
    Yh                       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          ZMdBd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 d0 d1          Z\ G d2 d3          Z] G d4 d5          Z^ G d6 d7          Z_ G d8 d9          Z`d: Zaejb        jc        d;             Zd G d< d=          Ze G d> d?          Zf G d@ dA          ZgdS )Cz8
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|R i | t          | j        |j                   d S N)npasarrayr   r   shape)resrefargskwargss       u/var/www/tools.fuzzalab.pt/emblema-extractor/venv/lib/python3.11/site-packages/scipy/stats/tests/test_multivariate.pyassert_closerE   /   sU    z#
3CC.t...v...CI&&&&&    c                   (   e Zd Zd Zej        ej        j        ej        j        ej        j	        d dZ
 ej         ee
                    Z ej        g d          g dg dg dg ej        g d          g d	g d
g dgdZeedd         eg d         edd         dZej                            dedd                   d             Zej                            d ee                    ej                            de          d                         Zej                            dd e            ddg          ej                            d ee                    ej                            de          d                                     Zej                            d e            dg          ej                            de          d                         Zd Zej                            d          d             Zd ZdS )TestCovariancec                    d}t          j        t          |          5  t          j        t          j        d                     d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j        t          j        d          t          j        d                     d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j        d           d d d            n# 1 swxY w Y   d	}t          j        t          |          5  t          j	        t          j        d                     d d d            n# 1 swxY w Y   d
}t          j        t          |          5  t          j
        dt          j        d          f           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j
        t          j        d          df           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          j
        g dt          j        d          f           d d d            d S # 1 swxY w Y   d S )Nz:The input `precision` must be a square, two-dimensional...match   z0`precision.shape` must equal `covariance.shape`.   )
covariancez7The input `diagonal` must be a one-dimensional array...alpacaz9The input `cholesky` must be a square, two-dimensional...z4The input `eigenvalues` must be a one-dimensional...z,The input `eigenvectors` must be a square...z9The shapes of `eigenvalues` and `eigenvectors` must be...r   rL   rM   )pytestr
   
ValueErrorr,   CovViaPrecisionr=   oneseyeCovViaDiagonalCovViaCholeskyCovViaEigendecompositionselfmessages     rD   test_input_validationz$TestCovariance.test_input_validation7   s:   N]:W555 	4 	4'

333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 E]:W555 	I 	I'q		bfQiiHHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I L]:W555 	1 	1&x000	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 	1 N]:W555 	3 	3&rwqzz222	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 	3 I]:W555 	H 	H0(BF1II1FGGG	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H 	H A]:W555 	I 	I0"'!**h1GHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I N]:W555 	I 	I0)))RVAYY1GHHH	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	I 	Is}   'AAA9;C  CC(D		DD1'E$$E(+E()GGG))HH"%H"+I>>JJc                 $    t          | d          S )NTallow_singular)r   )xs    rD   <lambda>zTestCovariance.<lambda>Y   s    %)!D%A%A%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|                                           } | ||                    } | ||                    }t          |          t          |          u sJ t          |	                    |          |	                    |                     d S )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    GIIIJJ;(@(@(@AA6}E*&Em.A.A.C.C&E&EFFgmmA&&''h}}Q''((CyyDII%%%%

1szz!}}55555rF   matrix_typec                 l   d| d| d}|| j         |         vrt          j        |           | j        |         }t	          t
          d|           }| j        |         }t          |d          } | ||                    }t          |j	        |j	                   t          |j        |j                   t          |j        t          j        |          j                   t          |j        t          j        |                     t          j                            d          }	|	                    d          }
|                    |
          }|
|j        z  }t          ||z  ||z             t)          |d	          r'd
|vr#t          |                    |          |
           |	                    d          }
|                    |
          }|
|j        z  }t          |dz                      d          |dz                      d                     t)          |d	          r'd
|vr#t          |                    |          |
           t)          |d	          rN|                    t          j        t1          |                              }t          |j        |z  |           d S d S )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  [    <<<K   N;';(@(@(@AA6}E1T*** XmmA..//
Z(#,777Z_ch///Z%rz!}}':;;;Z*BJqMM::: i##$788JJAJ""#%iS3Yc	***:{++ 	6
+0M0M,,S111555 JJIJ&&""#%ic1f\\r\**S!VLLbL,A,ABBB:{++ 	6
+0M0M,,S111555 :{++ 	)%%bfSVVnn55Ca(((((	) 	)rF   r   r   c                 z   d| d| d}|| j         |         vrt          j        |           | j        |         }t	          t
          d|           }| j        |         }g d} | ||                    }	t          }
t          ||d          }t          ||	d          }t          j	        
                    d          }|                    |||          }t          j	        
                    d          }|
                    ||	||	          }t          j	        
                    d          } |
||	|
                              |          }t          |	t
          j                  rEt          |t          j        |                     t          |t          j        |                     nDt!          |j        |j                   t!          |j        |j                   t          ||           t          |
                    |||	          |                    |                     t          |                    |          |                    |                     t          |
                    |||	          |                    |                     t          |                    |          |                    |                     t          |
                    ||	          |                                           t          |                                |                                           d S )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  [    <<<K   N;';(@(@(@AA6}EXmmA..//
!#D!DAAA#D*TJJJi##$788##D!$#77i##$788WWT:DsWCCi##$788Sz,,,00d0;;j+"788 	!RZ]]+++RZ]]++++17+++17+++R   SWWQj11599Q<<@@@UYYq\\599Q<<000SZZ444ell1ooFFFU\\!__ell1oo666S[[z22EMMOODDDU]]__emmoo66666rF   c                    d}| j         |         }t          t          d|           }| j        |         }g d} | ||                    }t          }	t	          ||d          }
t	          ||d          }t
          j                            d          }|                    |||          }t          |		                    |||          |
	                    |                     t          |	                    |          |
	                    |                     t          |	
                    |||          |

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

                    |                     d S )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[    +N;';(@(@(@AA6}EXmmA..//
!#D!DAAA#D*TJJJi##$788##D!$#77SWWQj11599Q<<@@@UYYq\\599Q<<000SZZ444ell1ooFFFU\\!__ell1oo66666rF   c                     d}t          j        t          |          5  t                       d d d            d S # 1 swxY w Y   d S )Nz7The `Covariance` class cannot be instantiated directly.rJ   )rQ   r
   NotImplementedErrorr-   rY   s     rD   test_covariance_instantiationz,TestCovariance.test_covariance_instantiation   s    K].g>>> 	 	LLL	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	s   :>>zignore::RuntimeWarningc                    t          j        g d          }|j        d         }t          j        |          }t	          j        t          d          5  t          ||                                           d d d            n# 1 swxY w Y   d}t           j	        
                    |          }t           j	        
                    |          }t          j        t           j                            |                    }t          ||          }|                    |          }	t          j        |||          }
t          |	|
           d S )N)r   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   sV   
 GMMM""GAJx{{ ]:-JKKK 	/ 	/a((,,...	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ 	/ #y$$T**y$$T**01B1BCC s++ff$f''!%dCdCCCS#s   #BB	Bc                    t          j        d          }t          j        t          j        d          t          j        d          f          }t          j                            ||          }|	                    d           }t          ||           t          j        j                            t          j        ddg          t          j        ddgddgg          f          }t          j                            ||          }|	                    d           }|d         |d         k    sJ |d         |d         k    sJ d S )	NrL   r   r   r         ?        g      y@r   r   )r=   rT   r-   r   r   rU   scipyr/   r   r   r   array)rZ   r   r   distr   s        rD   test_gh19197zTestCovariance.test_gh19197  s!   
 wqzz0"(1++rvayy1IJJ{..Dc.BBhhDh!!S$k$<<Xr2hB8b$Z*@!A!ABD D{..Dc.BBhhDh!!1va    1va      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 I I< .0W.0im-/Y-?79y~)B )B	!C !C %BHTT*C%D%DEE'.rwyyy'9'9'0yy)))YYY&G&-bgiii&8&8&0jj***iii%HJ JI )>'<QRR'@'<[[['I&;BCC&@B BJ
 [_.CCRC.HII6 6 JI6 []DDOO<<[_.CDD-) -) ED =<-)^ [VdEEGGQ	%BCC[]DDOO<<[_.CDD#7 #7 ED =< DC#7J [Veeggy%9::[_.CDD7 7 ED ;:70  
 [ 899  :9,! ! ! ! !rF   rH   Fc                    |                     | | f          }||j        z  }t          j                            |          \  }}|r|                    |           dk    }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	ACA9>>!DAq JJCJ((1,	i
bgenn
qs
"CJrF   c                     t           j                            | |           }t          j                            |          \  }}}|S r<   )r=   r   randnr   r   svd)r   Musr   s        rD   _sample_orthonormal_matrixr   #  s7    
	1Al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                 $   t                                                       || _        || _        || _        || _        t          j        | j        | j                  | _        t          j	        | j        d           | 
                                 d S Nr   )super__init__r   r   r   r   r=   outerr   fill_diagonalfind_target)rZ   r   r   r   r   	__class__s        rD   r   zMVNProblem.__init__F  sy    		XdlDL99

S)))rF   c                 &   t           j                            |          }t          j        |t           j                   }|                    dt          j        |          |          }|                    dd|          } | ||||          }|S )zDRandom lambdas, random upper bounds, infinite lower bounds.
        r   r         r   r   r   r   r   r=   r   r   fullinfr   sqrtclsr   r   r   r   r   rZ   s          rD   generate_semigeneralzMVNProblem.generate_semigeneralQ  s     i##C((gdRVG$${{3D{99++dCd+33s	
 
 
 rF   c                 p   t           j                            |          }t          j        |t           j                   }|                    dt          j        |          |          }t          j        |                    dd                    }t          j        ||          } | ||||          }|S )zVConstant off-diagonal covariance, random upper bounds, infinite lower bounds.
        r   r   r   r   r   )r  r   r   r   r   sigmar   rZ   s           rD   generate_constantzMVNProblem.generate_constantb  s     i##C((gdRVG$${{3D{99C--..'$&&s	
 
 
 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  sk     gdRVG$$x~~'#,,s	
 
 
 T!VrF   c                     t          dd          }|                    |           t          | j        fi |\  | _        | _        dS )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  sT     
 
 
 	
+/0D+J+J+J+J(rF   c           
      V   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     DL!O+,,wL$)dl1QQQ
]3C&CCuLMML$(T\!AAArzM2B%BBeKLLM
 
 
 	
rF   c                     t          j        |          }t          j        t          |          |                     |          z            S )zUnivariate integrand.
        )r=   
atleast_1dr   norm_pdfr  rZ   r  s     rD   r  zMVNProblem.univariate_func  s<     M!z(1++(=(=a(@(@@AAArF   c                 \   ddl m} t          j        ddd          }|                    |t          |          d           |                    ||                     |          d           |                    ||                     |          d	           |                                 d
S )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  s     	-,,,,,Kc4((HQKK|444D))!,,I>>>D((++3CDD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   )  sW          JJJ
*:jJ #Hut|"""	 	 	 	 	    [     ["    [$K K K	
 	
 	
B B 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d
S )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                     || _         || _        || _        t          j        |t          j                   | _        t          j        | j        | j                   | _        t          j	        | j        d           | 
                                 d S r   )r   r   r   r=   r   r   r   r   r   r   r   )rZ   r   r   r   s       rD   r   zSingularMVNProblem.__init__  su    		74"&))ht|T\:::

S)))rF   Nc                 l   t           j                            |          }|                    dt          j        |          |          }|                    t          j        |d                    }t          j        |d|z
  z            |                    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     i##C(({{3D{99MM"'$,,--'!qs)$$szz4+Dz'I'IIs
 
 

 rF   c                     t          dd          }|                    |           t          | j        fi |\  | _        | _        d S )Nr  r  r  r  r  s      rD   r   zSingularMVNProblem.find_target  sR    
 
 
 	
+/0D+J+J+J+J(rF   c           	         t          j        d| j        dz  z             }t          j        t	          j        | j        d| j        z  |d d t           j        f         z  z
  |z            d          }t          j        t	          j        | j         d| j        z  |d d t           j        f         z  z   |z            d          }|d| j        z  |z  z
  j	        S )Nr   rL   y              ?r   rk   )
r=   r  r   r  r  r  r   r  r   real)rZ   r  r  i1i2s        rD   r  z#SingularMVNProblem._univariate_term  s    DL!O+,,WL$)boa2:6F&FF%OPP
 
