a
    BCCfV                    @   s  d Z ddlZddlmZmZmZmZmZmZ ddl	Z	ddl	m
Z ddlmZ ddlZddlZddlZddlmZmZmZ ddlmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2 dd	lm3Z3m4Z4 dd
lm5Z5 ddl6m7Z7m8Z8m9Z9 ddl:m;Z; ddl<m=Z= ddl>m?Z? ddl@mAZA ddlBmCZC dd ZDG dd dZEd@ddZFdd ZGG dd dZHG dd dZIG dd dZJd d! ZKG d"d# d#ZLG d$d% d%ZMG d&d' d'ZNG d(d) d)ZOG d*d+ d+ZPG d,d- d-ZQG d.d/ d/ZRG d0d1 d1ZSG d2d3 d3ZTG d4d5 d5ZUG d6d7 d7ZVd8d9 ZWd:d; ZXG d<d= d=ZYG d>d? d?ZZdS )Az8
Test functions for multivariate normal distributions.

    N)assert_allcloseassert_almost_equalassert_array_almost_equalassert_equalassert_array_lessassert_)raises   )check_distribution_rvs)_PSD_lnBmultivariate_normal_frozen)multivariate_normalmultivariate_hypergeommatrix_normalspecial_ortho_grouportho_grouprandom_correlationunitary_group	dirichletbetawishartmultinomial
invwishartchi2invgammanormuniformks_2sampkstestbinom	hypergeommultivariate_tcauchy
normaltestrandom_tableuniform_directionvonmises_fisherdirichlet_multinomialvonmises)_covariance
Covariance)stats)rombqmc_quadtplquad)multigammaln)Version)check_random_state_property)_qsimvtv)patchc                 O   s@   t | t | } }t| |g|R i | t| j|j d S N)npasarrayr   r   shape)resrefargskwargs r=   _/var/www/html/django/DPS/env/lib/python3.9/site-packages/scipy/stats/tests/test_multivariate.pyassert_close,   s    r?   c                   @   s  e Zd Zdd Zejejjejjejj	dd dZ
eee
Zeg dg dg dg d	ge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d Zejdeeejdedd Zejdde ddgejdeeejdedd Zejde dgejdedd Zd d! Zejd"d#d$ Zd%d& ZdS )'TestCovariancec                 C   s  d}t jt|d  ttd W d    n1 s80    Y  d}t jt|d* tjtdtdd W d    n1 s0    Y  d}t jt|d td W d    n1 s0    Y  d	}t jt|d  t	td W d    n1 s0    Y  d
}t jt|d$ t
dtdf W d    n1 sL0    Y  d}t jt|d$ t
tddf W d    n1 s0    Y  d}t jt|d( t
g dtdf W d    n1 s0    Y  d S )Nz:The input `precision` must be a square, two-dimensional...match   z0`precision.shape` must equal `covariance.shape`.   )
covariancez7The input `diagonal` must be a one-dimensional array...Zalpacaz9The input `cholesky` must be a square, two-dimensional...z4The input `eigenvalues` must be a one-dimensional...z,The input `eigenvectors` must be a square...z9The shapes of `eigenvalues` and `eigenvectors` must be...r	   rC   rD   )pytestr   
ValueErrorr*   CovViaPrecisionr6   oneseyeZCovViaDiagonalZCovViaCholeskyZCovViaEigendecompositionselfmessager=   r=   r>   test_input_validation4   s*    .8(044z$TestCovariance.test_input_validationc                 C   s   t | ddS )NTallow_singular)r   xr=   r=   r>   <lambda>V   s    zTestCovariance.<lambda>)ZDiagonalZ	PrecisionZCholeskyZEigendecompositionZPSDrF   )   r	   rD   )r	         )rD   rW      )r	   r   rD   )rU   r   )rY   rU   r   r   r   r   )diagonal full rankzgeneral full rankzdiagonal singularzgeneral singularr	   N)r   rY   r\   cov_type_namerY   c           	      C   s   t g d}g d}ttd| }| j| }ttd|  }|||}|||}t|t|kspJ t|	||	| d S )NrF   )rC   rU   CovViaZfrom_)
r6   diaggetattrr*   _covariance_preprocessingr+   lowertyper   whiten)	rM   r]   ArS   cov_typepreprocessingfactoryr9   r:   r=   r=   r>   test_factoriesb   s    
zTestCovariance.test_factoriesmatrix_typec                 C   s  d| d| d}|| j | vr*t| | j| }ttd| }| j| }t|dd}|||}t|j	|j	 t
|j|j t
|jt|j t|jt| tjd}	|	jdd}
||
}|
|j }t|| ||  t|d	rd
|vrt|||
 |	jdd}
||
}|
|j }t|d jdd|d jdd t|d	rtd
|vrtt|||
 t|d	r|tt|}t|j| | d S )Nr_    does not support 	 matricesTrP      VGiVK rD   sizeZ	_colorizesingularrC   rW   rD   rC   rY   axis)
_cov_typesrG   skip	_matricesra   r*   rb   r   r?   log_pdetr   rankr8   r6   r7   rE   randomdefault_rngre   UhasattrZcolorizesumrK   lenT)rM   rk   r]   rN   rf   rg   rh   psd
cov_objectrngrS   r9   r:   r=   r=   r>   test_covariancep   s8    






"zTestCovariance.test_covariancerp   rr   c                 C   s  d| d| d}|| j | vr*t| | j| }ttd| }| j| }g d}|||}	t}
t||dd}t||	dd}tj	
d}|j|||d}tj	
d}|
j||	||d	}tj	
d}|
||	|d
j|d}t|	tjrt|t| t|t| n&t|j|j t|j|j t|| t|
|||	|| t|||| t|
|||	|| t|||| t|
||	|  t| |  d S )Nr_   rl   rm   皙?皙?333333?TrP   rn   ro   rp   random_stateseed)ru   rG   rv   rw   ra   r*   rb   r   r6   rz   r{   rvs
isinstanceZ	CovViaPSDr?   squeezer   r8   pdflogpdfentropy)rM   rp   rk   r]   rN   rf   rg   rh   meanr   mvndist0dist1r   rS   x1x2r=   r=   r>   test_mvn_with_covariance   s:    



z'TestCovariance.test_mvn_with_covariancec                 C   s   d}| j | }ttd| }| j| }g d}|||}t}	t||dd}
t||dd}tjd}|j|||d}t|		||||
	| t|	||
	| t|	
||||

