
                  dd      <   t        j                  |j                  |      }t        j                  |df      }|j                  j                  |      j                  |      j                         }t        ||      }t        ||	      }t        |j                         |j                                t        |j                         |j                                t        |j                         |j                                t        j                   d
dd      }	t        |j#                  |	      |j#                  |	             |j%                  |      }
|d|f}d}t'        d|||
       y )Nr  r  r$  rd   r
   rc   rf   r  rJ  r   r  r   r   rP  r   )r8   r   r   ro   r   r  r
  r   rO   r   r   r   r   r9  r   r   rI  r   r   r   )rU   r  r  r   rJ  lamdasigma_lamdar  r  r*  r   r=   r  s                r?   test_is_scaled_chisquaredz%TestWishart.test_is_scaled_chisquared  s`   
 			v		!Q'*,))A,booa2&'uww&Q ggkk%(,,U3;;=B$;' 	)!&&(+		QYY[1 KKB2&a!%%(+ eeen1[!vtUC8rA   N)	r   r   r   r  r  r`  r  r  r  r   rA   r?   r  r  P  s$    )5V/,b>@*4X=>!9rA   r  c                   h   e Zd Zd Zd Zd Zej                  j                  dddg      d        Z	d Z
d	 Zej                  j                  ddd
g      d        Zd Zej                  j                  dddg      d        Zd Zej                  j                  ddd
g      d        Zd Zd Zd Zy)TestMultinomialc                 b   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       y )NrH   rd   re   r   r  g&Mtyr  r<  rH   rd   r   r   r  ri   )r   logpmfr   r8   r  rt  )rU   vals1vals2vals3vals4s        r?   test_logpmfzTestMultinomial.test_logpmf<  s    ""5!Z81=""Aq61r2h7""Aq61r2h7zz""Aq61r1g6rvvD1rA   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       y )Nr  re   r  rH   r   r  r<  )rc         r   rG  rc   r   )r   r  r!   r   pmfrU   val1val2s      r?   test_reduces_binomialz%TestMultinomial.test_reduces_binomialI  sf     !!&!Z8||Aq#&d.vr:6yyB$d.rA   c                     dg d}}ddddddd	dd
dd
}|D ](  }t        t        j                  |||      ||   d       * y )NrH   )g      ?r\  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rH   )r
   r   rG   )rG   r   r
   )rH   r   r   r   r  rG   r
   r   )r   rG   r
   r  )r   rH   r   +=r  )r   r   r  )rU   r   pr_valsr[   s        r?   test_RzTestMultinomial.test_RT  s_     $1([([([([([	B
  	MAKOOAq!4fQieL	MrA   r   r   rH   c                     t        j                  |dgdz  dd      }t        j                  j	                  d      }|j                  |dgdz  d      }t        ||       y )Nr\  rH   re   {   r   r   )r   r   r8   r   RandomStater   )rU   r   sc_rvsrndmnp_rvss        r?   test_rvs_npzTestMultinomial.test_rvs_npe  sY     TF1H13Gyy$$S)!!!dVAXA!6VV$rA   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 y )N)rb   rb   r
   r
   r  r<  r  re   r  g5
?rH   r   r  rf   	   r  g*7?g<Wƌ?r   rG   r.  rd   rG   rH   rH   r   rc   )gUUUUUU?r`  r   gߦ?rg   r  )r   r  r   r8   rT  float64r   )	rU   vals0r  r  r[   r  r  vals5vals6s	            r?   test_pmfzTestMultinomial.test_pmfm  sJ   a.qt,q(31=1Q%1"a1a&0A BA (*I 6A?dKHHU"**-1h/UBHHRrzz:;1q(3qt,	1.?@~D9	1.?@zz	1.?@zzrA   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
       y )Nr
   rG   rH   r   rG  r   rj  gv?g~jt?r  r<  rd   r   )r   r  r   )rU   r  r  r  r  r  s         r?   test_pmf_broadcastingz%TestMultinomial.test_pmf_broadcasting  s   ARHr2h+?@d|$7AAR9ayt41a&1a&!1 2ABx@q	{6A1#sr2h?$!T:!Q!AQC5'RHE4)T:rA   rb   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       y )	N)r   r   rH  r   rj  r   rH  r  r  r<  r   r   r   )rU   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.rA   c                 `   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	
       y )Nrb   r   rG  r   rj  g?gܿgr  r<  rd   g
ףp=
?g
ףp=
׿r   r  rl  rM  gzG?gzGrF  g333333r  rU   r  r  cov3cov4cov5cov6s          r?   test_cov_broadcastingz%TestMultinomial.test_cov_broadcasting  s    qB8b"X"67tdC[)RIRy+ABd.1vBx0ttSk*c4[4+,FGd.1vR2r(';<8$x&9:8$x&9:<d.rA   rG   c                 x    t        j                  |ddg      }t        |t        j                  |d      d       y Nr   rj  r  r<  r   r   r   r!   )rU   r   ent0s      r?   r  zTestMultinomial.test_entropy  s1     ""1r2h/emmAr2>rA   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       y )NrG   rH   r   r   r  r<  re   r  r  rl  rM  r  )rU   r  ent1ent2s       r?   test_entropy_broadcastingz)TestMultinomial.test_entropy_broadcasting  s   ""Aq6B84u}}Q3U]]1b5IJ!	# ""Aq6RHr2h+?@u}}Q3U]]1b5IJ!	# ""QC!:R2r(/CD--2.a0DE--2.a0DEG!	#rA   c                 `    t        j                  |ddg      }t        ||dz  |dz  gd       y r  r   r   r   )rU   r   mean1s      r?   	test_meanzTestMultinomial.test_mean  s0      RH-"ad|$7rA   c                 `    t        j                  ddgddg      }t        |ddgddggd	
       y )Nrb   rc   r   rj  r   rK  g433333?g433333@r  r<  r  )rU   r  s     r?   test_mean_broadcastingz&TestMultinomial.test_mean_broadcasting  s5      !Q"b2ttTl;$GrA   c                    t         j                  j                  d       d}d}g dg dg dg dg dg}t        j                  |t         j                  	      }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                         t        j                  ||             y )
Nr      )r   r   r   rl  r   r   r   r  r   r   r
      r   r
   r
   r$  r
   r
   r
   r  r
   r
   rG   r  r.  )
r8   r   r   r9   r  r   r   r  r  r   )rU   r   pvalsr[   	mn_frozens        r?   r`  zTestMultinomial.test_frozen  s    
		t 
:i	BJJq

+5)		a(+//!Q*FG	((+[-?-?1e-LM	))+[-@-@E-JKrA   c                 (   d}t         j                  j                  d      }|j                  |      }d|d<   |t        j                  |      z  }t        j                  |      }t        j                  |||      }t        j                  |      sJ y )NX   l   iRZY gKH9rf   )r8   r   r   r   rO   r   r  isfinite)rU   r   r   r  r[   r  s         r?   test_gh_11860zTestMultinomial.test_gh_11860  sx    
 ii##$78JJqM"	RVVAYGGAJ##Aq!,{{6"""rA   N)r   r   r   r  r  r  rL   r   r   r  r  r  r  r  r  r  r  r  r`  r
  r   rA   r?   r  r  ;  s    2	/M" [[S1a&)% *%6;  [[S1a&)/ *// [[S1a&)? *?# [[S1a&)8 *8H
L#rA   r  c                   *    e Zd Zd Zd Zd Zd Zd Zy)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
                  |      }|j                  |        t        j                  |      j
                  }ddt        j                  ddd      fd||fg}|D ]  \  }}}t        ||      }t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j!                  |      t        j                   |||              y r  )r8   ro   r   r  r
  r   r	  r|  r   rI  r   r   r9  r   r  r   r   )	rU   r   rJ  r*  rA  r[   r  r  iws	            r?   r`  zTestInvwishart.test_frozen  s   
 		#q(),.IIc3q5k!m,DboocR()uww& q 	A		#!ax/0A,.IIc3q5k!m,DAboocR()qssAAHHQK		
 HHQKMM BKKR+,N


 ) 	ENRB&B:>>"e#<=JOOB$>?JOOB$>?BFF1Iz~~aU'CD	ErA   c                    t         j                  j                  d       d}d}t        j                  |      }t        j                  dddt
              }t        j                  dd	d	
      }|D ]  }t        ||      }t        |dz  d      }t        |j                         |j                                t        |j                         |j                                t        |j                  |      |j                  |             |j                  |      }	|dz  ddf}
d}t        d|
||	       t        |j                         |j                                 y )Nr  r  r
   rb      rG   r.  r   r$  r  rH  r  r   r   rP  r   )r8   r   r   rP   r   r1  rI  r   r   r   r9  r   r   r   r   r   )rU   r  r   rJ  r  r*  r  r  igr   r=   r  s               r?   test_1D_is_invgammaz"TestInvwishart.test_1D_is_invgamma  s   
 			vs99QAU3KKB2& 	8BB&B"Q$d+B BFFHbffh/BGGIrwwy1 BFF1Irvvay1 &&b&/CqD!T?DE":tUC@ BJJL"**,7%	8rA   c                    d}d}t        j                  |      }d|d<   d|d<   t        ||      }t         j                  j	                  d       t        j
                  ||      }t         j                  j	                  d       |j                         }t         j                  j	                  d       t         j                  j                  d      }t         j                  t         j                  j                  |dz
        t         j                  j                  |d	z
        t         j                  j                  |      f   dz  }t        j                  |      }	||	t        j                  |d
      <   t         j                  j                  |      }
t         j                  j                  |	j                  |
j                        j                  }t        j                  ||j                        }t!        ||       t!        ||       y )NrH   r$  rH  r   r  iHG	 r   rG   r
   rf   r  )r8   rP   r   r   r   r   r   r  r  ro   r  r   r   solver   r
  r   )rU   r   r  rJ  r  iw_rvsfrozen_iw_rvsr  r  ru   r  Lmanual_iw_rvss                r?   test_invwishart_2D_rvsz%TestInvwishart.test_invwishart_2D_rvs)  s    sc
c
 E" 			vE*
		v 			vii&&A&.EEII1%II1%II#%
 		 GGI(3"//#
$% IIu%IIOOACC%''q!## 	.}5rA   c                 h   d}d}dD ](  }t        j                  t        j                  |      dz         }t        j                  ||dz
  z  dz        |t        j                  |d      <   t        j                  |j
                  |      }t        ||      }|j                         }|j                         }||z  dz  }|j                  |d	
      }	|	j                  d      }
||dz   z  dz  }d|z  }t        j                  d|dz  z
        }t        j                  |
|z
  |z  d|      r)J  y)z1Test that sample mean consistent with known mean.r$   N  )r
   rb   r
   rG   rf   r  rH  r   r   r   r   rP  r  N)r8   ro   r   r  r
  r   r   r   r9  r   r   ppfrc  )rU   r  sample_sizer   rJ  r   	Xmean_expXvar_exp	Xmean_stdr*  	Xmean_estntests	fail_ratemax_diffs                 r?   test_sample_meanzTestInvwishart.test_sample_meanW  s$     	CGGBIIcNQ./E02		#q/A:M0NE"//#,-FF577E*Eb%(D		IxxzH!K/#5Ik=AAI#']A%FvIxxIM 12H;;Y&)3  !	rA   c                 l   t        j                  g dg dg dg dg      }t        j                  g dg dg dg dg      }d	}t        j                  |||      }|j                  d
   }t         j
                  j                  |      \  }}t         j
                  j                  |      \  }}t         j
                  j                  ||      }	|dz  |z  ||z  dz  t        j                  d      z  z
  t        |dz  |      z
  ||z   dz   dz  |z  z
  d|	j                         z  z
  }
t        ||
       y)zRegression test for gh-8844.)rG   r
   r   rH  )r
   rG   rH  rH  )r   rH  rH   r
   )rH  rH  r
   rG   )r  re   rH   r
   )re   r  rb   r
   )rH   rb   r  rG   )r
   r
   rG   r  rc   r   rG   r
   rH  N)r8   r   r   r   r:   r   r4  r  r   r1   tracer   )rU   r*  Psinuprobr  siglogdetX	logdetPsir   r0  s              r?   test_logpdf_4x4zTestInvwishart.test_logpdf_4x4r  s%   HHn&$&( ) hh$$$& '   B,GGAJyy((+W**3/YIIOOAs#T9$!tAvrvvay()"2a4+, Avz1nW,- !'')m	$
 	h'rA   N)r   r   r   r`  r  r  r%  r.  r   rA   r?   r  r    s    E@8B,6\6(rA   r  c                   *    e Zd Zd Zd Zd Zd Zd Zy)TestSpecialOrthoGroupc                 F   t         j                  j                  d       t        j                  d      }t        j
                  g dg dg dg      }t        ||       t         j                  j                  d      }t        j                  d|      }t        ||       y )N  rH   )g(fg^A.g*B?)g:d?g2ugi}?)gR#xlF?g^`D?g?r   r   )r8   r   r   r   r   r   r   r  )rU   r[   r0  r   s       r?   test_reproducibilityz*TestSpecialOrthoGroup.test_reproducibility  s    
		s##A&88CBAC D 	"!X.yy,,#,6##ALA!!X.rA   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y Nr  r
   r   )r   rM   r   r   rU   s    r?   test_invalid_dimz&TestSpecialOrthoGroup.test_invalid_dim  sN    j"5"9"94@j"5"9"96Bj"5"9"91=j"5"9"93?rA   c                     d}t        |      }|j                  d      }t        j                  |d      }t        ||       y )Nre   r   r   )r   r   r   )rU   r   r  r  r  s        r?   test_frozen_matrixz(TestSpecialOrthoGroup.test_frozen_matrix  s=    $S)zztz,"&&s>T4 rA   c                    t        dd      D cg c]'  }t        d      D ]  }t        j                  |       ) }}}|D cg c]!  }t        j                  j                  |      # }}t        |dgdz  d       |D ]L  }t        t        j                  ||j                        t        j                  |j                  d                N y c c}}w c c}w )	NrG   r  rH   r      vIh%<=r<  r   )r	  r   r   r8   r   r3  r   r   r
  r   rP   r:   )rU   r   rA  r  r[   detss         r?   test_det_and_orthoz(TestSpecialOrthoGroup.test_det_and_ortho  s    q!Qx! "%%c* !* ! !