 
 WL49*r$,qBJ7G'GG5PQQ
 
 
 b49_r))//rF   c                     t          j        |          }t          |          |                     |          z                                  S r<   )r=   r!  r"  r  r   r#  s     rD   r  z"SingularMVNProblem.univariate_func  s<    M!d33A666??AAArF   c                    ddl m} t          j        ddd          }|                    |t          |          d           |                    ||                     |          d           |                    ||                     |          d	           |                    d
d           |	                                 dS )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     	-,,,,,Kc4((HQKK|444D))!,,I>>>D((++3CDD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=    s          " JJJ
*:jJ      [K K K0 0 0B B 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                            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$d Z%d  Z&ej        j'        d!             Z(d" Z)ej                            d# e*dd$                    ej                            d%d&d'g          d(                         Z+ej                            d# e*dd)                    ej                            d%d&d'g          d*                         Z,ej                            d# e*d+d)                    ej                            d%d&d,g          d-                         Z-d. Z.d/ Z/ej                            d0d1          d2             Z0d3 Z1ej                            d4 ej2        d5           ej2        d6          g          d7             Z3ej                            d8 ej2        d9           ej2        d:           ej2        d;          g          d<             Z4d= Z5d> Z6d? Z7d@S )ATestMultivariateNormalc                 f   t          j        d          }t          j        d          }t          t          t
          j        d||           t          t          t
          j        d||           t          t          t
          j        d||           t          t          t
          j        d||           d S )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  s    Yq\\k!nnj"5"962sKKKj"5"99b#NNNj"5"962sKKKj"5"99b#NNNNNrF   c                 p   t           j                            d           d\  }}}t          j        |||          }t          |j        d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          |j        d           d\  }}}t          j	        |||          }t          |j        d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j	        |||          }t          |j        d           d S )N  )      ?g333333?      @r   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  sX   
	t %4!%as33SXq!!! IOOAyq!!fRY__Q''((!%as33SXq!!! %4!%as33SXq!!! IOOAyq!!fRY__Q''((!%as33SXq!!!!!rF   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          j        |||          }t          |t          j	        |                     d S 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IOOAyq!!fRY__Q''(( '455 $Qc22BF2JJ'''''rF   c                    t           j                            d           t           j                            d          }t	          j        |          }t	          j        |          }t	          j        |d d          }t	          j        |d d          }t          |t          j        |                     t          |t          j        |                     d S 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IOOA '** $Q'' '433 $Qa00BF2JJ'''BF2JJ'''''rF   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          j        |||          }t          j        |||          }t          |t          j	        |                     d S r^  )
r=   r   r   r   r[  r   r   r   r   r_  r`  s         rD   test_logcdfz"TestMultivariateNormal.test_logcdfE  rd  rF   c                    t           j                            d           t           j                            d          }t	          j        |          }t	          j        |          }t	          j        |d d          }t	          j        |d d          }t          |t          j        |                     t          |t          j        |                     d S rf  )	r=   r   r   r   r   r   r   r   r_  rg  s         rD   test_logcdf_default_valuesz1TestMultivariateNormal.test_logcdf_default_valuesO  rk  rF   c                 ~   t           j                            d           d}t           j                            |          }t	          d|dz             D ]h}t           j                            ||          }t          j        ||j                  }t          ||d          }t          |j	        j
        |           id S )NrX  ri   r   Tr^   )r=   r   r   r   rangedotr   r   r   r   r   )rZ   r   r   expected_rankr   r   distns          rD   	test_rankz TestMultivariateNormal.test_rank\  s    
	tyq!!"1a!e__ 	? 	?M	=11A&AC..C'c$GGGE).>>>>		? 	?rF   c           	         t          dd          D ]}t          j                            |          }t          d|          D ]}t          j                            ||          }t          j        ||j                  }t          j        ||f          }||d |d |f<   t          j        |          }|d |         |d |<   t          |          }t          j        |t          j        ||j                            }	t          j        ||          }
t          t          j        |          |d          }t          t          j        |          |d          }t          t          j        |          |	d          }t          |j
        j        |           t          |j
        j        |           t          |j
        j        |           |                    |d |                   }|                    |          }|                    |
          }t          ||           t          ||           |                    |d |                   }|                    |          }|                    |
          }t          ||           t          ||           |
|d d df         z   }|                    |          }|                    |          }t          |d           t          |t          j                    d S )Nr   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  s   q! 0	6 0	6A	""A1a[[ .6 .6IOOAq))13 1a&))!'rr2A2v HQKK"1""1" /q1126&!##6#677F1aLL /rx{{F>BD D D.rx{{F>BD D D.rx{{F>BD D DX05q999X05q999X05q999!ae,,!a!a//////$OOAbqbE22	$OOA..	$OOA..		9555	9555 Qqqq"uX&ll622!)!8!8 [#...^bfW5555].60	6 0	6rF   c                 L   d}t          dd          D ]}t          d|          D ]}t          j        |          }t          |          d d d |f         }t          j        ||j                  }t          j        |||          }t          j        |||d          }t          |j
        |           t          j        |dk              sJ t          j        |||d          }	t          |	j
        |           t          j        |	t          j         k              sJ d S )	N
   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! 	0 	0A1a[[ 0 0Xa[[.q11!!!RaR%8VAqs^^'+!DDD)-abb=AC C CSXq)))vcCi(((((,3ABBCGI I IV[!,,,vfw.//////0	0 	0rF   c                 f   d}d}d}t          j        ||z            }||z   }t          j        ||ft                    }t          j        ||           d|| d | d f<   t          t          j                            |          d           t          t          j                            |d |d |f                   t           j	                   t          t           j                            |d |d |f                   d|f           t          |          }t          |j        |           d S )Ng     @@d   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-   
 !f_t3445Lh1vU+++
k*** !UFGGeVWW 	U\%%c**A...U\%%c%4%$,&788"&AAA	))#eteUdUl*;<<O,	. 	. 	. 3iio66666rF   c                 |   t           j                            d          }d}|                    ||          }t          j        ||j                  }|                    |          }|                    dd|          }t          j        |||          }t          j        |||          }t          d          D ]}	t          d          D ]p}
t          j        ||	|
f         ||          }t          |||	|
f                    t          j        ||	|
f         ||          }t          |||	|
f         d           qd S )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  sD   i##D)) yyAfT46""yy|| IIaA *-as;;)-as;;q 	E 	EA1XX E E,01a4$DDAaC(8999,01a4$DDAaC(8tDDDDDE	E 	ErF   c                 6   t          j        ddd          }d\  }}|dz  }t          j        |||          }t	          j        |||          }t          ||           t          j        |||          }t	          j        |||          }t          ||           d S )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     K1b!!	cSXau%% $Qc22BXau%% $Qc22BrF   c                    t          j        ddg          }t          j        ddgddgg          }d}d|dz
  z  }t          j        d	d|          }t          j        ||          \  }}t          j        ||d
f          }||d d d d d	f<   ||d d d d df<   t          j        |||          }	t          |	|d	          }
t          |	|d          }t          j        ||d	         |d         dz            }t          j        ||d         |d         dz            }t          |
|dd           t          ||dd           d S )NrZ  g      @r	  r   333333?i  rh   r   r   rL   r   r   r   locr  )r   r   {Gz?r  atol)
r=   r   r/  meshgridemptyr   r   r3   r   r   )rZ   r   r   r   deltar   xvyvposr   margin_xmargin_ygauss_xgauss_ys                 rD   test_marginalizationz+TestMultivariateNormal.test_marginalization  sj    xc
##hS	C9-..QUK1a  Q""Bh1ay!!AAAqqq!GAAAqqq!G!%c455 U+++U+++ (1$q'Tc1ABBB(1$q'Tc1ABBB'4@@@@'4@@@@@@rF   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        t           j                            d                    }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                    |          t          j	        |||                     t          |
                    |          t          j
        |||                     d S r^  )r=   r   r   r   r[  r   r   r   r   r   r   )rZ   r`   r   r   norm_frozens        rD   test_frozenz"TestMultivariateNormal.test_frozen  s:   
	tIOOAyq!!fRY__Q''(()$44**,?,CAtS,Q,QRRR**1--+21dC@@	B 	B 	B**,?,CAtS,Q,QRRR**1--+21dC@@	B 	B 	B 	B 	BrF   rN   rL   r   c                     t          j        d          }t          j        d          }t          ||          }t          j        |j        |          sJ t          j        |j        |          sJ d S )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  sh     wt}}q		)$
;;{;+T22222{;?M:::::::rF   c           
         t           j                            d           d}t           j                            ||          }t          j        ||j                  }t          j                            |          \  }}t          j	        |d          }d|d<   d|d<   t          j        |t          j        t          j
        |          |j                            }d}t          ||	          }t          |j        |	          }t          |j        t          j        t          j        |d d                                        t          |j         |j                   d S )
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$  s    		tIOOAq!!fQnn|  %%1GAsOO!"fQrwqzz13//00 3T"""t,,, 	bfRVAcrcF^^&<&<=== 	x'899999rF   c                 L    g dg dg}t          t          t          |           d S )NrP   ri   rg   rh   rT  rR   r   rZ   r   s     rD   test_exception_nonsquare_covz3TestMultivariateNormal.test_exception_nonsquare_cov>  s,    yy)))$j$,,,,,rF   c                     ddgdt           j        gg}t          t          t          |           ddgdt           j        gg}t          t          t          |           d S )Nr   r   )r=   nanrT  rR   r   r   )rZ   cov_nancov_infs      rD   test_exception_nonfinite_covz3TestMultivariateNormal.test_exception_nonfinite_covB  sT    q6Arv;'j$000q6Arv;'j$00000rF   c                 L    ddgddgg}t          t          t          |           d S )Nr   r   rk   r  r  s     rD   test_exception_non_psd_covz1TestMultivariateNormal.test_exception_non_psd_covH  s,    1v2wj$,,,,,rF   c                    t           j                            d           t           j                            d          }t           j                            d          }t          j        d          }t           j        j        }t          |t          ||           t          |t          j	        |||           t          |t          j
        |||           t          |t          j        |||           t          |t          j        |||           ddgddgg}d}t          j        t           j        j        |          5  t          |           d d d            d S # 1 swxY w Y   d S )	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  sx   
	tIOOAyq!!gfooI!a,dC888a,0!T3???a,3QcBBBa,0!T3???a,3QcBBB Bx"b"@]290<<< 	) 	)C((((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)s   =EE"Ec                     t          j        g d          }t          j        ddd          }d|z  dz
  }|t          j        |          z   }t          j        |||g          j        }t          j        g dd          }t          j        g dg d	g d
gd          }t          j        |||          }t          ||d           t          j        g d          }	t          j        |||          }
t          |
|	d           t          j        g d          }t          j        ||g          j        }t          j        ddgd          }t          j        ddgddggd          }t          j        |||          }t          ||d           d S )N)g0Q-?gox'V?g[S, t?gDB?gc_.?r   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$TestMultivariateNormal.test_R_values_  s     6 6 6 7 7 K1a  EAIq		MHaAY!x			3''h			:::zzz:C@@!%as33U////  6 6 6 7 7 "%as33U....  3 3 3 4 4 Xq!f!Q%%x!Q!Q(#.."&r5$77f4000000rF   c                     t          j        d          }t          j        d          }t          ||d          }|                                }t	          |ddg           d S )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  sY    x{{Xf%%
#D*TJJJVaV$$$$$rF   c                    d}d}t          j        t          j        |          d|          }t	          |j        ||f           t          j        d t          j        ddgddgg          |          }t	          |j        |df           t          dd          }|                    |          }t	          |j        |f           d S )	Ni,  ri   r   r  rL   r   r   r   )r   r   r=   r   r   r?   r   )rZ   Nr  r  r   s        rD   test_rvs_shapez%TestMultivariateNormal.test_rvs_shape  s     $(bhqkkqqIIIV\Aq6***$(d-/X2wQ6H-I-I./1 1 1 	V\Aq6***QA...qV\A5)))))rF   c                    t           j                            d          }d}|                    |          }|                    ||          }t          j        ||j                  }d}t          j        ||||          }t          t          j	        |j                  |d           t          |
                    d          |d           d S )N  rM     r   r   r  r   )r=   r   r  r   rr  r   r   r   r   r   r   )rZ   r   r   r   r   r   r   r  s           rD   test_large_samplez(TestMultivariateNormal.test_large_sample  s     i##D))yy||IIaOOfQnn$(sDsKKKvx((#D9999A4888888rF   c                    t           j                            d          }d}|                    |          }|                    ||          }t          j        ||j                  }t          ||          }t          |                                t          j        ||                     t           j	        
                    |          d         }d|t          j        dt           j        z            dz   z  t          j        t          j        |                    z   z  }t          ||                                           d S )Nr  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    i##D))yy||IIaOOfQnn s++ 	BJJLL*=*EdC*P*PQQQ y}}S!!!$1q25y 1 1A 56t9M9MMNGRZZ\\22222rF   c                     t          j        g d          }d}t          t          j        t	          |                    |           d S )Nr   r   r   r	  )r=   r   r   r  r   )rZ   alphar  s      rD   test_lnBzTestMultivariateNormal.test_lnB  s@    ##BF4;;//99999rF   c                    t           j                            d          }ddg}t          j        d          }|                    d          dz  dz
  }|                    d          dz  dz
  }t	          j        ||||          }t	          j        |||          }t	          j        |||          }t          j        |ddd	f         |dd	df         fd
          }	t          j        |dd	df         |ddd	f         fd
          }
t	          j        |	||          }t	          j        |
||          }||z   |z
  |z
  }t          ||           d S )N   FYc@Y r   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  sX   i##$7881vfQiiJJy!!!#a'JJy!!!#a'"&q$CCC#'455#'455naQqSk1S!A#X;7bAAAnaQqSk1S!A#X;7bAAA%)#tS99%)#tS99u}w&0d#####rF   c                    t           j                            d          }|                    d          }|                    d          }||j        z  }|                    d          dz  dz
  }|                    d          dz  dz
  }t	          j        ||||          }t	          ||                              ||          }t          j        t	          j        ||||                    }t          j        t	          ||                              ||                    }	t          ||d           t          ||d           t          |	|d           d S )	Nr  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  sJ   i##$788zz!}}jj  CEkJJvq 1$JJvq 1$"&q$CCC"4--11!1CCv)0D#1MMMNNv)$44;;A1;MMNNd....d....d......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             d S )	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  s    x{{fQiiYY			999iii8YY			999iii8...11!%asBBBSVN233333rF   c                    d}t           j                            d          }|                    ||f          }|j        |z  }|                    |          }t          ||          }|                    dd|f          }|                    |          }t          dg|z  |          }	t          |	j        t           j	         g|z  ||z
            j
        }
t          ||
d	           d S )
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    i##C((KKdD\K**cAgKKTK"""s333KKBQdWK55hhqkk$1#d(<<<rvgYt^QU;;DU......rF   c                    t          dd          D ]r}t          j        ||fd          }t          j        |d           t	          dg|z  |          }t          |                    dg|z            dd|z   z  d           sd S )	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  s    !RLL 	 	D'4,,,CS"%%%&s4xS999D!T""b4i     		 	rF   r   r  r   l   >[= l	   HVqKWs.!) c                 j   t           j                            |          }t                              ||          }|j        t           j         k                                    sJ t          dg|z  |j	                  }|
                    |j        |          }t          ||j        d           d S 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     i##D))..Dc.BBRVG#((*****"DdjAAA((49#(..t<<<<<<rF      c                 j   t           j                            |          }t                              ||          }|j        t           j         k                                    sJ t          dg|z  |j	                  }|
                    |j        |          }t          ||j        d           d S 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     i##D))++3+??RVG#((*****"DdjAAA((49#(..t<<<<<<rF   ri   l	   HVqKWs.!) c                    t           j                            |          }t                              ||          }|j        t           j         k                                    sJ t          dg|z  |j	        dd|j	        j
        d         z            }|                    |j        |          }t          ||j        d           d S )	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    
 i##D))!77Ts7KKRVG#((*****"DdjQU*01A!1D*D
 
 
 ((49#(..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            n# 1 swxY w Y   t          j        t          |          5  t          ddg|           d d d            n# 1 swxY w Y   g d}t          j
        |g d|          }t          t          j
        ||          |           t          j
        |g d	|          }t          t          j
        |d|          |           d S )
Nr   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   GA+++,, 033
K]:W555 	< 	<'A
;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< ]:W555 	4 	4A
333	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 	4 OO!%aJ??(,QJ???EEE!%aJ??(,QzBBBCHHHHHs$   BBB'CC
C
c                     ddg}d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )Nr   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  s    1v2	]:Y777 	* 	*#D)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	*s   AAAr   )rM   rg   c                 J   t           j                            d          }|                    d|f          }t          j        |          \  }}t          j        |d          t          j        |j        d          }}t          ||d           t          ||d           d S )	N   @,Q| r  r   r   )ddofV瞯<r  r  )	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  s    i##$455JJSz""/3A66'GAA...qs0C0C0C'(7777u555555rF   c                     t          j        dd          }d}t          j        d          }t          j        |||          \  }}t          ||           t          ||           d S )N)rL   r   rM   r   )fix_meanfix_cov)r=   r   
atleast_2dr   rA  r   )rZ   r  
mean_fixed	cov_fixedr   r   s         rD   test_fit_both_parameters_fixedz5TestMultivariateNormal.test_fit_both_parameters_fixeds  so    wvq!!
M"%%	'+D:4=? ? ?	cT:&&&S)$$$$$rF   rN  r  rM   c                     d}t          j        t          |          5  t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nzd`fix_mean` must be a one-dimensional array the same length as the dimensionality of the vectors `x`.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|  s    C]:S111 	B 	B#BF1IIAAAA	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B   )AAArO  r  )rM   rL   )ri   ri   c                     d}t          j        t          |          5  t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nzn`fix_cov` must be a two-dimensional square array of same side length as the dimensionality of the vectors `x`.rJ   rM   rO  rW  )rZ   rO  r  s      rD   +test_fit_fix_cov_input_validation_dimensionzBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimension  s     ]:S111 	@ 	@#BF1IIw????	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@rY  c                     d}t          j        t          |          5  t          j        ddgddgg          }t          j        t          j        d          |           d d d            d S # 1 swxY w Y   d S )Nz2`fix_cov` must be symmetric positive semidefinite.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  s    H	]:Y777 	@ 	@hR2s)455G#BF1IIw????	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@ 	@s   AA..A25A2c                     t           j                            d          }|                    d          }|                    d          }t          j        ||j                  }t          j        ||d|          }t          j        |          \  }}t          j        |||          	                                }t          j        ||          \  }	}
t          |	|           t          j        ||	|
          	                                }||k     sJ |                    d          }dt          j        ||j                  z  }|
|z   }t          j        ||	|          	                                }||k     sJ d S )	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  s   i##$455jjmmJJvfQnn%)s#7:< < <15g>>	8'.wY3;= = ==@SUU 	/3GcJJJ'Xs###&-gH29; ; ;;>355 	 )#### JJv26!QS>>!!-4W:B9FH H H 8;suu 	 ((((((rF   c                    t           j                            d          }|                    d          }|                    d          }t          j        ||j                  }t          j        ||d|          }t          j        |          \  }}t          j        |||          	                                }t          j        ||          \  }	}
t          |	t          j        |d	                     t          |
|           t          j        ||	|
          	                                }||k     sJ |	d
|                    d          z  z   }t          j        |||
          	                                }||k     sJ d S )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  s   i##$455jjmmJJvfQnn%)s/2F F F15g>>	8'.wY3;= = ==@SUU 	/3GSIII'XrwwQ777888Wc"""&-gH29; ; ;;>355 	 )#### "D3::a==$88-4W:H9@B B B 8;suu 	 ((((((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 O O" " "6( ( (( ( (( ( (( ( (	? 	? 	?26 26 26h0 0 0,7 7 70E E E0     A A A2B B B [BF1II$J$aV,,	
 ; ; ;: : :4- - -1 1 1- - -) ) )&>1 >1 >1@% % %* * *"9 9 9"3 3 3$: : :$ $ $(/ / /$	4 	4 	4 [/ / /
 
 
 [VUU1b\\22[Vj2T%UVV= = WV 32= [VUU1b\\22[Vj2T%UVV= = WV 32= [VUU1b\\22[Vj2T%UVV= = WV 32=I I I&* * * [UF++6 6 ,+6% % % [Z("(6*:*:*2"(5//*; < <B B< <B [Y%)1&)9)9)1&)9)9); < <@ @< <@@ @ @) ) ):) ) ) ) )rF   rN  c                   >    e Zd Zd Zd Zd Zd Zd Zd Zd Z	d Z
d	S )
TestMatrixNormalc           
      \   d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t          t          t
          t          j        d                     t          t          t
          |t          j        d          |           t          t          t
          ||t          j        d                     t          t          t
          |||           t          t          t
          |||           t          t          t
          |j        ||           t           j        j	        }t          |t
          j
        ||t          j        ||f                     t          |t
          j
        |t          j        ||f          |           t          |t
          ||t          j        ||f                     t          |t
          |t          j        ||f          |           d S )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   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LL 	j-'1B1BCCCj-BHRLL!DDDj-Arx||DDDj-Aq999j-Aq999j-a;;;I!a*BGXx$899	; 	; 	;a*(H!566	; 	; 	; 	a1bgx6J.K.KLLLa27Hh3G+H+H!LLLL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
        |           d S )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:   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLHh)**Xxm$$Xq(m$$[""[""[^^]&AaBBBH)	+ 	+ 	+]&A...4)	+ 	+ 	+]&a0006]	$ 	$ 	$]&a0006]	$ 	$ 	$]&Aa888>)	+ 	+ 	+]&Aa888>)	+ 	+ 	+]&a:::@)	+ 	+ 	+ 	]***12666]***12666]!,,,12666]!,,,3R888]!,,,12666]!,,,3R888]!444;R@@@]!444;R@@@]!A666;Q?????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             d S )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*   GXx(#..WXs##WXs##[""[""]"R@@@GV	 	 	]"R@@@GV	 	 	]"R@@@GV	 	 	]"R@@@GV	 	 	 	 	rF   c                    t          dd          D ]m}t          dd          D ]X}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t	          |||          }|                    d          }t	          j        |||d	          }t          ||           |                    d          }	|                    |	          }
t	          j        |	|||          }t          |
|           |                    |	          }t	          j        |	|||          }t          ||           Zod S )
Nr   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&  s   q 	/ 	/A1QZZ / /GQqE3''"+a..(27Aa5#+>+>>"+a..(27Aa5#+>+>>&AaBBBzztz44$(a!6:< < <T4(((JJDJ11zz!}}$(1QGGGT4((( --**'.qq1MMMWg....)/	/ 	/rF   c                    t          dd          D ]}t          dd          D ]}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }t	          |||          }|                    d          }|                    |          }|                    |          }	|                                }
|j	        
                                }|j	        
                                }t          j        ||          }t          j        |||	          }t          j        |||	          }t          j        ||	          }t          ||d
           t          |	|d
           t          |
|           d S )Nr   rg   r   r	  rt  rz  rX  r   r   r  r  )rq  r=   r   rS  r   r   r   r   r   r   flattenkronr   r   )rZ   r  r  r   r   rw  r  r  r  r  entropy1vecXvecMr   r  r  entropy2s                    rD   test_matches_multivariatez*TestMatrixNormal.test_matches_multivariate>  s    q 	4 	4A1QZZ 4 4GQqE3''"+a..(27Aa5#+>+>>"+a..(27Aa5#+>+>>&AaBBBJJDJ11zz!}} --**!>>++s{{}}s{{}}gall*.t$CHHH-4T#NNN.6DcJJJd7777u====(3333)4	4 	4rF   c           	      X   d}d}t          j        ||fd          }dt          j        |          z  t          j        ||fd          z   }dt          j        |          z  t          j        ||fd          z   }d}t          |||          }|                    |d	          }|                    |d
	          }	t          j        |t           j        d d d d d d f         |	t           j        d d d d d d f         fd          }
t          |
j        d|||f           |	                    |
          }t          |j        d|f           t          d          D ]M}t          |          D ];}t          j	        |
||f         |||          }t          ||||f         d           <Nd S )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   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLAa:::ZZQTZ22ZZQTZ22NBrz!!!AAAaaa/0BJqqq1114D1EFQOOOQWq!Xx8999}}Q''\'!Q000q 	K 	KA1XX K K"/"6q1vA>?#K #K #Kac1BEJJJJK	K 	K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          |||          }|                    |d	          }t          j        |d
          }	t          |	|d           t          j        |                    ||z  |          j	                  }
t          |
|d           t          j        t          j
        |dd                              ||z  |          j	                  }t          ||d           d S )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  sb   GXh'--"+h'''"'8X2F*L*LL"+h'''"'8X2F*L*LLAa:::JJADJ11gaQ'''QS1111qyy8H==?@@qs3333r{1Qq119989(
8 M  MMNP Pqs33333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                            d          d	          }t          j        d
dgddggddgddggg          }t          ||           d S )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*++8aWr1g.//8aVaW-....q11
 