| t|
||

| d S )Nr[   r_   r   TrP   rn   ro   )rw   ra   r*   rb   r   r6   rz   r{   r?   cdflogcdf)rM   rp   r]   rk   rf   rg   rh   r   r   r   r   r   r   rS   r=   r=   r>   test_mvn_with_covariance_cdf   s    

z+TestCovariance.test_mvn_with_covariance_cdfc                 C   s<   d}t jt|d t  W d    n1 s.0    Y  d S )Nz7The `Covariance` class cannot be instantiated directly.rA   )rG   r   NotImplementedErrorr+   rL   r=   r=   r>   test_covariance_instantiation   s    z,TestCovariance.test_covariance_instantiationzignore::RuntimeWarningc                 C   s   t g d}|jd }t |}tjtdd t||  W d    n1 sT0    Y  d}t j	
|}t j	
|}tt j|}t||}|j|d}	tj|||d}
t|	|
 d S )N)r	   rC   g:0yEr   zThe input matrix must be...rA   l   .ypGw r   )r6   r`   r8   zerosrG   r   rH   r   r   rz   r{   r+   from_eigendecompositionlinalgeighr   )rM   rf   nr   r   Zrng1Zrng2covrvr9   r:   r=   r=   r>   test_gh9942   s    

,
zTestCovariance.test_gh9942c                 C   s   t d}tt dt df}tjj||d}|j	d d}t
|| tjjt ddgt ddgddggf}tjj||d}|j	d d}|d |d ksJ |d |d ksJ d S )	NrC   r   r   ro         ?        g      y@r   r	   )r6   rJ   r+   r   r   rK   scipyr,   r   r   r   array)rM   r   r   distr   r=   r=   r>   test_gh19197   s    

"zTestCovariance.test_gh19197)__name__
__module____qualname__rO   r6   r`   r   invcholeskyr   rb   r   listZ_all_covariance_typesrw   ru   rG   markparametrizerj   r   tupler   r   r   filterwarningsr   r   r=   r=   r=   r>   r@   2   sD   



/%

r@   Fc           	      C   s\   | | | f}||j }tj|\}}|rD|j| ddk}d||< |t| |j }|S )Nro   r   )rz   r   r6   r   r   normalr`   )	dimZevalsr   rq   rf   _vZ	zero_eigsr   r=   r=   r>   _random_covariance  s    
r   c                 C   s$   t j| | }tj|\}}}|S r5   )r6   rz   randnr   r   svd)r   Musr   r=   r=   r>   _sample_orthonormal_matrix   s    r   c                   @   s  e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zejdededdggd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Z d2d3 Z!d4d5 Z"d6d7 Z#d8d9 Z$d:d; Z%d<d= Z&d>d? Z'd@dA Z(ejdBdCdDdE Z)dFdG Z*ejdHe+dIe+dJgdKdL Z,ejdMe+dNe+dOe+dPgdQdR Z-dSdT Z.dUdV Z/dWdX Z0dYS )ZTestMultivariateNormalc                 C   s`   t d}t d}tttjd|| tttjd|| tttjd|| tttjd|| d S )NrD   rC   r   r	   r   r	   rC   )r6   arangeidentityassert_raisesrH   r   r   r   )rM   mur   r=   r=   r>   test_input_shape'  s    

z'TestMultivariateNormal.test_input_shapec                 C   s   t jd d\}}}t|||}t|jd t jd}t jd}t t jd}t|||}t|jd d\}}}t	|||}t|jd t jd}t jd}t t jd}t	|||}t|jd d S )N  )      ?g333333?      @r   rU   )
r6   rz   r   r   r   r   ndimr   absr   )rM   rS   r   r   r   r   r=   r=   r>   test_scalar_values/  s"    

z)TestMultivariateNormal.test_scalar_valuesc                 C   sf   t jd t jd}t jd}t t jd}t|||}t|||}t|t 	| d S Nr   rU   )
r6   rz   r   r   r   r   r   r   r   logrM   rS   r   r   d1d2r=   r=   r>   test_logpdfJ  s    z"TestMultivariateNormal.test_logpdfc                 C   sl   t jd t jd}t|}t|}t|d d}t|d d}t|t | t|t | d S Nr   rU   r	   )	r6   rz   r   r   r   r   r   r   r   rM   rS   r   r   Zd3Zd4r=   r=   r>   test_logpdf_default_valuesT  s    

z1TestMultivariateNormal.test_logpdf_default_valuesc                 C   sf   t jd t jd}t jd}t t jd}t|||}t|||}t|t 	| d S r   )
r6   rz   r   r   r   r   r   r   r   r   r   r=   r=   r>   test_logcdfa  s    z"TestMultivariateNormal.test_logcdfc                 C   sl   t jd t jd}t|}t|}t|d d}t|d d}t|t | t|t | d S r   )	r6   rz   r   r   r   r   r   r   r   r   r=   r=   r>   test_logcdf_default_valuesk  s    

z1TestMultivariateNormal.test_logcdf_default_valuesc                 C   sl   t jd d}t j|}td|d D ]<}t j||}t ||j}t||dd}t|j	j
| q*d S )Nr   rW   r	   TrP   )r6   rz   r   r   rangedotr   r   r   r   ry   )rM   r   r   Zexpected_rankr   r   Zdistnr=   r=   r>   	test_rankx  s    z TestMultivariateNormal.test_rankc              	   C   s  t ddD ]}tj|}t d|D ]}tj||}t||j}t||f}||d |d |f< t|}|d | |d |< t|}t|t||j}	t||}
tt||dd}tt||dd}tt||	dd}t	|j
j| t	|j
j| t	|j
j| ||d | }||}||
}t|| t|| ||d | }||}||
}t|| t|| |
|d d df  }||}||}t	|d t	|tj  q&q
d S )Nr	   rU   TrP   rY   r   )r   r6   rz   r   r   r   r   r   r   r   r   ry   r   r   r   inf)rM   r   zkr   Zcov_kkZcov_nnrS   r   Zcov_rryZdistn_kkZdistn_nnZdistn_rrZpdf_kkZpdf_nnZpdf_rrZ	logpdf_kkZ	logpdf_nnZ	logpdf_rrZy_orthZpdf_rr_orthZlogpdf_rr_orthr=   r=   r>   test_degenerate_distributions  sN    











