
    Џkh                       d Z ddlZddlmZ ddlmZmZmZmZm	Z	m
Z
 ddlZddlmZ ddlmZ ddlZddlZddlmZmZmZ dd	lmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4 dd
lm5Z5m6Z6 ddl7m8Z9 ddlm:Z: ddl;m<Z<m=Z=m>Z> ddl;m?Z?m@Z@mAZAmBZB ddlCmDZD ddlCmEZE ddlFmGZG ddlHmIZI ddlJmKZK d ZL G d d      ZMdAdZNd ZOe G d d             ZPe G d d             ZQ G d d      ZR G d d      ZS G d  d!      ZTd" ZU G d# d$      ZV G d% d&      ZW G d' d(      ZX G d) d*      ZY G d+ d,      ZZ G d- d.      Z[ G d/ d0      Z\ G d1 d2      Z] G d3 d4      Z^ G d5 d6      Z_ G d7 d8      Z`d9 Zaej                  j                  d:        Zd G d; d<      Ze G d= d>      Zf G d? d@      Zgy)Bz8
Test functions for multivariate normal distributions.

    N)	dataclass)assert_allcloseassert_almost_equalassert_array_almost_equalassert_equalassert_array_lessassert_)raises   )check_distribution_rvs)_PSD_lnBmultivariate_normal_frozen)multivariate_normalmultivariate_hypergeommatrix_normalspecial_ortho_grouportho_grouprandom_correlationunitary_group	dirichletbetawishartmultinomial
invwishartchi2invgammanormuniformks_2sampkstestbinom	hypergeommultivariate_tcauchy
normaltestrandom_tableuniform_directionvonmises_fisherdirichlet_multinomialvonmises)_covariance
Covariance)	_norm_pdf)stats)tanhsinhcubaturequad)rombqmc_quaddblquadtplquad)multigammaln)check_random_state_property)_qsimvtv)patchc                     t        j                  |       t        j                  |      }} t        | |g|i | t        | j                  |j                         y N)npasarrayr   r   shape)resrefargskwargss       _/var/www/teggl/fontify/venv/lib/python3.12/site-packages/scipy/stats/tests/test_multivariate.pyassert_closerE   /   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   $xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   y xY w)Nz:The input `precision` must be a square, two-dimensional...match   z0`precision.shape` must equal `covariance.shape`.   )
covariancez7The input `diagonal` must be a one-dimensional array...alpacaz9The input `cholesky` must be a square, two-dimensional...z4The input `eigenvalues` must be a one-dimensional...z,The input `eigenvectors` must be a square...z9The shapes of `eigenvalues` and `eigenvectors` must be...r   rL   rM   )pytestr
   
ValueErrorr,   CovViaPrecisionr=   oneseyeCovViaDiagonalCovViaCholeskyCovViaEigendecompositionselfmessages     rD   test_input_validationz$TestCovariance.test_input_validation7   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    rD   <lambda>zTestCovariance.<lambda>Y   s    %)!D%A rF   )Diagonal	PrecisionCholeskyEigendecompositionPSDrP   )   r   rM   )r         )rM   ri      )r   r   rM   )rg   r   )rk   rg   r   r   r   r   )diagonal full rankzgeneral full rankzdiagonal singularzgeneral singularr   N)r   rk   rn   cov_type_namerk   c                 |   t        j                  g d      }g d}t        t        d|       }| j                  |   }t        t
        d|j                                } | ||            } | ||            }t        |      t        |      u sJ t        |j                  |      |j                  |             y )NrP   )rL   rg   CovViafrom_)
r=   diaggetattrr,   _covariance_preprocessingr-   lowertyper   whiten)	rZ   ro   Ar`   cov_typepreprocessingfactoryr@   rA   s	            rD   test_factorieszTestCovariance.test_factoriese   s    GGI;&(@A66}E*m.A.A.C-D&EFmA&'}Q'(CyDI%%%

1szz!}5rF   matrix_typec                    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 )Nrr    does not support 	 matricesTr^      VGiVK rM   size	_colorizesingularrL   ri   rM   rL   rk   axis)
_cov_typesrQ   skip	_matricesru   r,   rv   r   rE   log_pdetr   rankr?   r=   r>   rN   randomdefault_rngry   UhasattrcolorizesumrU   lenT)rZ   r   ro   r[   rz   r{   r|   psd
cov_objectrngr`   r@   rA   s                rD   test_covariancezTestCovariance.test_covariances   s    M?*<[M J  <<KK NN;';&(@A66}E1T* mA./
Z((#,,7Z__chh/Z%%rzz!}':':;Z**BJJqM: ii##$78JJAJ"#%%iS3Yc	*:{+
+0M,,S115 JJIJ&"#%%ic1f\\r\*S!VLLbL,AB:{+
+0M,,S115 :{+%%bffSVn5Ca( ,rF   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 )Nrr   r   r   皙?皙?333333?Tr^   r   r   r   random_stateseed)r   rQ   r   r   ru   r,   rv   r   r=   r   r   rvs
isinstance	CovViaPSDrE   squeezer   r?   pdflogpdfentropy)rZ   r   r   ro   r[   rz   r{   r|   meanr   mvndist0dist1r   r`   x1x2s                    rD   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6rF   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 )Nrm   rr   r   Tr^   r   r   )r   ru   r,   rv   r   r=   r   r   rE   cdflogcdf)rZ   r   ro   r   rz   r{   r|   r   r   r   r   r   r   r`   s                 rD   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6rF   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.rJ   )rQ   r
   NotImplementedErrorr-   rY   s     rD   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   rL   g:0yEr   zThe input matrix must be...rJ   l   .ypGw r   )r=   rt   r?   zerosrQ   r
   rR   r   r   r   r   r-   from_eigendecompositionlinalgeighr   )rZ   rz   nr   r   rng1rng2covrvr@   rA   s              rD   test_gh9942zTestCovariance.test_gh9942   s    
 GGM"GGAJxx{ ]]:-JK 	/a(,,.	/ #yy$$T*yy$$T*001BC s+ff$f'!%%dCdCS#	/ 	/s   D//D8c                 r   t        j                  d      }t        j                  t        j                  d      t        j
                  d      f      }t        j                  j                  ||      }|j                  d       }t        ||       t        j                  j                  j                  t        j                  ddg      t        j                  ddgddgg      f      }t        j                  j                  ||      }|j                  d       }|d   |d   k7  sJ |d   |d   k(  sJ y )	NrL   r   r   r         ?        g      y@r   r   )r=   rT   r-   r   r   rU   scipyr/   r   r   r   array)rZ   r   r   distr   s        rD   test_gh19197zTestCovariance.test_gh19197  s   
 wwqz00"((1+rvvay1IJ{{..Dc.BhhDh!S$kk$$<<XXr2hB8b$Z*@!ABD{{..Dc.BhhDh!1va   1va   rF   )__name__
__module____qualname__r\   r=   rt   r   invcholeskyr   rv   r   list_all_covariance_typesr   r   rQ   markparametrizer~   r   tupler   r   r   filterwarningsr   r    rF   rD   rH   rH   5   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 :,!rF   rH   c                    |j                  | | f      }||j                  z  }t        j                  j	                  |      \  }}|r|j                  |       dkD  }d||<   |t        j                  |      z  |j                  z  }|S )Nr   r   )r   r   r=   r   r   normalrt   )	dimevalsr   r   rz   _v	zero_eigsr   s	            rD   _random_covariancer     s{     	

C:A	ACCA99>>!DAqJJCJ(1,	i
bggen
qss
"CJrF   c                     t         j                  j                  | |       }t        j                  j                  |      \  }}}|S r<   )r=   r   randnr   r   svd)r   Musr   s        rD   _sample_orthonormal_matrixr   #  s5    
		1Allq!GAq!HrF   c                       e Zd ZU dZeed<   ej                  ed<   ej                  ed<   ej                  ed<   ej                  ed<   eed<   eed<   d	Z	ed	z  ed
<    fdZ
edd       Zedd       Zedd       Zd Zd Zd Zd Z xZS )
MVNProblemaP  Instantiate a multivariate normal integration problem with special structure.

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

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

    References
    ----------
    .. [1] Tong, Y.L. "The Multivariate Normal Distribution".
           Springer-Verlag. p192. 1990.
    ndimlowhighlambdascovar
target_val
target_errNtrue_valc                    t         |           || _        || _        || _        || _        t        j                  | j
                  | j
                        | _        t        j                  | j                  d       | j                          y Nr   )super__init__r   r   r   r   r=   outerr   fill_diagonalfind_target)rZ   r   r   r   r   	__class__s        rD   r   zMVNProblem.__init__F  sd    		XXdllDLL9

S)rF   c                    t         j                  j                  |      }t        j                  |t         j                         }|j                  dt        j                  |      |      }|j                  dd|      } | ||||      }|S )zDRandom lambdas, random upper bounds, infinite lower bounds.
        r   r         r   r   r   r   r   r=   r   r   fullinfr   sqrtclsr   r   r   r   r   rZ   s          rD   generate_semigeneralzMVNProblem.generate_semigeneralQ  s{     ii##C(ggdRVVG${{3D{9++dCd+3	
 rF   c                 j   t         j                  j                  |      }t        j                  |t         j                         }|j                  dt        j                  |      |      }t        j                  |j                  dd            }t        j                  ||      } | ||||      }|S )zVConstant off-diagonal covariance, random upper bounds, infinite lower bounds.
        r   r   r   r   r   )r  r   r   r   r   sigmar   rZ   s           rD   generate_constantzMVNProblem.generate_constantb  s     ii##C(ggdRVVG${{3D{9C-.''$&	
 rF   c                     t        j                  |t         j                         }t        j                  |      }t        j                  d      } | ||||      }d|dz   z  |_        |S )zzOff-diagonal covariance of 0.5, negative orthant bounds.

        True analytically-derived answer is 1/(ndim+1).
              ?r   r   )r=   r   r   r   r  r   r  s          rD   generate_halveszMVNProblem.generate_halvest  s`     ggdRVVG$xx~''#,	
 T!VrF   c                     t        dd      }|j                  |       t        | j                  fi |\  | _        | _        y)z?Perform the simplified integral and store the results.
              "      "@abNdictupdater2   univariate_funcr   r   rZ   kwdsds      rD   r   zMVNProblem.find_target  s?     
 	
+/0D0D+J+J(rF   c           
         t        j                  d| j                  dz  z
        }t        j                  t	        j
                  | j                  | j                  |ddt         j                  f   z  z   |z        t	        j
                  | j                  | j                  |ddt         j                  f   z  z   |z        z
  d      S )z`The parameter-specific term of the univariate integrand,
        for separate plotting.
        r   rL   Nr   )	r=   r  r   prodspecialndtrr   newaxisr   )rZ   tdenoms      rD   _univariate_termzMVNProblem._univariate_term  s     DLL!O+,wwLL$))dll1Q

]3C&CCuLMLL$((T\\!ArzzM2B%BBeKLM
 	
rF   c                     t        j                  |      }t        j                  t        |      | j	                  |      z        S )zUnivariate integrand.
        )r=   
atleast_1dr   norm_pdfr  rZ   r  s     rD   r  zMVNProblem.univariate_func  s5     MM!zz(1+(=(=a(@@AArF   c                 $   ddl m} t        j                  ddd      }|j	                  |t        |      d       |j	                  || j                  |      d       |j	                  || j                  |      d	       |j                          y
)QPlot the univariate integrand and its component terms for understanding.
        r   pyplotr  r    	$\phi(t)$label$f(t)$$f(t)*phi(t)$N)	
matplotlibr'  r=   linspaceplotr"  r  r  legendrZ   pltr  s      rD   plot_integrandzMVNProblem.plot_integrand  ss     	-KKc4(HQK|4D))!,I>D((+3CD

rF   r<   )r   r   r   __doc__int__annotations__r=   ndarrayfloatr   r   classmethodr  r  r
  r   r  r  r4  __classcell__)r   s   @rD   r   r   )  s     J
**::jjJJ #Hut|"	     "  $K	
B	rF   r   c                       e Zd ZU dZeed<   ej                  ed<   ej                  ed<   ej                  ed<   ej                  ed<   eed<   eed<   d	 Z	e
dd       Zd Zd Zd Zd Zy
)SingularMVNProblemaH  Instantiate a multivariate normal integration problem with a special singular
    covariance structure.
    
    When covariance matrix is a correlation matrix where the off-diagonal entries
    ``covar[i, j] == -lambdas[i]*lambdas[j]`` for ``i != j``, and
    ``sum(lambdas**2 / (1+lambdas**2)) == 1``, then the matrix is singular, and
    the multidimensional integral reduces to a simpler univariate integral that 
    can be numerically integrated fairly easily.
    
    The lower bound must be infinite, though the upper bounds can be general.
    
    References
    ----------
    .. [1] Kwong, K.-S. (1995). "Evaluation of the one-sided percentage points of the
           singular multivariate normal distribution." Journal of Statistical
           Computation and Simulation, 51(2-4), 121-135. doi:10.1080/00949659508811627
    r   r   r   r   r   r   r   c                 B   || _         || _        || _        t        j                  |t        j
                         | _        t        j                  | j                  | j                         | _        t        j                  | j                  d       | j                          y r   )r   r   r   r=   r   r   r   r   r   r   r   )rZ   r   r   r   s       rD   r   zSingularMVNProblem.__init__  sl    		774"&&)hht||T\\::

S)rF   Nc                 T   t         j                  j                  |      }|j                  dt        j                  |      |      }|j                  t        j                  |d            }t        j                  |d|z
  z        |j                  ddg|      z  } | |||      }|S )z/Singular lambdas, random upper bounds.
        r   r   r   r   r   )r   r   r   )r=   r   r   r   r  r   r   choice)r  r   r   r   pr   rZ   s          rD   generate_semiinfinitez(SingularMVNProblem.generate_semiinfinite  s     ii##C({{3D{9MM"''$,-''!qs)$szz4+Dz'II

 rF   c                     t        dd      }|j                  |       t        | j                  fi |\  | _        | _        y )Nr  r  r  r  r  s      rD   r   zSingularMVNProblem.find_target  s=    
 	