 
 8!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 M M4%@ %@ %@N  ,/ / /04 4 44K K K.4 4 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dS )TestDirichletc           	         t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }t          |                                t          j        |                     t          |                                t          j        |                     t          |	                                t          j	        |                     d}t          |          D ]}t           j                            dd|          }|t          j        |          z  }t          |                    |d d                   t          j        |d d         |                     t          |                    |d d                   t          j        |d d         |                     d S Nr  r       &.>r  r  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  s   
	tIa$$	!!&#q11eQUUWWimE22333QVVXXy~e44555QYY[[)"3E":":;;;	y!! 	L 	LA	!!&#q11ANAq"v	afe(D(DEEE!CRC&))9+;AcrcFE+J+JKKKK		L 	LrF   c                 P   t           j                            d           t          j        g d          }t           j                            |d          }t          |j        d           t          t          t          j	        ||           t          t          t          j
        ||           t	          j	        |j        |           t	          j	        |j        d d         |           t	          j
        |j        |           t	          j
        |j        d d         |           d S )Nr  r          @      @rj   r   )rj   rM   rk   )r=   r   r   r   r   r   r?   rT  rR   r   r   r   rZ   r  r`   s      rD   "test_numpy_rvs_shape_compatibilityz0TestDirichlet.test_numpy_rvs_shape_compatibility  s    
	t))IA..QWf%%%j)-E:::j)"2Au===ac5!!!ac#2#h&&&e$$$SbS5)))))rF   c                 B   t           j                            d           g d}t           j                            t          j        d|          d          j        }t          t          t          j        ||           t          t          t          j	        ||           d S )Nr  )r   r   r  r  rj   r   
r=   r   r   r   maximumr   rT  rR   r   r   r  s      rD   test_alpha_with_zerosz#TestDirichlet.test_alpha_with_zeros  s{    
	tI
4 7 7a@@Bj)-E:::j)"2Au=====rF   c                 B   t           j                            d           g d}t           j                            t          j        d|          d          j        }t          t          t          j        ||           t          t          t          j	        ||           d S )Nr  )r   g       r  r  rj   r   r  r  s      rD    test_alpha_with_negative_entriesz.TestDirichlet.test_alpha_with_negative_entries  s}    
	t   I
4 7 7a@@Bj)-E:::j)"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                     d S )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    ---..H)))**aE"""---..IM!U33Q777I,Q66q		BBBBBrF   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )N)r   r	  r  r  r  r=   r   rT  rR   r   r   r   r  s      rD   $test_data_with_zeros_and_small_alphaz2TestDirichlet.test_data_with_zeros_and_small_alpha  a    ---..H)))**j)-E:::j)"2Au=====rF   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )Nr  )r   rJ  r   rt  r  r  s      rD   test_data_with_negative_entriesz-TestDirichlet.test_data_with_negative_entries  sa    ---..H***++j)-E:::j)"2Au=====rF   c                     t          j        g d          }t          j        g d          }t          t          t          j        ||           t          t          t          j        ||           d S )Nr  )r   rK  r   rt  r  r  s      rD    test_data_with_too_large_entriesz.TestDirichlet.test_data_with_too_large_entries  r  rF   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr  )rL   rj   rj   g$I$I?r=   r   r   rT  rR   r   r   r   r  s      rD   test_data_too_deep_cz"TestDirichlet.test_data_too_deep_c  sY    ))GIv&&j)-E:::j)"2Au=====rF   c                     t          j        ddgddgg          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr   r  r  r  )rL   rL   rj         ?r  r  s      rD   test_alpha_too_deepz!TestDirichlet.test_alpha_too_deep  sb    3*sCj122GIu%%j)-E:::j)"2Au=====rF   c                     t          j        g d          }t          j        dd          }t          j        ||           t          j        ||           d S )Nr  rM   rj   UUUUUU?)r=   r   r   r   r   r   r  s      rD   test_alpha_correct_depthz&TestDirichlet.test_alpha_correct_depth  sQ    ))GFE""aE"""""rF   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr  r  r	  r  r  s      rD   test_non_simplex_dataz#TestDirichlet.test_non_simplex_data  sY    ))GFE""j)-E:::j)"2Au=====rF   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr  )rL   rj   r	  r  r  s      rD   test_data_vector_too_shortz(TestDirichlet.test_data_vector_too_short  \    ---..GFE""j)-E:::j)"2Au=====rF   c                     t          j        g d          }t          j        dd          }t          t          t
          j        ||           t          t          t
          j        ||           d S )Nr  )rg   rj   r   r  r  s      rD   test_data_vector_too_longz'TestDirichlet.test_data_vector_too_long  r  rF   c                 B   t          j        g d          }t          |          }g d}g d}g dg dg dg}t          |                                |           t          |                                |           t          |                                |           d S )N)r   皙?r   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  s     ((e'---......///
 	"!&&((M:::!!%%''<888!!%%''<88888rF   c                    t          j        dg          }t          |          }t          |                                j        d           t          |                                j        d           t          |                    dg          j        d           t          |                    dg          j        d           d S )Nr   r   r   )	r=   r   r   r   r   r   r  r   r   )rZ   r  r  s      rD   r\  z TestDirichlet.test_scalar_values  s    #e 	QVVXX]A&&&QUUWW\1%%%QUUB4[[%q)))QXXrd^^(!,,,,,rF   c                    t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }d}t          |          D ]x}t           j                            dd|          }|t          j        |          z  }t          |	                    |d d                   |	                    |                     yd S 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Ia$$	!!&#q11e	y!! 	9 	9A	!!&#q11ANAafquuQxx8888	9 	9rF   c                    t           j                            d           t           j                            dd          }t           j                            dd|          }t          |          }d}d}d }t          |          D ]}t          |          D ]U}t           j                            dd|          }	|	t          j        |	          z  }	|t          j        ||	f          }S|	}V|	                    |j
                  }
d }|D ]1}|	                    |          }|t          j        ||          }/|}2t          |
|           d S )Nr  r   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  sK   
	tIa$$	!!&#q11e	y!! 	. 	.A<((  I%%fc155RVAYY>B7++BBBBrtBB  EE"II>2q))BBBB%b"----!	. 	.rF   c                    t           j                            d           t           j                            ddd          }t	          |          }t          |d         |d                   }d}t          |          D ]q}t           j                            ddd          }|t          j        |          z  }t          |	                    |          |	                    |g                     rt          |
                                |
                                d                    t          |                                |                                d                    d S )Nr  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1eq58$$	y!! 	6 	6A	!!&#q11ANAa!%%**5555AFFHHaffhhqk222AEEGGQUUWWQZ00000rF   N)r   r   r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r\  r  r  r  r   rF   rD   r  r    s7       L L L$
* 
* 
*> > >> > >C C C> > >> > >> > >> > >> > ># # #> > >> > >> > >9 9 9$	- 	- 	-9 9 9. . .:1 1 1 1 1rF   r  c                  P   t          j        ddg          } t          j        dgg          }t          t          t          | |           	 t	          | |           d S # t          $ r?}d}t          t          |          d t          |                   |           Y d }~d S d }~ww xY w)Nr   r   zDimension mismatch)r=   r   rT  rR   r   r   strr   )rU  r  r  r  s       rD   ,test_multivariate_normal_dimensions_mismatchr  a  s     
3*		BHseWE*12u===
-B&&&&& - - -"SVVISXXI&,,,,,,,,,-s   
A 
B%&4B  B%c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestWishartc                 h   t          j        dd          }ddgt          j        d          t           j        d         t          j        dd          g}|D ]F}t          d|          }t	          |j        |           t	          |j        j        |j                   Gt          j        ddgddgg          }ddgt           j        d         t          j        ddgddgg          g}|D ]F}t          d|          }t	          |j        |           t	          |j        j        |j                   Gt          t          t          dt          j	        d                     t          dt          j	        d                     t          j        dd          }t          t          t          d|           d S )Nr   rL   ndminr   r   rL   rK  rM   )
r=   r   r_r   r   r  r?   rT  rR   rU   )rZ   
true_scalescalesr  ws        rD   test_scale_dimensionsz!TestWishart.test_scale_dimensionsu  s    Xaq)))
CHQKKE!HHQa   
  	: 	:E5!!A*---
(89999 X!u !!u& ' '
 qEE#JHqee  
  	: 	:E5!!A*---
(89999 	j'1bfQii888 	RVAYY !$$$j'1e44444rF   c           
         ddgt          j        d          t           j        d         t          j        dd          t          j        dgd          g}t          dd          }|                    t          j        dd                    }|D ]%}t          |                    |          |           &g dt           j        d         t          j        g dd          g}t          dd          }|                    t          j        g dd                    }|D ]%}t          |                    |          |           &dddgt          j        d          t           j        d         t          j        ddgddgg          t          j        ddgddgg          d d d d t           j        f         g}t          dt          j        d                    }|                    t          j        ddgddgg          d d d d t           j        f                   }|D ]%}t          |                    |          |           &d S )Nr   rL   r  rM   rP   r  r   )r=   r   r  r   r   r   r  rU   )rZ   r  r	  densityr`   s        rD   test_quantile_dimensionsz$TestWishart.test_quantile_dimensions  sQ   
 CHQKKE!HHQa   HaS"""
 AaLL%%!,,,-- 	, 	,Aq7++++ GGE%LHWWWA&&&
 AaLL%%22233 	, 	,Aq7++++
 qEHQKKE#JHqee  Hqee  aa"*n.	
 AbfQii  %%1Q%#$Q%") * **+!!AAAbj.: ; ; 	, 	,Aq7++++	, 	,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        |          }|                    |           t          j        |          j        }ddt          j	        ddd          fd||fg}|D ]"\  }}}t          ||          }t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                    |          t          j        |||                     $d S 	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()),.IcSUmq6H,I,IbocR((()uw&& q 	 	A	#!ax/00A,.IcSUmq6H,I,IAbocR((()qsAAHHQKKKKHQKKM BKR++,N


 ) 	> 	>NRE""A'+b%"8"89997<E#:#:;;;7<E#:#:;;;gob%&@&@AAAq7;q"e#<#<====	> 	>rF   c                    d}d}t          j        |          }d|d<   d|d<   t          ||          }t           j                            d          }t          j        |||          }t           j                            d          }|                    |          }t           j                            d          }|                    d          }t           j        |                    |          |                    |d	z
            |                    |d
z
            f         dz  }	t          j	        |	          }
||
t          j
        |d          <   t           j                            |          }|                    |
          }t          j        ||j                  }t          ||           t          ||           d S )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  s    sc
c
 B i##F++BC888i##F++uu#u.. i##F++jjaj((EMM"MM"Q$MM"Q$!
 		 GI(3"/#
$
$
$% Iu%%UU1XXvb"$'' 	|,,,l33333rF   c                 (   t           j                            d          }d}d}t          j        |          }t          j        dddt
                    }t          j        ddd          }|D ]"}t          ||          }t          |          }	t          |
                                |	
                                           t          |                                |	                                           t          |                                |	                                           t          |                    |          |	                    |                     |                    ||	          }
|f}d
}t          d|||
           $d S )N^   r   r  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  sS   
 i##F++s9QAU333KB2&&& 	= 	=BE""ARA AEEGGQUUWW---AFFHHaffhh///AIIKK555 AEE!HHaeeAhh/// %%Rc%22C5DE"64<<<<!	= 	=rF   c                 J   t           j                            d          }d}d}d}t          j        t          j        d          dz             }t          j        d          |t          j        dd          <   t          j        |j        |          }t          j        |df          }|j                            |                              |          	                                }t          ||          }t          ||	          }	t          |                                |	                                           t          |                                |	                                           t          |                                |	                                           t          j        d
dd          }
t          |                    |
          |	                    |
                     |                    ||          }|d|f}d}t'          d|||           d S )Nr!  r"  r  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<  s   
 i##F++	!Q''*,)A,,boa2&&&'uw&&Q  gkk%((,,U33;;==B$$;''' 	)))!&&((+++		QYY[[111 KB2&&&a!%%((+++ ee#e..1[!vtUC88888rF   N)	r   r   r   r
  r  r  r  r(  r-  r   rF   rD   r  r  t  sr        )5 )5 )5V/, /, /,b> > >@*4 *4 *4X= = =>!9 !9 !9 !9 !9rF   r  c                      e Zd Zd Zd Zd Zej                            dddg          d             Z	d Z
d	 Zej                            ddd
g          d             Zd Zej                            dddg          d             Zd Zej                            ddd
g          d             Zd Zd Zd Zej                            dej        ej        g          d             ZdS )TestMultinomialc                 `   t          j        ddd          }t          |dd           t          j        ddgd	d
dg          }|t          j         k    sJ t          j        d	d	gd	d
dg          }|d	k    sJ t          j        ddgd	ddg          }t          |t          j        d           d S )NrM   ri   rj   r   rt  g&Mtyra  r  rM   ri   r   r   rt  rn   )r   logpmfr   r=   r   r  )rZ   vals1vals2vals3vals4s        rD   test_logpmfzTestMultinomial.test_logpmf`  s    "5!Z881===="Aq61r2h77"Aq61r2h77zzzz"Aq61r1g66rvD111111rF   c                     t          j        ddd          }t          j        ddd          }t          ||d           t          j        dd	d
          }t          j        dd	d          }t          ||d           d S )Nr1  rj   r2  rM   r   ra  r  )rh         r   r  rh   r   )r   r3  r"   r   pmfrZ   val1val2s      rD   test_reduces_binomialz%TestMultinomial.test_reduces_binomialm  s     !&!Z88|Aq#&&d....vr:66yB$$d......rF   c                     dg d}}ddddddd	dd
dd
}|D ].}t          t          j        |||          ||         d           /d S )NrM   )g      ?r  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rM   )r   r   rL   )rL   r   r   )rM   r   r   rQ  r  rL   r   r   )r   rL   r   r  )r   rM   r   +=r  )r   r   r=  )rZ   r   rA  r_valsr`   s        rD   test_RzTestMultinomial.test_Rx  s     $$$1([([([([([	B B
  	M 	MAKOAq!44fQieLLLLL	M 	MrF   r   r   rM   c                 t   d}t          j        t          |          5  t          j                            d          }t          j        |dgdz  dd          }|                    |dgdz  d          }t          ||           d d d            n# 1 swxY w Y   t          j        t          |          5  t          j                            d          }t          j        |dgd	z  dd          }|                    |dgd	z  d          }t          ||           d d d            d S # 1 swxY w Y   d S )
Nz,Some rows of `p` do not sum to 1.0 within...rJ   r#  r  rM   rj   r   r   rg   )	rQ   warnsFutureWarningr=   r   r  r   r   r   )rZ   r   r[   rndmsc_rvsnp_rvss         rD   test_rvs_npzTestMultinomial.test_rvs_np  s    A\-w777 	) 	)9((--D _QqqsKKKF%%a$%::F(((		) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)
 \-w777 	) 	)9((--D _QqqsKKKF%%a$%::F(((		) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	)s%   A(BBB8A(D--D14D1c                    t          j        ddd          }t          |dd           t          j        ddd	          }t          |d
d           t          j        ddgddggddgddgggdd          }t          |ddgddggd           t          j        dt          j                  }t          j        |dd	          }t          |t          j        g t          j                             t          j        ddgdd	          }t          |dd           t          j        g ddg d          }t          |dd           t          j        g ddg d          }|dk    sJ t          j        g ddg d          }|dk    sJ d S )N)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  s   a..qt,,,,q(331====1Q%1"a1a&0A BA (* *I 6A?dKKKKHU"*---1h//UBHRrz:::;;;1q(33qt,,,,			1.?.?.?@@~D9999			1.?.?.?@@zzzz			1.?.?.?@@zzzzzzrF   c                    t          j        ddgdddgddgg          }t          |dd	gd
           t          j        ddgddgddg          }t          |ddgd
           t          j        ddgddgggdddg          }t          |ddggd
           t          j        ddgdgdgggddg          }t          |dgdgggd
           t          j        ddgddggdggggddg          }t          |ddggggd
           d S )Nr   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  sM   ARHr2h+?@@d|$7777AAR99ayt44441a&1a&!1 2ABx@@q	{6666A1#sr2h??$!T::::!Q!AQC5'RHEE4)T::::::rF   rg   c                     t          j        |d          }|dz  dz  | dz  dz  | dz  dz  g| dz  dz  |dz  dz  | dz  dz  g| dz  dz  | dz  dz  |dz  dz  gg}t          ||d           d S )	N)r   r   r	  r   r  r   r	  rt  ra  r  r   r   r   )rZ   r   cov1r  s       rD   test_covzTestMultinomial.test_cov  s    q,//2b1"R%(QBrE"H-Br1R47QBrE"H-BrA2b58QrT"W-/ 	d......rF   c                 t   t          j        dddgddgg          }ddgddggddgddggg}t          ||d	
           t          j        ddgddg          }ddgddggddgddggg}t          ||d	
           t          j        ddgddgddgg          }ddgddggddgddggg}t          ||d	
           d S )Nrg   r   r  r   r  g?gܿgra  r  ri   g
ףp=
?g
ףp=
׿r   rt  r  r  gzG?gzGr  g333333r[  rZ   r\  r  cov3cov4cov5cov6s          rD   test_cov_broadcastingz%TestMultinomial.test_cov_broadcasting  s   qB8b"X"677tdC[)RIRy+ABd....1vBx00ttSk*c4[4+,FGd....1vR2r(';<<8$x&9:8$x&9:<d......rF   rL   c                 ~    t          j        |ddg          }t          |t          j        |d          d           d S Nr   r  ra  r  r   r   r   r"   )rZ   r   ent0s      rD   r  zTestMultinomial.test_entropy  sA     "1r2h//emAr22>>>>>>rF   c           	      `   t          j        ddgddg          }t          |t          j        dd          t          j        dd          gd           t          j        ddgd	d
gddgg          }t          |t          j        dd	          t          j        dd          gd           t          j        dgdggd	d
gddgg          }t          |t          j        dd	          t          j        dd          gt          j        dd	          t          j        dd          ggd           d S )NrL   rM   r   r  ra  r  rj   r:  r   rt  r  r  rg  )rZ   rh  ent1ent2s       rD   test_entropy_broadcastingz)TestMultinomial.test_entropy_broadcasting  sL   "Aq6B844u}Q33U]1b5I5IJ!	# 	# 	# 	# "Aq6RHr2h+?@@u}Q33U]1b5I5IJ!	# 	# 	# 	# "QC!:R2r(/CDD-2..a0D0DE-2..a0D0DEG!	# 	# 	# 	# 	# 	#rF   c                 h    t          j        |ddg          }t          ||dz  |dz  gd           d S rf  r   r   r   )rZ   r   mean1s      rD   	test_meanzTestMultinomial.test_mean  s?     RH--"ad|$777777rF   c                 h    t          j        ddgddg          }t          |ddgddggd	
           d S )Nrg   rh   r   r  r   r  g433333?g433333@ra  r  rn  )rZ   ro  s     rD   test_mean_broadcastingz&TestMultinomial.test_mean_broadcasting  sD     !Q"b22ttTl;$GGGGGGrF   c                    t           j                            d           d}d}g dg dg dg dg dg}t          j        |t           j        	          }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                                t          j	        ||                     d S )
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 ZZ