z4TestMultivariateNormal.test_degenerate_distributionsc           
      C   s   d}t ddD ]}t d|D ]}t|}t|d d d |f }t||j}tj|||d}tj|||dd}t	|j
| t|dksJ tj|||dd}	t	|	j
| t|	tj ksJ qqd S )	N
   rC   rV   r	   r   r   rp   T)r   r   rQ   r   )r   r6   r   r   r   r   r   r   r   r   rp   allr   r   )
rM   r   r   rZmnr   ZvrXr   r   r=   r=   r>   test_degenerate_array  s"    


z,TestMultivariateNormal.test_degenerate_arrayc                 C   s   d}d}d}t || }|| }t j||ftd}t || 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   rC   Zdtyper   r	   )r6   expr   floatZfill_diagonalr   r   r   detr   r   slogdetr   rx   )rM   Zlarge_total_logZnposZnzeroZlarge_entryr   r   r   r=   r=   r>   test_large_pseudo_determinant  s    $z4TestMultivariateNormal.test_large_pseudo_determinantc                 C   s   t jd d}t j||}t ||j}t j|}t jdd|}t|||}t|||}t	dD ]f}t	dD ]X}	t|||	f ||}
t
|
|||	f  t|||	f ||}
t
|
|||	f dd qxqld S )Nr   rW   rC   rD   MbP?rtol)r6   rz   r   r   r   r   r   r   r   r   r   )rM   r   datar   r   r   Zdesired_pdfZdesired_cdfijactualr=   r=   r>   test_broadcasting  s    z(TestMultivariateNormal.test_broadcastingc                 C   sn   t ddd}d\}}|d }t|||}t|||}t|| t|||}t|||}t|| d S )Nr   rC   r   )333333??      ?)r6   linspacer   r   r   r   r   )rM   rS   r   r   scaler   r   r=   r=   r>   test_normal_1D  s    
z%TestMultivariateNormal.test_normal_1Dc                 C   s  t ddg}t ddgddgg}d}d|d  }t d	d|}t ||\}}t ||d
f}||d d d d d	f< ||d d d d df< t|||}	t|	|d	d}
t|	|dd}tj||d	 |d d d}tj||d |d d d}t	|
|ddd t	||ddd d S )Nr   g      @r   r   333333?i  rV   r	   r   rC   rs   r   r   )locr   )r	   r	   {Gz?r   atol)
r6   r   r   Zmeshgridemptyr   r   r-   r   r   )rM   r   r   r   deltar   ZxvZyvposr   Zmargin_xZmargin_yZgauss_xZgauss_yr=   r=   r>   test_marginalization  s     z+TestMultivariateNormal.test_marginalizationc                 C   s   t jd t jd}t jd}t t jd}t||}t||t||| t||t||| t|	|t	||| t|
|t
||| d S r   )r6   rz   r   r   r   r   r   r   r   r   r   )rM   rS   r   r   norm_frozenr=   r=   r>   test_frozen$  s    


z"TestMultivariateNormal.test_frozenrE   rC   r	   c                 C   sF   t d}t d}t||}t |j|s0J t |j|sBJ d S )NrC   rC   )r6   rJ   rK   r   allcloser   r   )rM   rE   r   Zcov_should_ber
  r=   r=   r>   2test_frozen_multivariate_normal_exposes_attributes2  s
    


zITestMultivariateNormal.test_frozen_multivariate_normal_exposes_attributesc           	   	   C   s   t jd d}t j||}t ||j}tj|\}}t 	|d}d|d< d|d< t |t t 
||j}d}t||d	}t|j|d	}t|jt t |d d  t|j |j d S )
Nr   rX   r   r   r   Hz>rY   h㈵>)cond)r6   rz   r   r   r   r   r   r   r   fullr`   r   Zpinvr   rx   r~   r   )	rM   r   rS   r   r   r   r  r   Zpsd_pinvr=   r=   r>   test_pseudodet_pinv@  s     z*TestMultivariateNormal.test_pseudodet_pinvc                 C   s    g dg dg}t tt| d S )NrF   rW   rU   rV   r   rH   r   rM   r   r=   r=   r>   test_exception_nonsquare_covZ  s    z3TestMultivariateNormal.test_exception_nonsquare_covc                 C   s@   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   )r6   nanr   rH   r   r   )rM   Zcov_nanZcov_infr=   r=   r>   test_exception_nonfinite_cov^  s    z3TestMultivariateNormal.test_exception_nonfinite_covc                 C   s    ddgddgg}t tt| d S )Nr	   r   rY   r  r  r=   r=   r>   test_exception_non_psd_covd  s    z1TestMultivariateNormal.test_exception_non_psd_covc                 C   s   t jd t jd}t jd}t 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|d t|d W d    n1 s0    Y  d S )	Nr   rU   )rU   rU   r   r   z0When `allow_singular is False`, the input matrixrA   r   )r6   rz   r   r   rJ   r   LinAlgErrorr   r   r   r   r   r   rG   r   )rM   rS   r   r   emsgr=   r=   r>   test_exception_singular_covh  s    
z2TestMultivariateNormal.test_exception_singular_covc                 C   s"  t g d}t ddd}d| d }|t | }t |||gj}t g dd}t g dg d	g d
gd}t|||}t||dd t g d}	t|||}
t|
|	dd t g d}t ||gj}t ddgd}t ddgddggd}t|||}t||dd d S )N)g0Q-?gox'V?g[S, t?gDB?gc_.?r   rC   rU   rD   )r	   rD   rC   dr	   rC   r   )rC   rU   r   )r   r   rD   绽|=r  )gwk:E]?g̙Z?g0?gL8?gAG*?gh㈵>)gIى?gG?gƏ)?gėh?gEE?r	   r  )	r6   r   r   cosr   r   r   r   r   )rM   Zr_pdfrS   r   r   r   r   r   r   Zr_cdfr   Zr_cdf2r2mean2cov2cdf2r=   r=   r>   test_R_values{  s$    z$TestMultivariateNormal.test_R_valuesc                 C   s<   t d}t d}t||dd}| }t|ddg d S )NrC   rC   rC   TrP   r   )r6   r   r   r   r   )rM   r   rE   modelsampler=   r=   r>   ,test_multivariate_normal_rvs_zero_covariance  s
    