 +--Q		a --rd2gE2  	:A%bffQn&(ffQWWQZ&8:	:!
 .s   ,C&Cc                    d}d}d}t         j                  j                  d       t        j                  ||      }d}|D ci c]'  \  }}||ft        |D cg c]
  }||   |    c}      ) }	}}}|D 
cg c]  }
|D ]  }|
|kD  s	|
|f  }}
}|D cg c]  \  }}t        |	|   |	|         d    }}}t        |gt        |      z  |       y c c}w c c}}}w c c}}
w c c}}w )Nrb   r(  皙?r2  r   rN  r  )r
   rd   r  r
   )	r8   r   r   r   r   sortedr   r   r   rU   r   r  ks_probr  elserecr[   proje0e1pairsp0p1ks_testss                   r?   	test_haarzTestSpecialOrthoGroup.test_haar  s     
		s $$Sw7 +HKLLfb"R&R!8!B%)!899LL$'Ab#ABb"bAAADIJRHT"XtBx03JJ7)CJ.9 "9LAJ*   CC(	C:C"
C"C(CN)r   r   r   r3  r7  r9  r>  rO  r   rA   r?   r0  r0    s    
/@!::rA   r0  c                       e Zd Zd Zd Zd Zd Zej                  j                  dg d      d        Z
d Zej                  j                  d	        Zy
)TestOrthoGroupc                 \   d}t         j                  j                  |       t        j                  d      }t        j                  d|      }t        t         j                  j                  |      d       t        j                  g dg dg dg      }t        ||       t        ||       y )Nr2  rH   r   rf   )gm?gӠh"gEo?)g~7ݲC?g>Ŀg0J_ٿ)gݱ&ǿg 6qrg`X|[)
r8   r   r   r   r   r   r   r3  r   r   )rU   r   r[   r   r0  s        r?   r3  z#TestOrthoGroup.test_reproducibility  s    
		tOOA__QT2BIIMM!,b188<==? @ 	"!X.!"h/rA   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y r5  )r   rM   r   r   r6  s    r?   r7  zTestOrthoGroup.test_invalid_dim  sB    j+//48j+//6:j+//15j+//37rA   c                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                  d      }t        ||       t        ||       y )Nre   r   r   r   r
   r   )r   r   r   rU   r   r  frozen_seedr  r  rvs3s          r?   r9  z!TestOrthoGroup.test_frozen_matrix  sa    S!!#D1zztz,s6A&T4 T4 rA   c                    t        dd      D cg c].  }t        d      D cg c]  }t        j                  |       c}0 }}}t        j                  |D cg c]/  }|D cg c]!  }t        j
                  j                  |      # c}1 c}}      }t        t        j                  |      t        j                  |j                        d       |D ]S  }|D ]L  }t        t        j                  ||j                        t        j                  |j                  d                N U y c c}w c c}}w c c}w c c}}w )NrG   r  r$  r<  r<  r   )r	  r   r   r8   r   r   r3  r   fabsrO   r:   r   r
  r   rP   )rU   r   rA  r  xxr[   r=  s          r?   r>  z!TestOrthoGroup.test_det_and_ortho  s     q& b	# s# # & &
 xx"EBB7q"))--*7EFrwwtzz':G  	>B >)"&&ACC.*,&&*<>>	># &
 8Es-   D2D-D2	D=
#&D8	D=
-D28D=
r   )rG   rb   r$  r  c                 z   t         j                  j                  d      }t        |      }|j	                  d|      }t
        j                  j                  |      }t        j                  |dkD        }t        |      }t        j                  ||      }|j                  d      \  }	}
|	dcxk  r|
k  sJ  J y )	Nl   <`Lr r   r  r   r   gffffff?)confidence_levelrH  )r8   r   r   r   r   r   r   r3  r   r   r-   	binomtestproportion_ci)rU   r   r   r   r   r=  r  r   r;   lowhighs              r?   test_det_distribution_gh18272z,TestOrthoGroup.test_det_distribution_gh18272   s     ii##$78s#hhDsh3||$FF4!8Iooa#%%t%<	TS4rA   c                    d}d}d}t         j                  j                  d       t        j                  ||      }d}|D ci c]'  \  }}||ft        |D cg c]
  }||   |    c}      ) }	}}}|D 
cg c]  }
|D ]  }|
|kD  s	|
|f  }}
}|D cg c]  \  }}t        |	|   |	|         d    }}}t        |gt        |      z  |       y c c}w c c}}}w c c}}
w c c}}w )Nrb   r(  r@  i  r   rA  r
   )	r8   r   r   r   r   rB  r   r   r   rC  s                   r?   rO  zTestOrthoGroup.test_haar  s     
		s__Sw/ +HKLLfb"R&R!8!B%)!899LL$'Ab#ABb"bAAADIJRHT"XtBx03JJ7)CJ.9 "9LAJrP  c                 :   t         j                  j                  d       d }t        dd      D ]i  dfd	} ||      } |t        j
                  j                  j                        }t        j
                  j                  ||      \  }}t        d|       k y )Nr2  c                     t         j                  j                  t         j                  j	                  | | f            \  }}}t        j
                  ||      S Nr   )r8   r   r   r   r   r
  )r   r   _sr   s       r?   random_orthoz<TestOrthoGroup.test_pairwise_distances.<locals>.random_ortho-  s@    yy}}RYY%5%5C:%5%FGHAr166!Q<rA   rG   rc   c                    t        j                  t        |      D cg c]+  }t        j                   |        |       z
  dz        - c}      }|t         j                  j                  | ||j                        z  }|S c c}w )Nr]  rG   r   )r8   r   r	  r   r   r   r:   )r   r  epsr   r-   r   s        r?   generate_test_statisticszHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statistics2  sx    "1X" FFCCL33<7!;<" 
 **C45;;*GG"s   0Br@  )r(  r  )
r8   r   r   r	  r   r-   r   r   r   r   )rU   ri  rl  r0  rC  _Dr  r   s          @r?   test_pairwise_distancesz&TestOrthoGroup.test_pairwise_distances(  s     			s	  A; 	&C 0=H-ekk.E.E.I.IJFKK((6:EBc1%	&rA   N)r   r   r   r3  r7  r9  r>  rL   r   r   rc  rO  slowrn  r   rA   r?   rR  rR    s^    08
!> [[UN3
  4
 :6 [[& &rA   rR  c                   *    e Zd Zd Zd Zd Zd Zd Zy)TestRandomCorrelationc                    t         j                  j                  d       d}t        j                  |      }t        j                  |d      }t        j
                  g dg dg dg dg      }t        ||       t        ||       y )Nr2  rH  rj  rF  r   r   )r   ѓ2ǿA?Ϳ)rt  r   4($?R}%?)ru  rw  r   qTnƿ)rv  rx  ry  r   )r8   r   r   r   r   r   r   )rU   r  r[   r   r0  s        r?   r3  z*TestRandomCorrelation.test_reproducibilityD  sp    
		s!""4(##Ds;88A@@AC D 	"!X.!"h/rA   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       y )	Ntestr   r
   rG   rH   rd   g      )r
   rG   r   )r   rM   r   r   r6  s    r?   test_invalid_eigsz'TestRandomCorrelation.test_invalid_eigsP  s    j"4"8"8$?j"4"8"8&Aj"4"8"8#>j"4"8"83%@j"4"8"8Aa5!A-Hj"4"8"83*Ej"4"8"8*ErA   c                     d}t        |      }t        |d      }t        j                  |d      }|j                  d      }|j                         }t        ||       t        ||       y )Nrs  r2  r   r   )r   r   r   )rU   r  r  rW  r  r  rX  s          r?   r9  z(TestRandomCorrelation.test_frozen_matrixY  s_    !#D)(C8!%%d=zzsz+ T4 T4 rA   c           	      H   d }t         j                  j                  d       t        dd      D cg c])  } ||t         j                  j	                  |            + }}|j                  g d       |D cg c]  }dgt        |      z   }}|D cg c]  }t        j                  |       }}|D cg c]4  }t        j                  t         j                  j                  |            6 }}|D cg c]  }t        j                  |       }	}t        ||	dd	       |D cg c]  }t        j                  |       }
}t        |
|      D ]  \  }}t        ||d
        |D ]  }t        ||j                   d
        y c c}w c c}w c c}w c c}w c c}w c c}w )Nc                 $    | |z  t        |      z  S r7   )r   )rA  r}  s     r?   r   z3TestRandomCorrelation.test_definition.<locals>.normm  s    Q3s1v:rA   r  rG   rc   r   )rd   r   r   r   r   r<  rQ  r<  )r8   r   r   r	  r   r|  r   r   r   rZ  r   r3  prodr   ro   zipr   )rU   r   rA  r  r}  rO   r  r[   r=  
dets_knowndiagsr  r  s                r?   test_definitionz%TestRandomCorrelation.test_definitione  sf   	 			s<A!QKHqQ		))q)12HHI%)*SV**156A $$Q'66 466a		a()66*./Qbggaj/
/ju5A &((((t$ 	.DAqAqu-	.  	0AAqss/	0) I +6 7/ )s#   .F8FF69F5F&F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                  |j                               }t        ||j                  j                  |      j                  |             t        j                  d	dgdd
ggt              }t        j                  |j                               }t        ||j                  j                  |      j                  |             d d d        t        j                  ddgddggt              }t        j                  |j                               }t        |d   d       t        j                  ddgddggt              }t        j                  |j                               }t        |d   d       y # 1 sw Y   xY w)Nr   r   r
   r.  ignore)overrf   gu <7~rG  rV  rG   rN  gMk   @)r8   r   r1  r   _to_corrr   errstate	nextaftercopyr   r
  )rU   r  gm0s       r?   test_to_corrz"TestRandomCorrelation.test_to_corr  s    HHsAhA'u5''*288aVaX$678
 [[h' 		31a&2q'*+AE1:2<<1+='>?uMB"++BGGI6AAqsswwr{q12C<%6eDB"++BGGI6AAqsswwr{q12		3 XX1v1v&e4''	2#" XX!}q!f-U;''	2#"'		3 		3s   2D II
N)r   r   r   r3  r|  r9  r  r  r   rA   r?   rq  rq  C  s    
0F
!"0H#rA   rq  c                   ,   e Zd Zej                  j                  dddg      ej                  j                  dg d      d               Zej                  j                  dg d      d        Zd	 Zej                  j                  dg d
      d        Z	y)TestUniformDirectionr   r
   rH   r   Nr
   rb   )rb   rd   c                    t         j                  j                  d      }t        ||      }|j	                  |      }t        j
                  |      t        j                  |      }}|j                  |||      j                  }|j                  |k(  sJ t         j                  j                  |d      }	t        |	d       y )N   Sid)_i4 r   r   rf   r   r   )r8   r   r   r'   r   r   rP   r   r:   r   r   r   )
rU   r   r   r   uniform_direction_distr  r   r   expected_shapenormss