:::iii			BJq
+++5))		a((+/!Q*F*FGGG	((++[-?1e-L-LMMM	))++[-@E-J-JKKKKKrF   c                 *   d}t           j                            d          }|                    |          }d|d<   |t          j        |          z  }t          j        |          }t          j        |||          }t          j        |          sJ d S )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  s    
 i##$788JJqMM"	RVAYYGAJJ#Aq!,,{6"""""""rF   r  c                     d}t          j        g d|          }t          j        g d||          }t          j        g d||          }t           j                            ||d           d S )	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  s{     J00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 2 2	/ 	/ 	/M M M" [S1a&))) ) *))  6; ; ;  [S1a&))/ / *)// / / [S1a&))? ? *)?# # # [S1a&))8 8 *)8H H H
L 
L 
L# # # [Wrz2:&>??; ; @?; ; ;rF   r/  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestInvwishartc           	         d}t          j        t          j        |          dz             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }g }t          d          D ]}t          j        t          j        |          |dz   dz  z             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }|                    |           t          j        |          j        }ddt          j	        ddd          fd||fg}|D ]\  }}}t          ||          }t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     t          |                    |          t          j        |||                     d S r  )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()),.Ic3q5k!m,D,DbocR((()uw&& q 	 	A	#!ax/00A,.Ic3q5k!m,D,DAbocR((()qsAAHHQKKKKHQKKM BKR++,N


 ) 	E 	ENRB&&B:>"e#<#<===JOB$>$>???JOB$>$>???BFF1IIz~aU'C'CDDDD	E 	ErF   c                 <   t           j                            d          }d}d}t          j        |          }t          j        dddt
                    }t          j        dd	d	
          }|D ],}t          ||          }t          |dz  d          }	t          |
                                |	
                                           t          |                                |	                                           t          |                    |          |	                    |                     |                    ||          }
|dz  ddf}d}t          d|||
           t          |                                |	                                           .d S )Nr!  r"  r   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>  sh   
 i##F++s9QAU333KB2&&& 	8 	8BB&&B"Q$d+++B BFFHHbffhh///BGGIIrwwyy111 BFF1IIrvvayy111 &&bs&33CqD!T?DE":tUC@@@ BJJLL"**,,7777%	8 	8rF   c                    d}d}t          j        |          }d|d<   d|d<   t          ||          }t           j                            d          }t          j        |||          }t           j                            d          }|                    |          }t           j                            d          }|                    d          }t           j        |                    |d	z
            |                    |d
z
            |                    |          f         dz  }	t          j	        |	          }
||
t          j
        |d          <   t           j                            |          }t           j                            |
j        |j                  j        }t          j        ||j                  }t!          ||           t!          ||           d S )NrM   r  r	  rP  r  iHG	 r   r   rL   r   rk   r  )r=   rU   r   r   r  r   r   r  r  rt   r  r   r   solver   rr  r   )rZ   r   r  r  r  r   iw_rvsfrozen_iw_rvsr  r  rz   r  Lmanual_iw_rvss                 rD   test_invwishart_2D_rvsz%TestInvwishart.test_invwishart_2D_rvs_  s    sc
c
 E"" i##F++E<<<i##F++C00 i##F++jjaj((EMM"Q$MM"Q$MM"
 		 GI(3"/#
$
$
$% Iu%%IOOAC%%'q!# 	...}55555rF   c                 v   d}d}dD ]0}t          j        t          j        |          dz             }t          j        ||dz
  z  dz            |t          j        |d          <   t          j        |j        |          }t          ||          }|                                }|                                }||z  dz  }|	                    |d	
          }	|	                    d          }
||dz   z  dz  }d|z  }t          j        d|dz  z
            }t          j        |
|z
  |z  d|          sJ 2dS )z1Test that sample mean consistent with known mean.r   N  r   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  sR     	 	CGBIcNNQ.//E02	#q/A:M0N0NE"/#,,,-F57E**Eb%((D		IxxzzH!K/#5Ik==AAI#']A%FvIxIM 122H;Y&)3      !	 	rF   c                 z   t          j        g dg dg dg dg          }t          j        g dg dg dg dg          }d	}t          j        |||          }|j        d
         }t           j                            |          \  }}t           j                            |          \  }}t           j                            ||          }	|dz  |z  ||z  dz  t          j        d          z  z
  t          |dz  |          z
  ||z   dz   dz  |z  z
  d|	
                                z  z
  }
t          ||
           dS )zRegression test for gh-8844.)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  sa   Hnnn&&&$nn&&&( ) ) h$$$& ' '  B,,GAJy((++W**3//YIOOAs##T9$!tAvrvayy()"2a4++, Avz1nW,- !''))m	$
 	h'''''rF   N)r   r   r   r  r  r  r  r  r   rF   rD   r  r    se        E E E@8 8 8B,6 ,6 ,6\  6( ( ( ( (rF   r  c                   8    e Zd Zd Zd Zd Zd Zd Zd Zd Z	dS )	TestSpecialOrthoGroupc                     t          j        dt          j                            d                    }t          j        g dg dg dg          }t          ||           d S )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  ss    #ABI4I4I#4N4NOOO8CCCBBBCCCE F F 	"!X.....rF   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        d           d S Nr  rk   rZ  )rT  rR   r   r   rZ   s    rD   test_invalid_dimz&TestSpecialOrthoGroup.test_invalid_dim  s`    j"5"94@@@j"5"96BBBj"5"92>>>j"5"93?????rF   c                     d}t          |          }|                    d          }t          j        |d          }t          ||           d S )Nrj   rX  r   )r   r   r   )rZ   r   r  r  r  s        rD   test_frozen_matrixz(TestSpecialOrthoGroup.test_frozen_matrix  sR    $S))zztz,,"&s>>>T4     rF   c                    d t          dd          D             }d |D             }t          |dgdz  d           |D ]G}t          t          j        ||j                  t          j        |j        d	                              Hd S )
Nc                 Z    g | ](}t          d           D ]}t          j        |          )S rT  )rq  r   r   .0r   r  s      rD   
<listcomp>z<TestSpecialOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  sN     ! ! !Qxx! ! "%c** ! ! ! !rF   rL   r+  c                 L    g | ]!}t           j                            |          "S r   r=   r   r  r  r`   s     rD   r  z<TestSpecialOrthoGroup.test_det_and_ortho.<locals>.<listcomp>  s&    ---Q	a  ---rF   r      vIh%<=r  r   )rq  r   r   r=   rr  r   rU   r?   )rZ   r  detsr`   s       rD   test_det_and_orthoz(TestSpecialOrthoGroup.test_det_and_ortho  s    ! !q! ! !
 .-"---rd2gE2222  	: 	:A%bfQnn&(fQWQZ&8&8: : : :	: 	:rF   c                    d}d}d}t          j        ||t          j                            d                    dfdD             fdD             }fd	|D             }t          |gt          |          z  |           d S )
Nrg   r  皙?i  r   r  rQ  )r   ri   r  c                 X    i | ]$\  ft          fd D                       %S )c                 ,    g | ]}|                  S r   r   r  r`   ecers     rD   r  z>TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>  !    !8!8!8!B%)!8!8!8rF   sortedr  r  r  r  s    @@rD   
<dictcomp>z3TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>  E    LLLfb"R&!8!8!8!8!8R!8!8!899LLLrF   c                 .    g | ]}D ]}||k    ||fS r   r   r  e0e1elss      rD   r  z3TestSpecialOrthoGroup.test_haar.<locals>.<listcomp>  .    AAAb#AABb"brF   c                 Z    g | ]'\  }}t          |         |                   d          (S rO  r    r  p0p1projs      rD   r  z3TestSpecialOrthoGroup.test_haar.<locals>.<listcomp>  4    JJJRHT"XtBx003JJJrF   )r   r   r=   r   r   r   r   )	rZ   r   rb  ks_probpairsks_testsr  r  r  s	         @@@rD   	test_haarzTestSpecialOrthoGroup.test_haar  s      $gBI,A,A#,F,F
 
 
 +LLLLLLLAAAACAAAJJJJEJJJ7)CJJ.99999rF   c                 R    t          t          j        dd          dd           d S )Nr   r  r   r  r  )r   r   r   r  s    rD   test_one_by_onez%TestSpecialOrthoGroup.test_one_by_one	  s0     	+/===quMMMMMMrF   c                 X    t          t          j        dd          j        d           d S Nr   ri   r   )ri   r   r   r   r   r   r?   r  s    rD   test_zero_by_zeroz'TestSpecialOrthoGroup.test_zero_by_zero	  ,    (,QQ777=yIIIIIrF   N)
r   r   r   r  r  r  r  r  r  r  r   rF   rD   r  r    s        / / /@ @ @! ! !: : :: : :8N N N
J J J J JrF   r  c                       e Zd Zd Zd Zd Zd Zej        	                    dg d          d             Z
d Zd	 Zd
 Zej        j        d             ZdS )TestOrthoGroupc                 t   d}t           j                            |          }t          j        d|          }t          j        d|          }t          t           j                            |          d           t          j        g dg dg dg          }t          ||           t          ||           d S )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    i##D))OAC000_QT222BIMM!,,b1118<<<======? @ @ 	"!X...!"h/////rF   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        d           d S r  )rT  rR   r   r   r  s    rD   r  zTestOrthoGroup.test_invalid_dim	  sX    j+/4888j+/6:::j+/2666j+/377777rF   c                    d}t          |          }t          |d          }|                    d          }t          j        |d          }|                    d          }t          ||           t          ||           d S )Nrj   rX  r   r   r   r   )r   r   r   rZ   r   r  frozen_seedr  r  rvs3s          rD   r  z!TestOrthoGroup.test_frozen_matrix	  s    S!!!#D111zztz,,s666A&&T4   T4     rF   c           	         d t          dd          D             }t          j        d |D                       }t          t          j        |          t          j        |j                  d           |D ]L}|D ]G}t          t          j        ||j	                  t          j
        |j        d                              HMd S )Nc                 F    g | ]fd t          d          D             S )c                 8    g | ]}t          j                  S r   )r   r   )r  r  r   s     rD   r  z@TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>.<listcomp>,	  s3     # # # s## # # #rF   r  )rq  )r  r   s    @rD   r  z5TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>,	  sP     & & &# # # #b		# # # & & &rF   rL   r+  c                 &    g | ]}d  |D             S )c                 L    g | ]!}t           j                            |          "S r   r  r  s     rD   r  z@TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>.<listcomp>1	  s&    777q")--**777rF   r   )r  xxs     rD   r  z5TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>1	  s'    EEEB77B777EEErF   r  r  r   )rq  r=   r   r   fabsrT   r?   r   rr  r   rU   )rZ   r  r  r  r`   s        rD   r  z!TestOrthoGroup.test_det_and_ortho+	  s    & &q& & &
 xEE"EEEFFrwtz':':GGGG  	> 	>B > >)"&AC..*,&*<*<> > > >>	> 	>rF   r   )rL   rg   r  r  c                    t           j                            d          }t          |          }|                    d|          }t
          j                            |          }t          j        |dk              }t          |          }t          j        ||          }|                    d          \  }	}
|	dcxk     r|
k     sn J d S )	Nl   <`Lr )r   r  r   r   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     i##$788s###hhDsh33|$$F4!8IIoa##%%t%<<	TS4rF   c                   	 d}d}d}t           j                            d          }t          j        |||          	d	fdD             fdD             }fd	|D             }t          |gt          |          z  |           d S )
Nrg   r  r  i  r   r  c                 X    i | ]$\  ft          fd D                       %S )c                 ,    g | ]}|                  S r   r   r  s     rD   r  z7TestOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>]	  r  rF   r  r  s    @@rD   r  z,TestOrthoGroup.test_haar.<locals>.<dictcomp>]	  r  rF   c                 .    g | ]}D ]}||k    ||fS r   r   r  s      rD   r  z,TestOrthoGroup.test_haar.<locals>.<listcomp>^	  r  rF   c                 Z    g | ]'\  }}t          |         |                   d          (S rO  r  r  s      rD   r  z,TestOrthoGroup.test_haar.<locals>.<listcomp>_	  r  rF   )r=   r   r  r   r   r   r   )
rZ   r   rb  r  r   r  r  r  r  r  s
          @@@rD   r  zTestOrthoGroup.test_haarG	  s     i##C((_SwSAAA +LLLLLLLAAAACAAAJJJJEJJJ7)CJJ.99999rF   c                    d}t          j        |dt          j                            d                    }t          t          j        |          dd           t          j        |dk              }t          |          }t          j
        ||          }|                    d	          \  }}|d
cxk     r|k     sn J d S )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:TUUUr

AE2222F26NNGGoa##%%t%<<	TS4rF   c                 X    t          t          j        dd          j        d           d S r  r  r  s    rD   r  z TestOrthoGroup.test_zero_by_zerom	  r  rF   c                 B   t           j                            d          d	fd	}t          dd          D ]fd
fd	} ||          } |t          j        j        j                  }t          j                            ||          \  }}t          d|           gd S )Nr  c                     t           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>    y}}SZZc3ZZ%@%@AAHAr16!Q<<rF   rL   rh   r  r  c                      t          j         fdt          |          D                       }|t           j                            | ||j                  z  }|S )Nc           	      p    g | ]2}t          j                                z
  dz            3S ))r   r   rL   )r=   r   )r  r   r   r   r   s     rD   r  z\TestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statistics.<locals>.<listcomp>{	  si     " " "  FCCCc:::CCc:::;=>? @ @" " "rF   r   )r=   r   rq  r   r   r?   )r   r  epsr/   r   r   s   `   rD   generate_test_statisticszHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statisticsz	  sy     " " " " " " #1XX" " "   **C45;*GGGrF   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     i##C((	  	  	  	  	  	  A;; 	& 	&C       0/==H--ek.E.IJJFK((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  	  s        0 0 08 8 8
! 
! 
!> > > [UNNN33
  