zCTestMultivariateNormal.test_multivariate_normal_rvs_zero_covariancec                 C   s   d}d}t jt|d|d}t|j||f t jd tddgddgg|d}t|j|df t ddd}||}t|j|f d S )	Ni,  rW   r	   r   rC   r   r   r   )r   r   r6   r   r   r8   r   )rM   Nr   r,  r   r=   r=   r>   test_rvs_shape  s    
z%TestMultivariateNormal.test_rvs_shapec                 C   sx   t jd d}t j|}t j||}t ||j}d}t|||}tt	
|j|dd t|d|dd d S )N  rD     r   r   r   )r6   rz   r   r   r   r   r   r   r   numpyr   r   )rM   r   r   r   r   rp   r,  r=   r=   r>   test_large_sample  s    z(TestMultivariateNormal.test_large_samplec                 C   s   t jd d}t j|}t j||}t ||j}t||}t| t|| t j	
|d }d|t dt j d  t t |  }t||  d S )Nr0  rD   r   r   rC   r	   )r6   rz   r   r   r   r   r   r   r   r   Zeigr   pir~   )rM   r   r   r   r   r   eigsdesiredr=   r=   r>   test_entropy  s    
,z#TestMultivariateNormal.test_entropyc                 C   s*   t g d}d}tt t|| d S )Nr	   r	   r	   r   )r6   r   r   r   r   )rM   alphar6  r=   r=   r>   test_lnB  s    zTestMultivariateNormal.test_lnBc                 C   s   t jd}ddg}t d}|dd d }|dd d }tj||||d}t|||}t|||}t j|ddd	f |dd	df fd
d}	t j|dd	df |ddd	f fd
d}
t|	||}t|
||}|| | | }t|| d S )N   FYc@Y r   rC   )rW   rD   rC   rV   rD   lower_limit.r	   rY   rs   )r6   rz   r{   rK   r   r   concatenater   )rM   r   r   r   abcdf1Zcdf2aZcdf2bZab1Zab2Zcdf2ab1Zcdf2ab2r(  r=   r=   r>    test_cdf_with_lower_limit_arrays  s    
**z7TestMultivariateNormal.test_cdf_with_lower_limit_arraysc           
      C   s   t jd}|d}|d}||j }|dd d }|dd d }tj||||d}t||j||d}t tj||||d}t t||j||d}	t||dd t||dd t|	|dd d S )	Nr;  rD   rD   rD   rC   rD   rV   r<  -C6?r   )	r6   rz   r{   r   r   r   r   r   r   )
rM   r   r   r   r?  r@  rA  r(  Zcdf3Zcdf4r=   r=   r>   %test_cdf_with_lower_limit_consistency  s    


z<TestMultivariateNormal.test_cdf_with_lower_limit_consistencyc                 C   s   t d}t d}g dg dg dg dg}g dg dg dg dg}t g d}tj||||d}t||d |  d S )	NrD   r8  rZ   r	   r   r	   r   r	   r   r	   rY   rY   r	   r<  r   r6   r   rK   r   r   r   r   )rM   r   r   r@  r?  expected_signsr   r=   r=   r>   test_cdf_signs"  s    

z%TestMultivariateNormal.test_cdf_signsc                 C   s   t dt g d }t|}d}tjt|d  t	ddg| W d    n1 sZ0    Y  tjt|d tddg| W d    n1 s0    Y  g d}t
|g d|}ttj
||d| t
|g d	|}ttj
|d|d| d S )
Nr	   rF   z7`cov` represents a covariance matrix in 3 dimensions...rA   r   )r   r   r   rZ   r  r8  )r6   r`   r   r*   rI   rG   r   rH   r   r   r   r   )rM   Pr   rN   rS   r:   r=   r=   r>   test_mean_cov-  s    
.,z$TestMultivariateNormal.test_mean_covc                 C   sH   ddg}d}t jt|d t| W d    n1 s:0    Y  d S )Nr	   rD   z`x` must be two-dimensional.rA   )rG   r   rH   r   fit)rM   r   	error_msgr=   r=   r>   test_fit_wrong_fit_data_shape@  s    z4TestMultivariateNormal.test_fit_wrong_fit_data_shaper   )rD   rU   c                 C   sh   t jd}|d|f}t|\}}t j|ddt j|jdd }}t||dd t||dd d S )	N   @,Q| r   r   rs   )ZddofV瞯<r#  r   )	r6   rz   r{   r   rO  r   r   r   r   )rM   r   r   rS   Zmean_estZcov_estZmean_refZcov_refr=   r=   r>   test_fit_correctnessF  s     z+TestMultivariateNormal.test_fit_correctnessc                 C   sF   t dd}d}t d}tj|||d\}}t|| t|| d S )N)rC   r	   rD   r   )fix_meanfix_cov)r6   r  Z
atleast_2dr   rO  r   )rM   r   Z
mean_fixedZ	cov_fixedr   r   r=   r=   r>   test_fit_both_parameters_fixedO  s    


z5TestMultivariateNormal.test_fit_both_parameters_fixedrU  r*  rD   c                 C   sJ   d}t jt|d$ tjtd|d W d    n1 s<0    Y  d S )Nzd`fix_mean` must be a one-dimensional array the same length as the dimensionality of the vectors `x`.rA   rC   rU  rG   r   rH   r   rO  r6   rK   )rM   rU  r  r=   r=   r>   "test_fit_fix_mean_input_validationX  s    z9TestMultivariateNormal.test_fit_fix_mean_input_validationrV  r  )rD   rC   )rW   rW   c                 C   sJ   d}t jt|d$ tjtd|d W d    n1 s<0    Y  d S )Nzn`fix_cov` must be a two-dimensional square array of same side length as the dimensionality of the vectors `x`.rA   rD   rV  rZ  )rM   rV  r  r=   r=   r>   +test_fit_fix_cov_input_validation_dimension`  s    zBTestMultivariateNormal.test_fit_fix_cov_input_validation_dimensionc                 C   s`   d}t jt|d: tddgddgg}tjtd|d W d    n1 sR0    Y  d S )Nz2`fix_cov` must be symmetric positive semidefinite.rA   r   r   g      rC   r\  )rG   r   rH   r6   r   r   rO  rK   )rM   rP  rV  r=   r=   r>   *test_fit_fix_cov_not_positive_semidefinitej  s    zATestMultivariateNormal.test_fit_fix_cov_not_positive_semidefinitec                 C   s   t jd}|d}|d}t ||j}tj||d|d}t|\}}tj|||d	 }tj||d\}	}
t
|	| tj||	|
d	 }||k sJ |d}dt ||j }|
| }tj||	|d	 }||k sJ d S )	NrR  rD   rC  r   r   r   rp   r   r   rY  :0yE>)r6   rz   r{   r   r   r   r   rO  r   r~   r   )rM   r   r  rf   r   samples	mean_freecov_free	logp_freemean_fixcov_fixlogp_fixmZcov_perturbedlogp_perturbedr=   r=   r>   test_fit_fix_meanp  s2    