             r?   r1  z!TestUniformDirection.test_samples  s     ii##$78!23S!A(,,T2HHSM266#;c00s0FLL}}...		wR0r"rA   )Nr   r  r   c                     d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)NzMDimension of vector must be specified, and must be an integer greater than 0.rE   )rL   r	   rM   r'   r   )rU   r   rV   s      r?   r7  z%TestUniformDirection.test_invalid_dim  s:    <]]:W5 	'!!#&	' 	' 	's	   =Ac                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                         }t        ||       t        ||       y )Nrb   r2  r   r   )r'   r   r   rV  s          r?   test_frozen_distributionz-TestUniformDirection.test_frozen_distribution  s_    "3''#6zzsz+ $$Ss; T4 T4 rA   )rG   rb   r  c                    t         j                  j                  d      }t        ||      }|j	                  d      \  }}|||z  |z  z  }|t         j
                  j                  |      z  }t        ||z  dd       |j	                  d      }||z  }||z  }t        j                  ||      }	|	t         j                  z  }	|	dt         j                  z  z  }	t               }
t        |	|
j                        }|j                  d	kD  sJ y )
Nl   @9Y sr   rG   r   r   r  r  '  r@  )r8   r   r   r'   r   r   r   r   arctan2r  r   r    r   pvalue)rU   r   r   spherical_distv1v2r  s1s2anglesuniform_distkstest_results               r?   test_uniformz!TestUniformDirection.test_uniform  s    ii##$78*3S9###+B
b2gl
biinnR  R/ $$%$0r\r\B# 	"%%!BEE'yv|'7'78##d***rA   N)
r   r   r   rL   r   r   r1  r7  r  r  r   rA   r?   r  r    s    [[UQF+[[V%9:	# ; ,	# [[U$:;' <'
! [[UI.+ /+rA   r  c                   *    e Zd Zd Zd Zd Zd Zd Zy)TestUnitaryGroupc                    t         j                  j                  d       t        j                  d      }t        j                  dd      }t        j
                  g dg dg dg      }t        ||       t        ||       y )Nr2  rH   r   )y~p?yZ?y뉦?ĭ?y8Z?&4?)yEHξr?8i?ye??+ݓݿyu=ٿB۽'?)yqXQÿ?yN6ҿzܷy! 8l?2W'?)r8   r   r   r   r   r   r   )rU   r[   r   r0  s       r?   r3  z%TestUnitaryGroup.test_reproducibility  sg    
		sa qs388IHKM
 	"!X.!"h/rA   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y r5  )r   rM   r   r   r6  s    r?   r7  z!TestUnitaryGroup.test_invalid_dim  sJ    j-"3"3T:j-"3"3V<j-"3"3Q7j-"3"3S9rA   c                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                  d      }t        ||       t        ||       y )Nre   r2  r   r   r
   r   )r   r   r   rV  s          r?   r9  z#TestUnitaryGroup.test_frozen_matrix  sc    s##Cc2zzsz+  37A&T4 T4 rA   c                 N   t        dd      D cg c]'  }t        d      D ]  }t        j                  |       ) }}}|D ]\  }t        t	        j
                  ||j                         j                        t	        j                  |j                  d         d       ^ y c c}}w )NrG   r  rH   r   r  r  )
r	  r   r   r   r8   r
  conjr   rP   r:   )rU   r   rA  r  r[   s        r?   test_unitarityzTestUnitaryGroup.test_unitarity	  s    q!Qx! $ !$ ! !
  	SABFF1affhjj1266!''!*3EER	S!s   ,B!c                 "   d}d}t         j                  j                  d       t        j                  ||      }t        j
                  |D cg c]!  }t        j                  j                  |      # c}      }t        j                  |j                  |j                        }t        |j                         t        t         j                   dt         j                  z        j                         }t#        |j$                  dkD         y c c}w )Nrb   r(  r2  r   rG   r@  )r8   r   r   r   r   r{  r   r   eigvalsr  imagrealr    ravelr   r  r   r   r  )rU   r   r  r  r[   r  r;   s          r?   rO  zTestUnitaryGroup.test_haar	  s    
 
		ss1 yy2>a%,,..q1>?JJtyy$)),QWWY"%% 8 < <=

T!" ?s   &DN)r   r   r   r3  r7  r9  r  rO  r   rA   r?   r  r    s    0:
!S#rA   r  c                   z   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
                  j                  de      d        Zej
                  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
                  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
                  j                  d e      d#        Zd$ Zd% Zd& Zej
                  j                  d'd(d)g      ej
                  j                  d*g d+      ej
                  j                  d,d-d.ej0                  g      d/                      Zd0 Zej
                  j                  d*g d1      d2        Zej
                  j                  d*g d3      d4        ZdTd6Zd7 Zej
                  j                  d*g d8      ej
                  j                  d9g d:      ej
                  j                  d;d5d<g      d=                      Zd> Z d? Z!d@ Z"dA Z#ej
                  j                  d*dB      dC        Z$dD Z%ej
                  j                  d,g dE      dF        Z&ej
                  j                  dGdH ejN                  dd      dIdJfdK ej$                  dLdgddHgg      dMdNfg      dO        Z(ej
                  j                  dPg dQ      dR        Z)dS Z*y)UTestMultivariateTr
   rG   rd   rH   rb   r   )
|	ߌ?v
2R?r  g0$H?r  r  gO`?gՒXO?g	ߌ,?g8N8?)gHP?gQI?go_?)g9m4?g=U?gˡE?)g$C?ghs?gǺ?)g!uq?g%C?gS㥛?)gOec?gz,C?g	h"l?)rf   r
   2   )r   rH  r\  )rH  r   rS  )r\  rS  r   r  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 \    t        |||d      }|j                  |      }t        ||       y Nr   r   )r#   r   r   )rU   r[   rO  r:   r  ansr   vals           r?   test_pdf_correctnessz&TestMultivariateT.test_pdf_correctnessh	  s)    c5"15hhqk!#s+rA   c                     t        |||d      }|j                  |      }|j                  |      }t        t	        j
                  |      |       y r  )r#   r   r   r   r8   r   )	rU   r[   rO  r:   r  r  r   r  r  s	            r?   test_logpdf_correctz%TestMultivariateT.test_logpdf_correctn	  s>    c5"15xx{{{1~!"&&,5rA   c                 |    g d}t        j                  |d      }t        j                  |      }t        ||       y )N)
r  re   rd   r
   r  r   r  rf   rH   r
   r  )r#   r   r$   r   )rU   r[   r  r  s       r?   test_mvt_with_df_one_is_cauchyz0TestMultivariateT.test_mvt_with_df_one_is_cauchyv	  s0    -  q)jjm!#s+rA   c                    d}t        dddd      }|j                  d      }t        |      \  }}||kD  sJ t        ddgd	d
gd
d	ggdd      }|j                  d      }t        |      \  }}||kD  j                         sJ y )Nr   r   r
   順 r  r   r   ri   rH   r$  rf   *   )r#   r   r%   r&  )rU   	P_VAL_MINr   r  r   r  s         r?   &test_mvt_with_high_df_is_approx_normalz8TestMultivariateT.test_mvt_with_high_df_is_approx_normal|	  s    
 	avA6(((''"1Ir1gR2r(';#%'(((''"1Y##%&%rA   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 y )Nr   r
   re   r  r  rG   )r#   r8   r  r   r   r   
call_countr   )rU   mockr   s      r?   !test_mvt_with_inf_df_calls_normalz3TestMultivariateT.test_mvt_with_inf_df_calls_normal	  ss    arvvA6$ :;;;1(!###aBFF+!###rA   c                    d}t        j                  |      }t        j                  |      }d}t        j                  |      }t        |||      j	                  |      }t        j
                  |      sJ t        |||      j                  |      }t        j
                  |      sJ d}t         j                  j                  ||f      }t        |||      j	                  |      }|j                  |fk(  sJ t        |||      j                  |      }|j                  |fk(  sJ t        t        j                  d      t        j                  d      d      j                         }t        j
                  |      sJ d}t        t        j                  d      t        j                  d      d      j                  |      }|j                  |fk(  sJ y )Nrd         @re   r
   r   )
r8   r   rP   r#   r   isscalarr   r   r:   r   )	rU   r   rO  r:   r  r[   r;   	n_samplesr   s	            r?   test_shape_correctnessz(TestMultivariateT.test_shape_correctness	  s    hhsmsHHSMS%,003{{3S%,33A6{{3 	IIi-.S%,003		i\)*)S%,33A6		i\)*) RXXa["&&)Q7;;={{3 RXXa["&&)Q7;;;F		dW$%$rA   c                     t               }t        |j                  dg       t        |j                  dgg       |j                  dk(  sJ y )Nr   r
   r#   r   rO  r:   r  )rU   r   s     r?   test_default_argumentsz(TestMultivariateT.test_default_arguments	  s<    TXXs#TZZ1#'1rA   )NNNr   r
   r
   )NNre   r   r
   re   Nre   z*loc, shape, df, loc_ans, shape_ans, df_ansc                     t        |||      }t        |j                  |       t        |j                  |       |j                  |k(  sJ y )NrO  r:   r  r  rU   rO  r:   r  loc_ans	shape_ansdf_ansr   s           r?   test_default_argsz#TestMultivariateT.test_default_args	  s@     #Ur:TXXw'TZZ+6!"!rA   rf   c                     t        |||      }t        |j                  |       t        |j                  |       t        |j                  |       y r7   r  r  s           r?   &test_scalar_list_and_ndarray_argumentsz8TestMultivariateT.test_scalar_list_and_ndarray_arguments	  s<     c5"-TXXw'TZZ+TWWf%rA   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        |||       y )	Nr
   )rO  rG   rH   )rO  r:   rf   r  r   )r   rM   r#   dictr8   r   rP   )rU   rO  r:   r  s       r?   test_argument_error_handlingz.TestMultivariateT.test_argument_error_handling	  s    1vhj$	'	'
 Q!Q!Q(j$	4E2	4
 hhqkq	j$	;Eb9	; j$	;Eb9	;rA   c                 ,   t         j                  j                  d      }|j                  d      }t        j                  d      }t        ||dd      }t        ||dd      }|j                  d      }|j                  d      }t        ||       y )Nrd   rH   r   rG   r  r$  )r8   r   r  r   rP   r#   r   r   )rU   r   rO  r:   r   dist2samples1samples2s           r?   r3  z&TestMultivariateT.test_reproducibility	  s}    ii##A&kkqk!q	sEaa8sEaa899"9%99"9%Xx(rA   c                     t        ddgddgddggdd      }t        t        j                  j                  t