  43
 : : :6	  	  	 J J J [& & & & &rF   r  c                   ,    e Zd Zd Zd Zd Zd Zd ZdS )TestRandomCorrelationc                     t           j                            d          }d}t          j        ||          }t          j        |d          }t          j        g dg dg dg dg          }t          ||           t          ||           d S )Nr  r	  r  r  rY  r   )r   ѓ2ǿA?Ϳ)r  r   4($?R}%?)r  r  r   qTnƿ)r  r  r  r   )r=   r   r  r   r   r   r   )rZ   r   r   r`   r   r  s         rD   r  z*TestRandomCorrelation.test_reproducibility	  s    i##C((!"4c:::#Ds;;;8AAA@@@@@@AAAC D D 	"!X...!"h/////rF   c                    t          t          t          j        d            t          t          t          j        d           t          t          t          j        d           t          t          t          j        dg           t          t          t          j        ddgddgg           t          t          t          j        ddg           t          t          t          j        g d           d S )	NtestrZ  r   rL   rM   ri   g      )r   rL   r   )rT  rR   r   r   r  s    rD   test_invalid_eigsz'TestRandomCorrelation.test_invalid_eigs	  s    j"4"8$???j"4"8&AAAj"4"8#>>>j"4"83%@@@j"4"8Aa5!A-HHHj"4"83*EEEj"4"8***EEEEErF   c                 
   d}t          |          }t          |d          }t          j        |d          }|                    d          }|                                }t          ||           t          ||           d S )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88!%d===zzsz++  T4   T4     rF   c                   
 d 
t           j                            d          
fdt          dd          D             }|                    g d           d |D             }fd|D             }d	 |D             }d
 |D             }t          ||dd           d |D             }t          ||          D ]\  }}t          ||d           |D ]}	t          |	|	j        d           d S )Nc                 ,    | |z  t          |          z  S r<   )r   )r  r  s     rD   r   z3TestRandomCorrelation.test_definition.<locals>.norm	  s    Q3s1vv:rF   r#  c                 P    g | ]"} |                     |                     #S )r   )r   )r  r  r   r   s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s3    BBBQ++,,BBBrF   rL   rh   )ri   r   r   r   c                 4    g | ]}d gt          |          z  S )r   )r   r  r  s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s$    ***SVV***rF   c                 <    g | ]}t          j        |           S )r   )r   r   )r  r  r   s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s*    HHHa $QS999HHHrF   c                 p    g | ]3}t          j        t           j                            |                    4S r   )r=   r  r   r  r  s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s0    666a	a(())666rF   c                 6    g | ]}t          j        |          S r   )r=   r  r"  s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s     ///Qbgajj///rF   r  r  c                 6    g | ]}t          j        |          S r   )r=   rt   r  s     rD   r  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>	  s     ((((((rF   r  )r=   r   r  rq  r  r   zipr   )rZ   r   rT   r  r  
dets_knowndiagsr  r  r`   r   r   s             @@rD   test_definitionz%TestRandomCorrelation.test_definition	  sN   	 	 	 i##C((BBBBBeAqkkBBBIII**T***HHHH4HHH 762666//$///
ju5AAAA )(R(((t$$ 	. 	.DAqAqu-----  	0 	0AAqs/////	0 	0rF   c           	         t          j        ddgddggt                    }t          j        |          }t          |t          j        ddgddgg                     t          j        d          5  t          j        ddgddgg          }t          j        ddgdt          j        dd          ggt                    }t          j        |                                          }t          ||j	        
                    |          
                    |                     t          j        d	dgdd
ggt                    }t          j        |                                          }t          ||j	        
                    |          
                    |                     d d d            n# 1 swxY w Y   t          j        ddgddggt                    }t          j        |                                          }t          |d         d           t          j        ddgddggt                    }t          j        |                                          }t          |d         d           d S )Nr   r   r   r  ignore)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	  sU    HsAhA'u555'**28aVaX$677888
 [h''' 		3 		31a&2q'*++AE1:2<1+=+='>?uMMMB"+BGGII66AAqswwr{{q11222C<%6eDDDB"+BGGII66AAqswwr{{q11222		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 		3 X1v1v&e444'		22#""" X!}q!f-U;;;'		22#"""""s   3D2F11F58F5N)r   r   r   r  r  r  r*  r4  r   rF   rD   r  r  	  sc        
0 
0 
0F F F
! 
! 
!"0 "0 "0H# # # # #rF   r  c                   >   e Zd Zej                            dddg          ej                            dg d          d                         Zej                            dg d          d             Zd	 Zej                            dg d
          d             Z	dS )TestUniformDirectionr   r   rM   r   Nr   rg   )rg   ri   c                    t           j                            d          }t          ||          }|                    |          }t          j        |          t          j        |          }}|                    |||          j        }|j        |k    sJ t           j	        
                    |d          }	t          |	d           d S )N   Sid)_i4 r   r   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     i##$788!23S!A!A!A(,,T22HSMM26#;;c00s0FFL}....	wR00r"""""rF   )Nr   r  rZ  c                     d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )NzMDimension of vector must be specified, and must be an integer greater than 0.rJ   )rQ   r
   rR   r(   r   )rZ   r   r[   s      rD   r  z%TestUniformDirection.test_invalid_dim
  s    <]:W555 	' 	'!#&&&	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	' 	's   A  AAc                 
   d}t          |          }t          |d          }|                    d          }t          j        |d          }|                                }t          ||           t          ||           d S )Nrg   r  r   r   )r(   r   r   r  s          rD   test_frozen_distributionz-TestUniformDirection.test_frozen_distribution
  s    "3'''#666zzsz++ $Ss;;;  T4   T4     rF   )rL   rg   r:  c                 (   t           j                            d          }t          ||          }|                    d          \  }}|||z  |z  z  }|t           j                            |          z  }t          ||z  dd           |                    d          }||z  }||z  }t          j        ||          }	|	t           j	        z  }	|	dt           j	        z  z  }	t                      }
t          |	|
j                  }|j        d	k    sJ d S )
Nl   @9Y sr   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   i##$788*3S999###++B
b2gl
binnR   R//// $$%$00r\r\B## 	"%!BE'yyv|'788#d******rF   N)
r   r   r   rQ   r   r   r  r  r?  rK  r   rF   rD   r6  r6  	  s        [UQF++[V%9%9%9::	# 	# ;: ,+	# [U$:$:$:;;' ' <;'
! 
! 
! [UIII..+ + /.+ + +rF   r6  c                   2    e Zd Zd Zd Zd Zd Zd Zd ZdS )TestUnitaryGroupc                    t           j                            d          }t          j        d|          }t          j        dd          }t          j        g dg dg dg          }t          ||           t          ||           d S )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-
  s    i##C((ac222qs3338IIIHHHKK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           d S r  )rT  rR   r   r   r  s    rD   r  z!TestUnitaryGroup.test_invalid_dim;
  s\    j-"3T:::j-"3V<<<j-"3R888j-"3S99999rF   c                    d}t          |          }t          |d          }|                    d          }t          j        |d          }|                    d          }t          ||           t          ||           d S )Nrj   r  r   r   r   r   )r   r   r   r  s          rD   r  z#TestUnitaryGroup.test_frozen_matrixA
  s    s###Cc222zzsz++ 3777A&&T4   T4     rF   c                     d t          dd          D             }|D ][}t          t          j        ||                                j                  t          j        |j        d                   d           \d S )Nc                 Z    g | ](}t          d           D ]}t          j        |          )S rT  )rq  r   r   r  s      rD   r  z3TestUnitaryGroup.test_unitarity.<locals>.<listcomp>N
  sN     ! ! !Qxx! ! $$ ! ! ! !rF   rL   r+  r   rG  r  )rq  r   r=   rr  conjr   rU   r?   )rZ   r  r`   s      rD   test_unitarityzTestUnitaryGroup.test_unitarityM
  s    ! !q! ! !
  	S 	SABF1affhhj1126!'!*3E3EERRRRR	S 	SrF   c           	         dD ]}d}t          j        ||t          j                            d                    }t          j        d |D                       }t          j        |j        |j                  }t          |
                                t          t          j         dt          j        z            j                  }t          |j        dk               d S )Nr  r  r  r   c                 L    g | ]!}t           j                            |          "S r   )r   r   eigvalsr  s     rD   r  z.TestUnitaryGroup.test_haar.<locals>.<listcomp>d
  s(    BBB!el22155BBBrF   rL   r  )r   r   r=   r   r   r  rA  imagrE  r!   ravelr   r  r   r	   rB  )rZ   r   rb  r  r   r`   r@   s          rD   r  zTestUnitaryGroup.test_haarV
  s    
  	' 	'CG"'	0E0Ec0J0J  B 9BBrBBBCCD
49di00AGRUFAbeG$<$<$@AACCJ%&&&&	' 	'rF   c                 X    t          t          j        dd          j        d           d S r  )r   r   r   r?   r  s    rD   r  z"TestUnitaryGroup.test_zero_by_zeroi
  s+    ]&qq1117CCCCCrF   N)	r   r   r   r  r  r  rT  r  r  r   rF   rD   rM  rM  ,
  sv        0 0 0: : :
! 
! 
!S S S' ' '&D D D D DrF   rM  c                      e Zd Zddgddgddgddgddgddgddgddgddgddgg
ddgddgddggdg dfg dg d	g d
g dg dgg dg dg dg dgdg dfgZej                            de          d             Zej                            de          d             Zd Z	d Z
e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                            d e          d!             Zd"ddd"gdggdfd"gdgdd"gdggdf ej        d"g           ej        dg          dd"gdggdfgZej                            d e          d#             Zd$ Zd% Zd& Zej                            d'd(d)g          ej                            d*g d+          ej                            d,d-d.ej        g          d/                                     Zd0 Zej                            d*g d1          d2             Zej                            d*g d3          d4             ZdTd6Zd7 Zej                            d*g d8          ej                            d9g d:          ej                            d;d5d<g          d=                                     Z ej        j!        d>             Z"d? Z#d@ Z$dA Z%ej                            d*dB          dC             Z&dD Z'ej                            d,g dE          dF             Z(ej                            dGdH ej)        dd          dIdJfdK ej        dLdgddHgg          dMdNfg          dO             Z*ej                            dPg dQ          dR             Z+dS Z,dS )UTestMultivariateTr   rL   ri   rM   rg   r   )
|	ߌ?v
2R?r]  g0$H?r^  r^  gO`?gՒXO?g	ߌ,?g8N8?)gHP?gQI?go_?)g9m4?g=U?gˡE?)g$C?ghs?gǺ?)g!uq?g%C?gS㥛?)gOec?gz,C?g	h"l?)rk   r   2   )r   r	  r  )r	  r   rJ  )r  rJ  r   r:  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 v    t          |||d          }|                    |          }t          ||           d S Nr   r   )r$   r   r   )rZ   r`   r  r?   r  ansr   vals           rD   test_pdf_correctnessz&TestMultivariateT.test_pdf_correctness
  s=    c5"1555hhqkk!#s+++++rF   c                     t          |||d          }|                    |          }|                    |          }t          t	          j        |          |           d S ra  )r$   r   r   r   r=   r_  )	rZ   r`   r  r?   r  rb  r   r?  r@  s	            rD   test_logpdf_correctz%TestMultivariateT.test_logpdf_correct
  sT    c5"1555xx{{{{1~~!"&,,55555rF   c                     g d}t          j        |d          }t          j        |          }t          ||           d S )N)
rP  rj   ri   r   r$  rP  r   r$  rk   rM   r   r  )r$   r   r%   r   )rZ   r`   rc  rb  s       rD   test_mvt_with_df_one_is_cauchyz0TestMultivariateT.test_mvt_with_df_one_is_cauchy
  sE    --- q)))jmm!#s+++++rF   c                 J   d}t          dddd          }|                    d          }t          |          \  }}||k    sJ t          ddgd	d
gd
d	ggdd          }|                    d          }t          |          \  }}||k                                    sJ d S )Nr   r   r   順 r  r   r   rn   rM   r  rk   *   )r$   r   r&   r  )rZ   	P_VAL_MINr   rb  r   rA  s         rD   &test_mvt_with_high_df_is_approx_normalz8TestMultivariateT.test_mvt_with_high_df_is_approx_normal
  s    
 	avA666((('''""1Ir1gR2r(';#%' ' '((('''""1Y##%%&&&&&rF   z'scipy.stats.multivariate_normal._logpdfc                 "   t          ddt          j        d          }t          |t                    sJ t          j        dt          j                   |j        dk    sJ t          j        dt          j                   |j        dk    sJ d S )Nr   r   rj   rl  rh  rL   )r$   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
  s     arvA666$ :;;;;;1((((!####aBF++++!######rF   c                    d}t          j        |          }t          j        |          }d}t          j        |          }t          |||                              |          }t          j        |          sJ t          |||                              |          }t          j        |          sJ d}t           j                            ||f          }t          |||                              |          }|j        |fk    sJ t          |||                              |          }|j        |fk    sJ t          t          j        d          t          j        d          d          	                                }t          j        |          sJ d}t          t          j        d          t          j        d          d          	                    |          }|j        |fk    sJ d S )Nri         @rj   r   r   )
r=   r   rU   r$   r   isscalarr   r   r?   r   )	rZ   r   r  r?   r  r`   r@   	n_samplesr   s	            rD   test_shape_correctnessz(TestMultivariateT.test_shape_correctness
  s    hsmmsHSMMS%,,0033{3S%,,33A66{3 	Ii-..S%,,0033	i\))))S%,,33A66	i\)))) RXa[["&))Q77;;=={3 RXa[["&))Q77;;;FF	dW$$$$$$rF   c                     t                      }t          |j        dg           t          |j        dgg           |j        dk    sJ d S )Nr   r   r$   r   r  r?   r  )rZ   r   s     rD   test_default_argumentsz(TestMultivariateT.test_default_arguments  sJ    TXs###TZ1#'''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 d S )Nr  r?   r  rz  rZ   r  r?   r  loc_ans	shape_ansdf_ansr   s           rD   test_default_argsz#TestMultivariateT.test_default_args  sU     #Ur:::TXw'''TZ+++6!!!!!!rF   rk   c                     t          |||          }t          |j        |           t          |j        |           t          |j        |           d S r<   rz  r~  s           rD   &test_scalar_list_and_ndarray_argumentsz8TestMultivariateT.test_scalar_list_and_ndarray_arguments%  sQ     c5"--TXw'''TZ+++TWf%%%%%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          |||           d S )	Nr   )r  rL   rM   )r  r?   rk   r}  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$	4 	4E222	4 	4 	4
 hqkkq		j$	; 	;Eb999	; 	; 	; j$	; 	;Eb999	; 	; 	; 	; 	;rF   c                 \   t           j                            d          }|                    d          }t          j        d          }t          ||dd          }t          ||dd          }|                    d          }|                    d          }t          ||           d S )Nri   rM   r   rL   rl  r  )r=   r   r  r   rU   r$   r   r   )rZ   r   r  r?   r   dist2samples1samples2s           rD   r  z&TestMultivariateT.test_reproducibilityG  s    i##A&&kkqk!!q		sEaa888sEaa88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 | d S )Nr   r   F)r  r?   r  r_   )r  rT  r=   r   r  r$   )rZ   rB   s     rD   test_allow_singularz%TestMultivariateT.test_allow_singularQ  sK    1qeQqE]qOOObi+^DDtDDDDDrF   r   )r  rM   )rg   rh   ri   rM   r   )rL   rM   ri   rg   r  r   r  c                     t          t          j        |          t          j        |          |          }|                    |          }|j        ||fz   k    sJ d S r  )r$   r=   r   rU   r   r?   )rZ   r   r   r  r   r   s         rD   test_rvszTestMultivariateT.test_rvsV  sW     bhsmmRVC[["==hhDh!!yDC7N******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             d S )
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^  s    x{{fQiiYY			999iii8YY			999iii8...11!%asBAFFFSVN233333rF   )r   rL   rg   c                 0    |                      |           d S r<   cdf_against_mvn_testrZ   r   s     rD   $test_cdf_against_multivariate_normalz6TestMultivariateT.test_cdf_against_multivariate_normalj  s     	!!#&&&&&rF   )rM   rh   rP  c                 2    |                      dd           d S )NrM   Tr  r  s     rD   -test_cdf_against_multivariate_normal_singularz?TestMultivariateT.test_cdf_against_multivariate_normal_singularo  s      	!!!T*****rF   Fc           	      d   t           j                            d          }d}d|                    dd|          z  }t	          ||||          }d|                    dd|          z  t          j        |                    |                    z  }d|                    dd||f          z   |z   }d|                    dd||f          z  |z   }	t          j        	                    |	||d	|d
|          }
t          j
        	                    |	||d
|          }t          |
|d           d S )N   ]J>?a rM   r  rn   r   r   rk   rL   r:  T)r  r
  r_   r   )r_   r
  Mb@?r  )r=   r   r   r   r   signr   r/   r$   r   r   r   )rZ   r   r   r   r   r	  r   r   r  r  r@   rA   s               rD   r  z&TestMultivariateT.cdf_against_mvn_testt  sB   i##O44B,,, ah773;;r13;///"'#**#*:N:N2O2OOR!S2222T9BC111D8"&&q$16: ' N N'++AtS89 , ; ;St,,,,,,rF   c                 R   t           j                            d          }d}d}|                    dt          j        |                    }d}t
          j                            ||||t           j         |          }t
          j	                            |||t          j        |                    }t
          j
                            ||t          j        |                    }t          ||d	           t          j        t          j        ||z
            d
k              sJ d S )Nr  rL   r   r  )r   r  rM   )r
  r   r  r  r  )r=   r   r   r   r  r/   r$   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    i##O44JJBbgcllJ33"&&q$RbfW47 ' 9 9gkk!Rrws||44JNN1dBGCLL99	St,,,,vbfS9_--45555555rF   )rL   rM   rg   r  r   )   no l   m, l   sO l   U iOfYl   O_ r   Tc           	         |r|dk    rt          j        d           t          j                            |          }d|                    dd|          z  }t          ||||          }|                    |          }|                    |           }|                    |          }	|                                dz  }
t          j        	                    |	|||
|d	          }t          j
        d
          5  t          d|
|t          j        |z  |	|z
  |          d         }d d d            n# 1 swxY w Y   t          ||dd           t          j        	                    |	|||
||d          }t          j
        d
          5  t          d|
|||z
  |	|z
  |          d         }d d d            n# 1 swxY w Y   t          ||dd           d S )Nr  z4Agreement with qsimvtv is not great in singular caser  rn   rL   r   rg   T)r   r_   r,  )invalidr  r   g-C6*?r  r  r  )r
  r   r_   r  )rQ   r   r=   r   r   r   r   r/   r$   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  sz   
  	P
**KNOOOi##D))B,,, ah77zz#ZZ__JJsOOZZ\\A "&&q$Rc6: ' < <[*** 	G 	G5"c26!8QXsCCAFC	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	GSt$7777 "&&q$RQ47 ' N N[*** 	G 	G5"c1t8QXsCCAFC	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	G 	GSt$777777s$   :+D11D58D5
!F77F;>F;c           
        	