z(TestMultivariateNormal.test_fit_fix_meanc                 C   s   t jd}|d}|d}t ||j}tj||d|d}t|\}}tj|||d	 }tj||d\}	}
t
|	t j|dd	 t
|
| tj||	|
d	 }||k sJ |	d
|d  }tj|||
d	 }||k sJ d S )NrR  rD   rC  r   r_  r   r\  r   rs   r`  )r6   rz   r{   r   r   r   r   rO  r   r~   r   r   )rM   r   r  rf   r   ra  rb  rc  rd  re  rf  rg  Zmean_perturbedri  r=   r=   r>   test_fit_fix_cov  s0    





z'TestMultivariateNormal.test_fit_fix_covN)1r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	  r  rG   r   r   r6   rK   r+   Zfrom_diagonalr  r  r  r  r  r  r)  r-  r/  r3  r7  r:  rB  rF  rL  rN  rQ  rT  rW  r   r[  r]  r^  rj  rk  r=   r=   r=   r>   r   &  sh   

4
@
	

r   c                   @   sL   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dS )TestMatrixNormalc              	   C   s<  d}d}t ||fd}dt | t ||fd }dt | t ||fd }tttt d ttt|t d| ttt||t d ttt||| ttt||| ttt|j|| t jj	}t|tj
||t ||f t|tj
|t ||f| t|t||t ||f t|t|t ||f| d S )NrW   rD   r   r   ffffff?)rU   rW   rD   r   )r6   r  r   r   rH   r   r   r   r   r  r   rJ   )rM   num_rowsnum_colsr   r|   Vr  r=   r=   r>   test_bad_input  s(    zTestMatrixNormal.test_bad_inputc                 C   s  d}d}t ||fd}dt | t ||fd }dt | t ||fd }t ||f}t |df}t d|f}t |}	t |}
t d}ttj|||dj||f ttj|dj||f ttj|d	j|df ttj|d
jd|f ttj||dj||f ttj||dj||f ttj||dj||f tt|dj|	 tt|dj	|
 tt|d	j
| tt|d	j	| tt|d
j
| tt|d
j| tt||dj	|
 tt||dj|	 tt||dj
| d S )NrW   rD   r   r   rm  r	   r   rowcovcolcov)r   )rs  )rt  )r   rt  )r   rs  )rs  rt  )r6   r  r   r   r   r   r   r8   rs  rt  r   )rM   rn  ro  r   r|   rp  ZZZrZZcIrIcZI1r=   r=   r>   test_default_inputs  sR    


z$TestMatrixNormal.test_default_inputsc           
      C   s   d}d}t ||fd}t |d}d}t |d}d}t |}t |}	tt|||djd|  tt|||djd|	  tt|||djd|  tt|||djd|	  d S )NrW   rD   r   r   r   rr  )r6   r  r   r   r   rs  rt  )
rM   rn  ro  r   ZUvZUsZVvZVsrv  rw  r=   r=   r>   test_covariance_expansion  s*    

z*TestMatrixNormal.test_covariance_expansionc                 C   s   t ddD ]}t ddD ]}t||fd}dt| t||fd }dt| t||fd }t|||d}|jdd}tj|||dd	}t|| |jdd}	||	}
tj|	|||d}t|
| ||	}tj|	|||d}t|| qq
d S )
Nr	   rU   r   r   rm  rr  r   r   )r   rs  rt  r   )	r   r6   r  r   r   r   r   r   r   )rM   r   r   r   r|   rp  frozenrvs1rvs2r   pdf1pdf2logpdf1logpdf2r=   r=   r>   test_frozen_matrix_normal  s$    




z*TestMatrixNormal.test_frozen_matrix_normalc                 C   s  t ddD ]
}t ddD ]}t||fd}dt| t||fd }dt| t||fd }t|||d}|jdd}||}||}	| }
|j	
 }|j	
 }t||}tj|||d	}tj|||d	}tj||d	}t||d
d t|	|d
d t|
| qq
d S )Nr	   rU   r   r   rm  rr  r   r   r   r"  r   )r   r6   r  r   r   r   r   r   r   r   flattenZkronr   r   )rM   r   r   r   r|   rp  rz  r   r}  r  Zentropy1ZvecXZvecMr   r~  r  Zentropy2r=   r=   r>   test_matches_multivariate  s&    