        fi | y )Nr   r
   F)rO  r:   r  rZ   )r  r   r8   r   r|  r#   )rU   r=   s     r?   test_allow_singularz%TestMultivariateT.test_allow_singular
  s;    1qeQqE]qObii++^DtDrA   r   )r$  rH   )rb   rc   rd   rH   r   )rG   rH   rd   rb   r  r   r?  c                     t        t        j                  |      t        j                  |      |      }|j	                  |      }|j
                  ||fz   k(  sJ y rg  )r#   r8   r   rP   r   r:   )rU   r   r   r  r   r   s         r?   test_rvszTestMultivariateT.test_rvs
  sJ     bhhsmRVVC["=hhDh!yyDC7N***rA   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         y )
NrH   r$  r  rg   r  r  r  r  r   r  )rU   r   r   r  r  r  r  r   s           r?   r  z TestMultivariateT.test_cdf_signs
  sv    xx{ffQi	9i8	9i8.1!%%asBAFSVN23rA   )r
   rG   rb   r$  c                 &    | j                  |       y r7   cdf_against_mvn_testrU   r   s     r?   $test_cdf_against_multivariate_normalz6TestMultivariateT.test_cdf_against_multivariate_normal
  s     	!!#&rA   )rH   rc   r  c                 (    | j                  dd       y )NrH   Tr  r  s     r?   -test_cdf_against_multivariate_normal_singularz?TestMultivariateT.test_cdf_against_multivariate_normal_singular 
  s     	!!!T*rA   Fc           	      ,   t         j                  j                  d      }d}d|j                  dd|      z  }t	        ||||      }d|j                  dd|      z  t        j
                  |j                  |            z  }d|j                  dd||f      z   |z   }d|j                  dd||f      z  |z   }	t        j                  j                  |	||d	|d
|      }
t        j                  j                  |	||d
|      }t        |
|d       y )N   ]J>?a rH   r$  ri   r
   r   rf   rG   r  T)r  r  rZ   r   )rZ   r  Mb@?r  )r8   r   r   r   r   signr   r-   r#   r   r   r   )rU   r   r   r   r   r  r   r   r  r  r;   r<   s               r?   r  z&TestMultivariateT.cdf_against_mvn_test%
  s   ii##O4B,, ah73;;r13;//"''#**#*:N2OOR!S222T9BC11D8""&&q$16: ' N''++AtS89 , ;St,rA   c                 P   t         j                  j                  d      }d}d}|j                  dt        j                  |            }d}t
        j                  j                  ||||t         j                   |      }t
        j                  j                  |||t        j                  |            }t
        j                  j                  ||t        j                  |            }t        ||d	       t        j                  t        j                  ||z
        d
kD        sJ y )Nr  rG   r   r$  )r   rJ  rH   )r  r   r  r  r;  )r8   r   r   r   sqrtr-   r#   r   r  tr   r   r&  r   )	rU   r   r   r   r[   r  r;   r<   	incorrects	            r?   test_cdf_against_univariate_tz/TestMultivariateT.test_cdf_against_univariate_t7
  s    ii##O4JJBbggclJ3""&&q$RbffW47 ' 9ggkk!Rrwws|4JJNN1dBGGCL9	St,vvbffS9_-4555rA   )rG   rH   rb   r$  r   )   no l   m, l   sO l   U iOfYl   O_ r   Tc           	      P   |r|dk7  rt        j                  d       t        j                  j	                  |      }d|j                  dd|      z  }t        ||||      }|j                  |      }|j                  |       }|j                  |      }	|j                         dz  }
t        j                  j                  |	|||
|d	      }t        j                  d
      5  t        d|
|t        j                  |z  |	|z
  |      d   }d d d        t        |dd       t        j                  j                  |	|||
||d      }t        j                  d
      5  t        d|
|||z
  |	|z
  |      d   }d d d        t        ||dd       y # 1 sw Y   xY w# 1 sw Y   %xY w)Nr  z4Agreement with qsimvtv is not great in singular caser$  ri   rG   r   rb   T)r   rZ   r  )invalidr  r   g-C6*?r;  rR  r=  )r  r   rZ   r  )rL   r   r8   r   r   r   r   r-   r#   r   r  r4   r  r   )rU   r   r   r   r   r  r   r   r  r  r  r;   r<   s                r?   test_cdf_against_qsimvtvz*TestMultivariateT.test_cdf_against_qsimvtvF
  s   
 
*KKNOii##D)B,, ah7zz#ZZ_JJsOZZ\A ""&&q$Rc6: ' <[[* 	G5"c266!8QXsCAFC	GSt$7 ""&&q$RQ47 ' N[[* 	G5"c1t8QXsCAFC	GSt$7	G 	G	G 	Gs   #(FFFF%c           
        	
 d}t         j                  j                  d      }d|j                  dd|      z  }t	        |||d      	|j                  |      |j                  |       }|j                  |      }|j                         d	z  
t
        j                  j                  |	
||
      }	
fd}t        |||t
        j                  j                  ||            }t        ||j                  d       	
fd}t        ||d   |d   |d   |d   |d   |d         }t        ||d   d       y )NrH   l   	!y r$  rf   r
   r   T)r   rb   )r   r  c                 \    t         j                  j                  | j                        S r7   )r-   r#   r   r   )r[   r   r  r   s    r?   	integrandzITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrandq
  s$    ''++ACCsB??rA   )r  r   )qrngr;  r<  c                  T    t         j                  j                  | d d d         S )Nrf   )r-   r#   r   )zyxr   r  r   s    r?   r  zITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrandw
  s(    ''++C"ItS"EErA   r   rG   )r8   r   r   r   r   r-   r#   r   r/   qmcHaltonr   integralr0   )rU   r   r   r  r  r  r;   r  r<   r   r  r   s            @@@r?   $test_cdf_against_generic_integratorsz6TestMultivariateT.test_cdf_against_generic_integratorsc
  s)   ii##N3#++b!#+.. at<zz#ZZ_JJsOZZ\A""&&q$Rc34 ' 6	@ y!QUYY-=-=#-=-NOS\\5	F i1qtQqT1Q41qtDSV$/rA   c                     t         j                  j                  d      }t        j                  g dg dg dg      }d}t	        j
                  ||      }|j                  g d|      }d	}t        ||d
       y )Nl   Ja )go!@S<?^Ss@)r  gRP=@jT0@)r  r  gk`-3@gWK?r:   r  rg   r   g1%?r;  r<  )r8   r   r   r   r-   r#   r   r   )rU   r   r   r  r   r;   r<   s          r?   test_against_matlabz%TestMultivariateT.test_against_matlab}
  sr     ii##J/hh???A B  ###"5hhysh3St,rA   c                    d}t         j                  j                  |      }|j                  d      }|j                  d      |z   }t        j                  d      }|j                         }|||f}t         j                  j                  |      }t         j                  j                  |      }	t        j                  |d|i}
t        |
j                  |      t        j                  |g|d|	i       y )Nl   2m rH   r   r   r   )	r8   r   r   r   rP   r-   r#   r   r   )rU   r   r   rO  r[   r:   r  r=   
rng_frozenrng_unfrozenr   s              r?   r`  zTestMultivariateT.test_frozen
  s    ii##D)kkqk!KKQK#%q	ZZ\UBYY**40
yy,,T2##T;
;TXXa[#''LDL|L	NrA   c                   	
 d}d}t         j                  j                  d      j                  ||f      }||j                  z  j                  |      
j                  ||fz         }j                         dz  	t        j
                  j                  |
	      }	
fd}t        j                  |d|      }t        ||d	d
       y )Nrd   r  r  r   rb   r   c                 T    t        dt        j                   | z  | z
        d   S )Nr  r   )r4   r8   r  )r[   r   r  r   r   s    r?   _cdf_1dz2TestMultivariateT.test_vectorized.<locals>._cdf_1d
  s+    E2sRVVGAIqvsCAFFrA   rf   r  r;  r  )	r8   r   r   r   r-   r#   r   apply_along_axisr   )rU   r   r   ru   r[   r;   r  r<   r   r  r   r   s           @@@@r?   test_vectorizedz!TestMultivariateT.test_vectorized
  s    ii##O4JJS#JJ'!##gzz#JJqC6z"ZZ\A""&&q$Rc&J	G !!'2q1St$7rA   r_  c                    t         j                  j                  d      }t        j                  j                  dgdg|dz
  z  z         }t        j                  |      j                  dg|z  |      }d|dz   z  }t        ||d	       y )
Nr  r
   rH  )r  )r:   r   r   g-C6
?r<  )
r8   r   r   r   r   toeplitzr-   r#   r   r   )rU   r   r   ru   r;   r<   s         r?   test_against_analyticalz)TestMultivariateT.test_against_analytical
  s~    ii##O4LL!!QC3%37*;$;!<""+//c	/L37mSt,rA   c                     t        j                  dd      }t         j                  }t        j                  j                  ||      }t        j                  j                  d |      }||k(  sJ y )NrH   r  )r8   rP   r  r-   r#   r   r   )rU   r   r  mvt_entropymvn_entropys        r?   test_entropy_inf_dfz%TestMultivariateT.test_entropy_inf_df
  s[    ffQlVV**222D//77cBk)))rA   )r
   r$  r-  c                     t         j                  j                  d|      }t         j                  j                  |      }t	        ||d       y )Nr   r  r  r<  r<  )r-   r#   r   r  r   )rU   r  r  	t_entropys       r?   test_entropy_1dz!TestMultivariateT.test_entropy_1d
  s=    **222CGGOOrO*	YU;rA   zdf, cov, ref, tolr$  g}M@r  r-  rH  gNfh@r  c                     t        j                  d      }t        j                  |||      }t	        |j                         ||       y )Nrb  r<  )r8   r   r-   r#   r   r   )rU   r  r   r<   tolrO  mvts          r?   %test_entropy_vs_numerical_integrationz7TestMultivariateT.test_entropy_vs_numerical_integration
  s7    
 hhuo""3R0s5rA   zdf, dim, ref, tol))r$  r
   gDdVW?r  )r-  r
   gU?r<  )r  r
   g/+?r  )@xDr
   Z_2?r  )}Ô%ITr
   r'  r  )r$  r$  gzg#.@r  )r(  r$  gD:f,@r<  )r&  r$  1>`,@r  )r(  r$  r)  r  )r$  r-  g8d?b@r  )r(  r-  g-YҺa@r  )r&  r-  ZGra@r  )r(  r-  r*  r  c                     t        j                  t        j                  |      |      }t	        |j                         ||       y )Nr  r<  )r-   r#   r8   rP   r   r   )rU   r  r   r<   r#  r$  s         r?   test_extreme_entropyz&TestMultivariateT.test_extreme_entropy
  s1    F ""<s5rA   c                    t        j                  g dg dg dg dg dg      }||j                  z  }d}t        j                  j                  ||      }t        d |      j                         }t        ||d	