 d}t           j                            d          }d|                    dd|          z  }t	          |||d          	|                    |          |                    |           }|                    |          }|                                d	z  
t
          j                            |	
||
          }	
fd}t          |||t
          j	        
                    ||                    }t          ||j        d           	
fd}t          ||d         |d         |d         |d         |d         |d                   }t          ||d         d           d S )NrM   l   	!y r  rk   r   r   T)r   rg   )r   r
  c                 R    t           j                            | j                  S r<   )r/   r$   r   r   )r`   r   r  r   s    rD   	integrandzITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand  s"    '++ACsB???rF   )r  r   )qrngr  r  c                  Z    t           j                            | d d d                   S )Nrk   )r/   r$   r   )zyxr   r  r   s    rD   r  zITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand  s*    '++C"ItS"EEErF   r   rL   )r=   r   r   r   r   r/   r$   r   r4   qmcHaltonr   integralr6   )rZ   r   r   r	  r  r  r@   r  rA   r   r  r   s            @@@rD   $test_cdf_against_generic_integratorsz6TestMultivariateT.test_cdf_against_generic_integrators  s    i##N33#++b!#+... at<<<zz#ZZ__JJsOOZZ\\A"&&q$Rc34 ' 6 6	@ 	@ 	@ 	@ 	@ 	@ 	@ y!QUY-=-=#-=-N-NOOOS\5555	F 	F 	F 	F 	F 	F 	F i1qtQqT1Q41qtDDSV$//////rF   c                    t           j                            d          }t          j        g dg dg dg          }d}t	          j        ||          }|                    g d|          }d	}t          ||d
           d S )Nl   Ja )go!@S<?^Ss@)r  gRP=@jT0@)r  r  gk`-3@gWK?r?   r  rl   r   g1%?r  r  )r=   r   r   r   r/   r$   r   r   )rZ   r   r   r  r   r@   rA   s          rD   test_against_matlabz%TestMultivariateT.test_against_matlab  s     i##J//h?????????A B B  ##"555hhyyysh33St,,,,,,rF   c                 
   d}t           j                            |          }|                    d          }|                    d          |z   }t          j        d          }|                                }|||f}t           j                            |          }t           j                            |          }	t          j        |d|i}
t          |
                    |          t          j        |g|R d|	i           d S )Nl   2m rM   r   r   r   )	r=   r   r   r   rU   r/   r$   r   r   )rZ   r   r   r  r`   r?   r  rB   
rng_frozenrng_unfrozenr   s              rD   r  zTestMultivariateT.test_frozen  s    i##D))kkqk!!KKQK#%q		ZZ\\UBY**400
y,,T22#T;
;;TXXa[[#'LDLLL|LL	N 	N 	N 	N 	NrF   c                   	
 d}d}t           j                            d                              ||f          }||j        z                      |          
                    ||fz             }                                dz  	t          j                            |
	          }	
fd}t          j        |d|          }t          ||d	d
           d S )Nri   r  r  r   rg   r   c                 Z    t          dt          j         | z  | z
            d         S )Nr:  r   )r9   r=   r   )r`   r   r  r   r   s    rD   _cdf_1dz2TestMultivariateT.test_vectorized.<locals>._cdf_1d  s,    E2sRVGAIqvsCCAFFrF   rk   r  r  r  )	r=   r   r   r   r/   r$   r   apply_along_axisr   )rZ   r   r   rz   r`   r@   r  rA   r   r  r   r   s           @@@@rD   test_vectorizedz!TestMultivariateT.test_vectorized  s   i##O44JJS#JJ''!#gzz#JJqC6z""ZZ\\A"&&q$Rc&JJ	G 	G 	G 	G 	G 	G 	G 	G !'2q11St$777777rF   r  c                 *   t           j                            d          }t          j                            dgdg|dz
  z  z             }t          j        |                              dg|z  |          }d|dz   z  }t          ||d	           d S )
Nr  r   r	  )r'  )r?   r   r   r,  r  )
r=   r   r   r   r   toeplitzr/   r$   r   r   )rZ   r   r   rz   r@   rA   s         rD   test_against_analyticalz)TestMultivariateT.test_against_analytical  s    i##O44L!!QC3%37*;$;!<<"+++//c	/LL37mSt,,,,,,rF   c                     t          j        dd          }t           j        }t          j                            ||          }t          j                            d |          }||k    sJ d S )NrM   r  )r=   rU   r   r/   r$   r   r   )rZ   r   r  mvt_entropymvn_entropys        rD   test_entropy_inf_dfz%TestMultivariateT.test_entropy_inf_df  sb    fQllV*222DD/77cBBk))))))rF   )r   r  r  c                     t           j                            d|          }t           j                            |          }t	          ||d           d S )Nr   r  rh  r  r  )r/   r$   r   r  r   )rZ   r  r  	t_entropys       rD   test_entropy_1dz!TestMultivariateT.test_entropy_1d  sM    *222CCGOOrO**	YU;;;;;;rF   zdf, cov, ref, tolr  g}M@rD  r  r	  gNfh@ra  c                     t          j        d          }t          j        |||          }t	          |                                ||           d S )Nr  r  )r=   r   r/   r$   r   r   )rZ   r  r   rA   tolr  mvts          rD   %test_entropy_vs_numerical_integrationz7TestMultivariateT.test_entropy_vs_numerical_integration"  sH    
 huoo"3R00s555555rF   zdf, dim, ref, tol))r  r   gDdVW?rG  )r  r   gU?r  )r"  r   g/+?rD  )@xDr   Z_2?rG  )}Ô%ITr   r  rG  )r  r  gzg#.@rG  )r  r  gD:f,@r  )r  r  1>`,@rG  )r  r  r  rG  )r  r  g8d?b@rG  )r  r  g-YҺa@rD  )r  r  ZGra@rG  )r  r  r  rG  c                     t          j        t          j        |          |          }t	          |                                ||           d S )Nr  r  )r/   r$   r=   rU   r   r   )rZ   r  r   rA   r  r  s         rD   test_extreme_entropyz&TestMultivariateT.test_extreme_entropy+  sE    F "<<<s555555rF   c                    t          j        g dg dg dg dg dg          }||j        z  }d}t          j                            ||          }t          d |                                          }t          ||d	
           d}d}t          j                            ||          }t          j                            ||          }	t          ||	d
           d S )N)gQ?g
ףp=
?g\(\߿(\?gGz?)gGzg{GzgQ?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    X+++---,,,,,,,,,
   24i ,44324FF.t===EEGG'7eDDDD (00ss0CC	(00ss0CC		94888888rF   F)-r   r   r   	PDF_TESTSrQ   r   r   rd  rf  ri  ro  thread_unsafer:   rs  rx  r{  DEFAULT_ARGS_TESTSr  r=   r   ARGS_SHAPES_TESTSr  r  r  r  r   r  r!  r  r  r  r  r  rp  r  r  r  r  r  r  r  rU   r  r  r  r   rF   rD   r\  r\  m
  s1        FFFFFFFFFF	
 
A FF	

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

4 
4 
4 [UIII..' ' /.' [UIII..+ + /.+- - - -$6 6 6 [UMMM22[V &J &J &J K K[Z%778 8 87K K 3282 [0 0 04- - -"N N N8 8 8$ [UF++- - ,+-* * * [T<<<00< < 10<& [0!626!Q<<1CUK"HBHsAhB-@$A$A/789 96 6	9 96
 [	
 	
 	
 $6 6% $6(9 9 9 9 9rF   r\  c                   :   e Zd Zej                            dddgddgddfddgddgdej         fd	dgddgdej         fddgd
dgdej        fddgddggddgd
dggddgej        ej        gfd	dgd
dgdej        fddgddgdej        fddgddgdej        fddgddgdej        fddgddgdej         fg
          d             Z	d Z
d Zd Zej                            dg ddfg ddfddgdfdgdff          d             Zej                            ddgdgddfddgddgddfddgddggddgddgggddgddgddggdd gdd!ggf ej        g e"           ej        g e"          dg fddgddgddfg d#g d$d%d&fg          d'             Zej                            dddgddgdd(ggddd)gfdgdggdgdggddgd*d+gfdgdgggdgdggddgd*d+ggfdgdggdggggddgd*d+gggfg          d,             Zd- Zd. Zd/ Zd0 Zd1 Zd2 Zd3 Zd4 Zd5 Zd6 Zd7 Zd8S )9TestMultivariateHypergeomzx, m, n, expectedrM   ri   rg   r  rj   gr   r$  r   rL   rq   iir6  r+  rk   ic                 V    t          j        |||          }t          ||d           d S )Nư>r  )r   r3  r   rZ   r`   r&  r   r  valss         rD   r8  z%TestMultivariateHypergeom.test_logpmfq  s3    6 &,Q155hT222222rF   c                    t          j        ddgddgd          }t          j        dddd          }t          ||d	
           t          j        ddgddgd          }t          j        dddd          }t          ||d	
           d S )NrM   r   r  rg   ri   )r`   r&  r      )rx  r   r   r  ra  r  rj      )r   r=  r#   r   r>  s      rD   test_reduces_hypergeomz0TestMultivariateHypergeom.test_reduces_hypergeom  s     &)QFr1gCCC}qB!r222d....%)QFr2h"EEE}qB"333d......rF   c                     t          ddgd          }|                    dd          }t          |                    d          |                                d	
           d S )NrM   rg   ri   r&  r   r  r#  r   r   r  r  r   r   r   r   rZ   r   r   s      rD   r  z"TestMultivariateHypergeom.test_rvs  s\     $q!f222ff$Sf11RWWYYT::::::rF   c                     t          ddgddggddg          }|                    dd	          }t          |                    d
          |                                d           d S )NrM   rg   r  ri   rP  r  r  rL   r#  r   r   r  r  r  r  s      rD   test_rvs_broadcastingz/TestMultivariateHypergeom.test_rvs_broadcasting  sg    #1v2w&7Aq6BBBff)#f66RWWYYT::::::rF   zm, n)r   r   r  r   r   )r   r   r   r   r   c                     t          j        ||          }t          j        |          }|                                }|||dk    <   t          ||           d S )Nr   )r   r   r=   r>   r1  r   )rZ   r&  r   r@   res_exs        rD   test_rvs_gh16171z*TestMultivariateHypergeom.test_rvs_gh16171  sS    
 %(A..JqMMqAvS&!!!!!rF   g zl?r:  rP  gQ?gE|?g
y?r  rR  )rg   rh   rj   rh   gzp?c                 V    t          j        |||          }t          ||d           d S Nr  r  r   r=  r   r  s         rD   rW  z"TestMultivariateHypergeom.test_pmf  s3    " &)!Q22hT222222rF   r  g ?r   r   c                 V    t          j        |||          }t          ||d           d S r  r  r  s         rD   rY  z/TestMultivariateHypergeom.test_pmf_broadcasting  s3     &)!Q22hT222222rF   c                 p    t          j        g dd          }g dg dg dg}t          ||d           d S )	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  sZ    %)JJJ"===6666666668 	d......rF   c                 j   t          j        ddgddggddg          }dd	gd	dggd
dgdd
ggg}t          ||d           t          j        dgdggddg          }dggdggg}t          ||d           t          j        ddgddg          }dd	gd	dggddgddggg}t          ||d           d S )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JJ..0d....%)aS1#J1a&AAA"d....%)QFq"g>>>.'"Wf$568d......rF   c                     t          j        ddgd          }t          j        ddd          }t          ||d           d S )	Nr  rg   ri   r  r  r   r   r  ra  r  )r   r  r#   r   )rZ   var0var1s      rD   test_varz"TestMultivariateHypergeom.test_var  sL    %)RGq999}rQ"---d......rF   c                    t          j        ddgddg          }t          j        ddgd          }t          j        ddgd          }t          |d         |d           t          |d	         |d           t          j        ddgdd
ggddg          }ddgddgg}t          ||d           t          j        dgdggddg          }dgdgg}t          ||d           d S )Nr  rg   ri   r:  r  r   ra  r  r   r;  g̍3eY?gI{?r   )r   r  r   )rZ   r   r  var2var3var4var5var6s           rD   test_var_broadcastingz/TestMultivariateHypergeom.test_var_broadcasting  s   %)RG1v>>>%)RGq999%)RGq999QD1111QD1111%)b!Wr2h,?Aq6JJJI&8(<=d....%)aS2$KAr7CCCrd|d......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	           d S )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  s    &+r1g;;;qB///a%d3333&+r1g<<<j)u4000000rF   c                 v    t          j        ddgddggddg          }ddgd	d
gg}t          ||d           d S )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  sW    &+1vAw.?Aq6JJJH%
I'>?u4000000rF   c                 @   t          j        g dd          }t          |g d           t          j        g dd          }t          |t          j        t          j        t          j        g           t          j        g dg dgd          }t          |t          j        t          j        t          j        gg dgd	
           t          j        t          j        g t                    d          }t          |g            t          |j	        dk               d S )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   &+iii1===ULLL)))&+iii1===URVRVRV4555&+yyy))).DJJJ 8,,,G"	$ 	$ 	$ 	$ '+bhr.E.E.EKKKUBu$%%%%%rF   c                 D   t          j        g dd          }t          |g dd           t          j        g dd          }t          |t          j        t          j        t          j        g           t          j        g dg d	gd          }t          |t          j        t          j        t          j        gg dgd
           t          j        t	          j        g t                    d          }t          |g            t          |j	        dk               d S )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   %)III;;;lll7777%)III;;;TBFBFBF3444%)YYY			,BaHHH7F"	$ 	$ 	$ 	$ &)BHRs,C,C,CqIIIT2
e#$$$$$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        	                              dd          }t          ||d           t          |j
        d
k               d S )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   %)III;;;lllLLL9d////%)III;;;lllLLL9T4   %)BHRs,C,C,CqIIIx"*---55a;;d////
f$%%%%%rF   c                 x   t           j                            d           d}g d}g dg dg dg dg dg}t          j        |t          	          }t          ||          }t          |                    |          t          j        |||                     t          |                    |          t          j        |||                     t          |	                                t          j	        ||                     t          |
                                t          j
        ||                     d S )
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NN]]MMM===\\<<<)Jq$$$+Aq11

q)).21a;;	= 	= 	=
))!,,.5aA>>	@ 	@ 	@
((*@*DQ*J*JKKK
((*@*DQ*J*JKKKK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           d S )	Nrg   r  ri   g      @ru  r  g      %@g      /@)rT  rR   r   r=  	TypeErrorr  s    rD   test_invalid_paramsz-TestMultivariateHypergeom.test_invalid_paramsH  s    j"8"<aQGGGj"8"<a"qIIIj"8"<q!frdANNNi!7!;c3Z2h	# 	# 	#i!7!;aVTlA	' 	' 	'i!7!;aV2h	% 	% 	% 	% 	%rF   N)r   r   r   rQ   r   r   r=   r   r  r8  r  r  r  r  r   r6  rW  rY  r]  rd  r  r	  rp  rr  r  r  r  r  r  r   rF   rD   r  r  p  sV       [ VaWa+VaWa"&)!Wq"gq26'*Vb"Xq"&)!fq!fR2s)4Vbfbf%' !Wr2h26*Wr1gr26*Wr2hBF+VaWb"&)VaWa"&)+	
 43 35 43	/ 	/ 	/; ; ;; ; ;
 [V			13
Qqc1X&  " "	 " [S1#q!VaWa+1v1v"a1a& 12W1v1v&+&I79 RXb$$$hbhr&=&=&=q"EVaVQ"YY			1j1	
  3 3!  3 [Vq"gBx(!i-CDcA3Z1#saVb"X6sQCj\QC!:1vRz:cA3ZQC5'QFr2hZL9		
 3 3 3/ / // / // / // / /1 1 11 1 1
& & &% % %& & &L L L 	% 	% 	% 	% 	%rF   r  c                      e Zd Zd Zd Zej                            dd          d             Zd Z	ej                            dd          ej                            d	d          d
                         Z
ej                            dd          d             Zd Zej                            dd          d             Zej                            dd          d             Zej                            dd          d             Zej                            dd          ej                            dg dgf          ej                            dg dgf          d                                     Zej                            dd          d             Zd Zej                            dd          d             ZdS )TestRandomTablec                 @    t           j                            d          S )Nl   OfE)r=   r   r   r  s    rD   get_rngzTestRandomTable.get_rngU  s    y$$%7888rF   c                    d}t          j        t          |          5  t          ddggddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgddgg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgdd	g           d d d            n# 1 swxY w Y   d
}t          j        t          |          5  t          ddgddg           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgg d           d d d            n# 1 swxY w Y   d}t          j        t          |          5  t          ddgg d           d d d            n# 1 swxY w Y   ddg}g d}t          j        ddgg d          \  }}}t          ||           t          ||           |t          j        |          k    sJ d S )Nz`row` must be one-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  s6   1]:W555 	+ 	+1a&Aq6***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 2]:W555 	+ 	+!Q1a&***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ ?]:W555 	* 	*!R1a&)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* ?]:W555 	* 	*!Q!R)))	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* 	* <]:W555 	) 	)!Q!Q(((	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) 	) =]:W555 	0 	0#sYYY///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 =]:W555 	0 	0!Q///	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 	0 !fii2Aq6999EE1aS!S!BF3KKs}   A  AA(B