+/0D0D+J+J(rF   c           	         t        j                  d| j                  dz  z         }t        j                  t	        j
                  | j                  d| j                  z  |d d t         j                  f   z  z
  |z        d      }t        j                  t	        j
                  | j                   d| j                  z  |d d t         j                  f   z  z   |z        d      }|d| j                  z  |z  z
  j                  S )Nr   rL   y              ?r   rk   )
r=   r  r   r  r  r  r   r  r   real)rZ   r  r  i1i2s        rD   r  z#SingularMVNProblem._univariate_term  s    DLL!O+,WWLL$))boa2::6F&FF%OP
 WWLL499*r$,,qBJJ7G'GG5PQ
 b499_r))///rF   c                     t        j                  |      }t        |      | j                  |      z  j	                         S r<   )r=   r!  r"  r  r   r#  s     rD   r  z"SingularMVNProblem.univariate_func  s3    MM!d33A66??AArF   c                 H   ddl m} t        j                  ddd      }|j	                  |t        |      d       |j	                  || j                  |      d       |j	                  || j                  |      d	       |j                  d
d       |j                          y)r%  r   r&  r  r  r(  r)  r*  r,  r-  皙皙?N)
r.  r'  r=   r/  r0  r"  r  r  ylimr1  r2  s      rD   r4  z!SingularMVNProblem.plot_integrand  s     	-KKc4(HQK|4D))!,I>D((+3CDs

rF   r<   )r   r   r   r5  r6  r7  r=   r8  r9  r   r:  rB  r   r  r  r4  r   rF   rD   r=  r=    sq    " J
**::jjJJ  K0B
rF   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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&ej$                  jN                  d!        Z(d" Z)ej$                  j'                  d# e*dd$            ej$                  j'                  d%d&d'g      d(               Z+ej$                  j'                  d# e*dd)            ej$                  j'                  d%d&d'g      d*               Z,ej$                  j'                  d# e*d+d)            ej$                  j'                  d%d&d,g      d-               Z-d. Z.d/ Z/ej$                  j'                  d0d1      d2        Z0d3 Z1ej$                  j'                  d4 ejd                  d5       ejd                  d6      g      d7        Z3ej$                  j'                  d8 ejd                  d9       ejd                  d:       ejd                  d;      g      d<        Z4d= Z5d> Z6d? Z7y@)A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 )NrM   rL   r   r   r   r   rL   )r=   arangeidentityassert_raisesrR   r   r   r   )rZ   mur   s      rD   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#NrF   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   rg   )
r=   r   r   r   r   r   r   r   absr   )rZ   r`   r   r   r   r   s         rD   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!rF   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 NrX  rg   )
r=   r   r   r   r[  r   r   r   r   logrZ   r`   r   r   d1d2s         rD   test_logpdfz"TestMultivariateNormal.test_logpdf.      
		tIIOOAyyq!ffRYY__Q'( ''45 $$Qc2BFF2J'rF   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 NrX  rg   r   )	r=   r   r   r   r   r   r   r   r_  rZ   r`   ra  rb  d3d4s         rD   test_logpdf_default_valuesz1TestMultivariateNormal.test_logpdf_default_values8       			tIIOOA ''* $$Q' ''43 $$Qa0BFF2J'BFF2J'rF   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        j                  |||      }t        j                  |||      }t        |t        j                  |             y r^  )
r=   r   r   r   r[  r   r   r   r   r_  r`  s         rD   test_logcdfz"TestMultivariateNormal.test_logcdfE  rd  rF   c                    t         j                  j                  d       t         j                  j                  d      }t	        j
                  |      }t	        j                  |      }t	        j
                  |d d      }t	        j                  |d d      }t        |t        j                  |             t        |t        j                  |             y rf  )	r=   r   r   r   r   r   r   r   r_  rg  s         rD   test_logcdf_default_valuesz1TestMultivariateNormal.test_logcdf_default_valuesO  rk  rF   c                    t         j                  j                  d       d}t         j                  j                  |      }t	        d|dz         D ]p  }t         j                  j                  ||      }t        j
                  ||j                        }t        ||d      }t        |j                  j                  |       r y )NrX  ri   r   Tr^   )r=   r   r   r   rangedotr   r   r   r   r   )rZ   r   r   expected_rankr   r   distns          rD   	test_rankz TestMultivariateNormal.test_rank\  s    
		tyyq!"1a!e_ 	?M		=1A&&ACC.C'c$GE))..>		?rF   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   rg   Tr^   rk   r   )rq  r=   r   r   rr  r   r   r   r   r   r   r   r   r   r   r   )rZ   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                          rD   test_degenerate_distributionsz4TestMultivariateNormal.test_degenerate_distributionsg  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	6rF   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
   rL   rh   r   r   r   r   T)r   r   r_   r   )rq  r=   r   r   rr  r   r   r   r   r   r   allr   r   )
rZ   rx  r   rmnr   vrXr   r   s
             rD   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	0rF   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   rL   dtyper   r   )r=   expr   r9  r   r   r   r   detr   r   slogdetr   r   )rZ   large_total_lognposnzerolarge_entryr   r   r   s           rD   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6rF   c                 F   t         j                  j                  d      }d}|j                  ||      }t        j                  ||j
                        }|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 )NrX  ri   rL   rM   MbP?rtol)r=   r   RandomStater   rr  r   r   r   r   rq  r   )rZ   r   r   datar   r   r  desired_pdfdesired_cdfijactuals               rD   test_broadcastingz(TestMultivariateNormal.test_broadcasting  s   ii##D) yyAffT466"yy| IIaA *--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rF   c                 .   t        j                  ddd      }d\  }}|dz  }t        j                  |||      }t	        j                  |||      }t        ||       t        j                  |||      }t	        j                  |||      }t        ||       y )Nr   rL   r  )333333??r	  )r=   r/  r   r   r   r   r   )rZ   r`   r   r   scalera  rb  s          rD   test_normal_1Dz%TestMultivariateNormal.test_normal_1D  s     KK1b!	cSXXau% $$Qc2BXXau% $$Qc2BrF   c                 b   t        j                  ddg      }t        j                  ddgddgg      }d}d|dz
  z  }t        j                  d	d|      }t        j                  ||      \  }}t        j                  ||d
f      }||d d d d d	f<   ||d d d d df<   t        j                  |||      }	t        |	|d	      }
t        |	|d      }t        j                  ||d	   |d   dz        }t        j                  ||d   |d   dz        }t        |
|dd       t        ||dd       y )NrZ  g      @r	  r   333333?i  rh   r   r   rL   r   r   r   locr  )r   r   {Gz?r  atol)
r=   r   r/  meshgridemptyr   r   r3   r   r   )rZ   r   r   r   deltar   xvyvposr   margin_xmargin_ygauss_xgauss_ys                 rD   test_marginalizationz+TestMultivariateNormal.test_marginalization  s)    xxc
#hhS	C9-.QUKK1a Q"Bhh1ay!Aq!GAq!G!%%c45 U+U+ ((1$q'Tc1AB((1$q'Tc1AB'4@'4@rF   c                    t         j                  j                  d       t         j                  j                  d      }t         j                  j                  d      }t        j                  t         j                  j                  d            }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             y r^  )r=   r   r   r   r[  r   r   r   r   r   r   )rZ   r`   r   r   norm_frozens        rD   test_frozenz"TestMultivariateNormal.test_frozen  s    
		tIIOOAyyq!ffRYY__Q'()$4*,?,C,CAtS,QR**1-+221dC@	B*,?,C,CAtS,QR**1-+221dC@	BrF   rN   rL   r   c                     t        j                  d      }t        j                  d      }t        ||      }t        j                  |j
                  |      sJ t        j                  |j                  |      sJ y )NrL   rL   )r=   rT   rU   r   allcloser   r   )rZ   rN   r   cov_should_ber  s        rD   2test_frozen_multivariate_normal_exposes_attributeszITestMultivariateNormal.test_frozen_multivariate_normal_exposes_attributes  s\     wwt}q	)$
;{{;++T222{{;??M:::rF   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 )
NrX  rj   r	  r   r   Hz>rk   h㈵>)cond)r=   r   r   r   rr  r   r   r   r   r   rt   r   pinvr   r   r   r_  )	rZ   r   r`   r   r   r   r  r   psd_pinvs	            rD   test_pseudodet_pinvz*TestMultivariateNormal.test_pseudodet_pinv$  s    			tIIOOAq!ffQn||  %1GGAsO!"ffQrwwqz133/0 3T"t, 	bffRVVAcrF^&<= 	x'8'89rF   c                 >    g dg dg}t        t        t        |       y )NrP   ri   rg   rh   rT  rR   r   rZ   r   s     rD   test_exception_nonsquare_covz3TestMultivariateNormal.test_exception_nonsquare_cov>  s    )$j$,rF   c                     ddgdt         j                  gg}t        t        t        |       ddgdt         j
                  gg}t        t        t        |       y )Nr   r   )r=   nanrT  rR   r   r   )rZ   cov_nancov_infs      rD   test_exception_nonfinite_covz3TestMultivariateNormal.test_exception_nonfinite_covB  sF    q6Arvv;'j$0q6Arvv;'j$0rF   c                 >    ddgddgg}t        t        t        |       y )Nr   r   rk   r  r  s     rD   test_exception_non_psd_covz1TestMultivariateNormal.test_exception_non_psd_covH  s     1v2wj$,rF   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)	NrX  rg   )rg   rg   r   r   z0When `allow_singular is False`, the input matrixrJ   r   )r=   r   r   r   rT   r   LinAlgErrorrT  r   r   r   r   r   rQ   r
   )rZ   r`   r   r   emsgs         rD   test_exception_singular_covz2TestMultivariateNormal.test_exception_singular_covL  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   rL   rg   rM   )r   rM   rL   r  r   rL   r   )rL   rg   r	  )r   r	  rM   绽|=r  )gwk:E]?g̙Z?g0?gL8?gAG*?gh㈵>)gIى?gG?gƏ)?gėh?gEE?r   r  )	r=   r   r/  cosr   r   r   r   r   )rZ   r_pdfr`   r|  rw  r  r   r   r   r_cdfr   r_cdf2r2mean2cov2cdf2s                   rD   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0rF   c                     t        j                  d      }t        j                  d      }t        ||d      }|j                         }t	        |ddg       y )NrL   rL   rL   Tr^   r   )r=   r   r   r   r   )rZ   r   rN   modelsamples        rD   ,test_multivariate_normal_rvs_zero_covariancezCTestMultivariateNormal.test_multivariate_normal_rvs_zero_covariance  sD    xx{XXf%
#D*TJVaV$rF   c                    d}d}t        j                  t        j                  |      d|      }t	        |j
                  ||f       t        j                  d t        j                  ddgddgg      |      }t	        |j
                  |df       t        dd      }|j                  |      }t	        |j
                  |f       y )	Ni,  ri   r   r  rL   r   r   r   )r   r   r=   r   r   r?   r   )rZ   Nr  r  r   s        rD   test_rvs_shapez%TestMultivariateNormal.test_rvs_shape  s     $((bhhqkqqIV\\Aq6*$((d-/XX2wQ6H-I./1 	V\\Aq6*QA.qV\\A5)rF   c                    t         j                  j                  d      }d}|j                  |      }|j                  ||      }t        j                  ||j
                        }d}t        j                  ||||      }t        t        j                  |j
                        |d       t        |j                  d      |d       y )N  rM     r   r   r  r   )r=   r   r  r   rr  r   r   r   r   r   r   )rZ   r   r   r   r   r   r   r  s           rD   test_large_samplez(TestMultivariateNormal.test_large_sample  s     ii##D)yy|IIaOffQn$((sDsKvxx(#D9A48rF   c                 h   t         j                  j                  d      }d}|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  rM   r   r	  rL   r   )r=   r   r  r   rr  r   r   r   r   r   eigr_  pir   )	rZ   r   r   r   r   r   r   eigsdesireds	            rD   test_entropyz#TestMultivariateNormal.test_entropy  s    ii##D)yy|IIaOffQn s+ 	BJJL*=*E*EdC*PQ yy}}S!!$1q255y 1A 56t9MMNGRZZ\2rF   c                     t        j                  g d      }d}t        t        j                  t	        |            |       y )Nr   r   r   r	  )r=   r   r   r  r   )rZ   alphar  s      rD   test_lnBzTestMultivariateNormal.test_lnB  s,    #BFF4;/9rF   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   rL   )ri   rM   rL   rh   rM   lower_limit.r   rk   r   )r=   r   r   rU   r   r   concatenater   )rZ   r   r   r   r  r  cdf1cdf2acdf2bab1ab2cdf2ab1cdf2ab2r  s                 rD    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#rF   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  rM   rM   rM   rL   rM   rh   r	  -C6?r  )	r=   r   r   r   r   r   r  r   r   )
rZ   r   r   r   r  r  r  r  cdf3cdf4s
             rD   %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.rF   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 )	NrM   r  rl   r   r   r   r   r   r   r   rk   rk   r   r	  r   r=   r   rU   r   r   r   r   )rZ   r   r   r  r  expected_signsr   s          rD   test_cdf_signsz%TestMultivariateNormal.test_cdf_signs  so    xx{ffQi	9i8	9i8.1!%%asBSVN23rF   c                    d}t         j                  j                  d      }|j                  ||f      }|j                  |z  }|j                  |      }t        ||      }|j                  dd|f      }|j                  |      }t        dg|z  |      }	t        |	j                  t         j                   g|z  ||z
        j                  }
t        ||
d	       y )
NrM   {   r   r   )r   r   r   r   gh㈵>r  )r=   r   r   r   r   r   r   r1   r   r   estimater   )rZ   r   r   r  r   mr   r`   r   dist_icdf_is              rD   test_cdf_vs_cubaturez+TestMultivariateNormal.test_cdf_vs_cubature  s    ii##C(KKdD\K*ccAgKKTK""s3KKBQdWK5hhqk$1#d(<rvvgYt^QU;DDU.rF   c                     t        dd      D ]h  }t        j                  ||fd      }t        j                  |d       t	        dg|z  |      }t        |j                  dg|z        dd|z   z  d       j y )	NrL      r	  r   r   r  -C6
?r  )rq  r=   r   r   r   r   r   )rZ   r   r   r   s       rD   test_cdf_knownz%TestMultivariateNormal.test_cdf_known  sv    !RL 	D''4,,CS"%&s4xS9D!T"b4i 		rF   r   r  r   l   >[= l	   HVqKWs.!) c                 l   t         j                  j                  |      }t        j	                  ||      }|j
                  t         j                   k(  j                         sJ t        dg|z  |j                        }|j                  |j                  |      }t        ||j                  d       y Nr   r   r   r   r   r,  r  )r=   r   r   r   r  r   r   r  r   r   r   r   r   r   rZ   r   r   r   caser   cdf_vals          rD   test_cdf_vs_univariatez-TestMultivariateNormal.test_cdf_vs_univariate+  s     ii##D)..Dc.BRVVG#((***"DdjjA((499#(.t<rF      c                 l   t         j                  j                  |      }t        j	                  ||      }|j
                  t         j                   k(  j                         sJ t        dg|z  |j                        }|j                  |j                  |      }t        ||j                  d       y r/  )r=   r   r   r   r  r   r   r  r   r   r   r   r   r   r2  s          rD   test_cdf_vs_univariate_2z/TestMultivariateNormal.test_cdf_vs_univariate_26  s     ii##D)++3+?RVVG#((***"DdjjA((499#(.t<rF   ri   l	   HVqKWs.!) c                    t         j                  j                  |      }t        j	                  ||      }|j
                  t         j                   k(  j                         sJ t        dg|z  |j                  dd|j                  j                  d   z        }|j                  |j                  |      }t        ||j                  d       y )	Nr0  r   T'  )r   r   r_   maxptsr1  r  r  )r=   r   r   r=  rB  r   r   r  r   r   r?   r   r   r   r   r2  s          rD   test_cdf_vs_univariate_singularz6TestMultivariateNormal.test_cdf_vs_univariate_singularA  s    
 ii##D)!77Ts7KRVVG#((***"DdjjQU*01A1A!1D*D
 ((499#(.t<rF   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   rP   z7`cov` represents a covariance matrix in 3 dimensions...rJ   r   )r	  r	  r	  rl   r  r  )r=   rt   r   r,   rS   rQ   r
   rR   r   r   r   r   )rZ   Pr   r[   r`   rA   s         rD   test_mean_covz$TestMultivariateNormal.test_mean_covQ  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   rM   z`x` must be two-dimensional.rJ   )rQ   r
   rR   r   fit)rZ   r  	error_msgs      rD   test_fit_wrong_fit_data_shapez4TestMultivariateNormal.test_fit_wrong_fit_data_shaped  sA    1v2	]]:Y7 	*##D)	* 	* 	*s   AA
r   )rM   rg   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  )	r=   r   r   r   rA  r   r   r   r   )rZ   r   r   r`   mean_estcov_estmean_refcov_refs           rD   test_fit_correctnessz+TestMultivariateNormal.test_fit_correctnessj  sy    ii##$45JJSz"/33A6'GGAA.qss0C'(7u5rF   c                     t        j                  dd      }d}t        j                  d      }t        j                  |||      \  }}t        ||       t        ||       y )N)rL   r   rM   r   )fix_meanfix_cov)r=   r   
atleast_2dr   rA  r   )rZ   r  
mean_fixed	cov_fixedr   r   s         rD   test_fit_both_parameters_fixedz5TestMultivariateNormal.test_fit_both_parameters_fixeds  sT    wwvq!
MM"%	'++D:4=?	cT:&S)$rF   rN  r  rM   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`.rJ   rL   rN  rQ   r
   rR   r   rA  r=   rU   )rZ   rN  r  s      rD   "test_fit_fix_mean_input_validationz9TestMultivariateNormal.test_fit_fix_mean_input_validation|  sI    C]]:S1 	B##BFF1IA	B 	B 	B   +AArO  r  )rM   rL   )ri   ri   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`.rJ   rM   rO  rW  )rZ   rO  r  s      rD   +test_fit_fix_cov_input_validation_dimensionzBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimension  sJ     ]]:S1 	@##BFF1Iw?	@ 	@ 	@rY  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.rJ   r   r   r   rL   r[  )rQ   r
   rR   r=   r   r   rA  rU   )rZ   rB  rO  s      rD   *test_fit_fix_cov_not_positive_semidefinitezATestMultivariateNormal.test_fit_fix_cov_not_positive_semidefinite  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 )	NrE  rM   r  r  r   r   r   r   r   rV  :0yE>)r=   r   r   rr  r   r   r   rA  r   r   r   )rZ   r   r  rz   r   samples	mean_freecov_free	logp_freemean_fixcov_fixlogp_fixr&  cov_perturbedlogp_perturbeds                  rD   test_fit_fix_meanz(TestMultivariateNormal.test_fit_fix_mean  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 	 (((rF   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 )NrE  rM   r  r  r`  r   r[  r   r   ra  )r=   r   r   rr  r   r   r   rA  r   r   r   r   )rZ   r   r  rz   r   rb  rc  rd  re  rf  rg  rh  mean_perturbedrj  s                 rD   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 	 (((rF   N)8r   r   r   rV  r\  rc  rj  rm  ro  ru  r  r  r  r  r  r  r  rQ   r   r   r=   rU   r-   from_diagonalr  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  slowr)  r-  rq  r5  r8  r<  r?  rC  rL  rS  r   rX  r\  r^  rk  rn  r   rF   rD   rN  rN  
  s   O"6((((	?26h0,70E0 A2B [[BFF1I$J$$aV,	
;;:4-1-)&>1@%*"9"3$:$(/$	4 [[/ /
 [[VU1b\2[[Vj2T%UV= W 3= [[VU1b\2[[Vj2T%UV= W 3= [[VU1b\2[[Vj2T%UV= W 3=I&* [[UF+6 ,6% [[Z("((6*:*2"((5/*; <B<B [[Y%)1&)9)1&)9); <@<@@):)rF   rN  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 )Nri   rM   r   r	  ffffff?)rg   ri   rM   r  )r=   r   rS  rT  rR   r   r   r   r   r  r   rT   )rZ   num_rowsnum_colsr   r   Vr  s          rD   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!LrF   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 )Nri   rM   r   r	  rt  r   r   rowcovcolcov)r   )r{  )r|  )r   r|  )r   r{  )r{  r|  )r=   r   rS  r   r   r   r   r?   r{  r|  r   )rZ   ru  rv  r   r   rw  ZZrZcIrIcI1s               rD   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?rF   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 )Nri   rM   r   r   r   rz  )r=   r   rS  r   r   r{  r|  )
rZ   ru  rv  r   UvUsVvVsr  r  s
             rD   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	rF   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   rg   r   r	  rt  rz  rX  r   )r   r{  r|  r   )	rq  r=   r   rS  r   r   r   r   r   )rZ   r  r  r   r   rw  frozenrvs1rvs2r  pdf1pdf2logpdf1logpdf2s                 rD   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!}$((1QGT4( --*'..qq1MWg.)/	/rF   c                 Z   t        dd      D ]  }t        dd      D ]  }t        j                  ||fd      }dt        j                  |      z  t        j                  ||fd      z   }dt        j                  |      z  t        j                  ||fd      z   }t	        |||      }|j                  d      }|j                  |      }|j                  |      }	|j                         }
|j                  j                         }|j                  j                         }t        j                  ||      }t        j                  |||	      }t        j                  |||	      }t        j                  ||	      }t        ||d
       t        |	|d
       t        |
|         y )Nr   rg   r   r	  rt  rz  rX  r   r   r  r  )rq  r=   r   rS  r   r   r   r   r   r   flattenkronr   r   )rZ   r  r  r   r   rw  r  r  r  r  entropy1vecXvecMr   r  r  entropy2s                    rD   test_matches_multivariatez*TestMatrixNormal.test_matches_multivariate>  s\    q 	4A1QZ 4GGQqE3'"++a.(277Aa5#+>>"++a.(277Aa5#+>>&AaBJJDJ1zz!} --*!>>+ss{{}ss{{}ggal*..t$CH-44T#N.66DcJd7u=(3)4	4rF   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 )Nri   rM   r   r	  rt  r  rz  rX  r   i  r   r   rL   r  )r=   r   rS  r   r   r  r  r   r?   r   rq  r   )rZ   ru  rv  r   r   rw  r  r  X1X2r  array_logpdfr  r  separate_logpdfs                  rD   test_array_inputz!TestMatrixNormal.test_array_inputX  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rF   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 )Nri   rM   r   r	  rt    rz  rX  r   r   r   r   r  r   rL   )r=   r   rS  r   r   r   r   r   reshaper   swapaxes)rZ   ru  rv  r   r   rw  r  r  r  sample_meansample_colcovsample_rowcovs               rD   test_momentszTestMatrixNormal.test_momentso  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3rF   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   rL   rM   ri   rk   rg   r  r   )r   r{  r|  r   r   g6?gǀgcϿ@g"'@gI2͖@g^jy%@gDn3@g|\3@)r   r   r=   r   r   r   r   )rZ   r  expecteds      rD   test_sampleszTestMatrixNormal.test_samples  s     ""Aq6Aq6*+88aWr1g./88aVaW-...q1
 88!23!124!23!1245
 	)rF   N)r   r   r   rx  r  r  r  r  r  r  r  r   rF   rD   rr  rr    s.    M4%@N,/044K.4,*rF   rr  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  rk   )r=   r   r   randintr   r   r   varr   r   rq  r   r   r   rZ   r   r  r  	num_testsr  r`   s          rD   test_frozen_dirichletz#TestDirichlet.test_frozen_dirichlet  s0   
		tIIa$		!!&#q1eQUUWimmE23QVVXy~~e45QYY[)"3"3E":;	y! 	LA		!!&#q1ANAq"v	afe(DE!CR&)9+;+;AcrFE+JK		LrF   c                 j   t         j                  j                  d       t        j                  g d      }t         j                  j	                  |d      }t        |j                  d       t        t        t        j                  ||       t        t        t        j                  ||       t	        j                  |j                  |       t	        j                  |j                  d d |       t	        j                  |j                  |       t	        j                  |j                  d d |       y )Nr  r          @      @rj   r   )rj   rM   rk   )r=   r   r   r   r   r   r?   rT  rR   r   r   r   rZ   r  r`   s      rD   "test_numpy_rvs_shape_compatibilityz0TestDirichlet.test_numpy_rvs_shape_compatibility  s    
		t)IIA.QWWf%j)--E:j)"2"2Au=acc5!acc#2h&e$Sb5)rF   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  r  rj   r   
r=   r   r   r   maximumr   rT  rR   r   r   r  s      rD   test_alpha_with_zerosz#TestDirichlet.test_alpha_with_zeros  sg    
		tII