       d}d}t        j                  j                  ||      }t        j                  j                  ||      }	t        ||	d
       y )N)gQ?g
ףp=
?g\(\߿(\?gGz?)gGzg{GzgQ?rl  gQ)gQ?g)\(?gQѿg)\(ܿg(\?)g      gGzgq=
ףpg\(\?g)r.  g{Gzg\(\?g{GzԿg(\?r&  r  r{  r  r<  i  i   rh  )r8   r   r   r-   r#   r   r   r   )
rU   _Ar   r  mul_t_entropymul_norm_entropydf1df2	_entropy1	_entropy2s
             r?   test_entropy_with_covariancez.TestMultivariateT.test_entropy_with_covariance  s     XX+-,,,
  244i ,,44324F.t=EEG'7eD ((00ss0C	((00ss0C		948rA   F)+r   r   r   	PDF_TESTSrL   r   r   r  r  r  r  r5   r  r  r  DEFAULT_ARGS_TESTSr  r8   r   ARGS_SHAPES_TESTSr  r  r3  r  r  r  r  r  r  r  r  r  r	  r  r`  r  r  r  r!  rP   r%  r,  r6  r   rA   r?   r  r  	  sD    FFFFFFFFFF	
 
A FF	

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

4 [[UM2' 3' [[UI.+ /+-$6 [[UM2[[V &J K[[Z%78 8K 38204-"N8$ [[UF+- ,-* [[T<0< 1<& [[0!6266!Q<1CUK"HBHHsAhB-@$A/7896	96
 [[	
$6%$6(9rA   r  c                      e Zd Zej                  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                  j                  dg ddfg ddfddgdfdgdff      d        Zej                  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$d%d&fg      d'        Zej                  j                  dddgddgdd(ggddd)gfdgdggdgdggddgd*d+gfdgdgggdgdggddgd*d+ggfdgdggdggggddgd*d+gggfg      d,        Zd- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zy8)9TestMultivariateHypergeomzx, m, n, expectedrH   rd   rb   r$  re   gr   r  r
   rG   rl   iir  r  rf   ic                 N    t        j                  |||      }t        ||d       y )Ngư>r<  )r   r  r   rU   r[   r  r   r0  valss         r?   r  z%TestMultivariateHypergeom.test_logpmf!  s$    6 &,,Q15hT2rA   c                    t        j                  ddgddgd      }t        j                  dddd      }t        ||d	
       t        j                  ddgddgd      }t        j                  dddd      }t        ||d	
       y )NrH   r
   r$  rb   rd   )r[   r  r      )r  r   r   r  r  r<  re      )r   r  r"   r   r  s      r?   test_reduces_hypergeomz0TestMultivariateHypergeom.test_reduces_hypergeom?  s|     &))QFr1gC}}qB!r2d.%))QFr2h"E}}qB"3d.rA   c                     t        ddgd      }|j                  dd      }t        |j                  d      |j                         d	
       y )NrH   rb   rd   r  r   r(  r  r   r   rP  r<  r   r   r   r   rU   r   r   s      r?   r  z"TestMultivariateHypergeom.test_rvsJ  s@     $q!f2ff$Sf1RWWYT:rA   c                     t        ddgddggddg      }|j                  dd	      }t        |j                  d
      |j                         d       y )NrH   rb   r$  rd   r  rF  r(  rG   r  r   r   rP  r<  rG  rH  s      r?   test_rvs_broadcastingz/TestMultivariateHypergeom.test_rvs_broadcastingQ  sK    #1v2w&7Aq6Bff)#f6RWWYT:rA   zm, n)r   r   r  r   r   )r   r   r   r   r   c                     t        j                  ||      }t        j                  |      }|j	                         }|||dk7  <   t        ||       y )Nr   )r   r   r8   r9   r  r   )rU   r  r   r;   res_exs        r?   test_rvs_gh16171z*TestMultivariateHypergeom.test_rvs_gh16171V  sE    
 %((A.JJqMqAvS&!rA   g zl?r  r  gQ?gE|?g
y?r.  r  )rb   rc   re   rc   gzp?c                 N    t        j                  |||      }t        ||d       y Nrg  r<  r   r  r   r?  s         r?   r  z"TestMultivariateHypergeom.test_pmfa  s$    " &))!Q2hT2rA   rB  g ?r   r   c                 N    t        j                  |||      }t        ||d       y rP  rQ  r?  s         r?   r  z/TestMultivariateHypergeom.test_pmf_broadcastingu  s$     &))!Q2hT2rA   c                 h    t        j                  g dd      }g dg dg dg}t        ||d       y )	N)rH   re   r$  r  rF  )gf_?&BUп疈Cx@ؿ)rT  ggs>d?ZsK)rU  rV  g35?r  r<  r   r   r   )rU   r  r  s      r?   r  z"TestMultivariateHypergeom.test_cov  s2    %))J"=6668 	d.rA   c                 V   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       y )Nre   r  r$  rB  r  r  rF  g?gg(\?g(\r  r<  rd   rb   r   g333333?g333333rW  r  s          r?   r  z/TestMultivariateHypergeom.test_cov_broadcasting  s    %))aVb"X,>1b'J..0d.%))aS1#J1a&A"d.%))QFq"g>.'"Wf$568d.rA   c                     t        j                  ddgd      }t        j                  ddd      }t        ||d       y )	Nr$  rb   rd   rF  rB  r   r   r  r  r<  )r   r9  r"   r   )rU   var0var1s      r?   test_varz"TestMultivariateHypergeom.test_var  s6    %))RGq9}}rQ"-d.rA   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       y )Nr$  rb   rd   r  rF  r   r  r<  r
   r  g̍3eY?gI{?r   )r   r9  r   )rU   r[  r\  var2var3var4var5var6s           r?   test_var_broadcastingz/TestMultivariateHypergeom.test_var_broadcasting  s    %))RG1v>%))RGq9%))RGq9QD1QD1%))b!Wr2h,?Aq6JI&8(<=d.%))aS2$KAr7Crd|d.rA   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	       y )Nr$  rb   rd   rF  rB  rZ  r   r  r<  r  r  g      @rK  )r   r   r"   r   rU   mean0r  r  mean3s        r?   r  z#TestMultivariateHypergeom.test_mean  sf    &++r1g;qB/a%d3&++r1g<j)u40rA   c                 n    t        j                  ddgddggddg      }ddgd	d
gg}t        ||d       y )NrH   rb   r$  rd   r  rF  r   r   gUUUUUU@gUUUUUU@r  r<  )r   r   r   )rU   rg  r  s      r?   r  z0TestMultivariateHypergeom.test_mean_broadcasting  sE    &++1vAw.?Aq6JH%
I'>?u40rA   c                 V   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(         y )Nrg   r   rF  r   r   r   r
   r   r   rG   r  )r   r   r   FFg<r<  r.  r   )
r   r   r   r8   rt  r   r   intr   r:   rf  s        r?   test_mean_edge_casesz.TestMultivariateHypergeom.test_mean_edge_cases  s    &++i1=UL)&++i1=URVVRVVRVV45&++y).DJ 8,G"	$ '++bhhr.EKUBu$%rA   c                 Z   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(         y )Nrg   r   rF  rk  gؗҜ<r<  rl  rG   r  rm  r.  rn  )
r   r9  r   r   r8   rt  r   ro  r   r:   )rU   r[  r\  r_  r`  s        r?   test_var_edge_casesz-TestMultivariateHypergeom.test_var_edge_cases  s    %))I;l7%))I;TBFFBFFBFF34%))Y	,BaH7F"	$ &))BHHRs,CqIT2

e#$rA   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                  	      j                  dd      }t        ||d       t        |j                  d
k(         y )Nrl  r
   rF  rk  rm  r<  rg   r   r.  rN  )r   r   r   r   r8   r   ro  r  r)  r   r:   )rU   cov0r  r  r  r  r  s          r?   test_cov_edge_casesz-TestMultivariateHypergeom.test_cov_edge_cases  s    %))I;lL9d/%))I;lL9T4 %))BHHRs,CqIxx"**-55a;d/

f$%rA   c                 6   t         j                  j                  d       d}g d}g dg dg dg dg dg}t        j                  |t        	      }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             y )
Nr   r  )re   r  r     r  r   r  r  r  r.  )r8   r   r   r9   ro  r   r   r  r  r9  r   )rU   r   r  r[   
mhg_frozens        r?   r`  z%TestMultivariateHypergeom.test_frozen  s    
		tM=<)JJq$+Aq1

q).221a;	=
))!,.55aA>	@
(*@*D*DQ*JK
(*@*D*DQ*JKrA   c                    t        t        t        j                  ddd       t        t        t        j                  ddgd       t        t        t        j                  ddgdgd       t        t        t        j                  ddgddgd       t        t        t        j                  ddgddgd       t        t        t        j                  ddgddgd       y )	Nrb   r$  rd   g      @r  rB  g      %@g      /@)r   rM   r   r  	TypeErrorr6  s    r?   test_invalid_paramsz-TestMultivariateHypergeom.test_invalid_params  s    j"8"<"<aQGj"8"<"<a"qIj"8"<"<q!frdANi!7!;!;c3Z2h	#i!7!;!;aVTlA	'i!7!;!;aV2h	%rA   N)r   r   r   rL   r   r   r8   r  rt  r  rD  r  rK  rN  r   ro  r  r  r  r  r]  rd  r  r  rp  rr  ru  r`  r{  r   rA   r?   r<  r<     s|   [[ VaWa+VaWa"&&)!Wq"gq266'*Vb"Xq"&&)!fq!fR2s)4Vbffbff%' !Wr2h266*Wr1gr266*Wr2hBFF+VaWb"&&)VaWa"&&)+	
43543	/;;
 [[V	13
Qqc1X& "	" [[S1#q!VaWa+1v1v"a1a& 12W1v1v&+&I79 RXXb$hbhhr&=q"EVaVQ"	1j1	
 3! 3 [[Vq"gBx(!i-CDcA3Z1#saVb"X6sQCj\QC!:1vRz:cA3ZQC5'QFr2hZL9		
33////11
&%&L 	%rA   r<  c                   T   e Zd Zd Zd Zej                  j                  dd      d        Zd Z	ej                  j                  dd      ej                  j                  d	d      d
               Z
ej                  j                  dd      d        Zd Zej                  j                  dd      d        Zej                  j                  dd      d        Zej                  j                  dd      d        Zej                  j                  dd      ej                  j                  dg dgf      ej                  j                  dg dgf      d                      Zej                  j                  dd      d        Zd Zej                  j                  dd      d        Zy)TestRandomTablec                 @    t         j                  j                  d      S )Nl   OfE)r8   r   r   r6  s    r?   get_rngzTestRandomTable.get_rng  s    yy$$%788rA   c                 ^   d}t        j                  t        |      5  t        ddggddg       d d d        d}t        j                  t        |      5  t        ddgddgg       d d d        d}t        j                  t        |      5  t        ddgddg       d d d        d}t        j                  t        |      5  t        ddgdd	g       d d d        d
}t        j                  t        |      5  t        ddgddg       d d d        d}t        j                  t        |      5  t        ddgg d       d d d        d}t        j                  t        |      5  t        ddgg d       d d d        ddg}g d}t        j                  ddgg d      \  }}}t        ||       t        ||       |t        j                  |      k(  sJ y # 1 sw Y   xY w# 1 sw Y   ~xY w# 1 sw Y   UxY w# 1 sw Y   ,xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w)Nz`row` must be one-dimensionalrE   r