z*TestMatrixNormal.test_matches_multivariatec                 C   sF  d}d}t ||fd}dt | t ||fd }dt | t ||fd }d}t|||d}|j|dd	}|j|d
d	}	t j|t jd d d d d d f |	t jd d d d d d f fdd}
t|
jd|||f |	|
}t|jd|f t
dD ]B}t
|D ]4}tj	|
||f |||d}t||||f d q
qd S )NrW   rD   r   r   rm  r   rr  r   r   i  r   rs   rC   r"  )r6   r  r   r   r   r>  newaxisr   r8   r   r   r   )rM   rn  ro  r   r|   rp  r.  rz  ZX1ZX2r   Zarray_logpdfr   r   Zseparate_logpdfr=   r=   r>   test_array_input4  s&    F
z!TestMatrixNormal.test_array_inputc                 C   s   d}d}t ||fd}dt | t ||fd }dt | t ||fd }d}t|||d}|j|dd	}t j|d
d}	t|	|dd t ||| |j	}
t|
|dd t t 
|dd|| |j	}t||dd d S )NrW   rD   r   r   rm    rr  r   r   r   rs   r   r#  r	   rC   )r6   r  r   r   r   r   r   r   reshaper   Zswapaxes)rM   rn  ro  r   r|   rp  r.  rz  r   Zsample_meanZsample_colcovZsample_rowcovr=   r=   r>   test_momentsK  s     zTestMatrixNormal.test_momentsc                 C   s   t jtddgddggtddgddggtddgddggtjddd	}td
dgddggddgddggg}t|| d S )Nr	   rC   rD   rW   rY   rU   r   r   )r   rs  rt  r   rp   g6?gǀgcϿ@g"'@gI2͖@g^jy%@gDn3@g|\3@)r   r   r6   r   rz   r{   r   )rM   r   expectedr=   r=   r>   test_samplesa  s"    
zTestMatrixNormal.test_samplesN)r   r   r   rq  rx  ry  r  r  r  r  r  r=   r=   r=   r>   rl    s   'rl  c                   @   s   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'S )(TestDirichletc                 C   s   t jd t jdd}t jdd|}t|}t| t| t| t| t|	 t	| d}t
|D ]r}t jdd|}|t | }t||d d t|d d | t||d d t|d d | qzd S Nr0  r	       &.>r   r   rY   )r6   rz   r   randintr   r   r   varr   r   r   r~   r   r   rM   r   r9  r   	num_testsr   rS   r=   r=   r>   test_frozen_dirichletv  s    (z#TestDirichlet.test_frozen_dirichletc                 C   s   t jd t g d}t jj|dd}t|jd tttj	|| tttj
|| t	|j| t	|jd d | t
|j| t
|jd d | d S )Nr0  r          @      @rX   ro   )rX   rD   rY   )r6   rz   r   r   r   r   r8   r   rH   r   r   r   rM   r9  rS   r=   r=   r>   "test_numpy_rvs_shape_compatibility  s    z0TestDirichlet.test_numpy_rvs_shape_compatibilityc                 C   sR   t jd g d}t jjt d|ddj}tttj|| tttj	|| d S )Nr0  )r   r   r  r  rX   ro   
r6   rz   r   r   maximumr   r   rH   r   r   r  r=   r=   r>   test_alpha_with_zeros  s
    z#TestDirichlet.test_alpha_with_zerosc                 C   sR   t jd g d}t jjt d|ddj}tttj|| tttj	|| d S )Nr0  )r   g       r  r  rX   ro   r  r  r=   r=   r>    test_alpha_with_negative_entries  s
    z.TestDirichlet.test_alpha_with_negative_entriesc                 C   sp   t g d}t g d}t|| t|| t g d}tt||d tt||t d d S )Nr   r  r        @r   r   r   rm  )r   r   r   r   rV   )r6   r   r   r   r   r   r   r  r=   r=   r>   test_data_with_zeros  s    z"TestDirichlet.test_data_with_zerosc                 C   s@   t g d}t g d}tttj|| tttj|| d S )N)r   r   r  r  r  r6   r   r   rH   r   r   r   r  r=   r=   r>   $test_data_with_zeros_and_small_alpha  s    z2TestDirichlet.test_data_with_zeros_and_small_alphac                 C   s@   t g d}t g d}tttj|| tttj|| d S )Nr  )r   皙r   rm  r  r  r=   r=   r>   test_data_with_negative_entries  s    z-TestDirichlet.test_data_with_negative_entriesc                 C   s@   t g d}t g d}tttj|| tttj|| d S )Nr  )r   皙?r   rm  r  r  r=   r=   r>    test_data_with_too_large_entries  s    z.TestDirichlet.test_data_with_too_large_entriesc                 C   s>   t g d}t dd}tttj|| tttj|| d S )Nr  )rC   rX   rX   g$I$I?r6   r   r  r   rH   r   r   r   r  r=   r=   r>   test_data_too_deep_c  s    z"TestDirichlet.test_data_too_deep_cc                 C   sF   t ddgddgg}t dd}tttj|| tttj|| d S )Nr   r  r  r  )rC   rC   rX         ?r  r  r=   r=   r>   test_alpha_too_deep  s    z!TestDirichlet.test_alpha_too_deepc                 C   s6   t g d}t dd}t|| t|| d S )Nr  rD   rX   UUUUUU?)r6   r   r  r   r   r   r  r=   r=   r>   test_alpha_correct_depth  s    z&TestDirichlet.test_alpha_correct_depthc                 C   s>   t g d}t dd}tttj|| tttj|| d S )Nr  r  r   r  r  r=   r=   r>   test_non_simplex_data  s    z#TestDirichlet.test_non_simplex_datac                 C   s>   t g d}t dd}tttj|| tttj|| d S )Nr  )rC   rX   r   r  r  r=   r=   r>   test_data_vector_too_short  s    z(TestDirichlet.test_data_vector_too_shortc                 C   s>   t g d}t dd}tttj|| tttj|| d S )Nr  )rU   rX   r   r  r  r=   r=   r>   test_data_vector_too_long  s    z'TestDirichlet.test_data_vector_too_longc                 C   sj   t 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  )r6   r   r   r   r   r  r   )rM   r9  r   Zexpected_meanZexpected_varZexpected_covr=   r=   r>   test_mean_var_cov  s    zTestDirichlet.test_mean_var_covc                 C   s`   t dg}t|}t| jd t| jd t|dgjd t|dgjd d S )Nr   r   r   )	r6   r   r   r   r   r   r  r   r   )rM   r9  r   r=   r=   r>   r     s    z TestDirichlet.test_scalar_valuesc                 C   s   t jd t jdd}t jdd|}t|}d}t|D ]@}t jdd|}|t | }t|	|d d |	| q>d S r  )
r6   rz   r   r  r   r   r   r~   r   r   r  r=   r=   r>    test_K_and_K_minus_1_calls_equal   s    z.TestDirichlet.test_K_and_K_minus_1_calls_equalc                 C   s   t jd t jdd}t jdd|}t|}d}d}d }t|D ]}t|D ]>}t jdd|}	|	t |	 }	|d urt ||	f}qR|	}qR|	|j
}
d }|D ](}|	|}|d urt ||}q|}qt|
| qFd S )Nr0  r	   r  r  r   r   rU   )r6   rz   r   r  r   r   r   r~   vstackr   r   appendr   )rM   r   r9  r   r  Znum_multipleZxmr   rh  rS   Zrmrsxsr   r=   r=   r>   test_multiple_entry_calls  s,    
z'TestDirichlet.test_multiple_entry_callsc                 C   s   t jd t jddd}t|}t|d |d }d}t|D ]:}t jddd}|t | }t|	||	|g qBt|
 |
 d  t| | d  d S )Nr0  r  r   rC   r   r	   r   )r6   rz   r   r   r   r   r   r~   r   r   r   r  )rM   r9  r   r@  r  r   rS   r=   r=   r>   test_2D_dirichlet_is_beta,  s    z'TestDirichlet.test_2D_dirichlet_is_betaN)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  t  s&   	r  c               
   C   s   t ddg} t dgg}ttt| | zt| | W nB tyz } z*d}tt|d t| | W Y d }~n
d }~0 0 d S )Nr   r   zDimension mismatch)r6   r   r   rH   r   r   strr   )r   sigmar  r  r=   r=   r>   ,test_multivariate_normal_dimensions_mismatch=  s    r  c                   @   s<   e Zd Zdd Zdd Zdd Zdd Zd	d
 Zdd ZdS )TestWishartc                 C   s  t jddd}ddgt dt jd t jdddg}|D ]*}td|}t|j| t|jj|j q8t ddgddgg}ddgt jd t ddgddggg}|D ]*}td|}t|j| t|jj|j qtttdt 	d tdt 	d t jddd}tttd| d S )Nr	   rC   Zndminr   r	   rC   r  rD   )
r6   r   r_r   r   r   r8   r   rH   rK   )rM   Z
true_scalescalesr   wr=   r=   r>   test_scale_dimensionsQ  s8    