4 7a@BBj)--E:j)"2"2Au=rF   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  r  rj   r   r  r  s      rD    test_alpha_with_negative_entriesz.TestDirichlet.test_alpha_with_negative_entries  sg    
		t II

4 7a@BBj)--E:j)"2"2Au=rF   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   rt  )r   r   r   r   rh   )r=   r   r   r   r   r   r_  r  s      rD   test_data_with_zerosz"TestDirichlet.test_data_with_zeros  s    -.HH)*aE"-.IMM!U3Q7I,,Q6q	BrF   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )N)r   r	  r  r  r  r=   r   rT  rR   r   r   r   r  s      rD   $test_data_with_zeros_and_small_alphaz2TestDirichlet.test_data_with_zeros_and_small_alpha  F    -.HH)*j)--E:j)"2"2Au=rF   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )Nr  )r   rJ  r   rt  r  r  s      rD   test_data_with_negative_entriesz-TestDirichlet.test_data_with_negative_entries  sF    -.HH*+j)--E:j)"2"2Au=rF   c                     t        j                  g d      }t        j                  g d      }t        t        t        j
                  ||       t        t        t        j                  ||       y )Nr  )r   rK  r   rt  r  r  s      rD    test_data_with_too_large_entriesz.TestDirichlet.test_data_with_too_large_entries  r  rF   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr  )rL   rj   rj   g$I$I?r=   r   r   rT  rR   r   r   r   r  s      rD   test_data_too_deep_cz"TestDirichlet.test_data_too_deep_c  sF    )GGIv&j)--E:j)"2"2Au=rF   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  r  )rL   rL   rj         ?r  r  s      rD   test_alpha_too_deepz!TestDirichlet.test_alpha_too_deep  sS    3*sCj12GGIu%j)--E:j)"2"2Au=rF   c                     t        j                  g d      }t        j                  dd      }t        j                  ||       t        j
                  ||       y )Nr  rM   rj   UUUUUU?)r=   r   r   r   r   r   r  s      rD   test_alpha_correct_depthz&TestDirichlet.test_alpha_correct_depth  s>    )GGFE"aE"rF   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr  r  r	  r  r  s      rD   test_non_simplex_dataz#TestDirichlet.test_non_simplex_data  sF    )GGFE"j)--E:j)"2"2Au=rF   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr  )rL   rj   r	  r  r  s      rD   test_data_vector_too_shortz(TestDirichlet.test_data_vector_too_short  G    -.GGFE"j)--E:j)"2"2Au=rF   c                     t        j                  g d      }t        j                  dd      }t        t        t
        j                  ||       t        t        t
        j                  ||       y )Nr  )rg   rj   r   r  r  s      rD   test_data_vector_too_longz'TestDirichlet.test_data_vector_too_long  r  rF   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   r	  皙?r   )UUUUUU?{Gz?Q?)r  )r  r  O贁N)r  r  r  )r=   r   r   r   r   r  r   )rZ   r  r  expected_meanexpected_varexpected_covs         rD   test_mean_var_covzTestDirichlet.test_mean_var_cov  sh     (e'-../
 	"!&&(M:!!%%'<8!!%%'<8rF   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   )	r=   r   r   r   r   r   r  r   r   )rZ   r  r  s      rD   r\  z TestDirichlet.test_scalar_values  sy    #e 	QVVX]]A&QUUW\\1%QUUB4[%%q)QXXrd^((!,rF   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 r  )
r=   r   r   r  r   r   rq  r   r   r   r  s          rD    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	9rF   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   r  r  r  r  rg   )r=   r   r   r  r   r   rq  r   vstackr   r   appendr   )rZ   r   r  r  r  num_multiplexmr  r&  r`   rmrsxsr  s                 rD   test_multiple_entry_callsz'TestDirichlet.test_multiple_entry_calls3  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"-!	.rF   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  r  r  rL   r   r   r  )r=   r   r   r   r   r   rq  r   r   r   r   r  )rZ   r  r  r  r  r  r`   s          rD   test_2D_dirichlet_is_betaz'TestDirichlet.test_2D_dirichlet_is_betaP  s    
		t		!!&#q1eq58$	y! 	6A		!!&#q1ANAa!%%*5	6
 	AFFHaffhqk2AEEGQUUWQZ0rF   N)r   r   r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r\  r  r  r  r   rF   rD   r  r    sc    L$
*>>C>>>>>#>>>9$	-9.:1rF   r  c                     t        j                  ddg      } t        j                  dgg      }t        t        t        | |       	 t	        | |       y # t        $ r-}d}t        t        |      d t        |       |       Y d }~y d }~ww xY w)Nr   r   zDimension mismatch)r=   r   rT  rR   r   r   strr   )rU  r  r  r  s       rD   ,test_multivariate_normal_dimensions_mismatchr  a  sw     
3*	BHHseWE*12u=
-B& -"SVISX&,,-s   A 	B	#BB	c                   0    e Zd Zd Zd Zd Zd Zd Zd Zy)TestWishartc                    t        j                  dd      }ddgt        j                  d      t         j                  d   t        j                  dd      g}|D ]N  }t        d|      }t	        |j
                  |       t	        |j
                  j                  |j                         P t        j                  ddgddgg      }ddgt         j                  d   t        j                  ddgddgg      g}|D ]N  }t        d|      }t	        |j
                  |       t	        |j
                  j                  |j                         P t        t        t        dt        j                  d             t        dt        j                  d             t        j                  dd      }t        t        t        d|       y )Nr   rL   ndminr   r   rL   rK  rM   )
r=   r   r_r   r   r  r?   rT  rR   rU   )rZ   
true_scalescalesr  ws        rD   test_scale_dimensionsz!TestWishart.test_scale_dimensionsu  st    XXaq)
CHHQKEE!HHHQa 
  	:E5!A*-
(8(89	: XX!u !!u& '
 qEEE#JHHqee 
  	:E5!A*-
(8(89	: 	j'1bffQi8 	RVVAY !$j'1e4rF   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   rL   r  rM   rP   r  r   )r=   r   r  r   r   r   r  rU   )rZ   r  r	  densityr`   s        rD   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+	,rF   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 	Nri   r   rL   rk   rx  rg   r  r   )r=   rt   rR  tril_indicesrr  r   rq  r  r   r/  r   r   r  r   moder   r   )	rZ   r   r  r  r  r`   
parametersdfr	  s	            rD   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#<=	>rF   c                 Z   d}d}t        j                  |      }d|d<   d|d<   t        ||      }t         j                  j	                  d      }t        j
                  |||      }t         j                  j	                  d      }|j                  |      }t         j                  j	                  d      }|j                  d      }t         j                  |j                  |      |j                  |d	z
        |j                  |d
z
        f   dz  }	t        j                  |	      }
||
t        j                  |d      <   t         j                  j                  |      }|j                  |
      }t        j                  ||j                        }t        ||       t        ||       y )NrM   r  r	  rP  r   r   i r   r   r   rL   rk   r  )r=   rU   r   r   r  r   r   r  	chisquarert   r  r   r   rr  r   r   )rZ   r   r  r  r	  r   w_rvsfrozen_w_rvscovariances	variancesrz   DDAmanual_w_rvss                 rD   test_wishart_2D_rvszTestWishart.test_wishart_2D_rvs  sh    sc
c
 B ii##F+BC8ii##F+uu#u. ii##F+jjaj(EEMM"MM"Q$MM"Q$!
 		 GGI(3"//#
$% IIu%UU1Xvvb"$$' 	|,l3rF   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  rL   r  r   numr   r  r   )r=   r   r   rU   rR  r9  r/  r   r   r   r  r   r   r   r   r   )rZ   r   snr   r  df_ranger  r  r	  cr   rB   r  s                rD   test_1D_is_chisquaredz!TestWishart.test_1D_is_chisquared  s   
 ii##F+s99QAU3KKB2& 	=BE"ARA AEEGQUUW-AFFHaffh/AIIK5 AEE!HaeeAh/ %%Rc%2C5DE"64<!	=rF   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  ri   r   rh   rk   r  r  r   r#  r   r   r  r   )r=   r   r   rt   rR  r  rr  r   rT   r   r   r   r   r  r   r   r/  r   r   r   )rZ   r   r%  r  r   r  lamdasigma_lamdar	  r'  r  r   rB   r  s                 rD   test_is_scaled_chisquaredz%TestWishart.test_is_scaled_chisquared<  sg   
 ii##F+		!Q'*,))A,booa2&'uww&Q ggkk%(,,U3;;=B$;' 	)!&&(+		QYY[1 KKB2&a!%%(+ ee#e.1[!vtUC8rF   N)	r   r   r   r
  r  r  r  r(  r-  r   rF   rD   r  r  t  s$    )5V/,b>@*4X=>!9rF   r  c                      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ej                  j                  dej*                  ej,                  g      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rM   ri   rj   r   rt  g&Mtyra  r  rM   ri   r   r   rt  rn   )r   logpmfr   r=   r   r  )rZ   vals1vals2vals3vals4s        rD   test_logpmfzTestMultinomial.test_logpmf`  s    ""5!Z81=""Aq61r2h7""Aq61r2h7zz""Aq61r1g6rvvD1rF   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 )Nr1  rj   r2  rM   r   ra  r  )rh         r   r  rh   r   )r   r3  r"   r   pmfrZ   val1val2s      rD   test_reduces_binomialz%TestMultinomial.test_reduces_binomialm  sf     !!&!Z8||Aq#&d.vr:6yyB$d.rF   c                     dg d}}ddddddd	dd
dd
}|D ](  }t        t        j                  |||      ||   d       * y )NrM   )g      ?r  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rM   )r   r   rL   )rL   r   r   )rM   r   r   rQ  r  rL   r   r   )r   rL   r   r  )r   rM   r   +=r  )r   r   r=  )rZ   r   rA  r_valsr`   s        rD   test_RzTestMultinomial.test_Rx  s_     $1([([([([([	B
  	MAKOOAq!4fQieL	MrF   r   r   rM   c                 H   d}t        j                  t        |      5  t        j                  j                  d      }t        j                  |dgdz  dd      }|j                  |dgdz  d      }t        ||       d d d        t        j                  t        |      5  t        j                  j                  d      }t        j                  |dgd	z  dd      }|j                  |dgd	z  d      }t        ||       d d d        y # 1 sw Y   xY w# 1 sw Y   y xY w)
Nz,Some rows of `p` do not sum to 1.0 within...rJ   r#  r  rM   rj   r   r   rg   )	rQ   warnsFutureWarningr=   r   r  r   r   r   )rZ   r   r[   rndmsc_rvsnp_rvss         rD   test_rvs_npzTestMultinomial.test_rvs_np  s    A\\-w7 	)99((-D __QqqsKF%%a$%:F(		)
 \\-w7 	)99((-D __QqqsKF%%a$%:F(		) 	)	) 	)
	) 	)s   A!D"A!DDD!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)rg   rg   r   r   ra  r  r1  rj   r2  g5
?rM   r   r:  rk   	   r<  g*7?g<Wƌ?r   rL   r  ri   rL   rM   rM   r   rh   )gUUUUUU?r  r   gߦ?rl   rC  )r   r=  r   r=   r  float64r   )	rZ   vals0r4  r5  r`   r6  r7  vals5vals6s	            rD   test_pmfzTestMultinomial.test_pmf  sJ   a.qt,q(31=1Q%1"a1a&0A BA (*I 6A?dKHHU"**-1h/UBHHRrzz:;1q(3qt,	1.?@~D9	1.?@zz	1.?@zzrF   c                    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   rL   rM   r   r  r   r  gv?g~jt?ra  r  ri   r   )r   r=  r   )rZ   rT  r4  r5  r6  r7  s         rD   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?$!T:!Q!AQC5'RHE4)T:rF   rg   c                     t        j                  |d      }|dz  dz  | dz  dz  | dz  dz  g| dz  dz  |dz  dz  | dz  dz  g| dz  dz  | dz  dz  |dz  dz  gg}t        ||d       y )	N)r   r   r	  r   r  r   r	  rt  ra  r  r   r   r   )rZ   r   cov1r  s       rD   test_covzTestMultinomial.test_cov  s    q,/2b1"R%(QBrE"H-Br1R47QBrE"H-BrA2b58QrT"W-/ 	d.rF   c                 `   t        j                  dddgddgg      }ddgddggddgddggg}t        ||d	
       t        j                  ddgddg      }ddgddggddgddggg}t        ||d	
       t        j                  ddgddgddgg      }ddgddggddgddggg}t        ||d	
       y )Nrg   r   r  r   r  g?gܿgra  r  ri   g
ףp=
?g
ףp=
׿r   rt  r  r  gzG?gzGr  g333333r[  rZ   r\  r  cov3cov4cov5cov6s          rD   test_cov_broadcastingz%TestMultinomial.test_cov_broadcasting  s    qB8b"X"67tdC[)RIRy+ABd.1vBx0ttSk*c4[4+,FGd.1vR2r(';<8$x&9:8$x&9:<d.rF   rL   c                 x    t        j                  |ddg      }t        |t        j                  |d      d       y Nr   r  ra  r  r   r   r   r"   )rZ   r   ent0s      rD   r  zTestMultinomial.test_entropy  s1     ""1r2h/emmAr2>rF   c           	      \   t        j                  ddgddg      }t        |t        j                  dd      t        j                  dd      gd       t        j                  ddgd	d
gddgg      }t        |t        j                  dd	      t        j                  dd      gd       t        j                  dgdggd	d
gddgg      }t        |t        j                  dd	      t        j                  dd      gt        j                  dd	      t        j                  dd      ggd       y )NrL   rM   r   r  ra  r  rj   r:  r   rt  r  r  rg  )rZ   rh  ent1ent2s       rD   test_entropy_broadcastingz)TestMultinomial.test_entropy_broadcasting  s   ""Aq6B84u}}Q3U]]1b5IJ!	# ""Aq6RHr2h+?@u}}Q3U]]1b5IJ!	# ""QC!:R2r(/CD--2.a0DE--2.a0DEG!	#rF   c                 `    t        j                  |ddg      }t        ||dz  |dz  gd       y rf  r   r   r   )rZ   r   mean1s      rD   	test_meanzTestMultinomial.test_mean  s0      RH-"ad|$7rF   c                 `    t        j                  ddgddg      }t        |ddgddggd	
       y )Nrg   rh   r   r  r   r  g433333?g433333@ra  r  rn  )rZ   ro  s     rD   test_mean_broadcastingz&TestMultinomial.test_mean_broadcasting  s5      !Q"b2ttTl;$GrF   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 )
NrX  r+  )r   r   r   r  r   r   r   r+  r   r   r   r6  r   r   r   r  r   r   r   rP  r   r   rL   r:  r  )
r=   r   r   r>   rS  r   r   r=  r3  r   )rZ   r   pvalsr`   	mn_frozens        rD   r  zTestMultinomial.test_frozen  s    
		t 
:i	BJJq