   rG   z`col` must be one-dimensionalz*each element of `row` must be non-negativerf   z*each element of `col` must be non-negativeri   z'sums over `row` and `col` must be equalr   z(each element of `row` must be an integer @)r
   r
   rG   z(each element of `col` must be an integer)rV  rV  r
   rH   rG   r
   r
   )rL   r	   rM   r&   _process_parametersr   r8   r   )rU   rV   rowcolr'  r  r   s          r?   test_process_parametersz'TestRandomTable.test_process_parameters  s   1]]:W5 	+1a&Aq6*	+ 2]]:W5 	+!Q1a&*	+ ?]]:W5 	*!R1a&)	* ?]]:W5 	*!Q!R)	* <]]:W5 	)!Q!Q(	) =]]:W5 	0#sY/	0 =]]:W5 	0!Q/	0 !f22Aq69E1aS!S!BFF3KA	+ 	+	+ 	+	* 	*	* 	*	) 	)	0 	0	0 	0sS   GG#G0G=8H
.H$H#G #G-0G:=H
HH #H,zscale,method))r
   boyett)r-  	patefieldc                     t        j                  ddg      |z  }t        j                  g d      |z  }t        }|j                  |||d      }|j                  ||d d      }t	        ||       y )Nr
   rH   r  methodr   )r8   r   r&   r   r   )rU   rJ  r  r  r  ctr0  gots           r?   test_process_rvs_method_on_Nonez/TestRandomTable.test_process_rvs_method_on_None,  si     hh1v&hhy!E)66#s66BffS#df;Xs#rA   c                     ddg}g d}d}t        j                  t        |      5  t        j                  ||d       d d d        y # 1 sw Y   y xY w)Nr
   rH   r  z$'foo' not recognized, must be one ofrE   foo)r  )rL   r	   rM   r&   r   )rU   r  r  rV   s       r?   $test_process_rvs_method_bad_argumentz4TestRandomTable.test_process_rvs_method_bad_argument8  sL    !f 9]]:W5 	5S#e4	5 	5 	5s   AAr  )TFr   c                    | j                         }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          |j                  d|j                  dd  z         } ||      }	|	j                  dk(  sJ t        |	j                  d         D ]A  }t        |	j                  d         D ]$  }|	||f   }|||f   } ||      }t        ||       & C g dg dg}t        t	        j                  |d              ||      }	|	dk(  sJ g dg dg}t        t	        j                  |d              ||      }	|	dk(  sJ d}t        j                  t         |      5   |dg       d d d        d}t        j                  t         |      5   |dgg       d d d        d}t        j                  t         |      5   |t        j"                  gg       d d d        d}t        j                  t         |      5   |dgg       d d d        d}t        j                  t         |      5   |g dg       d d d        d }t        j                  t         |      5   |ddgd!d"gg       d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   oxY w# 1 sw Y   y xY w)#NrG   rc   r
   rH   rd   r(  r  r   r  r   r  r  c                      |       S r7   r   )r[   r  original_methodr  s    r?   r  z/TestRandomTable.test_pmf_logpmf.<locals>.methodR  s    &q#s33rA   c                 :    t        j                   |             S r7   )r8   r0  )r[   r  s    r?   r\   z1TestRandomTable.test_pmf_logpmf.<locals>.<lambda>T  s    q	* rA   r   Tr   return_countsr   r<  )r$  r-  r
   )r   r
   r
   )rG   r
   rH   rf   r   r   )r
   rG   rG   ri   z$`x` must be at least two-dimensionalrE   z%`x` must contain only integral valuesrV  z)`x` must contain only non-negative valuesz"shape of `x` must agree with `row`rK   z"shape of `x` must agree with `col`rH   rd   )r  r&   r   rp   r8   uniquer   r   r   r   r)  r:   r	  r   rL   r	   rM   rt  )rU   r  r   r   r   objr  
unique_rvscountsr  p2rvs_ndrA  rB  pijrvijqijr[   rV   r  r  r  r  s                      @@@@r?   test_pmf_logpmfzTestRandomTable.test_pmf_logpmfA  s(    lln!fsCd&.SB )/l3$L#h59$O4/2*YYs$G
F 
OCHf37 jm$%R1 Y1267Kww)###qwwqz" 	'A1771:& '1gad|$iS#&	'	' 	"RVVAB'-FAvv 	"RVVAB'-FAvv 9]]:W5 	H	 :]]:W5 	#L	 :]]:W5 	"&&
O	 >]]:W5 	"K	 7]]:W5 		 7]]:W5 	!QQ 	 	)	 		 		 		 		 		 	sH   2
L!LL!L-?L90MLL!L*-L69MMr  )r  r  c                    | j                         }ddg}g d}t        j                  ||d||      }t        j                  ||      }t	        t        j                  |      t        j                  |             t        |j                  d      |d       t	        |j                  d	
      t        j                  |d             t	        |j                  d
      t        j                  |d             y )NrG   rc   r  r(  r  r   r@  r  rf   r   rJ  ri   )r(  rH   )	r  r&   r   r   r   r8   r   r   broadcast_to)rU   r  r   r  r  r   r   s          r?   test_rvs_meanzTestRandomTable.test_rvs_mean  s     lln!fsCd6,/1  c*RVVD\266#;/T5SWW"W%rsI'FGSWW"W%rsI'FGrA   c                    | j                         }ddg}g d}t        j                  ||dd|      }t        j                  ||dd|      }t        j                  |d	      }t        j                  |d	      }t        ||d
       y )NrG   rc   r  r  r  r  r  r   r   {Gz?r  )r  r&   r   r8   r9  r   )rU   r   r  r  r  r  r  r  s           r?   test_rvs_covzTestRandomTable.test_rvs_cov  s     lln!fSuX-02Su[-02vvd#vvd#d.rA   c           	      (   ddg}g d}t        j                  |||| j                               }|j                  dk(  sJ t        j                  ||d|| j                               }|j                  dk(  sJ t	        ||d	          t        j                  ||d	|| j                               }|j                  d
k(  sJ t        j                  ||d|| j                               }|j                  dk(  sJ t        j                  ||d|| j                               }|j                  dk(  sJ t        |j                  ddd      |d       d}	t        j                  t        |	      5  t        j                  ||d|| j                                d d d        t        j                  t        |	      5  t        j                  ||t        j                  || j                                d d d        y # 1 sw Y   dxY w# 1 sw Y   y xY w)NrG   rc   r  r  r  r
   r  rK   r   )r   rG   rH   r  )r  rG   rH   )rd   rb   )rd   rb   rG   rH   rH   r  r<  z/`size` must be a non-negative integer or `None`rE   rf   )r&   r   r  r:   r   r   r)  rL   r	   rM   r8   rt  )
rU   r  r  r  r   rv2rv3rv4rv5rV   s
             r?   test_rvs_sizezTestRandomTable.test_rvs_size  s   !f c3v+/<<>;xx6!!! sCa,0LLN<yyI%%%RQ  sCa,0LLN<yyI%%% sCb,0LLN<yyJ&&&sCfV,0LLN<yyL(((B1-s? D]]:W5 	:S#Bv*.,,.:	: ]]:W5 	:S#BFF6*.,,.:	: 	:		: 	:	: 	:s   0)G<<7H<HHc                     ddg}g d}t         }|j                  ||d|| j                               }t        j                  |dd      \  }}|j                  |||      }t        |t        |      z  |d	
       y )NrG   rc   r  r  r  r   Tr  r  r<  )r&   r   r  r8   r  r  r   r   )	rU   r  r  r  r  r   r  r  r  s	            r?   test_rvs_methodzTestRandomTable.test_rvs_method  s|     !fffS#F6"&,,.  2  YYs$G
F FF:sC(CHf48rA   c                     g d}g d}t        ||      }|j                  d|| j                               }t        j                  dt        |      t        |      f      }g dg dg dg|d<   t        ||       y )Nr  )r
   r   r   r   r(  r  )r   r   r   r   .r&   r   r  r8   r   r   r   rU   r  r  r  r  r   r0  s          r?   test_rvs_with_zeros_in_col_rowz.TestRandomTable.test_rvs_with_zeros_in_col_row  so    c"UU4T\\^UD88T3s8SX67%%%' 	R"rA   )Nr  r  r  r   r  c                     t        ||      }|j                  d|| j                               }t        j                  dt        |      t        |      f      }t        ||       y )Nr$  r  r  r  s          r?   test_rvs_with_edge_casesz(TestRandomTable.test_rvs_with_edge_cases  sQ     c"UU2f4<<>UB88RS3s845R"rA   r   r  c                    dd l mc m} t        j                  ddgt        j
                        }t        j                  g dt        j
                        }t        |d|       }t        j                  |      } ||||d| j                               }|j                  dt        |      t        |      fk(  sJ t        j                  |      |k(  sJ y )Nr   r
   rH   r.  r  	rvs_rcont)scipy.stats._rcontr-   _rcontr8   r   int64rp   r   r  r:   r   )rU   r   r  r  r  r   ntotresults           r?   test_rvs_rcontzTestRandomTable.test_rvs_rcont  s     	,+hh1vRXX.hhy1f	!o.vvc{S#tQ7||3s8SX6666vvf~%%%rA   c                    ddg}g d}t        ||| j                               }|j                         }t        j                  ||      }t	        ||j                                t        j
                  |||      }t	        ||j                  |             t        j                  |||      }t	        ||j                  |             y )NrG   rc   r  r   )r&   r  r   r   r   r  r  )rU   r  r  r  r  r0  s         r?   r`  zTestRandomTable.test_frozen  s    !fc7$$S#.Xqvvx(##FC5XquuV}-&&vsC8Xqxx/0rA   c                     ddg}g d}t        ||| j                               }t        j                  ||d|| j                               }|j                  d|      }t        ||       y )NrG   rc   r  r   r$  r  )r   r  )r&   r  r   r   )rU   r  r  r  r  r0  r  s          r?   test_rvs_frozenzTestRandomTable.test_rvs_frozen#  sb    !fc7##C2f15AeeFe+Xs#rA   N)r   r   r   r  r  rL   r   r   r  r  r  r  r  r  r  r  r  r  r`  r  r   rA   r?   r}  r}    s   9" H [[^@B$B$5 [[X}5[[UM2L 3 6L\ [[X'>?H @H/ [[X'>?': @':R [[X'>?9 @9( [[X'>?	# @	# [[X'DE[[UR!I.[[UR!I.# / / F# [[S&)& *& 1  [[X'>?$ @$rA   r}  c                    | j                   }d| _          | j                  |ddi t        j                  |       } | j                  |ddi}t        j                  |      } |j                  |ddi}t        ||       || _         y )Nr   r   r  )r   r   pickledumpsloadsr   )distfnr=   r  r   r0	unpickledr1s          r?   check_picklingr  /  s    
 DFFJJ1VA	T	"	"BQI		%1	%BR FrA   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        ||        y )NrH   rH  r   r  r   r   r$  rb   rk  rb  )r8   rP   r   r   r   r   r   r   r   r   r3   r  )rJ  distsr  r=   s       r?   test_random_state_propertyr  C  s    FF1IEE$KE$K	b!	RXXrd^&'	2u+	b%[!	q/*+	d	d#E  %#FD1vt$%rA   c                      e Zd Zej                  j                  dg d      ej                  j                  dg d      d               Zej                  j                  dddg      ej                  j                  dg d	      d