z!TestWishart.test_scale_dimensionsc              
   C   s  ddgt dt jd t jdddt jdgddg}tdd}|t jddd}|D ]}t||| qVg dt jd t jg dddg}tdd}|t jg ddd}|D ]}t||| qdddgt dt jd t ddgddggt ddgddggd d d d t jf g}tdt d}|t ddgddggd d d d t jf }|D ]}t||| qfd S )Nr	   rC   r  rD   rF   r*  r   )r6   r   r  r   r   r   r  rK   )rM   r   r  ZdensityrS   r=   r=   r>   test_quantile_dimensions|  sP    	



z$TestWishart.test_quantile_dimensionsc           	      C   sn  d}t t |d }t ||d  d |t j|dd< t |j|}g }tdD ]\}t t ||d d  }t ||d  d |t j|dd< t |j|}|| qVt |j}ddt 	dddfd||fg}|D ]\}}}t
||}t| t
|| t| t
|| t| t
|| t| t
|| t||t
||| qd S 	NrW   r	   rC   rY   r   rU   r   r   )r6   r`   r   tril_indicesr   r   r   r  r   r   r   r   r  r   moder   r   )	rM   r   r   r   r   rS   
parametersdfr  r=   r=   r>   r    s*    $$
zTestWishart.test_frozenc                 C   s   d}d}t |}d|d< d|d< t||}t jd t||}t jd | }t jd t jjdd}t jt j|t j|d t j|d	 f d }t 	|}	||	t j
|d
d< t j|}
|
|	}t ||j}t|| t|| d S )NrD   r   r   r   r	   r   i ro   r	   rC   rY   r  )r6   rK   r   rz   r   r   r   r  	chisquarer`   r  r   r   r   r   r   )rM   r   r  r   r  Zw_rvsZfrozen_w_rvscovariances	variancesrf   DZDAZmanual_w_rvsr=   r=   r>   test_wishart_2D_rvs  s6    





zTestWishart.test_wishart_2D_rvsc                 C   s   t jd d}d}t |}t jdddtd}t jdddd}|D ]}t||}t|}t	|
 |
  t	| |  t	| |  t	|||| |j|d	}	|f}
d
}td|
||	 qDd S )N^   r	   r   rC   r   r   numro   r  r   )r6   rz   r   rK   r   r   r   r   r   r   r  r   r   r   r   r
   )rM   snr   r   df_ranger   r  r  cr   r;   r9  r=   r=   r>   test_1D_is_chisquared  s"    

z!TestWishart.test_1D_is_chisquaredc                 C   s  t jd d}d}d}t t dd }t d|t jddd< t |j|}t |df}|j||	 }t
||}t||d	}t| |  t| |  t| |  t jd
ddd}	t||	||	 |j|d}
|d|f}d}td|||
 d S )Nr  r  r   rW   r	   rV   rY   r  r   r   r  ro   r   r  r   )r6   rz   r   r`   r   r  r   r   rJ   r   r   r   r   r  r   r   r   r   r   r
   )rM   r  r  r   r   ZlamdaZsigma_lamdar  r  r   r   r;   r9  r=   r=   r>   test_is_scaled_chisquared  s(    