+5)		a(+//!Q*FG	((+[-?-?1e-LM	))+[-@-@E-JKrF   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 gKH9rk   )r=   r   r   r   rT   r   r3  isfinite)rZ   r   r   rA  r`   r3  s         rD   test_gh_11860zTestMultinomial.test_gh_11860  sx    
 ii##$78JJqM"	RVVAYGGAJ##Aq!,{{6"""rF   r  c                     d}t        j                  g d|      }t        j                  g d||      }t        j                  g d||      }t         j                  j                  ||d       y )	N   )r   r   r   r   r   r  )r   rL   rg   rj   ri   )r`   r   rA  )r   rL   ri   rg   rj   rG  r  )r=   r>   r   r=  testingr   )rZ   r  r   rA  res1res2s         rD   test_gh_22565zTestMultinomial.test_gh_22565  sW     JJ0>A;A;


""4E":rF   N)r   r   r   r8  rA  rF  rQ   r   r   rM  rW  rY  r]  rd  r  rl  rp  rr  r  r~  r=   float32rS  r  r   rF   rD   r/  r/  _  s   2	/M" [[S1a&)) *)6;  [[S1a&)/ *// [[S1a&)? *?# [[S1a&)8 *8H
L# [[Wrzz2::&>?; @;rF   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  )r=   rt   rR  r  rr  r   rq  r  r   r/  r   r   r  r   r  r   r   )	rZ   r   r  r  r  r`   r  r  iws	            rD   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rF   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   rg      rL   r  r   r  r#  r	  r*  r   r   r  r   )r=   r   r  rU   rR  r9  r/  r   r   r   r  r   r   r   r   r   )rZ   r   r%  r   r  r&  r  r  r  igr   rB   r  s                rD   test_1D_is_invgammaz"TestInvwishart.test_1D_is_invgamma>  s   
 ii##F+s99QAU3KKB2& 	8BB&B"Q$d+B BFFHbffh/BGGIrwwy1 BFF1Irvvay1 &&bs&3CqD!T?DE":tUC@ BJJL"**,7%	8rF   c                    d}d}t        j                  |      }d|d<   d|d<   t        ||      }t         j                  j	                  d      }t        j
                  |||      }t         j                  j	                  d      }|j                  |      }t         j                  j	                  d      }|j                  d      }t         j                  |j                  |d	z
        |j                  |d
z
        |j                  |      f   dz  }	t        j                  |	      }
||
t        j                  |d      <   t         j                  j                  |      }t         j                  j                  |
j                  |j                        j                  }t        j                  ||j                        }t!        ||       t!        ||       y )NrM   r  r	  rP  r  iHG	 r   r   rL   r   rk   r  )r=   rU   r   r   r  r   r   r  r  rt   r  r   r   solver   rr  r   )rZ   r   r  r  r  r   iw_rvsfrozen_iw_rvsr  r  rz   r  Lmanual_iw_rvss                 rD   test_invwishart_2D_rvsz%TestInvwishart.test_invwishart_2D_rvs_  s|    sc
c
 E" ii##F+E<ii##F+C0 ii##F+jjaj(EEMM"Q$MM"Q$MM"
 		 GGI(3"//#
$% IIu%IIOOACC%''q!## 	.}5rF   c                 h   d}d}dD ](  }t        j                  t        j                  |      dz         }t        j                  ||dz
  z  dz        |t        j                  |d      <   t        j                  |j
                  |      }t        ||      }|j                         }|j                         }||z  dz  }|j                  |d	
      }	|	j                  d      }
||dz   z  dz  }d|z  }t        j                  d|dz  z
        }t        j                  |
|z
  |z  d|      r)J  y)z1Test that sample mean consistent with known mean.r   N  r   rg   r   rL   rk   r  r	  rX  r   r   r   r  r  N)r=   rt   rR  r  rr  r   r   r   r  r   r   ppfr  )rZ   r  sample_sizer   r  r   	Xmean_expXvar_exp	Xmean_stdr  	Xmean_estntests	fail_ratemax_diffs                 rD   test_sample_meanzTestInvwishart.test_sample_mean  s$     	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  !	rF   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.)rL   r   r   r	  )r   rL   r	  r	  )r   r	  rM   r   )r	  r	  r   rL   )rP  rj   rM   r   )rj   rP  rg   r   )rM   rg   r:  rL   )r   r   rL   rP  rh   r   rL   r   r	  N)r=   r   r   r   r?   r   r  r  r_  r7   tracer   )rZ   r  PsinuprobrA  siglogdetX	logdetPsir   r  s              rD   test_logpdf_4x4zTestInvwishart.test_logpdf_4x4  s%   HHn&$&( ) hh$$$& '   B,GGAJyy((+W**3/YIIOOAs#T9$!tAvrvvay()"2a4+, Avz1nW,- !'')m	$
 	h'rF   N)r   r   r   r  r  r  r  r  r   rF   rD   r  r    s    E@8B,6\6(rF   r  c                   6    e Zd Zd Zd Zd Zd Zd Zd Zd Z	y)	TestSpecialOrthoGroupc                     t        j                  dt        j                  j	                  d            }t        j
                  g dg dg dg      }t        ||       y )NrM     r   )gDbgMPFh?g,׿)g7?g++?guC))g?gg]Qg^ɿ)r   r   r=   r   r   r   r   )rZ   r`   r  s      rD   test_reproducibilityz*TestSpecialOrthoGroup.test_reproducibility  sM    ##ABII4I4I#4NO88CBCE F 	"!X.rF   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y Nr  rk   rZ  )rT  rR   r   r   rZ   s    rD   test_invalid_dimz&TestSpecialOrthoGroup.test_invalid_dim  sN    j"5"9"94@j"5"9"96Bj"5"9"92>j"5"9"93?rF   c                     d}t        |      }|j                  d      }t        j                  |d      }t        ||       y )Nrj   rX  r   )r   r   r   )rZ   r   r  r  r  s        rD   test_frozen_matrixz(TestSpecialOrthoGroup.test_frozen_matrix  s=    $S)zztz,"&&s>T4 rF   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 )	NrL   r+  rM   r      vIh%<=r  r   )rq  r   r   r=   r   r  r   r   rr  r   rU   r?   )rZ   r   r  r  r`   detss         rD   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                  ||t        j                  j	                  d            }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 )Nrg   r  皙?i  r   r  rQ  )r   ri   r  r   )	r   r   r=   r   r   sortedr    r   r   )rZ   r   rb  ks_probr  elserecr`   proje0e1pairsp0p1ks_testss                   rD   	test_haarzTestSpecialOrthoGroup.test_haar  s      $$gBII,A,A#,F
 +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Js*   CC'	C9C!	C!C'Cc                 J    t        t        j                  dd      dd       y )Nr   r  r   r  r  )r   r   r   r  s    rD   test_one_by_onez%TestSpecialOrthoGroup.test_one_by_one	  s     	+//=quMrF   c                 Z    t        t        j                  dd      j                  d       y Nr   ri   r   )ri   r   r   r   r   r   r?   r  s    rD   test_zero_by_zeroz'TestSpecialOrthoGroup.test_zero_by_zero	       (,,QQ7==yIrF   N)
r   r   r   r  r  r  r  r  r  r  r   rF   rD   r  r    s(    /@!::8N
JrF   r  c                       e Zd Zd Zd Zd Zd Zej                  j                  dg d      d        Z
d Z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 )Nr  rM   r   rk   )gm?gӠh"gEo?)g~7ݲC?g>Ŀg0J_ٿ)gݱ&ǿg 6qrg`X|[)
r=   r   r  r   r   r   r   r  r   r   )rZ   r   r   r`   r   r  s         rD   r  z#TestOrthoGroup.test_reproducibility	  s    ii##D)OOAC0__QT2BIIMM!,b188<==? @ 	"!X.!"h/rF   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y r  )rT  rR   r   r   r  s    rD   r  zTestOrthoGroup.test_invalid_dim	  sB    j+//48j+//6:j+//26j+//37rF   c                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                  d      }t        ||       t        ||       y )Nrj   rX  r   r   r   r   )r   r   r   rZ   r   r  frozen_seedr  r  rvs3s          rD   r  z!TestOrthoGroup.test_frozen_matrix	  sa    S!!#D1zztz,s6A&T4 T4 rF   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 )NrL   r+  r  r  r  r   )rq  r   r   r=   r   r   r  r   fabsrT   r?   r   rr  r   rU   )rZ   r   r  r  xxr`   r  s          rD   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   )rL   rg   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   ffffff?confidence_levelr	  )r=   r   r   r   r   r   r   r  r   r   r/   	binomtestproportion_ci)rZ   r   r   r   r   r  rx  r   r@   r   r   s              rD   test_det_distribution_gh18272z,TestOrthoGroup.test_det_distribution_gh18272:	  s     ii##$78s#hhDsh3||$FF4!8Iooa#%%t%<	TS4rF   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 )Nrg   r  r  i  r   r  r   )	r=   r   r  r   r   r  r    r   r   )rZ   r   rb  r  r   r  r  r  r  r`   r  r  r  r  r  r  r  s                    rD   r  zTestOrthoGroup.test_haarG	  s     ii##C(__SwSA +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Js*   CC)	C;C#C#C)Cc                 p   d}t        j                  |dt        j                  j	                  d            }t        t        j                  |      dd       t        j                  |dkD        }t        |      }t        j                  ||      }|j                  d	      \  }}|d
cxk  r|k  sJ  J y )Nr   r  r  r   r  r  r   r  r  r	  )r   r   r=   r   r   r   r[  r   r   r/   r  r  )rZ   r   r  rx  r   r@   r   r   s           rD   r  zTestOrthoGroup.test_one_by_oneb	  s    __St")):O:OPS:TUr
AE2FF26NGooa#%%t%<	TS4rF   c                 Z    t        t        j                  dd      j                  d       y r  r  r  s    rD   r  z TestOrthoGroup.test_zero_by_zerom	  r  rF   c                 D   t         j                  j                  d      dfd	}t        dd      D ]j  dfd	} ||      } |t        j
                  j                  j                        }t        j
                  j                  ||      \  }}t        d|       l y )	Nr  c                     t         j                  j                  j                  | | f            \  }}}t        j                  ||      S Nr   )r=   r   r   r   rr  )r   r   r   _sr   r   s        rD   random_orthoz<TestOrthoGroup.test_pairwise_distances.<locals>.random_orthou	  s:    yy}}SZZc3ZZ%@AHAr166!Q<rF   rL   rh   c                    t        j                  t        |      D cg c]-  }t        j                   |        |       z
  dz        / c}      }|t         j                  j                  | ||j                        z  }|S c c}w )N)r   r   rL   r   )r=   r   rq  r   r   r   r?   )r   r  epsr   r/   r   r   s        rD   generate_test_statisticszHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statisticsz	  s     #1X"  FFCCc:Cc:;=>? @"  **C45;;*GG"s   2B	r  r<   )r  r  )
r=   r   r  rq  r   r/   r   r   r    r   )	rZ   r  r  r  r  _DrA  r   r   s	          @@rD   test_pairwise_distancesz&TestOrthoGroup.test_pairwise_distancesp	  s     ii##C(	  A; 	&C 0=H-ekk.E.E.I.IJFKK((6:EBc1%!	&rF   N)r   r   r   r  r  r  r  rQ   r   r   r  r  r  r  rp  r  r   rF   rD   r  r  	  si    08
!> [[UN3
  4
 :6	 J [[& &rF   r  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 )Nr  r	  r  r  rY  r   )r   ѓ2ǿA?Ϳ)r  r   4($?R}%?)r  r  r   qTnƿ)r  r  r  r   )r=   r   r  r   r   r   r   )rZ   r   r   r`   r   r  s         rD   r  z*TestRandomCorrelation.test_reproducibility	  sv    ii##C(!""4c:##Ds;88A@@AC D 	"!X.!"h/rF   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testrZ  r   rL   rM   ri   g      )r   rL   r   )rT  rR   r   r   r  s    rD   test_invalid_eigsz'TestRandomCorrelation.test_invalid_eigs	  s    j"4"8"8$?j"4"8"8&Aj"4"8"8#>j"4"8"83%@j"4"8"8Aa5!A-Hj"4"8"83*Ej"4"8"8*ErF   c                     d}t        |      }t        |d      }t        j                  |d      }|j                  d      }|j                         }t        ||       t        ||       y )Nr  r  r   r   )r   r   r   )rZ   r   r  r  r  r  r  s          rD   r  z(TestRandomCorrelation.test_frozen_matrix	  s_    !#D)(C8!%%d=zzsz+ T4 T4 rF   c           	      0   d }t         j                  j                  d      }t        dd      D cg c]  } |||j	                  |             }}|j                  g d       |D cg c]  }dgt        |      z   }}|D cg c]  }t        j                  ||       }}|D cg c]4  }t        j                  t         j                  j                  |            6 }	}|D cg c]  }t        j                  |       }
}t        |	|
d	d	
       |D cg c]  }t        j                  |       }}t        ||      D ]  \  }}t        ||d	        |D ]  }t        ||j                   d	        y c c}w c c}w c c}w c c}w c c}w c c}w )Nc                 $    | |z  t        |      z  S r<   )r   )r  r  s     rD   r   z3TestRandomCorrelation.test_definition.<locals>.norm	  s    Q3s1v:rF   r#  rL   rh   r   )ri   r   r   r   r   r   r  r  r  )r=   r   r  rq  r   r  r   r   r   r  r   r  r  r   rt   zipr   )rZ   r   r   r  r   r  rT   r  r`   r  
dets_knowndiagsr  r  s                 rD   test_definitionz%TestRandomCorrelation.test_definition	  se   	 ii##C(6;AqkBQ+,BBI%)*SV**CGHa $$QS9HH 466a		a()66*./Qbggaj/
/ju5A &((((t$ 	.DAqAqu-	.  	0AAqss/	0) C +H 7/ )s#    E:*E?F*9F	)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)overrk   gu <7~r  rK  rL   r  gMk   @)r=   r   r9  r   _to_corrr   errstate	nextaftercopyr   rr  )rZ   r&  gm0s       rD   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   r  r  r  r  r  r   rF   rD   r  r  	  s    
0F
!"0H#rF   r  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   rM   r   Nr   rg   )rg   ri   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   rk   r   r   )r=   r   r   r(   r   r   rU   r   r?   r   r   r   )
rZ   r   r   r   uniform_direction_distrb  r   r   expected_shapenormss
             rD   r  z!TestUniformDirection.test_samples	  s     ii##$78!23S!A(,,T2HHSM266#;c00s0FLL}}...		wR0r"rF   )Nr   r  rZ  c                     d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)NzMDimension of vector must be specified, and must be an integer greater than 0.rJ   )rQ   r
   rR   r(   r   )rZ   r   r[   s      rD   r  z%TestUniformDirection.test_invalid_dim
  s:    <]]:W5 	'!!#&	' 	' 	's	   =Ac                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                         }t        ||       t        ||       y )Nrg   r  r   r   )r(   r   r   r  s          rD   test_frozen_distributionz-TestUniformDirection.test_frozen_distribution
  s_    "3''#6zzsz+ $$Ss; T4 T4 rF   )rL   rg   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   rL   r   r   rD  r  r:  r  )r=   r   r   r(   r   r   r   r   arctan2r  r   r!   r   pvalue)rZ   r   r   spherical_distv1v2rb  s1s2anglesuniform_distkstest_results               rD   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***rF   N)
r   r   r   rQ   r   r   r  r  r  r%  r   rF   rD   r  r  	  s    [[UQF+[[V%9:	# ; ,	# [[U$:;' <'
! [[UI.+ /+rF   r  c                   0    e Zd 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 )Nr  rM   r   )y~p?yZ?y뉦?ĭ?y8Z?&4?)yEHξr?8i?ye??+ݓݿyu=ٿB۽'?)yqXQÿ?yN6ҿzܷy! 8l?2W'?)r=   r   r  r   r   r   r   )rZ   r   r`   r   r  s        rD   r  z%TestUnitaryGroup.test_reproducibility-
  sm    ii##C(ac2qs388IHKM
 	"!X.!"h/rF   c                     t        t        t        j                  d        t        t        t        j                  d       t        t        t        j                  d       t        t        t        j                  d       y r  )rT  rR   r   r   r  s    rD   r  z!TestUnitaryGroup.test_invalid_dim;
  sJ    j-"3"3T:j-"3"3V<j-"3"3R8j-"3"3S9rF   c                     d}t        |      }t        |d      }|j                  d      }t        j                  |d      }|j                  d      }t        ||       t        ||       y )Nrj   r  r   r   r   r   )r   r   r   r  s          rD   r  z#TestUnitaryGroup.test_frozen_matrixA
  sc    s##Cc2zzsz+  37A&T4 T4 rF   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 )NrL   r+  rM   r   rG  r  )
rq  r   r   r   r=   rr  conjr   rU   r?   )rZ   r   r  r  r`   s        rD   test_unitarityzTestUnitaryGroup.test_unitarityM
  s    q!Qx! $ !$ ! !
  	SABFF1affhjj1266!''!*3EER	S!s   ,B!c           	      .   dD ]
  }d}t        j                  ||t        j                  j	                  d            }t        j
                  |D cg c]!  }t        j                  j                  |      # c}      }t        j                  |j                  |j                        }t        |j                         t        t        j                   dt        j                  z        j                         }t#        |j$                  dkD          y c c}w )Nr  r  r  r   rL   r  )r   r   r=   r   r   r  r   r   eigvalsr  imagrE  r!   ravelr   r  r   r	   r  )rZ   r   rb  r  r`   r   r@   s          rD   r  zTestUnitaryGroup.test_haarV
  s    
  	'CG""'		0E0Ec0JB 99rB!ell2215BCD