BB2CCC;DD #D E%%E),E)F..F25F2G77G;>G;zscale,method))r   boyett)r  	patefieldc                     t          j        ddg          |z  }t          j        g d          |z  }t          }|                    |||d          }|                    ||d d          }t	          ||           d S )Nr   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|  s     h1v&hyyy!!E)66#s66BBffS#df;;Xs#####rF   c                     ddg}g d}d}t          j        t          |          5  t          j        ||d           d d d            d S # 1 swxY w Y   d S )Nr   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  s    !fii 9]:W555 	5 	5S#e4444	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5 	5s   AAAr  )TFr_  c                 n   |                                  }ddgg dt          j        dd|          }|rt                    nt          }t          ||rdnd          |s	fd	|rfd
n}t	          j        |dd          \  }} ||          }	t          |	t          |          z  |d            |t          |d                             }
t          |
|	d                    |
                    d|j        dd          z             } ||          }	|	j        dk    sJ t          |	j        d                   D ]N}t          |	j        d                   D ]1}|	||f         }|||f         } ||          }t          ||           2Og dg dg}t          t	          j        |d                      ||          }	|	dk    sJ g dg dg}t          t	          j        |d                      ||          }	|	dk    sJ d}t          j        t           |          5   |dg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |dgg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |t          j        gg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |dgg           d d d            n# 1 swxY w Y   d}t          j        t           |          5   |g dg           d d d            n# 1 swxY w Y   d }t          j        t           |          5   |ddgd!d"gg           d d d            d S # 1 swxY w Y   d S )#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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    llnn!fiisCd&.SB B B )/@l3$$$L#8hh599 	4$O4 4 4 4 4 4 4/2>*****Ys$GGG
F C
OOCHHf37777 Sjm$$%%R1 Y122677CKKw)####qwqz"" 	' 	'A171:&& ' '1gad|c$iiS#&&&&	' YY			"RVAB'''---CFFAvvvv YY			"RVAB'''---CFFAvvvv 9]:W555 	 	CHHH	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 :]:W555 	 	C#LLL	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 :]:W555 	 	C"&
OOO	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 >]:W555 	 	C"KKK	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 7]:W555 	 	C	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 7]:W555 	 	C!QQ   	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	 	sl   7III8JJJ:KK"%K"L  L$'L$M##M'*M'N**N.1N.r/  )r+  r,  c                 (   |                                  }ddg}g d}t          j        ||d||          }t          j        ||          }t	          t          j        |          t          j        |                     t          |                    d          |d           t	          |                    d	
          t          j        |d                     t	          |                    d
          t          j        |d                     d S )NrL   rh   r7  r  r8  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     llnn!fiisCd6,/1 1 1 c**RVD\\26#;;///T5555SWW"W%%rsI'F'FGGGSWW"W%%rsI'F'FGGGGGrF   c                    |                                  }ddg}g d}t          j        ||dd|          }t          j        ||dd|          }t          j        |d	          }t          j        |d	          }t          ||d
           d S )NrL   rh   r7  r:  r+  r8  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     llnn!fiiSuX-02 2 2Su[-02 2 2vd###vd###d......rF   c           	      P   ddg}g d}t          j        ||||                                           }|j        dk    sJ t          j        ||d||                                           }|j        dk    sJ t	          ||d	                    t          j        ||d	||                                           }|j        d
k    sJ t          j        ||d||                                           }|j        dk    sJ t          j        ||d||                                           }|j        dk    sJ t          |                    ddd          |d           d}	t          j        t          |	          5  t          j        ||d||                                            d d d            n# 1 swxY w Y   t          j        t          |	          5  t          j        ||t          j        ||                                            d d d            d S # 1 swxY w Y   d S )NrL   rh   r7  r.  r  r   r8  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ii c3v+/<<>>; ; ;x6!!!! sCa,0LLNN< < <yI%%%%RQ    sCa,0LLNN< < <yI%%%% sCb,0LLNN< < <yJ&&&&sCfV,0LLNN< < <yL((((B1--s???? D]:W555 	: 	:S#Bv*.,,..: : : :	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: ]:W555 	: 	:S#BF6*.,,..: : : :	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	: 	:s$   :,F22F69F66HH"Hc                 "   ddg}g d}t           }|                    ||d||                                           }t          j        |dd          \  }}|                    |||          }t          |t          |          z  |d	
           d S )NrL   rh   r7  rk  r8  r   Tr<  rL  r  )r'   r   r#  r=   r>  r=  r   r   )	rZ   r/  r(  r)  r0  r   r@  rA  rA  s	            rD   test_rvs_methodzTestRandomTable.test_rvs_method(  s     !fiiffS#F6"&,,..  2 2  Ys$GGG
F FF:sC((CHHf4888888rF   c                 (   g d}g d}t          ||          }|                    d||                                           }t          j        dt          |          t          |          f          }g dg dg dg|d<   t          ||           d S )Nr  )r   r   r   r   r  r.  )r   r   r   r   .r'   r   r#  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=  s    iillc""UU4T\\^^UDD8T3s88SXX677%%%' 	R"""""rF   )Nr+  r,  r)  r   r(  c                     t          ||          }|                    d||                                           }t          j        dt          |          t          |          f          }t          ||           d S )Nr  r.  rW  rX  s          rD   test_rvs_with_edge_casesz(TestRandomTable.test_rvs_with_edge_casesI  sj     c""UU2f4<<>>UBB8RS3s8845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	        dt          |          t          |          fk    sJ t          j        |          |k    sJ d S )Nr   r   rM   r  r&  	rvs_rcont)scipy.stats._rcontr/   _rcontr=   r   int64ru   r   r#  r?   r   )rZ   r   r_  r(  r)  r   ntotresults           rD   test_rvs_rcontzTestRandomTable.test_rvs_rcontR  s     	,++++++++h1vRX...hyyy111fo!oo..vc{{S#tQ77|3s88SXX66666vf~~%%%%%%rF   c                    ddg}g d}t          |||                                           }|                                }t          j        ||          }t	          ||                                           t          j        |||          }t	          ||                    |                     t          j        |||          }t	          ||                    |                     d S )NrL   rh   r7  r   )r'   r#  r   r   r   r=  r3  )rZ   r(  r)  r  r  r  s         rD   r  zTestRandomTable.test_frozenc  s    !fiic777$S#..Xqvvxx(((#FC55XquuV}}---&vsC88Xqxx//00000rF   c                    ddg}g d}t          |||                                           }t          j        ||d||                                           }|                    d|          }t          ||           d S )NrL   rh   r7  r   r  r8  )r   r/  )r'   r#  r   r   )rZ   r/  r(  r)  r  r  r1  s          rD   test_rvs_frozenzTestRandomTable.test_rvs_frozens  s    !fiic777#C2f15A A AeeFe++Xs#####rF   N)r   r   r   r#  r*  rQ   r   r   r2  r5  rG  rJ  rM  rS  rU  rY  r[  rc  r  rf  r   rF   rD   r!  r!  T  s       9 9 9"  "  " H [^@B B$ $B B$5 5 5 [X}55[UM22L L 32 65L\ [X'>??H H @?H/ / / [X'>??': ': @?':R [X'>??9 9 @?9( [X'>??	# 	# @?	# [X'DEE[UR!I..[UR!I..# # /. /. FE# [S&))& & *)& 1 1 1  [X'>??$ $ @?$ $ $rF   r!  c                     | j         }d| _          | j        |ddi t          j        |           } | j        |ddi}t          j        |          } |j        |ddi}t          ||           || _         d S )NrX  r   r:  )r   r   pickledumpsloadsr   )distfnrB   rJ  r   r0	unpickledr1s          rD   check_picklingro    s    
 DFFJ1VA	T	"	"	"BQI		%1	%	%BR FrF   c                 >   t          j        d          }d|d<   d|d<   t          dgt          t          j        dg          fgt
          d|fgt          d|fgt          dg d	fgt          d
gt          d
gg}|D ]%\  }}t          ||           t          ||           &d S )NrM   r	  rP  r  r   r   r  rg   r  r  )r=   rU   r   r   r   r   r   r   r   r   r8   ro  )num_parallel_threadsr  distsrk  rB   s        rD   test_random_state_propertyrs    s    F1IIEE$KE$K	b!	RXrd^^&'	2u+	b%[!	q///*+	d	d#E  % %#FD111vt$$$$% %rF   c                   "   e Zd Zej                            dg d          ej                            dg d          d                         Zej                            dddg          ej                            dg d	          d
                         Zd Zd Z	d Z
ej                            dddg          d             Zej                            dddg          d             Zej                            dej        ej        g          d             Zej                            dej        ej        g          d             Zej                            d ej        g d           ej        g d          ddf ej        g d           ej        g d          ddf ej        g d           ej        g d          ddf ej        g d           ej        g d          dd f ej        g d           ej         ej        d!           ej        d"          dg          d#d$f ej        g d           ej        g d          d#d%f ej        g d&           ej        g d&          d#d'f ej        g d&           ej         ej        d!           ej        d"          dddg          d#d(f ej        g d&           ej         ej        d)           ej        d*          dddg          d#d+fg	          d,             Zej                            d ej        g d           ej        g d          dd-f ej        g d           ej        g d          dd.f ej        g d           ej        g d          dd/f ej        g d           ej        g d          dd0f ej        g d           ej         ej        d!           ej        d"          dg          d#d1f ej        g d           ej        g d          d#d2f ej        g d&           ej        g d&          d#d3f ej        g d&           ej         ej        d!           ej        d"          dddg          d#d4f ej        g d&           ej         ej        d)           ej        d*          dddg          d#d5fg	          d6             Zej                            d7g d8          d9             Zej                            dej        ej        g          d:             Zd; Zej                            dg d<          ej                            d=g d>          d?                         Zd@ ZdA ZdB ZdCS )DTestVonMises_Fisherr   )rL   rM   ri   rh   r   r7  c                    t           j                            d          }t          j        |fdt          j        |          z            }t          |d|          }|                    |          }t          j        |          t          j        |          }}|	                    |||          j
        }	|j
        |	k    sJ t           j                            |d          }
t          |
d           d S )Nr9  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     i##$788WcWan--"2qs333,,t$$HSMM26#;;c00s0FFL}....	wR00r"""""rF   rg   r:  kappa)g  4&kCr  gꌠ9Y>)Fc                     t           j                            d          }t          j        |fdt          j        |          z            }t          |||          }|                    d           d S )Nr9  r   r   r  )r=   r   r   r   r  r)   r   )rZ   r   rx  r   rU  rw  s         rD    test_sampling_high_concentrationz4TestVonMises_Fisher.test_sampling_high_concentration  se     i##$788WcWan--"2u3777RrF   c                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )Nr  z%'mu' must have one-dimensional shape.rJ   r   r=   rT   rQ   r
   rR   r)   rZ   rU  r  s      rD   test_two_dimensional_muz+TestVonMises_Fisher.test_two_dimensional_mu  s    WV__5]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#   AAAc                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )Nr  z%'mu' must be a unit vector of norm 1.rJ   r   r|  r}  s      rD   test_wrong_norm_muz&TestVonMises_Fisher.test_wrong_norm_mu  s    WU^^5]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r  c                     t          j        d          }d}t          j        t          |          5  t          |d           d d d            d S # 1 swxY w Y   d S )NrO  z$'mu' must have at least two entries.rJ   r   r|  r}  s      rD   test_one_entry_muz%TestVonMises_Fisher.test_one_entry_mu  s    WU^^4]:S111 	# 	#B"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r  rk   )rg   rM   c                     d}t          j        t          |          5  t          ddg|           d d d            d S # 1 swxY w Y   d S )Nz"'kappa' must be a positive scalar.rJ   r   r   rQ   r
   rR   r)   rZ   rx  r  s      rD   test_kappa_validationz)TestVonMises_Fisher.test_kappa_validation  s    2]:S111 	+ 	+QFE***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+   >AAr   r   c                     d}t          j        t          |          5  t          ddg|           d d d            d S # 1 swxY w Y   d S )NzFor 'kappa=0' the von Mises-Fisher distribution becomes the uniform distribution on the sphere surface. Consider using 'scipy.stats.uniform_direction' instead.rJ   r   r   r  r  s      rD   test_kappa_zeroz#TestVonMises_Fisher.test_kappa_zero  s     ]:S111 	+ 	+QFE***	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+ 	+r  r/  c                     t          j        g d          }d}t          j        t          |          5   ||ddgd           d d d            d S # 1 swxY w Y   d S )Nr   r   r   znThe dimensionality of the last axis of 'x' must match the dimensionality of the von Mises Fisher distribution.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  s     H[[[!! ]:S111 	! 	!F1q!fa   	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	!   AAAc                     t          j        ddg          }d}t          j        t          |          5   ||ddgd           d d d            d S # 1 swxY w Y   d S )Nr	  r   8'x' must be unit vectors of norm 1 along last dimension.rJ   r   r   r  r  s       rD   test_unnormalized_inputz+TestVonMises_Fisher.test_unnormalized_input  s     Hc2YH]:S111 	! 	!F1q!fa   	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	! 	!r  zx, mu, kappa, reference)r   r   r   r  g0_?r  )r   r   r   g7m0_?r  gLI/@gFK:h*7g\(\?rL  i  g3pB>g7Ks@)r   r   r   r   r   go齿@gW+x\(?r  r   gS-c                 p    t          ||                              |          }t          ||d           d S )Nr  r  )r)   r   r   )rZ   r`   rU  rx  	referencer   s         rD   test_pdf_accuracyz%TestVonMises_Fisher.test_pdf_accuracy  s<    4 b%((,,Q//YU333333rF   g[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 p    t          ||                              |          }t          ||d           d S )NrD  r  )r)   r   r   )rZ   r`   rU  rx  r  r   s         rD   test_logpdf_accuracyz(TestVonMises_Fisher.test_logpdf_accuracy(  s<    4 !U++22155	66666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          ||                                          }t          ||d           d S )Nr   g+=r  )r=   r   r  r)   r   r   )rZ   r   rx  r  rU  r   s         rD   test_entropy_accuracyz)TestVonMises_Fisher.test_entropy_accuracyS  sY     WcWan--!"e,,4466777777rF   c           	         d}t           j                            d          }t          d                              ||          }t          j        ddt          j        d          z            }d} ||||          }|j        |k    sJ t          |d                   D ]L}t          |d                   D ]4}	 ||||	d d f         ||          }
t          |
|||	f         d	
           5Md S )Nr  r9  rM   r   rT  r   rg   r   rG  r  )
r=   r   r   r(   r   r   r  r?   rq  r   )rZ   r/  	testshaper   r`   rU  rx  
result_allr  r  current_vals              rD   r  z%TestVonMises_Fisher.test_broadcasting]  s    	i##$788a  $$YS$AAWUAbgajjL))VAr5))
9,,,,y|$$ 	K 	KA9Q<(( K K$fQq!QQQwZU;;Z1-=EJJJJJK	K 	KrF   c                    t           j                            d          }t          j        ddg          }t          j        |d         |d                   }d}t          ||          }t          ||          }t          d                              d|          }t          j        |d d df         |d d df                   }t          |
                                |
                                           t          |                    |          |                    |                     t          |                    |          |                    |                     d S )	Nr9  r   r   r  )r  rx  rL   r  r   )r=   r   r   r   rA  r)   r+   r(   r   r   r   r   r   )	rZ   r   rU  mu_anglerx  vmfvonmises_distvectorsrH  s	            rD   test_vs_vonmises_2dz'TestVonMises_Fisher.test_vs_vonmises_2dm  s3    i##$788Xq!f:beRU++b%(( XU;;;#A&&**2C*@@GAAAqDM7111a4=99--//???))&1137773C3CDDD,,V44cjj6I6IJJJJJrF   )rL   rM   rh   zkappa, mu_tol, kappa_tol))r   r  r  )r  r  r  )r  {Gzt?rL  )r  r  rL  c                    t          j        |fdt          j        |          z            }t          ||          }t           j                            d          }d}|                    ||          }	t          j        |	          \  }
}t          j        |	                    |
                    }t          |d|d           t          |||           d S )	Nr   r9  r:  r   r   r   r  r  )r=   r   r  r)   r   r   r   rA  arccosrr  r   )rZ   r   rx  mu_tol	kappa_tolrU  rw  r   rw  rb  mu_fit	kappa_fitangular_errors                rD   test_fit_accuracyz%TestVonMises_Fisher.test_fit_accuracy|  s     WcWan--"2u--i##$788	,,ys,;;+/88		"&&..11rQ????yy999999rF   c                     t          j        d          }d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )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  s    HUOO,]:S111 	# 	#"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#   AAAc                     t          j        d          }d}t          j        t          |          5  t          j        |           d d d            d S # 1 swxY w Y   d S )Nr  r  rJ   )r=   rT   rQ   r
   rR   r)   rA  r  s      rD    test_fit_error_unnormalized_dataz4TestVonMises_Fisher.test_fit_error_unnormalized_data  s    GFOOH]:S111 	# 	#"""	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	# 	#r  c                 <   t          j        g d          }d}t          ||          }t          ||d          }|                    d          }t          j        ||d          }|                                }t	          ||           t	          ||           d S )N)r   r   r   rg   r  r   r   )r=   r   r)   r   r   )rZ   rU  rx  r  r  r  r  r  s           rD   r?  z,TestVonMises_Fisher.test_frozen_distribution  s    Xiii   U++%b%c:::zzsz++"2u3???  T4   T4     rF   N)r   r   r   rQ   r   r   r  rz  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   ru  ru    s       [ULLL11[V%9%9%9::
# 
# ;: 21
# [UQF++[W&8&8&899  :9 ,+# # ## # ## # # [Wr6l33+ + 43+
 [Wq"g..+ + /.+ [X(;(7(>(@ A A! !A A! [X(;(7(>(@ A A! !A A!$ [6'rx55xrx7M7M#%79'rx44hbh|||6L6L#%8:'rx55xrx7M7M"$68'rx44hbh|||6L6L"$9;'rx55'rxr(JKK#%:<  (rx44hbh|||6L6L#%68'rx(<(<(<=='rx(<(<(<==#%79  (rx(<(<(<=='rxr)*B)0  1  1#%;=  (rx(<(<(<=='rxwrws||R)*B)0  1  1#%;=)>? ?24 43? ?24" [6'rx55xrx7M7M#%8:'rx44hbh|||6L6L#%8:'rx55xrx7M7M"$57'rx44hbh|||6L6L"$68'rx55'rxr(JKK#%8:  (rx44hbh|||6L6L#%68'rx(<(<(<=='rx(<(<(<==#%79  (rx(<(<(<=='rxr)*B)0  1  1#%79  (rx(<(<(<=='rxwrws||R)*B)0  1  1#%8:);< <27 73< <27$ [4: : :; ;
8 8; ;
8
 [X(;(7(>(@ A AK KA AKK K K [UIII..[72 2 23 3
	: 	:3 3 /.	:# # ## # #! ! ! ! !rF   ru  c                   ~   e Zd Zed             Zd Zd Zd Zd Zd Z	e
j                            ddd	g          d
             Ze
j                            dddg          d             Zd Zd Ze
j                            ddd	g          d             Ze
j                            dg d          d             ZdS )TestDirichletMultinomialc                     t           j                            d          }|                    ddd          }|                    dd|df          }|                    d	          }|||||fS )
N   t7)r   r  rL   r   r   r  rk   r   )r=   r   r   r   integersr   )rZ   r&  r   r  r`   r   s         rD   
get_paramsz#TestDirichletMultinomial.get_params  sl    i##$566As++LLBaVL,,EErENNAua""rF   c                    t           j                            d          }|                    ddd          }|                    ddd          }t          j        |d          }t          ||          }t          |                    |          t          j        |||                     t          |	                    |          t          j	        |||                     t          |
                                t          j
        ||                     t          |                                t          j        ||                     t          |                                t          j        ||                     d S )Nr  r   r  r  rk   r   )r=   r   r   r   r  r   r*   r   r3  r=  r   r  r   )rZ   r   r  r`   r   r  s         rD   r  z$TestDirichletMultinomial.test_frozen  s1   i##$566AsB''LLB##F12!%++QXXa[["7">q%"K"KLLLQUU1XX48E1EEFFFQVVXX49%CCDDDQUUWW37qAABBBQUUWW37qAABBBB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n J t           j	        
                    d          }|                    ddd          }|                    ddd          }t          j        |d	
          }t          ||                              |          }t          j        |||          }d}t          ||           t          |t          j        |                     d S )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  so   
 HYYYF1II###'5!44&-a::!S!!!s,,,yFL....B...... i##$566AsB''LLB##F12#E1--11!44&-a::"S!!!s,,,,,rF   c                    |                      d          \  }}}}}|dz  }t          t          ||                              |          d           t          t          ||                              |          t
          j                    |                      d          \  }}}}}|                    d          dk    }t          j        ||         dz            ||<   t          t          ||                              |          |         d           t          t          ||                              |          |         t
          j                    t          j	        t          ||                              |          |          dk              sJ t          j	        t          ||                              |          |          t
          j         k              sJ d S )Nr   r   r  r   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0Qq!	Q*5!4488;;Q???*5!44;;A>>HHH"oob11Qq!JJBJ#%x!q!!!*5!4488;;A>BBB*5!44;;A>>qABF7KKKv+E15599!<<aR@1DEEEEEv+E155<<Q??CrvgMNNNNNNNrF   c                 `   d}dg}t          j        |g          }t          ||          }t          |                    |          d           t          |                    |dz             d           t          |                    |          d           t          |                    |dz             t           j                    t          |                                |           t          |                                d           t          |	                                d           d S )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    JsOO$UA..TXXa[[!$$$TXXac]]A&&&T[[^^Q'''T[[1%%w///TYY[[!$$$TXXZZ###TXXZZ#####rF   c                    d}t          j        ddg          }t          j        ddg          }t          ||          }t          |                    |          d           t          |                    |dz             d           t          |                    |          d           t          |                    |dz             t           j                    t          |                                ddg           t          |                                ddg           t          |	                                ddgddgg           d S )Nr   r   r   r  r  s        rD   test_n_is_zeroz'TestDirichletMultinomial.test_n_is_zero  s   
B8$$J1v$UA..TXXa[[!$$$TXXac]]A&&&T[[^^Q'''T[[1%%w///TYY[[1a&)))TXXZZ!Q(((TXXZZ1a&1a&!122222rF   method_namer=  r3  c                 $   |                      d          \  }}}}}t          t          ||          |          }t          t          j        |g|j        R  |          } ||          }	 ||j        d                   }
t          |	|
           d S 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  s    "ooc22Qq!.ua88+FFU_Q9999;GG
fQiijQ  S!!!!!rF   r   r  c                    |                      d          \  }}}}}t          t          ||          |          }t          t          j        |g|j        R  |          } |            d d df         }	 |            }
t          |	|
           d S r  r  r  s              rD   test_against_betabinom_momentsz7TestDirichletMultinomial.test_against_betabinom_moments  s    "ooc22Qq!.ua88+FFU_Q9999;GG
fhhqqq!tnjllS!!!!!rF   c                    t           j                            d          }d}|                    dd          }|                    |          dz  }t	          ||          }d}|                    ||          }|                    |||          }t          |                                t          j        |d	          d
           t          |	                                t          j	        |d	          d           |                                j
        |	                                j
        cxk    r|fk    sn J |                                }	|	j
        ||fk    sJ t          |	t          j        |j                  d           t          t          j        |	          |	                                           t          j        t           j                            |	          d         dk              sJ d S )Nr  rg   r   r  r   r  rk  r   r   r  r  r  rL  )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!  s   i##$566LLC  