               Zd Zd Z	d Z
ej                  j                  dddg      d        Zej                  j                  dddg      d        Zej                  j                  dej                  ej                  g      d        Zej                  j                  dej                  ej                  g      d        Zej                  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                  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                  j                  d7g d8      d9        Zej                  j                  dej                  ej                  g      d:        Zd; Zej                  j                  dg d<      ej                  j                  d=g d>      d?               Zd@ ZdA ZdB ZyC)DTestVonMises_Fisherr   )rG   rH   rd   rc   r   r  c                    t         j                  j                  d      }t        j                  |fdt        j                  |      z        }t        |d|      }|j                  |      }t        j                  |      t        j                  |      }}|j                  |||      j                  }	|j                  |	k(  sJ t         j                  j                  |d      }
t        |
d       y )Nr  r
   r   r   rf   r   r   )r8   r   r   rj  r  r(   r   r   rP   r   r:   r   r   r   )rU   r   r   r   r   vmf_distr  r   r   r  r  s              r?   r1  z TestVonMises_Fisher.test_samplesV  s     ii##$78WWcWan-"2qs3,,t$HHSM266#;c00s0FLL}}...		wR0r"rA   rb   r  kappa)g  4&kCr&  gꌠ9Y>)Fc                     t         j                  j                  d      }t        j                  |fdt        j                  |      z        }t        |||      }|j                  d       y )Nr  r
   r   r$  )r8   r   r   rj  r  r(   r   )rU   r   r  r   r   r  s         r?    test_sampling_high_concentrationz4TestVonMises_Fisher.test_sampling_high_concentrationd  sQ     ii##$78WWcWan-"2u37RrA   c                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)Nr  z%'mu' must have one-dimensional shape.rE   r
   r8   rO   rL   r	   rM   r(   rU   r   r~  s      r?   test_two_dimensional_muz+TestVonMises_Fisher.test_two_dimensional_mum  sA    WWV_5]]:S1 	#B"	# 	# 	#   A		Ac                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)Nrb  z%'mu' must be a unit vector of norm 1.rE   r
   r  r  s      r?   test_wrong_norm_muz&TestVonMises_Fisher.test_wrong_norm_mus  sA    WWU^5]]:S1 	#B"	# 	# 	#r  c                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)Nr  z$'mu' must have at least two entries.rE   r
   r  r  s      r?   test_one_entry_muz%TestVonMises_Fisher.test_one_entry_muy  sA    WWU^4]]:S1 	#B"	# 	# 	#r  rf   )rb   rH   c                     d}t        j                  t        |      5  t        ddg|       d d d        y # 1 sw Y   y xY w)Nz"'kappa' must be a positive scalar.rE   r
   r   rL   r	   rM   r(   rU   r  r~  s      r?   test_kappa_validationz)TestVonMises_Fisher.test_kappa_validation  s8    2]]:S1 	+QFE*	+ 	+ 	+   6?r   r   c                     d}t        j                  t        |      5  t        ddg|       d d d        y # 1 sw Y   y xY w)NzFor 'kappa=0' the von Mises-Fisher distribution becomes the uniform distribution on the sphere surface. Consider using 'scipy.stats.uniform_direction' instead.rE   r
   r   r  r  s      r?   test_kappa_zeroz#TestVonMises_Fisher.test_kappa_zero  s<     ]]:S1 	+QFE*	+ 	+ 	+r  r  c                     t        j                  g d      }d}t        j                  t        |      5   ||ddgd       d d d        y # 1 sw Y   y xY w)Nr   r   r   znThe dimensionality of the last axis of 'x' must match the dimensionality of the von Mises Fisher distribution.rE   r
   r   r8   r   rL   r	   rM   rU   r  r[   r~  s       r?   test_invalid_shapes_pdf_logpdfz2TestVonMises_Fisher.test_invalid_shapes_pdf_logpdf  sN     HH[! ]]:S1 	!1q!fa 	! 	! 	!   AAc                     t        j                  ddg      }d}t        j                  t        |      5   ||ddgd       d d d        y # 1 sw Y   y xY w)NrH  r   8'x' must be unit vectors of norm 1 along last dimension.rE   r
   r   r  r  s       r?   test_unnormalized_inputz+TestVonMises_Fisher.test_unnormalized_input  sN     HHc2YH]]:S1 	!1q!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\(?rj  r   gS-c                 V    t        ||      j                  |      }t        ||d       y )Nr<  r<  )r(   r   r   )rU   r[   r   r  	referencer   s         r?   test_pdf_accuracyz%TestVonMises_Fisher.test_pdf_accuracy  s'    4 b%(,,Q/YU3rA   g[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 V    t        ||      j                  |      }t        ||d       y )Nr  r<  )r(   r   r   )rU   r[   r   r  r  r   s         r?   test_logpdf_accuracyz(TestVonMises_Fisher.test_logpdf_accuracy  s'    4 !U+2215	6rA   zdim, kappa, reference))rH   r  g?@)rH   r-  gp&F)rb   r  gT;ӷ&)r  r
   goZ@c                     t        j                  |fdt        j                  |      z        }t        ||      j	                         }t        ||d       y )Nr
   g+=r<  )r8   rj  r  r(   r   r   )rU   r   r  r  r   r   s         r?   test_entropy_accuracyz)TestVonMises_Fisher.test_entropy_accuracy  sC     WWcWan-!"e,4467rA   c           	         d}t         j                  j                  d      }t        d      j	                  ||      }t        j
                  ddt        j                  d      z        }d} ||||      }|j                  |k(  sJ t        |d         D ]:  }t        |d         D ]'  }	 ||||	d d f   ||      }
t        |
|||	f   d	
       ) < y )Nr  r  rH   r   r  r
   rb   r   r  r<  )
r8   r   r   r'   r   rj  r  r:   r	  r   )rU   r  	testshaper   r[   r   r  
result_allrA  rB  current_vals              r?   rD  z%TestVonMises_Fisher.test_broadcasting  s     	ii##$78a $$YS$AWWUAbggajL)Ar5)
9,,,y|$ 	KA9Q<( K$Qq!QwZU;Z1-=EJK	KrA   c                 V   t         j                  j                  d      }t        j                  ddg      }t        j                  |d   |d         }d}t        ||      }t        ||      }t        d      j                  d|      }t        j                  |d d df   |d d df         }t        |j                         |j                                t        |j                  |      |j                  |             t        |j                  |      |j                  |             y )	Nr  r   r
   r  )rO  r  rG   r$  r   )r8   r   r   r   r  r(   r*   r'   r   r   r   r   r   )	rU   r   r   mu_angler  vmfvonmises_distvectorsr  s	            r?   test_vs_vonmises_2dz'TestVonMises_Fisher.test_vs_vonmises_2d  s     ii##$78XXq!f::beRU+b%( XU;#A&**2C*@GAqDM71a4=9--/?))&137773CD,,V4cjj6IJrA   )rG   rH   rc   zkappa, mu_tol, kappa_tol))r
   r@  r@  )r$  rP  rP  )r-  {Gzt?r  )r(  r;  r  c                    t        j                  |fdt        j                  |      z        }t        ||      }t         j                  j                  d      }d}|j                  ||      }	t        j                  |	      \  }
}t        j                  |j                  |
            }t        |d|d       t        |||       y )	Nr
   r  r  r   r   r   r  r<  )r8   rj  r  r(   r   r   r   r  arccosr
  r   )rU   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     WWcWan-"2u-ii##$78	,,ys,;+//8			"&&.1rQ?yy9rA   c                     t        j                  d      }d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)Nr  z'x' must be two dimensional.rE   )r8   r   rL   r	   rM   r(   r  rU   r[   r~  s      r?   #test_fit_error_one_dimensional_dataz7TestVonMises_Fisher.test_fit_error_one_dimensional_data<  sE    HHUO,]]:S1 	#"	# 	# 	#   AAc                     t        j                  d      }d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)Nr  r  rE   )r8   rO   rL   r	   rM   r(   r  r
  s      r?    test_fit_error_unnormalized_dataz4TestVonMises_Fisher.test_fit_error_unnormalized_dataB  sE    GGFOH]]:S1 	#"	# 	# 	#r  c                    t        j                  g d      }d}t        ||      }t        ||d      }|j                  d      }t        j                  ||d      }|j                         }t	        ||       t	        ||       y )N)r   r   r
   rb   r2  r   r   )r8   r   r(   r   r   )rU   r   r  r  rW  r  r  rX  s           r?   r  z,TestVonMises_Fisher.test_frozen_distributionH  ss    XXi  U+%b%c:zzsz+""2u3? T4 T4 rA   N)r   r   r   rL   r   r   r1  r  r  r  r  r  r  r(   r   r   r  r  r8   r   r  r  r  r  rD  r  r  r  r  r  r   rA   r?   r  r  U  s   [[UL1[[V%9:
# ; 2
# [[UQF+[[W&89 : ,### [[Wr6l3+ 4+
 [[Wq"g.+ /+ [[X(;(;(7(>(>(@ A!A! [[X(;(;(7(>(>(@ A!A!$ [[6'rxx5xrxx7M#%79'rxx4hbhh|6L#%8:'rxx5xrxx7M"$68'rxx4hbhh|6L"$9;'rxx5'rxxr(JK#%:<  (rxx4hbhh|6L#%68'rxx(<='rxx(<=#%79  (rxx(<='rxxr)*B)0  1#%;=  (rxx(<='rxxwrwws|R)*B)0  1#%;=)>?243?24" [[6'rxx5xrxx7M#%8:'rxx4hbhh|6L#%8:'rxx5xrxx7M"$57'rxx4hbhh|6L"$68'rxx5'rxxr(JK#%8:  (rxx4hbhh|6L#%68'rxx(<='rxx(<=#%79  (rxx(<='rxxr)*B)0  1#%79  (rxx(<='rxxwrwws|R)*B)0  1#%8:);<273<27$ [[4:;
8;
8
 [[X(;(;(7(>(>(@ AKAKK [[UI.[[723
	:3 /	:##!rA   r  c                   `   e Zd Zed        Zd Zd Zd Zd Ze	j                  j                  dddg      d	        Ze	j                  j                  dd
dg      d        Zd Zd Ze	j                  j                  dddg      d        Ze	j                  j                  dg d      d        Zy)TestDirichletMultinomialc                     t         j                  j                  d      }|j                  ddd      }|j	                  dd|df      }|j                  d	      }|||||fS )
N   t7)r   r-  rG   r   r
   r  rf   r   )r8   r   r   r   integersr   )rU   r  r   r  r[   r   s         r?   