499dii0AGRUUFAbeeG$<$@$@ACCJJ%&	' Cs   &D
c                 Z    t        t        j                  dd      j                  d       y r  )r   r   r   r?   r  s    rD   r  z"TestUnitaryGroup.test_zero_by_zeroi
  s    ]&&qq177CrF   N)	r   r   r   r  r  r  r-  r  r  r   rF   rD   r'  r'  ,
  s"    0:
!S'&DrF   r'  c                      e Zd Zddgddgddgddgddgddgddgddgddgddgg
ddgddgddggdg dfg dg d	g d
g dg dgg dg dg dg dgdg dfgZej
                  j                  de      d        Zej
                  j                  de      d        Zd Z	d Z
ej
                  j                   ed      d               Zd Zd ZdddddgddggdddgddgddggdfdddgddggdddgddgddggdfddgddddgddgddggdfddgddddgddgddggdfddgddgddggdddgddgddggdfddgddgddggdddgddgddggdfgZej
                  j                  d e      d!        Zd"ddd"gdggdfd"gdgdd"gdggdf ej&                  d"g       ej&                  dg      dd"gdggdfgZej
                  j                  d e      d#        Zd$ 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j2                  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 ej
                  jB                  d>        Z"d? Z#d@ Z$dA Z%ej
                  j                  d*dB      dC        Z&dD Z'ej
                  j                  d,g dE      dF        Z(ej
                  j                  dGdH ejR                  dd      dIdJfdK ej&                  dLdgddHgg      dMdNfg      dO        Z*ej
                  j                  dPg dQ      dR        Z+dS Z,y)UTestMultivariateTr   rL   ri   rM   rg   r   )
|	ߌ?v
2R?r5  g0$H?r6  r6  gO`?gՒXO?g	ߌ,?g8N8?)gHP?gQI?go_?)g9m4?g=U?gˡE?)g$C?ghs?gǺ?)g!uq?g%C?gS㥛?)gOec?gz,C?g	h"l?)rk   r   2   )r   r	  r  )r	  r   rJ  )r  rJ  r   r:  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 \    t        |||d      }|j                  |      }t        ||       y Nr   r   )r$   r   r   )rZ   r`   r  r?   r  ansr   vals           rD   test_pdf_correctnessz&TestMultivariateT.test_pdf_correctness
  s)    c5"15hhqk!#s+rF   c                     t        |||d      }|j                  |      }|j                  |      }t        t	        j
                  |      |       y r9  )r$   r   r   r   r=   r_  )	rZ   r`   r  r?   r  r:  r   r?  r@  s	            rD   test_logpdf_correctz%TestMultivariateT.test_logpdf_correct
  s>    c5"15xx{{{1~!"&&,5rF   c                 |    g d}t        j                  |d      }t        j                  |      }t        ||       y )N)
rP  rj   ri   r   r$  rP  r   r$  rk   rM   r   r  )r$   r   r%   r   )rZ   r`   r;  r:  s       rD   test_mvt_with_df_one_is_cauchyz0TestMultivariateT.test_mvt_with_df_one_is_cauchy
  s0    -  q)jjm!#s+rF   c                    d}t        dddd      }|j                  d      }t        |      \  }}||kD  sJ t        ddgd	d
gd
d	ggdd      }|j                  d      }t        |      \  }}||kD  j                         sJ y )Nr   r   r   順 r  r   r   rn   rM   r  rk   *   )r$   r   r&   r  )rZ   	P_VAL_MINr   rb  r   rA  s         rD   &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##%&%rF   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   rj   rD  r@  rL   )r$   r=   r   r   r   r   
call_countr   )rZ   mockr   s      rD   !test_mvt_with_inf_df_calls_normalz3TestMultivariateT.test_mvt_with_inf_df_calls_normal
  su     arvvA6$ :;;;1(!###aBFF+!###rF   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 )Nri         @rj   r   r   )
r=   r   rU   r$   r   isscalarr   r   r?   r   )	rZ   r   r  r?   r  r`   r@   	n_samplesr   s	            rD   test_shape_correctnessz(TestMultivariateT.test_shape_correctness
  s    hhsmsHHSMS%,003{{3S%,33A6{{3 	IIi-.S%,003		i\)*)S%,33A6		i\)*) RXXa["&&)Q7;;={{3 RXXa["&&)Q7;;;F		dW$%$rF   c                     t               }t        |j                  dg       t        |j                  dgg       |j                  dk(  sJ y )Nr   r   r$   r   r  r?   r  )rZ   r   s     rD   test_default_argumentsz(TestMultivariateT.test_default_arguments  s<    TXXs#TZZ1#'1rF   )NNNr   r   r   )NNrj   r   r   rj   Nrj   z*loc, shape, df, loc_ans, shape_ans, df_ansc                     t        |||      }t        |j                  |       t        |j                  |       |j                  |k(  sJ y )Nr  r?   r  rR  rZ   r  r?   r  loc_ans	shape_ansdf_ansr   s           rD   test_default_argsz#TestMultivariateT.test_default_args  s@     #Ur:TXXw'TZZ+6!"!rF   rk   c                     t        |||      }t        |j                  |       t        |j                  |       t        |j                  |       y r<   rR  rV  s           rD   &test_scalar_list_and_ndarray_argumentsz8TestMultivariateT.test_scalar_list_and_ndarray_arguments%  s<     c5"-TXXw'TZZ+TWWf%rF   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   )r  rL   rM   )r  r?   rk   rU  r   )rT  rR   r$   r  r=   r   rU   )rZ   r  r?   r  s       rD   test_argument_error_handlingz.TestMultivariateT.test_argument_error_handling.  s    1vhj$	'	'
 Q!Q!Q(j$	4E2	4
 hhqkq	j$	;Eb9	; j$	;Eb9	;rF   c                 ,   t         j                  j                  d      }|j                  d      }t        j                  d      }t        ||dd      }t        ||dd      }|j                  d      }|j                  d      }t        ||       y )Nri   rM   r   rL   rD  r  )r=   r   r  r   rU   r$   r   r   )rZ   r   r  r?   r   dist2samples1samples2s           rD   r  z&TestMultivariateT.test_reproducibilityG  s}    ii##A&kkqk!q	sEaa8sEaa899"9%99"9%Xx(rF   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)r  r?   r  r_   )r  rT  r=   r   r  r$   )rZ   rB   s     rD   test_allow_singularz%TestMultivariateT.test_allow_singularQ  s;    1qeQqE]qObii++^DtDrF   r   )r  rM   )rg   rh   ri   rM   r   )rL   rM   ri   rg   r  r   r  c                     t        t        j                  |      t        j                  |      |      }|j	                  |      }|j
                  ||fz   k(  sJ y r  )r$   r=   r   rU   r   r?   )rZ   r   r   r  r   r   s         rD   test_rvszTestMultivariateT.test_rvsV  sJ     bhhsmRVVC["=hhDh!yyDC7N***rF   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 )
NrM   r  r  rl   r  r  r  r	  r   r  )rZ   r   r   r  r  r  r   r   s           rD   r!  z TestMultivariateT.test_cdf_signs^  sv    xx{ffQi	9i8	9i8.1!%%asBAFSVN23rF   )r   rL   rg   c                 &    | j                  |       y r<   cdf_against_mvn_testrZ   r   s     rD   $test_cdf_against_multivariate_normalz6TestMultivariateT.test_cdf_against_multivariate_normalj  s     	!!#&rF   )rM   rh   rP  c                 (    | j                  dd       y )NrM   Tri  rk  s     rD   -test_cdf_against_multivariate_normal_singularz?TestMultivariateT.test_cdf_against_multivariate_normal_singularo  s     	!!!T*rF   Fc           	      ,   t         j                  j                  d      }d}d|j                  dd|      z  }t	        ||||      }d|j                  dd|      z  t        j
                  |j                  |            z  }d|j                  dd||f      z   |z   }d|j                  dd||f      z  |z   }	t        j                  j                  |	||d	|d
|      }
t        j                  j                  |	||d
|      }t        |
|d       y )N   ]J>?a rM   r  rn   r   r   rk   rL   r:  T)r  r
  r_   r   )r_   r
  Mb@?r  )r=   r   r   r   r   signr   r/   r$   r   r   r   )rZ   r   r   r   r   r	  r   r   r  r  r@   rA   s               rD   rj  z&TestMultivariateT.cdf_against_mvn_testt  s   ii##O4B,, ah73;;r13;//"''#**#*:N2OOR!S222T9BC11D8""&&q$16: ' N''++AtS89 , ;St,rF   c                 P   t         j                  j                  d      }d}d}|j                  dt        j                  |            }d}t
        j                  j                  ||||t         j                   |      }t
        j                  j                  |||t        j                  |            }t
        j                  j                  ||t        j                  |            }t        ||d	       t        j                  t        j                  ||z
        d
kD        sJ y )Nrp  rL   r   r  )r   r  rM   )r
  r   rq  r  r  )r=   r   r   r   r  r/   r$   r   r   r  r   r   r  r[  )	rZ   r   r   r   r`   r  r@   rA   	incorrects	            rD   test_cdf_against_univariate_tz/TestMultivariateT.test_cdf_against_univariate_t  s    ii##O4JJBbggclJ3""&&q$RbffW47 ' 9ggkk!Rrwws|4JJNN1dBGGCL9	St,vvbffS9_-4555rF   )rL   rM   rg   r  r   )   no l   m, l   sO l   U iOfYl   O_ r   Tc           	      P   |r|dk7  rt        j                  d       t        j                  j	                  |      }d|j                  dd|      z  }t        ||||      }|j                  |      }|j                  |       }|j                  |      }	|j                         dz  }
t        j                  j                  |	|||
|d	      }t        j                  d
      5  t        d|
|t        j                  |z  |	|z
  |      d   }d d d        t        |dd       t        j                  j                  |	|||
||d      }t        j                  d
      5  t        d|
|||z
  |	|z
  |      d   }d d d        t        ||dd       y # 1 sw Y   xY w# 1 sw Y   %xY w)Nrv  z4Agreement with qsimvtv is not great in singular caser  rn   rL   r   rg   T)r   r_   r  )invalidr  r   g-C6*?r  r  r  )r
  r   r_   r  )rQ   r   r=   r   r   r   r   r/   r$   r   r	  r9   r   r   )rZ   r   r   r   r   r	  r   r   r  r  r  r@   rA   s                rD   test_cdf_against_qsimvtvz*TestMultivariateT.test_cdf_against_qsimvtv  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 )NrM   l   	!y r  rk   r   r   T)r   rg   )r   r
  c                 \    t         j                  j                  | j                        S r<   )r/   r$   r   r   )r`   r   r  r   s    rD   	integrandzITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand  s$    ''++ACCsB??rF   )r  r   )qrngr  r  c                  T    t         j                  j                  | d d d         S )Nrk   )r/   r$   r   )zyxr   r  r   s    rD   r}  zITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand  s(    ''++C"ItS"EErF   r   rL   )r=   r   r   r   r   r/   r$   r   r4   qmcHaltonr   integralr6   )rZ   r   r   r	  r  r  r@   r}  rA   r   r  r   s            @@@rD   $test_cdf_against_generic_integratorsz6TestMultivariateT.test_cdf_against_generic_integrators  s+    ii##N3#++b!#+.. at<zz#ZZ_JJsOZZ\A""&&q$Rc34 ' 6	@ y!QUYY-=-=#-=-NOS\\5	F i1qtQqT1Q41qtDSV$/rF   c                     t         j                  j                  d      }t        j                  g dg dg dg      }d}t	        j
                  ||      }|j                  g d|      }d	}t        ||d
       y )Nl   Ja )go!@S<?^Ss@)r  gRP=@jT0@)r  r  gk`-3@gWK?r?   r  rl   r   g1%?r  r  )r=   r   r   r   r/   r$   r   r   )rZ   r   r   r  r   r@   rA   s          rD   test_against_matlabz%TestMultivariateT.test_against_matlab  sr     ii##J/hh???A B  ###"5hhysh3St,rF   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 rM   r   r   r   )	r=   r   r   r   rU   r/   r$   r   r   )rZ   r   r   r  r`   r?   r  rB   
rng_frozenrng_unfrozenr   s              rD   r  zTestMultivariateT.test_frozen  s    ii##D)kkqk!KKQK#%q	ZZ\UBYY**40
yy,,T2##T;
;TXXa[#''LDL|L	NrF   c                   	
 d}d}t         j                  j                  d      j                  ||f      }||j                  z  j                  |      
j                  ||fz         }j                         dz  	t        j
                  j                  |
	      }	
fd}t        j                  |d|      }t        ||d	d
       y )Nri   r  rp  r   rg   r   c                 T    t        dt        j                   | z  | z
        d   S )Nr:  r   )r9   r=   r   )r`   r   r  r   r   s    rD   _cdf_1dz2TestMultivariateT.test_vectorized.<locals>._cdf_1d  s+    E2sRVVGAIqvsCAFFrF   rk   r  r  ry  )	r=   r   r   r   r/   r$   r   apply_along_axisr   )rZ   r   r   rz   r`   r@   r  rA   r   r  r   r   s           @@@@rD   test_vectorizedz!TestMultivariateT.test_vectorized  s    ii##O4JJS#JJ'!##gzz#JJqC6z"ZZ\A""&&q$Rc&J	G !!'2q1St$7rF   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 )
Nrp  r   r	  )r'  )r?   r   r   r,  r  )
r=   r   r   r   r   toeplitzr/   r$   r   r   )rZ   r   r   rz   r@   rA   s         rD   test_against_analyticalz)TestMultivariateT.test_against_analytical  s~    ii##O4LL!!QC3%37*;$;!<""+//c	/L37mSt,rF   c                     t        j                  dd      }t         j                  }t        j                  j                  ||      }t        j                  j                  d |      }||k(  sJ y )NrM   r  )r=   rU   r   r/   r$   r   r   )rZ   r   r  mvt_entropymvn_entropys        rD   test_entropy_inf_dfz%TestMultivariateT.test_entropy_inf_df  s[    ffQlVV**222D//77cBk)))rF   )r   r  r  c                     t         j                  j                  d|      }t         j                  j                  |      }t	        ||d       y )Nr   r  r@  r  r  )r/   r$   r   r  r   )rZ   r  r  	t_entropys       rD   test_entropy_1dz!TestMultivariateT.test_entropy_1d  s=    **222CGGOOrO*	YU;rF   zdf, cov, ref, tolr  g}M@rD  r  r	  gNfh@ra  c                     t        j                  d      }t        j                  |||      }t	        |j                         ||       y )Nr  r  )r=   r   r/   r$   r   r   )rZ   r  r   rA   tolr  mvts          rD   %test_entropy_vs_numerical_integrationz7TestMultivariateT.test_entropy_vs_numerical_integration"  s7    
 hhuo""3R0s5rF   zdf, dim, ref, tol))r  r   gDdVW?rG  )r  r   gU?r  )r"  r   g/+?rD  )@xDr   Z_2?rG  )}Ô%ITr   r  rG  )r  r  gzg#.@rG  )r  r  gD:f,@r  )r  r  1>`,@rG  )r  r  r  rG  )r  r  g8d?b@rG  )r  r  g-YҺa@rD  )r  r  ZGra@rG  )r  r  r  rG  c                     t        j                  t        j                  |      |      }t	        |j                         ||       y )Nr  r  )r/   r$   r=   rU   r   r   )rZ   r  r   rA   r  r  s         rD   test_extreme_entropyz&TestMultivariateT.test_extreme_entropy+  s1    F ""<s5rF   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?r  gQ)gQ?g)\(?gQѿg)\(ܿg(\?)g      gGzgq=
ףpg\(\?g)r  g{Gzg\(\?g{GzԿg(\?r  r  r  rG  r  i  i   r  )r=   r   r   r/   r$   r   r   r   )
rZ   _Ar   r  mul_t_entropymul_norm_entropydf1df2	_entropy1	_entropy2s
             rD   test_entropy_with_covariancez.TestMultivariateT.test_entropy_with_covarianceQ  s     XX+-,,,
  244i ,,44324F.t=EEG'7eD ((00ss0C	((00ss0C		948rF   F)-r   r   r   	PDF_TESTSrQ   r   r   r<  r>  rA  rG  thread_unsafer:   rK  rP  rS  DEFAULT_ARGS_TESTSrZ  r=   r   ARGS_SHAPES_TESTSr\  r^  r  rd  r   rf  r!  rl  rn  rj  ru  rz  rp  r  r  r  r  r  r  r  rU   r  r  r  r   rF   rD   r4  r4  m
  so    FFFFFFFFFF	
 