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

BF11$5$5$5DAAAAyy{{ DHHJJ$4>>>>>>>>>>hhjjyS#J&&&&RVAC[[t4444RWS\\488::...vel'',,Q/!34444444rF   c                    t          j        g d          }t          j        |          }t          j        g d          }d}t          t          |          5  t          j        g d||           d d d            n# 1 swxY w Y   t          t          |          5  t          j        g d||           d d d            n# 1 swxY w Y   d}t          t          |          5  t          j        |g d|           d d d            n# 1 swxY w Y   t          t          |          5  t          j        |g d	|           d d d            n# 1 swxY w Y   d
}t          t          |          5  t          j        ||d           d d d            n# 1 swxY w Y   t          t          |          5  t          j        ||d           d d d            n# 1 swxY w Y   t          j        g d          }t          j        g d          }d}t          t          |          5  t          j        |||                                           d d d            d S # 1 swxY w Y   d S )NrP   r  z,`x` must contain only non-negative integers.rJ   )r   rk   rM   )r   r%  rM   z*`alpha` must contain only positive values.)rM   r   ri   )rM   rk   ri   z#`n` must be a non-negative integer.ǧH@rk   )r   rL   rM   ri   z&`x` and `alpha` must be broadcastable.)r=   r   r   rT  rR   r*   r3  )rZ   x0n0alpha0textr`   r  s          rD   r\   z.TestDirichletMultinomial.test_input_validation7  s)   Xiii  VBZZ)))$$=:T222 	A 	A!(VR@@@	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A 	A:T222 	B 	B!(fbAAA	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B 	B <:T222 	< 	<!(YYY;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	<:T222 	= 	=!(ZZZ<<<	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 	= 5:T222 	; 	;!(VT:::	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	; 	;:T222 	9 	9!(VR888	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 	9 H\\\""##7:T222 	< 	<!(E15577;;;	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	< 	<s~   A>>BBCCC'DDD-EEE5FFF9GG #G +)I!!I%(I%r/  c           	         t          j        g dg dg dg dg          }t          j        dgdgdgg          }t          j        g dg d	g                              d
          }t          t          |          } ||||          }|j        dk    sJ t          t          |                    D ]}t          t          |                    D ]}t          t          |                    D ]r}||||f         }	 |||                                         ||                                         ||                                                   }
t          |	|
           sd S )Nr  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  si   )))YYY			:::FGGHqcA3_%%Hiii+,,44\BB.77fQq!!yI%%%%s1vv 	2 	2A3q66]] 2 2s5zz** 2 2A!!Q'lG &1q1A1A1C1CQqT\\^^TTC#GS111122	2 	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k    r|j        d	k    snnJ t          t          |                    D ]w}t          t          |                    D ]X}|||f         } |||                                         ||                                                   }	t          ||	           Yxd S )
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   )))YYY			:::FGGHqcA3_%%.<<fUA)4)=)=syI%%%%%%s1vv 	. 	.A3u::&& . .ad)fU1X--//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    sj       # # [#C C C- - ->O O O $ $ $3 3 3 []UH,=>>" " ?>" []VUO<<" " =<"5 5 5,< < << [Xx'8992 2 :92 [],B,B,BCC
. 
. DC
. 
. 
.rF   r  c                      e Zd Zd Zd Zd Zd Zd Zej	        j
        ej	                            d          d                         Zej	                            dej        ej        ej        ej        g          d	             Zd
S )TestNormalInverseGammac           	      X   t           j                            d          }|                    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          }|
                    |          }	t          |j        |	                               d|          }t          j        |d
         |j                  \  }
}|dk    sJ d S )N   &( ri   rL   r   r  r  rg   r6  c                 0                         ||           S r<   r   )rG  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   rB  r  s               @rD   test_marginal_xz&TestNormalInverseGamma.test_marginal_xt  s    i##J//**Q--E1a3Bq!DDGAaCRqUQ)?)?'?@@@ KAr"">>>>26QRPTUUUeeAhhc***   e# >>N3q61511	6||||||rF   c                 0   t           j                            d          }|                    d          \  }}}}t          j        ||||          t          j        ||          }t          j        ddd          }t          fdt           j         t           j        |f          }|	                    |          }	t          |j        |	                               d|	          }t          j        |d
         |j                  \  }
}|dk    sJ d S )Nr  ri   r*  r   r  c                 0                         | |          S r<   r  )r`   rG  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_gammarG  r@   rA   r   rB  r  s               @rD   test_marginal_s2z'TestNormalInverseGamma.test_marginal_s2  s    i##J//**Q--E1a3Bq!DDN1A...	 [b"%%>>>>wbU4 4 4mmBc***   e# >>N3q69=99	6||||||rF   c                    t           j                            d          }|                    d          dz
  \  }}}}|                    d          dz
  \  }}t          j        ||||                              ||          }t          j                            ||||||          }	t          |t          j        |	                     d S )Nr  )ri   r  r  )rL   r  r   )	r=   r   r   r/   r  r   r   r   r  )
rZ   r   rU  r  r  r  r`   rG  r@   rA   s
             rD   test_pdf_logpdfz&TestNormalInverseGamma.test_pdf_logpdf  s    i##J//**W--4E1a


((4/2(UAq99==aDD(//2r5!QGGRVC[[)))))rF   c                    t           j                            d          }|                    d          \  }}}}|                    d          \  }}t          j        t           j        |||                              ||          }t          |t           j                   t          j        |d||                              ||          }t          |t           j                   t          j        ||d|                              ||          }t          |t           j                   t          j        |||d                              ||          }t          |t           j                   t          j        ||||                              |d          }t          |d           t          j        |dt           j        g||                              |d          }t          |t           j                   t          j        |d||                                          }t          |t           j        t           j        f           t          j        ||d|          	                                }t          |t           j        t           j        f           t          j        t          d          5  t          j        |||d                                           d d d            d S # 1 swxY w Y   d S )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`   rG  r@   s	            rD   test_invalid_and_special_casesz5TestNormalInverseGamma.test_invalid_and_special_cases  s   i##J//**Q--E1a

12(1==AA!RHHS"&!!!(RA66::1bAAS"&!!!(UAq99==aDDS"&!!!(UAr::>>q"EES"&!!!(UAq99==aDDS! (b"&\1a@@DDQKKS"&!!!(RA66;;==S2626*+++(UB::>>@@S2626*+++]:-KLLL 	? 	?&r5!R88<<>>>	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	? 	?s   5*K,,K03K0c                    t           j                            d          }|                    d          }|                    d          dz   }|                    d          }|                    d          }|                    d          }|                    d          }t          j        ||||          }t          j        ||||||          }	d |	D             }
|                    ||          }|j        |	d	         j        k    sJ t          |	                                t          j        j        |
            |
                    ||          }|j        |	d	         j        k    sJ t          |	                                t          j        j
        |
            t          j        ||||          }	d
 |	D             }
|                                }|d	         j        |	d	         j        k    sJ t          |d	         	                                |d         	                                ft          j        j        |
            |                                }|d	         j        |	d	         j        k    sJ t          |d	         	                                |d         	                                ft          j        j        |
            d}t           j                            d          }|                    ||          }t           j                            d          }d}t          j        j        |
||d}t          |d	                             |          |d                             |          f|           d S )Nr  rL   )rM   r   )ri   r   r   )rg   r   r   r   )rh   r   r   r   r   )rj   r   r   r   r   r   c                 6    g | ]}t          j        |          S r   r=   rY  r  arrs     rD   r  z<TestNormalInverseGamma.test_broadcasting.<locals>.<listcomp>       DDDrx}}DDDrF   r   c                 6    g | ]}t          j        |          S r   r  r  s     rD   r  z<TestNormalInverseGamma.test_broadcasting.<locals>.<listcomp>  r  rF   r   )rh   rg   ri   rM   rL   l   Mr   )rh   x   )r=   r   r   r/   r  broadcast_arraysr   r?   r   rY  r   r   r  r   r  )rZ   r   r  r  r  rU  rG  r`   r   broadcastedbroadcasted_raveledr@   r   r?   rA   s                  rD   r  z(TestNormalInverseGamma.test_broadcasting  s1    i##J//JJqMMJJv"

9%%ZZ%%ZZ((JJ)**)"eQ:: )!RUAqAADDDDDhhq"ooyKN00000		268KL	N 	N 	N kk!R  yKN00000		29;NO	Q 	Q 	Q )"eQ::DDDDDiikk1v|{1~33333QQ8279LM	O 	O 	O hhjj1v|{1~33333QQ8268KL	N 	N 	N i##M22hhDsh33i##M22(,.A:=? ? ?Q..Au0E0EFLLLLLrF   r  c                 &   t           j                            d          }|                    d          \  }}}}|dz  }t          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           d S )
Nr  ri   rL   c                 6                         ||           |z  S r<   r  rG  r`   r   s     rD   ra   z5TestNormalInverseGamma.test_moments.<locals>.<lambda>  s    DHHQOOa$7 rF   r   r  r  c                 6                         ||           | z  S r<   r  r  s     rD   ra   z5TestNormalInverseGamma.test_moments.<locals>.<lambda>  s    DHHQOOb$8 rF   r   )	r=   r   r   r/   r  r   r5   r   r   )	rZ   r   rU  r  r  r  r@   rA   r   s	           @rD   r  z#TestNormalInverseGamma.test_moments  s     i##J//**Q--E1a	Q)"eQ::iikk7777"&"&!RVTTAAT2222888826'261bfUUAAT222222rF   r  c                    t           j        dk     rt          j        d           t           j                            d          }|                    ddd                              |          \  }}}}}}t          j        d|          }	t          j
        ||||          }
|
                                d	         j        |	k    sJ |
                                d
         j        |	k    sJ |
                                d	         j        |	k    sJ |
                                d
         j        |	k    sJ |
                                d	         j        |	k    sJ |
                                d
         j        |	k    sJ |
                    ||          j        |	k    sJ |
                    ||          j        |	k    sJ d S )N2z*Scalar dtypes only respected after NEP 50.r  rM   r  rh   r   r   r   r   )r=   __version__rQ   r   r   r   r   astyperesult_typer/   r  r   r  r   r  r   r   )rZ   r  r   r`   rG  rU  r  r  r  	dtype_outr   s              rD   
test_dtypez!TestNormalInverseGamma.test_dtype  s   >CKDEEEi##J//!$Q!;!;!B!B5!I!I2r5!QN3..	)"eQ::xxzz!}"i////xxzz!}"i////yy{{1~#y0000yy{{1~#y0000xxzz!}"i////xxzz!}"i////{{1b!!'94444xx2$	111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 1M 1Mf [[23 3  3 [WrxRZ&TUU2 2 VU2 2 2rF   r  r  )hr5  rh  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$   r%   r&   r'   r(   r)   r*   r+   r,   r-   scipy.stats._continuous_distnsr.   r"  r/   scipy.integrater0   r1   r2   r3   r4   r5   r6   scipy.specialr7   r  common_testsr8   	data._mvtr9   unittest.mockr:   rE   rH   r   r   r   r=  rN  rr  r  r  r  r/  r  r  r  r  r6  rM  r\  r  r!  ro  r   r  rs  ru  r  r  r   rF   rD   <module>r     sm     ! ! ! ! ! !7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7  * * * * * * 9 9 9 9 9 9        C C C C C C C C C C: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 0 / / / / / / / @ @ @ @ @ @       4 4 4 4 4 4 4 4 4 4 < < < < < < < < < < < < & & & & & &       5 5 5 5 5 5            ' ' ']! ]! ]! ]! ]! ]! ]! ]!@      A A A A A A A AH X X X X X X X Xv@) @) @) @) @) @) @) @)FH* H* H* H* H* H* H* H*VF1 F1 F1 F1 F1 F1 F1 F1R- - -&i9 i9 i9 i9 i9 i9 i9 i9V{; {; {; {; {; {; {; {;|a( a( a( a( a( a( a( a(HGJ GJ GJ GJ GJ GJ GJ GJT~& ~& ~& ~& ~& ~& ~& ~&Bd# d# d# d# d# d# d# d#N6+ 6+ 6+ 6+ 6+ 6+ 6+ 6+r>D >D >D >D >D >D >D >DB@9 @9 @9 @9 @9 @9 @9 @9Fa% a% a% a% a% a% a% a%Hh$ h$ h$ h$ h$ h$ h$ h$V	  ( % % %$~! ~! ~! ~! ~! ~! ~! ~!BH. H. H. H. H. H. H. H.Vk2 k2 k2 k2 k2 k2 k2 k2 k2 k2rF   