get_paramsz#TestDirichletMultinomial.get_paramsW  sc    ii##$56As+LLBaVL,EErENAua""rA   c                    t         j                  j                  d      }|j                  ddd      }|j	                  ddd      }t        j
                  |d      }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             y )Nr  r   r-  r$  rf   r   )r8   r   r   r   r  r   r)   r   r  r  r   r9  r   )rU   r   r  r[   r   r  s         r?   r`  z$TestDirichletMultinomial.test_frozen_  s    ii##$56AsB'LLB#FF12!%+QXXa["7">">q%"KLQUU1X488E1EFQVVX499%CDQUUW377qABQUUW377qABrA   c                    t        j                  g d      }t        j                  |      }t        j                  g d      }t        j                  |||      }t        j
                  |||      }d}t        ||       t        |t        j                  |             |j                  |j                  cxk(  rdk(  sJ  J t         j                  j                  d      }|j                  ddd      }|j                  ddd      }t        j                  |d	
      }t        ||      j	                  |      }t        j
                  |||      }d}t        ||       t        |t        j                  |             y )NrK   rH   rd   rb   gp.U.?r   r  r   r-  r$  rf   r   g+T<)r8   r   r   r)   r  r  r   r   r:   r   r   r   r  )rU   r[   r   r  r;   logresr<   r   s           r?   test_pmf_logpmf_against_Rz2TestDirichletMultinomial.test_pmf_logpmf_against_Rm  s.   
 HHYFF1I##''5!4&--a:!S!s,yyFLL.B..... ii##$56AsB'LLB#FF12#E1-11!4&--a:"S!s,rA   c                 :   | j                  d      \  }}}}}|dz  }t        t        ||      j                  |      d       t        t        ||      j	                  |      t
        j                          | j                  d      \  }}}}}|j                  d      dkD  }t        j                  ||   dz        ||<   t        t        ||      j                  |      |   d       t        t        ||      j	                  |      |   t
        j                          t        j                  t        ||      j                  |      |    dkD        sJ t        j                  t        ||      j	                  |      |    t
        j                   kD        sJ y )Nr
   r   r$  r   rH  rG   )
r  r   r)   r  r  r8   r  r   roundr&  )rU   r   r  r  r   r[   rA  s          r?   test_pmf_logpmf_supportz0TestDirichletMultinomial.test_pmf_logpmf_support  s`    #ooa0Qq!	Q*5!488;Q?*5!4;;A>H"oob1Qq!JJBJ#%xx!q!!*5!488;A>B*5!4;;A>qABFF7Kvv+E1599!<aR@1DEEEvv+E15<<Q?CrvvgMNNNrA   c                    d}dg}t        j                  |g      }t        ||      }t        |j	                  |      d       t        |j	                  |dz         d       t        |j                  |      d       t        |j                  |dz         t         j                          t        |j                         |       t        |j                         d       t        |j                         d       y )Nrc   r$  r
   r   )
r8   r9   r)   r   r  r  r  r   r9  r   )rU   r   r  r[   r   s        r?   test_dimensionality_onez0TestDirichletMultinomial.test_dimensionality_one  s    JJsO$UA.TXXa[!$TXXac]A&T[[^Q'T[[1%w/TYY[!$TXXZ#TXXZ#rA   method_namer  r  c                    | j                  d      \  }}}}}t        t        ||      |      }t        t        j                  |g|j
                   |      } ||      }	 ||j
                  d         }
t        |	|
       y Nr-  r   r  rp   r)   r-   	betabinomr   r   rU   r   r   r  r  r   r[   r  
ref_methodr;   r<   s              r?   test_against_betabinom_pmfz3TestDirichletMultinomial.test_against_betabinom_pmf  sr    "ooc2Qq!.ua8+FU__Q99;G
QiQ S!rA   r   r9  c                     | j                  d      \  }}}}}t        t        ||      |      }t        t        j                  |g|j
                   |      } |       d d df   }	 |       }
t        |	|
       y r"  r#  r%  s              r?   test_against_betabinom_momentsz7TestDirichletMultinomial.test_against_betabinom_moments  sm    "ooc2Qq!.ua8+FU__Q99;G
hq!tnlS!rA   c                 (   d}t        t        j                        t        d      k  rt        j                  |       t        j
                  j                  d      }d}|j                  dd      }|j                  |      d	z  }t        ||      }d
}|j                  ||      }|j                  |||      }	t        |j                         t        j                  |	d      d       t        |j                         t        j                  |	d      d       |j                         j                  |j                         j                  cxk(  r|fk(  sJ  J |j                         }
|
j                  ||fk(  sJ t        |
t        j                  |	j                         d       t#        t        j$                  |
      |j                                t        j&                  t(        j*                  j-                  |
      d   dkD        sJ y )Nz/Needs NumPy 1.22.0 for multinomial broadcastingz1.22.0)reasonr  rb   r
   r-  r   r$  r  r   r   r   r<  rP  r  )r2   r8   __version__rL   r   r   r   r  r)   r   r   r   r   r9  r:   r   r   r   ro   r&  r   r   r   )rU   rV   r   r   r   r  r   r  r  r[   r   s              r?   r.  z%TestDirichletMultinomial.test_moments  s   C2>>"WX%66KKw'ii##$56LLC 


$r)$UA. MM%aM(OOAqqO)		RWWQQ%7dC
BFF11$5DAyy{  DHHJ$4$4>>>>>>hhjyyS#J&&&RVVACC[t4RWWS\488:.vvell'',Q/!3444rA   c                    t        j                  g d      }t        j                  |      }t        j                  g d      }d}t        t        |      5  t        j                  g d||       d d d        t        t        |      5  t        j                  g d||       d d d        d}t        t        |      5  t        j                  |g d|       d d d        t        t        |      5  t        j                  |g d	|       d d d        d
}t        t        |      5  t        j                  ||d       d d d        t        t        |      5  t        j                  ||d       d d d        t        j                  g d      }t        j                  g d      }d}t        t        |      5  t        j                  |||j                                d d d        y # 1 sw Y   yxY w# 1 sw Y   SxY w# 1 sw Y   +xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   y xY w)NrK   r  z,`x` must contain only non-negative integers.rE   )r
   rf   rH   )r
   r  rH   z*`alpha` must contain only positive values.)rH   r   rd   )rH   rf   rd   z`n` must be a positive integer.ǧH@r   )r
   rG   rH   rd   z&`x` and `alpha` must be broadcastable.)r8   r   r   r   rM   r)   r  )rU   x0n0alpha0textr[   r  s          r?   rW   z.TestDirichletMultinomial.test_input_validation  s   XXi VVBZ)$=:T2 	A!((VR@	A:T2 	B!((fbA	B <:T2 	<!((Y;	<:T2 	=!((Z<	= 1:T2 	;!((VT:	;:T2 	8!((VQ7	8 HH\"#7:T2 	<!((E1557;	< 	<)	A 	A	B 	B	< 	<	= 	=	; 	;	8 	8	< 	<sT   G(
G5?H2H'HH(9&H4(G25G?HHH%(H14H=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      j                  d
      }t        t        |      } ||||      }|j
                  dk(  sJ t        t        |            D ]  }t        t        |            D ]l  }t        t        |            D ]S  }||||f   }	 |||   j                         ||   j                         ||   j                               }
t        |	|
       U n  y )Nr  ro  rb   rb   re   r  r  r$  rc   re   r  rK   )rG   rG   rH   )rG   r
   r
   rH   )rG   rH   rd   )
r8   r   r)  rp   r)   r:   r	  r   r   r   )rU   r  r  r   r[   r;   rA  rB  r  res_ijkr<   s              r?   test_broadcasting_pmfz.TestDirichletMultinomial.test_broadcasting_pmf  s   )Y	:FGHHqcA3_%HHi+,44\B.7Qq!yyI%%%s1v 	2A3q6] 2s5z* 2A!!Q'lG 1q1A1A1CQqT\\^TC#GS122	2rA   )r   r9  r   c                    t        j                  g dg dg dg dg      }t        j                  dgdgdgg      }t        t        |      } |||      }|dk7  r|j                  d	k(  sJ 	 t        t        |            D ]Y  }t        t        |            D ]@  }|||f   } |||   j                         ||   j                               }	t        ||	       B [ y )
Nr  ro  r3  r4  rc   re   r  r   )rH   rd   rH   )	r8   r   rp   r)   r:   r	  r   r   r   )
rU   r   r  r   r  r;   rB  r  r5  r<   s
             r?   test_broadcasting_momentsz2TestDirichletMultinomial.test_broadcasting_moments  s    )Y	:FGHHqcA3_%.<UA)4)=syyI%OO<s1v 	.A3u:& .ad)U1X--/1@-.	.rA   N)r   r   r   classmethodr  r`  r  r  r  rL   r   r   r'  r)  r.  rW   r6  r8  r   rA   r?   r  r  V  s    # #C->O $ [[]UH,=>" ?" [[]VUO<" ="54<< [[Xx'892 :2 [[],BC
. D
.rA   r  r7  )[__doc__r  numpy.testingr   r   r   r   r   r   rL   r	   r   test_continuous_basicr   r  r8   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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   scipy.integrater.   r/   r0   scipy.specialr1   scipy._lib._pep440r2   common_testsr3   	data._mvtr4   unittest.mockr5   r@   rC   r   r   r   r  r3  r  r  r  r  r0  rR  rq  r  r  r  r<  r}  r  r  r  r  r   rA   r?   <module>rF     st   7 7  * 9   C C: : : : : : : : 0  3 3 & & 5  ']! ]!@@
) @
)FH* H*VF1 F1R-&i9 i9Vj# j#Xa( a(HC: C:Lo& o&dd# d#N6+ 6+r9# 9#x~9 ~9Ba% a%Hh$ h$V	(%$~! ~!B}. }.rA   