A FF	

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

4 [[UI.' /' [[UI.+ /+-$6 [[UM2[[V &J K[[Z%78 8K 382 [[0 04-"N8$ [[UF+- ,-* [[T<0< 1<& [[0!6266!Q<1CUK"HBHHsAhB-@$A/7896	96
 [[	
$6%$6(9rF   r4  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$d%d&fg      d'        Zej                  j                  dddgddgdd(ggddd)gfdgdggdgdggddgd*d+gfdgdgggdgdggddgd*d+ggfdgdggdggggddgd*d+gggfg      d,        Zd- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zy8)9TestMultivariateHypergeomzx, m, n, expectedrM   ri   rg   r  rj   gr   r$  r   rL   rq   iir6  r+  rk   ic                 N    t        j                  |||      }t        ||d       y )Nư>r  )r   r3  r   rZ   r`   r&  r   r  valss         rD   r8  z%TestMultivariateHypergeom.test_logpmfq  s$    6 &,,Q15hT2rF   c                    t        j                  ddgddgd      }t        j                  dddd      }t        ||d	
       t        j                  ddgddgd      }t        j                  dddd      }t        ||d	
       y )NrM   r   r  rg   ri   )r`   r&  r      )rx  r   r   r  ra  r  rj      )r   r=  r#   r   r>  s      rD   test_reduces_hypergeomz0TestMultivariateHypergeom.test_reduces_hypergeom  s|     &))QFr1gC}}qB!r2d.%))QFr2h"E}}qB"3d.rF   c                     t        ddgd      }|j                  dd      }t        |j                  d      |j                         d	
       y )NrM   rg   ri   r&  r   r  r#  r   r   r  r  r   r   r   r   rZ   r   r   s      rD   rf  z"TestMultivariateHypergeom.test_rvs  s@     $q!f2ff$Sf1RWWYT:rF   c                     t        ddgddggddg      }|j                  dd	      }t        |j                  d
      |j                         d       y )NrM   rg   r  ri   rP  r  r  rL   r#  r   r   r  r  r  r  s      rD   test_rvs_broadcastingz/TestMultivariateHypergeom.test_rvs_broadcasting  sK    #1v2w&7Aq6Bff)#f6RWWYT:rF   zm, n)r   r   r  r   r   )r   r   r   r   r   c                     t        j                  ||      }t        j                  |      }|j	                         }|||dk7  <   t        ||       y )Nr   )r   r   r=   r>   r  r   )rZ   r&  r   r@   res_exs        rD   test_rvs_gh16171z*TestMultivariateHypergeom.test_rvs_gh16171  sE    
 %((A.JJqMqAvS&!rF   g zl?r:  rP  gQ?gE|?g
y?r  rR  )rg   rh   rj   rh   gzp?c                 N    t        j                  |||      }t        ||d       y Nr  r  r   r=  r   r  s         rD   rW  z"TestMultivariateHypergeom.test_pmf  s$    " &))!Q2hT2rF   r  g ?r   r   c                 N    t        j                  |||      }t        ||d       y r  r  r  s         rD   rY  z/TestMultivariateHypergeom.test_pmf_broadcasting  s$     &))!Q2hT2rF   c                 h    t        j                  g dd      }g dg dg dg}t        ||d       y )	N)rM   rj   r  r+  r  )gf_?&BUп疈Cx@ؿ)r  ggs>d?ZsK)r  r  g35?ra  r  r   r   r   )rZ   r\  r  s      rD   r]  z"TestMultivariateHypergeom.test_cov  s2    %))J"=6668 	d.rF   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 )Nrj   rP  r  r  r:  r+  r  g?gg(\?g(\ra  r  ri   rg   r   g333333?g333333r  r_  s          rD   rd  z/TestMultivariateHypergeom.test_cov_broadcasting  s    %))aVb"X,>1b'J..0d.%))aS1#J1a&A"d.%))QFq"g>.'"Wf$568d.rF   c                     t        j                  ddgd      }t        j                  ddd      }t        ||d       y )	Nr  rg   ri   r  r  r   r   r  ra  r  )r   r  r#   r   )rZ   var0var1s      rD   test_varz"TestMultivariateHypergeom.test_var  s6    %))RGq9}}rQ"-d.rF   c                    t        j                  ddgddg      }t        j                  ddgd      }t        j                  ddgd      }t        |d   |d       t        |d	   |d       t        j                  ddgdd
ggddg      }ddgddgg}t        ||d       t        j                  dgdggddg      }dgdgg}t        ||d       y )Nr  rg   ri   r:  r  r   ra  r  r   r;  g̍3eY?gI{?r   )r   r  r   )rZ   r  r  var2var3var4var5var6s           rD   test_var_broadcastingz/TestMultivariateHypergeom.test_var_broadcasting  s    %))RG1v>%))RGq9%))RGq9QD1QD1%))b!Wr2h,?Aq6JI&8(<=d.%))aS2$KAr7Crd|d.rF   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  rg   ri   r  r  r  r   ra  r  r+  r:  g      @r  )r   r   r#   r   rZ   mean0ro  r  mean3s        rD   rp  z#TestMultivariateHypergeom.test_mean  sf    &++r1g;qB/a%d3&++r1g<j)u40rF   c                 n    t        j                  ddgddggddg      }ddgd	d
gg}t        ||d       y )NrM   rg   r  ri   r:  r  rY  rZ  gUUUUUU@gUUUUUU@ra  r  )r   r   r   )rZ   r  ro  s      rD   rr  z0TestMultivariateHypergeom.test_mean_broadcasting  sE    &++1vAw.?Aq6JH%
I'>?u40rF   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 )Nrl   r   r  r   r   r   r   r   r   rL   r  )r   r   r   FFg<r  r  r   )
r   r   r   r=   r  r   r   r6  r	   r?   r  s        rD   test_mean_edge_casesz.TestMultivariateHypergeom.test_mean_edge_cases  s    &++i1=UL)&++i1=URVVRVVRVV45&++y).DJ 8,G"	$ '++bhhr.EKUBu$%rF   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 )Nrl   r   r  r  gؗҜ<r  r  rL   r  r  r  r  )
r   r  r   r   r=   r  r   r6  r	   r?   )rZ   r  r  r  r  s        rD   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#$rF   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 )Nr  r   r  r  r  r  rl   r   r  r  )r   r   r   r   r=   r   r6  rS  r  r	   r?   )rZ   cov0r\  r`  ra  rb  rc  s          rD   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$%rF   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 )
NrX  r+  )rj   rP  r6     rt  ru  rv  rw  rx  r  )r=   r   r   r>   r6  r   r   r=  r3  r  r   )rZ   r   r&  r`   
mhg_frozens        rD   r  z%TestMultivariateHypergeom.test_frozen8  s    
		tM=<)JJq$+Aq1

q).221a;	=
))!,.55aA>	@
(*@*D*DQ*JK
(*@*D*DQ*JKrF   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 )	Nrg   r  ri   g      @rM  r  g      %@g      /@)rT  rR   r   r=  	TypeErrorr  s    rD   test_invalid_paramsz-TestMultivariateHypergeom.test_invalid_paramsH  s    j"8"<"<aQGj"8"<"<a"qIj"8"<"<q!frdANi!7!;!;c3Z2h	#i!7!;!;aVTlA	'i!7!;!;aV2h	%rF   N)r   r   r   rQ   r   r   r=   r   r  r8  r  rf  r  r  r   r6  rW  rY  r]  rd  r  r  rp  rr  r  r  r  r  r  r   rF   rD   r  r  p  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$hbhhr&=q"EVaVQ"	1j1	
 3! 3 [[Vq"gBx(!i-CDcA3Z1#saVb"X6sQCj\QC!:1vRz:cA3ZQC5'QFr2hZL9		
33////11
&%&L 	%rF   r  c                   T   e Zd Zd Zd Zej                  j                  dd      d        Zd Z	ej                  j                  dd      ej                  j                  d	d      d
               Z
ej                  j                  dd      d        Zd Zej                  j                  dd      d        Zej                  j                  dd      d        Zej                  j                  dd      d        Zej                  j                  dd      ej                  j                  dg dgf      ej                  j                  dg dgf      d                      Zej                  j                  dd      d        Zd Zej                  j                  dd      d        Zy)TestRandomTablec                 @    t         j                  j                  d      S )Nl   OfE)r=   r   r   r  s    rD   get_rngzTestRandomTable.get_rngU  s    yy$$%788rF   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-dimensionalrJ   r   rL   z`col` must be one-dimensionalz*each element of `row` must be non-negativerk   z*each element of `col` must be non-negativern   z'sums over `row` and `col` must be equalr   z(each element of `row` must be an integer @)r   r   rL   z(each element of `col` must be an integer)rK  rK  r   rM   rL   r   r   )rQ   r
   rR   r'   _process_parametersr   r=   r   )rZ   r[   rowcolr  r'  r   s          rD   test_process_parametersz'TestRandomTable.test_process_parametersX  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   rM   r  methodr   )r=   r   r'   r   r   )rZ   r  r  r   r  ctr  gots           rD   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#rF   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   rM   r  z$'foo' not recognized, must be one ofrJ   foo)r  )rQ   r
   rR   r'   r   )rZ   r   r  r[   s       rD   $test_process_rvs_method_bad_argumentz4TestRandomTable.test_process_rvs_method_bad_argument  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 ]$  }|	||f   }|||f   } ||      }t        ||       & C g dg dg}t        t	        j                  |d              ||      }	|	dk(  sJ g dg dg}t        t	        j                  |d              ||      }	|	dk(  sJ d}t        j                  t         |      5   |dg       d d d        d}t        j                  t         |      5   |dgg       d d d        d}t        j                  t         |      5   |t        j"                  gg       d d d        d}t        j                  t         |      5   |dgg       d d d        d}t        j                  t         |      5   |g dg       d d d        d }t        j                  t         |      5   |ddgd!d"gg       d d d        y # 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   oxY w# 1 sw Y   y xY w)#NrL   rh   r   rM   ri   r  r  r   r  r   r3  r=  c                      |       S r<   r   )r`   r  original_methodr   s    rD   r  z/TestRandomTable.test_pmf_logpmf.<locals>.method  s    &q#s33rF   c                 :    t        j                   |             S r<   )r=   r  )r`   r  s    rD   ra   z1TestRandomTable.test_pmf_logpmf.<locals>.<lambda>  s    q	* rF   r   Tr   return_countsr   r  )r  r  r   )r   r   r   )rL   r   rM   rk   r   rQ  )r   rL   rL   rn   z$`x` must be at least two-dimensionalrJ   z%`x` must contain only integral valuesrK  z)`x` must contain only non-negative valuesz"shape of `x` must agree with `row`rP   z"shape of `x` must agree with `col`rM   ri   )r  r'   r   ru   r=   uniquer   r   r   r   r  r?   rq  r   rQ   r
   rR   r  )rZ   r  r_  r   r   objr=  
unique_rvscountsrA  p2rvs_ndr  r  pijrvijqijr`   r[   r  r  r  r   s                      @@@@rD   test_pmf_logpmfzTestRandomTable.test_pmf_logpmf  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 )NrL   rh   r  r  r  r   r  r  rk   r   r  rn   )r  rM   )	r  r'   r   r   r   r=   r   r   broadcast_to)rZ   r  r   r   r  r   r   s          rD   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GrF   c                    | j                         }ddg}g d}t        j                  ||dd|      }t        j                  ||dd|      }t        j                  |d	      }t        j                  |d	      }t        ||d
       y )NrL   rh   r  r:  r  r  r  r   r   {Gz?r  )r  r'   r   r=   r  r   )rZ   r   r   r  r  r  r\  r  s           rD   test_rvs_covzTestRandomTable.test_rvs_cov  s     lln!fSuX-02Su[-02vvd#vvd#d.rF   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)NrL   rh   r  r  r  r   r  rP   r   )r   rL   rM   r  )r  rL   rM   )ri   rg   )ri   rg   rL   rM   rM   rG  r  z/`size` must be a non-negative integer or `None`rJ   rk   )r'   r   r  r?   r   r   r  rQ   r
   rR   r=   r  )
rZ   r  r   r  r   rv2rv3rv4rv5r[   s
             rD   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 )NrL   rh   r  rC  r  r   Tr  r$  r  )r'   r   r  r=   r  r=  r   r   )	rZ   r  r   r  r  r   r  r  rA  s	            rD   test_rvs_methodzTestRandomTable.test_rvs_method(  s|     !fffS#F6"&,,.  2  YYs$G
F FF:sC(CHf48rF   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  r=   r   r   r   rZ   r  r   r  r  r   r  s          rD   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"rF   )Nr  r  r  r   r   c                     t        ||      }|j                  d|| j                               }t        j                  dt        |      t        |      f      }t        ||       y )Nr  r  r/  r0  s          rD   test_rvs_with_edge_casesz(TestRandomTable.test_rvs_with_edge_casesI  sQ     c"UU2f4<<>UB88RS3s845R"rF   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   rM   r  r  	rvs_rcont)scipy.stats._rcontr/   _rcontr=   r   int64ru   r   r  r?   r   )rZ   r   r7  r   r  r   ntotresults           rD   test_rvs_rcontzTestRandomTable.test_rvs_rcontR  s     	,+hh1vRXX.hhy1f	!o.vvc{S#tQ7||3s8SX6666vvf~%%%rF   c                    ddg}g d}t        ||| j                               }|j                         }t        j                  ||      }t	        ||j                                t        j
                  |||      }t	        ||j                  |             t        j                  |||      }t	        ||j                  |             y )NrL   rh   r  r   )r'   r  r   r   r   r=  r3  )rZ   r   r  r  r  r  s         rD   r  zTestRandomTable.test_frozenc  s    !fc7$$S#.Xqvvx(##FC5XquuV}-&&vsC8Xqxx/0rF   c                     ddg}g d}t        ||| j                               }t        j                  ||d|| j                               }|j                  d|      }t        ||       y )NrL   rh   r  r   r  r  )r   r  )r'   r  r   r   )rZ   r  r   r  r  r  r	  s          rD   test_rvs_frozenzTestRandomTable.test_rvs_frozens  sb    !fc7##C2f15AeeFe+Xs#rF   N)r   r   r   r  r  rQ   r   r   r
  r  r  r"  r%  r+  r-  r1  r3  r;  r  r>  r   rF   rD   r  r  T  s   9" H [[^@B$B$5 [[X}5[[UM2L 3 6L\ [[X'>?H @H/ [[X'>?': @':R [[X'>?9 @9( [[X'>?	# @	# [[X'DE[[UR!I.[[UR!I.# / / F# [[S&)& *& 1  [[X'>?$ @$rF   r  c                    | j                   }d| _          | j                  |ddi t        j                  |       } | j                  |ddi}t        j                  |      } |j                  |ddi}t        ||       || _         y )NrX  r   r:  )r   r   pickledumpsloadsr   )distfnrB   rJ  r   r0	unpickledr1s          rD   check_picklingrG    s    
 DFFJJ1VA	T	"	"BQI		%1	%BR FrF   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 )NrM   r	  rP  r  r   r   r  rg   r  r  )r=   rU   r   r   r   r   r   r   r   r   r8   rG  )num_parallel_threadsr  distsrC  rB   s        rD   test_random_state_propertyrK    s    FF1IEE$KE$K	b!	RXXrd^&'	2u+	b%[!	q/*+	d	d#E  %#FD1vt$%rF   c                      e Zd Zej                  j                  dg d      ej                  j                  dg d      d               Zej                  j                  dddg      ej                  j                  dg d	      d
               Zd Zd Z	d Z
ej                  j                  dddg      d        Zej                  j                  dddg      d        Zej                  j                  dej                  ej                  g      d        Zej                  j                  dej                  ej                  g      d        Zej                  j                  d ej&                  g d       ej&                  g d      ddf ej&                  g d       ej&                  g d      ddf ej&                  g d       ej&                  g d      ddf ej&                  g d       ej&                  g d      dd f ej&                  g d       ej&                   ej(                  d!       ej(                  d"      dg      d#d$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   )rL   rM   ri   rh   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   rk   r   r   )r=   r   r   r   r  r)   r   r   rU   r   r?   r   r   r   )rZ   r   r   r   rU  vmf_distrb  r   r   r  r  s              rD   r  z TestVonMises_Fisher.test_samples  s     ii##$78WWcWan-"2qs3,,t$HHSM266#;c00s0FLL}}...		wR0r"rF   rg   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  )r=   r   r   r   r  r)   r   )rZ   r   rP  r   rU  rO  s         rD    test_sampling_high_concentrationz4TestVonMises_Fisher.test_sampling_high_concentration  sQ     ii##$78WWcWan-"2u37RrF   c                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)Nr  z%'mu' must have one-dimensional shape.rJ   r   r=   rT   rQ   r
   rR   r)   rZ   rU  r  s      rD   test_two_dimensional_muz+TestVonMises_Fisher.test_two_dimensional_mu  sA    WWV_5]]:S1 	#B"	# 	# 	#   A		Ac                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)Nr  z%'mu' must be a unit vector of norm 1.rJ   r   rT  rU  s      rD   test_wrong_norm_muz&TestVonMises_Fisher.test_wrong_norm_mu  sA    WWU^5]]:S1 	#B"	# 	# 	#rW  c                     t        j                  d      }d}t        j                  t        |      5  t        |d       d d d        y # 1 sw Y   y xY w)NrO  z$'mu' must have at least two entries.rJ   r   rT  rU  s      rD   test_one_entry_muz%TestVonMises_Fisher.test_one_entry_mu  sA    WWU^4]]:S1 	#B"	# 	# 	#rW  rk   )rg   rM   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.rJ   r   r   rQ   r
   rR   r)   rZ   rP  r  s      rD   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.rJ   r   r   r]  r^  s      rD   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.rJ   r   r   r=   r   rQ   r
   rR   rZ   r  r`   r  s       rD   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)Nr	  r   8'x' must be unit vectors of norm 1 along last dimension.rJ   r   r   re  rf  s       rD   test_unnormalized_inputz+TestVonMises_Fisher.test_unnormalized_input  sN     HHc2YH]]:S1 	!1q!fa 	! 	! 	!rh  zx, mu, kappa, reference)r   r   r   r  g0_?rd  )r   r   r   g7m0_?r  gLI/@gFK:h*7g\(\?r$  i  g3pB>g7Ks@)r   r   r   r   r   go齿@gW+x\(?r  r   gS-c                 V    t        ||      j                  |      }t        ||d       y )Nr  r  )r)   r   r   )rZ   r`   rU  rP  	referencer   s         rD   test_pdf_accuracyz%TestVonMises_Fisher.test_pdf_accuracy  s'    4 b%(,,Q/YU3rF   g[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 V    t        ||      j                  |      }t        ||d       y )NrD  r  )r)   r   r   )rZ   r`   rU  rP  rm  r   s         rD   test_logpdf_accuracyz(TestVonMises_Fisher.test_logpdf_accuracy(  s'    4 !U+2215	6rF   zdim, kappa, reference))rM   r  g?@)rM   r  gp&F)rg   r  gT;ӷ&)r:  r   goZ@c                     t        j                  |fdt        j                  |      z        }t        ||      j	                         }t        ||d       y )Nr   g+=r  )r=   r   r  r)   r   r   )rZ   r   rP  rm  rU  r   s         rD   test_entropy_accuracyz)TestVonMises_Fisher.test_entropy_accuracyS  sC     WWcWan-!"e,4467rF   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  rM   r   rT  r   rg   r   rG  r  )
r=   r   r   r(   r   r   r  r?   rq  r   )rZ   r  	testshaper   r`   rU  rP  
result_allr  r  current_vals              rD   r  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rF   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  )r  rP  rL   r  r   )r=   r   r   r   r  r)   r+   r(   r   r   r   r   r   )	rZ   r   rU  mu_anglerP  vmfvonmises_distvectorsr"  s	            rD   test_vs_vonmises_2dz'TestVonMises_Fisher.test_vs_vonmises_2dm  s     ii##$78XXq!f::beRU+b%( XU;#A&**2C*@GAqDM71a4=9--/?))&137773CD,,V4cjj6IJrF   )rL   rM   rh   zkappa, mu_tol, kappa_tol))r   r  r  )r  r  r  )r  {Gzt?r$  )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   ry  r  )r=   r   r  r)   r   r   r   rA  arccosrr  r   )rZ   r   rP  mu_tol	kappa_tolrU  rO  r   rO  rb  mu_fit	kappa_fitangular_errors                rD   test_fit_accuracyz%TestVonMises_Fisher.test_fit_accuracy|  s     WWcWan-"2u-ii##$78	,,ys,;+//8			"&&.1rQ?yy9rF   c                     t        j                  d      }d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)NrT  z'x' must be two dimensional.rJ   )r=   r   rQ   r
   rR   r)   rA  rZ   r`   r  s      rD   #test_fit_error_one_dimensional_dataz7TestVonMises_Fisher.test_fit_error_one_dimensional_data  sE    HHUO,]]:S1 	#"	# 	# 	#   AAc                     t        j                  d      }d}t        j                  t        |      5  t        j                  |       d d d        y # 1 sw Y   y xY w)Nr  rj  rJ   )r=   rT   rQ   r
   rR   r)   rA  r  s      rD    test_fit_error_unnormalized_dataz4TestVonMises_Fisher.test_fit_error_unnormalized_data  sE    GGFOH]]:S1 	#"	# 	# 	#r  c                    t        j                  g d      }d}t        ||      }t        ||d      }|j                  d      }t        j                  ||d      }|j                         }t	        ||       t	        ||       y )N)r   r   r   rg   r  r   r   )r=   r   r)   r   r   )rZ   rU  rP  r  r  r  r  r  s           rD   r  z,TestVonMises_Fisher.test_frozen_distribution  ss    XXi  U+%b%c:zzsz+""2u3? T4 T4 rF   N)r   r   r   rQ   r   r   r  rR  rV  rY  r[  r_  rb  r)   r   r   rg  rk  r=   r   r  rn  rp  rr  r  r|  r  r  r  r  r   rF   rD   rM  rM    s   [[UL1[[V%9:
# ; 2
# [[UQF+[[W&89 : ,### [[Wr6l3+ 4+
 [[Wq"g.+ /+ [[X(;(;(7(>(>(@ A!A! [[X(;(;(7(>(>(@ A!A!$ [[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 /	:##!rF   rM  c                   f   e Zd Zed        Z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  rL   r   r   r  rk   r   )r=   r   r   r   integersr   )rZ   r&  r   r  r`   r   s         rD   
get_paramsz#TestDirichletMultinomial.get_params  sc    ii##$56As+LLBaVL,EErENAua""rF   c                    t         j                  j                  d      }|j                  ddd      }|j	                  ddd      }t        j
                  |d      }t        ||      }t        |j                  |      t        j                  |||             t        |j                  |      t        j                  |||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             t        |j                         t        j                  ||             y )Nr  r   r  r  rk   r   )r=   r   r   r   r  r   r*   r   r3  r=  r   r  r   )rZ   r   r  r`   r   r  s         rD   r  z$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BrF   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 )NrP   rM   ri   rg   gp.U.?r   r  r   r  r  rk   r   g+T<)r=   r   r   r*   r=  r3  r   r_  r?   r   r   r   r  )rZ   r`   r   r  r@   logresrA   r   s           rD   test_pmf_logpmf_against_Rz2TestDirichletMultinomial.test_pmf_logpmf_against_R  s.   
 HHYFF1I##''5!4&--a:!S!s,yyFLL.B..... ii##$56AsB'LLB#FF12#E1-11!4&--a:"S!s,rF   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   r	  rL   )
r  r   r*   r=  r3  r=   r   r   roundr  )rZ   r   r&  r  r   r`   r  s          rD   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NrF   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 )Nrh   r  r   r   
r=   r>   r*   r   r=  r3  r   r   r  r   rZ   r   r  r`   r   s        rD   test_dimensionality_onez0TestDirichletMultinomial.test_dimensionality_one  s    JJsO$UA.TXXa[!$TXXac]A&T[[^Q'T[[1%w/TYY[!$TXXZ#TXXZ#rF   c                 .   d}t        j                  ddg      }t        j                  ddg      }t        ||      }t        |j	                  |      d       t        |j	                  |dz         d       t        |j                  |      d       t        |j                  |dz         t         j                          t        |j                         ddg       t        |j                         ddg       t        |j                         ddgddgg       y )Nr   r   r   r  r  s        rD   test_n_is_zeroz'TestDirichletMultinomial.test_n_is_zero  s    

B8$JJ1v$UA.TXXa[!$TXXac]A&T[[^Q'T[[1%w/TYY[1a&)TXXZ!Q(TXXZ1a&1a&!12rF   method_namer=  r3  c                    | j                  d      \  }}}}}t        t        ||      |      }t        t        j                  |g|j
                   |      } ||      }	 ||j
                  d         }
t        |	|
       y Nr  r   r  ru   r*   r/   	betabinomr   r   rZ   r  r   r&  r  r   r`   r  
ref_methodr@   rA   s              rD   test_against_betabinom_pmfz3TestDirichletMultinomial.test_against_betabinom_pmf  sr    "ooc2Qq!.ua8+FU__Q99;G
QiQ S!rF   r   r  c                     | j                  d      \  }}}}}t        t        ||      |      }t        t        j                  |g|j
                   |      } |       d d df   }	 |       }
t        |	|
       y r  r  r  s              rD   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!rF   c                    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 )Nr  rg   r   r  r   r  rC  r   r   r}  r  r  r$  )r=   r   r   r  r*   r   r   r   r   r  r?   r   r   r   rt   r  r   r   r   )
rZ   r   r   r   r  r   r&  rA  r`   r   s
             rD   r  z%TestDirichletMultinomial.test_moments!  sc   ii##$56LLC 


$r)$UA. MM%aM(OOAqqO)		RWWQQ%7dC
BFF11$5DAyy{  DHHJ$4$4>>>>>>hhjyyS#J&&&RVVACC[t4RWWS\488:.vvell'',Q/!3444rF   c                    t        j                  g d      }t        j                  |      }t        j                  g d      }d}t        t        |      5  t        j                  g d||       d d d        t        t        |      5  t        j                  g d||       d d d        d}t        t        |      5  t        j                  |g d|       d d d        t        t        |      5  t        j                  |g d	|       d d d        d
}t        t        |      5  t        j                  ||d       d d d        t        t        |      5  t        j                  ||d       d d d        t        j                  g d      }t        j                  g d      }d}t        t        |      5  t        j                  |||j                                d d d        y # 1 sw Y   yxY w# 1 sw Y   SxY w# 1 sw Y   +xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   xY w# 1 sw Y   y xY w)NrP   r  z,`x` must contain only non-negative integers.rJ   )r   rk   rM   )r   r  rM   z*`alpha` must contain only positive values.)rM   r   ri   )rM   rk   ri   z#`n` must be a non-negative integer.ǧH@rk   )r   rL   rM   ri   z&`x` and `alpha` must be broadcastable.)r=   r   r   rT  rR   r*   r3  )rZ   x0n0alpha0textr`   r  s          rD   r\   z.TestDirichletMultinomial.test_input_validation7  s   XXi VVBZ)$=:T2 	A!((VR@	A:T2 	B!((fbA	B <:T2 	<!((Y;	<:T2 	=!((Z<	= 5:T2 	;!((VT:	;:T2 	9!((VR8	9 HH\"#7:T2 	<!((E1557;	< 	<)	A 	A	B 	B	< 	<	= 	=	; 	;	9 	9	< 	<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  r  rg   rg   rj   r:  rP  r  rh   rj   r:  rP   )rL   rL   rM   )rL   r   r   rM   )rL   rM   ri   )
r=   r   r  ru   r*   r?   rq  r   r   r   )rZ   r  r  r   r`   r@   r  r  rx  res_ijkrA   s              rD   test_broadcasting_pmfz.TestDirichletMultinomial.test_broadcasting_pmfU  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	2rF   )r   r  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  r  r  r  rh   rj   r:  r   )rM   ri   rM   )	r=   r   ru   r*   r?   rq  r   r   r   )
rZ   r  r  r   r  r@   r  rx  r  rA   s
             rD   test_broadcasting_momentsz2TestDirichletMultinomial.test_broadcasting_momentsd  s    )Y	:FGHHqcA3_%.<UA)4)=syyI%OO<s1v 	.A3u:& .ad)U1X--/1@-.	.rF   N)r   r   r   r:  r  r  r  r  r  r  rQ   r   r   r  r  r  r\   r  r  r   rF   rD   r  r    s    # #C->O $3 [[]UH,=>" ?" [[]VUO<" ="5,<< [[Xx'892 :2 [[],BC
. D
.rF   r  c                   :   e Zd Zd Zd Zd Zd Zd Zej                  j                  ej                  j                  d      d               Zej                  j                  dej                  ej                   ej"                  ej$                  g      d	        Zy
)TestNormalInverseGammac           	      L   t         j                  j                  d      }|j                  d      \  }}}}t        j                  ||||      t        j
                  d|z  |dt        j                  ||z  |z        z        }t        j                  ddd      }t        fd	d
t         j                  |f      }|j                  |      }	t        |j                  |	       j                  d|      }t        j                  |d
   |j                        \  }
}|dkD  sJ y )N   &( ri   rL   r   r  r  rg   r6  c                 (    j                  ||       S r<   r   )r!  r`   norm_inv_gammas     rD   ra   z8TestNormalInverseGamma.test_marginal_x.<locals>.<lambda>      ^%7%72%> rF   r   rB   r:  r   r   )r=   r   r   r/   normal_inverse_gammar  r  r/  r0   r   r   r   r  r   ks_1sampr   )rZ   r   rU  lmbdar  r  r  r`   r@   rA   r   r  r  s               @rD   test_marginal_xz&TestNormalInverseGamma.test_marginal_xt  s     ii##J/**Q-E1a33Bq!DGGAaCRqUQ)?'?@ KKAr">266QRPTUeeAhc*   e# >NN3q61551	6||rF   c                 *   t         j                  j                  d      }|j                  d      \  }}}}t        j                  ||||      t        j
                  ||      }t        j                  ddd      }t        fdt         j                   t         j                  |f      }|j                  |      }	t        |j                  |	       j                  d|	      }t        j                  |d
   |j                        \  }
}|dkD  sJ y )Nr  ri   r*  r   r  c                 (    j                  | |      S r<   r  )r`   r!  r  s     rD   ra   z9TestNormalInverseGamma.test_marginal_s2.<locals>.<lambda>  r  rF   r  r:  r   r   )r=   r   r   r/   r  r   r/  r0   r   r   r   r  r   r  r   )rZ   r   rU  r  r  r  	inv_gammar!  r@   rA   r   r  r  s               @rD   test_marginal_s2z'TestNormalInverseGamma.test_marginal_s2  s     ii##J/**Q-E1a33Bq!DNN1A.	 [[b"%>wbU4mmBc*   e# >NN3q69==9	6||rF   c                 z   t         j                  j                  d      }|j                  d      dz
  \  }}}}|j                  d      dz
  \  }}t        j                  ||||      j                  ||      }t        j                  j                  ||||||      }	t        |t        j                  |	             y )Nr  )ri   r  r  )rL   r  r   )	r=   r   r   r/   r  r   r   r   r  )
rZ   r   rU  r  r  r  r`   r!  r@   rA   s
             rD   test_pdf_logpdfz&TestNormalInverseGamma.test_pdf_logpdf  s    ii##J/**W-4E1a


(4/2((UAq9==aD((//2r5!QGRVVC[)rF   c                    t         j                  j                  d      }|j                  d      \  }}}}|j                  d      \  }}t        j                  t         j
                  |||      j                  ||      }t        |t         j
                         t        j                  |d||      j                  ||      }t        |t         j
                         t        j                  ||d|      j                  ||      }t        |t         j
                         t        j                  |||d      j                  ||      }t        |t         j
                         t        j                  ||||      j                  |d      }t        |d       t        j                  |dt         j
                  g||      j                  |d      }t        |t         j
                         t        j                  |d||      j                         }t        |t         j
                  t         j
                  f       t        j                  ||d|      j                         }t        |t         j
                  t         j
                  f       t        j                  t        d      5  t        j                  |||d      j                          d d d        y # 1 sw Y   y xY w)Nr  ri   rL   rk   r   zDomain error in arguments...rJ   )r=   r   r   r/   r  r  r   r   r   r  rQ   r
   rR   r   )	rZ   r   rU  r  r  r  r`   r!  r@   s	            rD   test_invalid_and_special_casesz5TestNormalInverseGamma.test_invalid_and_special_cases  s   ii##J/**Q-E1a

12((1=AA!RHS"&&!((RA6::1bAS"&&!((UAq9==aDS"&&!((UAr:>>q"ES"&&!((UAq9==aDS! ((b"&&\1a@DDQKS"&&!((RA6;;=S266266*+((UB:>>@S266266*+]]:-KL 	?&&r5!R8<<>	? 	? 	?s   !'KKc                    t         j                  j                  d      }|j                  d      }|j                  d      dz   }|j                  d      }|j                  d      }|j                  d      }|j                  d      }t        j                  ||||      }t        j
                  ||||||      }	|	D 
cg c]  }
t        j                  |
       }}
|j                  ||      }|j                  |	d   j                  k(  sJ t        |j                         t        j                  j                  |        |j                  ||      }|j                  |	d   j                  k(  sJ t        |j                         t        j                  j                  |        t        j
                  ||||      }	|	D 
cg c]  }
t        j                  |
       }}
|j                         }|d   j                  |	d   j                  k(  sJ t        |d   j                         |d	   j                         ft        j                  j                  |        |j                         }|d   j                  |	d   j                  k(  sJ t        |d   j                         |d	   j                         ft        j                  j                  |        d
}t         j                  j                  d      }|j                  ||      }t         j                  j                  d      }d}t        j                  j                  |||d}t        |d   j                  |      |d	   j                  |      f|       y c c}
w c c}
w )Nr  rL   )rM   r   )ri   r   r   )rg   r   r   r   )rh   r   r   r   r   )rj   r   r   r   r   r   r   r   )rh   rg   ri   rM   rL   l   Mr   )rh   x   )r=   r   r   r/   r  broadcast_arraysr1  r   r?   r   r   r   r  r   r  )rZ   r   r  r  r  rU  r!  r`   r   broadcastedarrbroadcasted_raveledr@   r   r?   rA   s                   rD   r  z(TestNormalInverseGamma.test_broadcasting  s    ii##J/JJqMJJv"

9%ZZ%ZZ(JJ)*))"eQ: ))!RUAqA8CDrxx}DDhhq"oyyKN00000		22668KL	N kk!R yyKN00000		2299;NO	Q ))"eQ:8CDrxx}DDiik1v||{1~33333QQ822779LM	O hhj1v||{1~33333QQ822668KL	N ii##M2hhDsh3ii##M2((,,.A:=?Q.Au0EFLE E Es   ?M=Nr  c                    t         j                  j                  d      }|j                  d      \  }}}}|dz  }t        j                  ||||      j                         }t        fdt         j                   t         j                  dt         j                        }t        |d   |d   d       t        fdt         j                   t         j                  dt         j                        }t        |d	   |d   d       y )
Nr  ri   rL   c                 .    j                  ||       |z  S r<   r  r!  r`   r   s     rD   ra   z5TestNormalInverseGamma.test_moments.<locals>.<lambda>  s    DHHQOa$7 rF   r   r  r  c                 .    j                  ||       | z  S r<   r  r  s     rD   ra   z5TestNormalInverseGamma.test_moments.<locals>.<lambda>  s    DHHQOb$8 rF   r   )	r=   r   r   r/   r  r   r5   r   r   )	rZ   r   rU  r  r  r  r@   rA   r   s	           @rD   r  z#TestNormalInverseGamma.test_moments  s     ii##J/**Q-E1a	Q))"eQ:iik7"&&"&&!RVVTAAT28266'2661bffUAAT2rF   r  c                 ^   t         j                  dk  rt        j                  d       t         j                  j                  d      }|j                  ddd      j                  |      \  }}}}}}t        j                  d|      }	t        j                  ||||      }
|
j                         d	   j                  |	k(  sJ |
j                         d
   j                  |	k(  sJ |
j                         d	   j                  |	k(  sJ |
j                         d
   j                  |	k(  sJ |
j                         d	   j                  |	k(  sJ |
j                         d
   j                  |	k(  sJ |
j                  ||      j                  |	k(  sJ |
j!                  ||      j                  |	k(  sJ y )N2z*Scalar dtypes only respected after NEP 50.r  rM   r  rh   r   r   r   r   )r=   __version__rQ   r   r   r   r   astyperesult_typer/   r  r   r  r   r  r   r   )rZ   r  r   r`   r!  rU  r  r  r  	dtype_outr   s              rD   
test_dtypez!TestNormalInverseGamma.test_dtype  sr   >>CKKDEii##J/!$Q!;!B!B5!I2r5!QNN3.	))"eQ:xxz!}""i///xxz!}""i///yy{1~##y000yy{1~##y000xxz!}""i///xxz!}""i///{{1b!''9444xx2$$	111rF   N)r   r   r   r  r  r  r  r  rQ   r   rp  	fail_slowr  r   r=   int32float16r  rS  r  r   rF   rD   r  r  r  s    *,* ?D1Mf [[[[23  3 [[WrxxRZZ&TU2 V2rF   r  r  )hr5  r@  dataclassesr   numpy.testingr   r   r   r   r   r	   rQ   r
   rT  test_continuous_basicr   numpyr=   scipy.linalgr   scipy.stats._multivariater   r   r   scipy.statsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   scipy.stats._continuous_distnsr.   r"  r/   scipy.integrater0   r1   r2   r3   r4   r5   r6   scipy.specialr7   r  common_testsr8   	data._mvtr9   unittest.mockr:   rE   rH   r   r   r   r=  rN  rr  r  r  r  r/  r  r  r  r  r  r'  r4  r  r  rG  r   r  rK  rM  r  r  r   rF   rD   <module>r     s    !7 7  * 9  C C: : : : : : : : 0 @  4 4 < < &  5  ']! ]!@ A A AH X X Xv@) @)FH* H*VF1 F1R-&i9 i9V{; {;|a( a(HGJ GJT~& ~&Bd# d#N6+ 6+r>D >DB@9 @9Fa% a%Hh$ h$V	( % %$~! ~!BH. H.Vk2 k2rF   