z%TestWishart.test_is_scaled_chisquaredN)	r   r   r   r  r  r  r  r  r  r=   r=   r=   r>   r  P  s   +1 ,r  c                   @   s   e Zd Zdd Zdd Zdd Zejddd	gd
d Z	dd Z
dd Zejdddgdd Zdd Zejdddgdd Zdd Zejdddgdd Zdd Zdd Zd d! Zd"S )#TestMultinomialc                 C   s   t ddd}t|ddd t ddgd	d
dg}|tj ksBJ t d	d	gd	d
dg}|d	ksdJ t ddgd	ddg}t|tjdd d S )NrD   rW   rX   r   rm  g&Mtyr`  r   rD   rW   r   r   rm  r\   )r   logpmfr   r6   r   r  )rM   vals1vals2vals3vals4r=   r=   r>   test_logpmf<  s    zTestMultinomial.test_logpmfc                 C   sX   t ddd}tddd}t||dd t dd	d
}tdd	d}t||dd d S )Nr  rX   r  rD   r   r`  r   )rV         r   r   rV   r   )r   r  r    r   pmfrM   val1val2r=   r=   r>   test_reduces_binomialI  s    z%TestMultinomial.test_reduces_binomialc                 C   sR   dg d }}ddddddd	dd
dd
}|D ] }t t||||| dd q,d S )NrD   )g      ?r  g      ?g     @?g     ?g      ?g      `?g     ?g      ?g      ?g      ?g      ?)
)r   r   rD   )r	   r   rC   )rC   r   r	   )rD   r   r   r   r8  rC   r	   r   )r   rC   r	   r!  )r   rD   r   +=r#  )r   r   r  )rM   r   pZr_valsrS   r=   r=   r>   test_RT  s    zTestMultinomial.test_Rr   r   rD   c                 C   sH   t j|dgd ddd}tjd}|j |dgd dd}t|| d S )Nr  rD   rX   {   r   ro   )r   r   r6   rz   RandomStater   )rM   r   Zsc_rvsrndmZnp_rvsr=   r=   r>   test_rvs_npe  s    zTestMultinomial.test_rvs_npc           	      C   s@  t ddd}t|ddd t ddd	}t|d
dd t 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d tjdtjd}t |dd	}t|tjg tjd t ddgdd	}t|ddd t g ddg d}t|ddd t g ddg d}|dksJ t g ddg d}|dks<J d S )N)rU   rU   r	   r	   r`  r   r  rX   r  g5
?rD   r   r  rY   	   r  g*7?g<Wƌ?r   rC   r   rW   rC   rD   rD   r   rV   )gUUUUUU?r  r   gߦ?rZ   r  )r   r  r   r6   r  float64r   )	rM   vals0r  r  rS   r  r  Zvals5Zvals6r=   r=   r>   test_pmfm  s&    $zTestMultinomial.test_pmfc                 C   s
  t ddgdddgddgg}t|dd	gd
d t ddgddgddg}t|ddgd
d t ddgddgggdddg}t|ddggd
d t ddgdgdgggddg}t|dgdgggd
d t ddgddggdggggddg}t|ddggggd
d d S )Nr	   rC   rD   r   r   r   r  gv?g~jt?r`  r   rW   r   )r   r  r   )rM   r  r  r  r  r  r=   r=   r>   test_pmf_broadcasting  s      &z%TestMultinomial.test_pmf_broadcastingrU   c                 C   s   t |d}|d d | d d | d d g| d d |d d | d d g| d d | d d |d d gg}t||dd d S )	N)r   r   r   r   r  r   r   rm  r`  r   r   r   r   )rM   r   cov1r'  r=   r=   r>   test_cov  s    $$$zTestMultinomial.test_covc                 C   s   t 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	d
 t ddgddg}ddgddggddgddggg}t||d	d
 t 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
 d S )NrU   r   r   r   r  g?gܿgr`  r   rW   g
ףp=
?g
ףp=
׿r   rm  r  r   gzG?gzGr   g333333r  rM   r  r'  cov3cov4cov5cov6r=   r=   r>   test_cov_broadcasting  s      z%TestMultinomial.test_cov_broadcastingrC   c                 C   s*   t |ddg}t|t|ddd d S Nr   r  r`  r   r   r   r   r    )rM   r   ent0r=   r=   r>   r7    s    zTestMultinomial.test_entropyc                 C   s   t ddgddg}t|tddtddgdd t ddgdd	gd
dgg}t|tddtdd
gdd t dgdggdd	gd
dgg}t|tddtdd
gtddtdd
ggdd d S )NrC   rD   r   r   r`  r   rX   r  rm  r  r   r  )rM   r  Zent1Zent2r=   r=   r>   test_entropy_broadcasting  s     z)TestMultinomial.test_entropy_broadcastingc                 C   s.   t |ddg}t||d |d gdd d S r  r   r   r   )rM   r   mean1r=   r=   r>   	test_mean  s    zTestMultinomial.test_meanc                 C   s2   t ddgddg}t|ddgddggd	d
 d S )NrU   rV   r   r  r   r  g433333?g433333@r`  r   r  )rM   r  r=   r=   r>   test_mean_broadcasting  s    z&TestMultinomial.test_mean_broadcastingc                 C   s   t jd d}d}g dg dg dg dg dg}t j|t jd	}t||}t||t||| t||t||| t|	 t	|| d S )
Nr      )r   r   r   r  r   r   r   r  r   r   r	      r   r	   r	   r   r	   r	   r	   r  r	   r	   rC   r  r   )
r6   rz   r   r7   r   r   r   r  r  r   )rM   r   ZpvalsrS   Z	mn_frozenr=   r=   r>   r    s    "
zTestMultinomial.test_frozenc                 C   sZ   d}t jd}||}d|d< |t | }t |}t|||}t |sVJ d S )NX   l   iRZY gKH9rY   )r6   rz   r{   r~   rJ   r   r  isfinite)rM   r   r   r  rS   r  r=   r=   r>   test_gh_11860  s    

zTestMultinomial.test_gh_11860N)r   r   r   r  r  r  rG   r   r   r  r  r  r  r  r7  r  r  r  r  r  r=   r=   r=   r>   r  ;  s$   



r  c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestInvwishartc           	      C   sX  d}t t |d }t ||d  d |t j|dd< t |j|}g }tdD ]\}t t ||d d  }t ||d  d |t j|dd< t |j|}|| qVt |j}ddt 	dddfd||fg}|D ]p\}}}t
||}t| t
|| t| t
|| t| t
|| t||t
||| qd S r  )r6   r`   r   r  r   r   r   r  r   r   r   r   r  r   r  r   r   )	rM   r   r   r   r   rS   r  r  iwr=   r=   r>   r    s(    $$
zTestInvwishart.test_frozenc                 C   s   t jd d}d}t |}t jdddtd}t jdd	d	d
}|D ]}t||}t|d dd}t	|
 |
  t	| |  t	|||| |j|d}	|d ddf}
d}td|
||	 t	| |  qDd S )Nr  r  r	   rU      rC   r   r   r   r  r   r  ro   r   r  r   )r6   rz   r   rK   r   r   r   r   r   r   r  r   r   r   r
   r   )rM   r  r   r   r  r   r  r   Zigr   r;   r9  r=   r=   r>   test_1D_is_invgamma  s"    

z"TestInvwishart.test_1D_is_invgammac                 C   s  d}d}t |}d|d< d|d< t||}t jd t||}t jd | }t jd t jjdd}t jt j|d t j|d	 t j|f d }t 	|}	||	t j
|d
d< t j|}
t j|	j|
jj}t ||j}t|| t|| d S )NrD   r   r   r   r  iHG	 ro   rC   r	   rY   r  )r6   rK   r   rz   r   r   r   r  r  r`   r  r   r   solver   r   r   )rM   r   r  r   r   Ziw_rvsZfrozen_iw_rvsr  r  rf   r  LZmanual_iw_rvsr=   r=   r>   test_invwishart_2D_rvs)  s6    

	


z%TestInvwishart.test_invwishart_2D_rvsc                 C   s   d}d}dD ]}t t |d }t ||d  d |t j|dd< t |j|}t||}| }| }|| d }|j	|d	d
}	|	jdd}
||d  d }d| }t
d|d  }t j|
| | d|dsJ qdS )z1Test that sample mean consistent with known mean.r    N  )r	   rU   r	   rC   rY   r  r   r   r   r   rs   r  r#  N)r6   r`   r   r  r   r   r   r   r  r   r   Zppfr  )rM   r  Zsample_sizer   r   r   Z	Xmean_expZXvar_expZ	Xmean_stdr   Z	Xmean_estZntestsZ	fail_rateZmax_diffr=   r=   r>   test_sample_meanW  s(    $

zTestInvwishart.test_sample_meanc                 C   s   t g dg dg dg dg}t g dg dg dg dg}d	}t|||}|jd
 }t j|\}}t j|\}}t j||}	|d | || d t d  t	|d | || d d |  d|	
   }
t||
 dS )zRegression test for gh-8844.)rC   r	   r   r   )r	   rC   r   r   )r   r   rD   r	   )r   r   r	   rC   )r  rX   rD   r	   )rX   r  rU   r	   )rD   rU   r  rC   )r	   r	   rC   r  rV   r   rC   r	   r   N)r6   r   r   r   r8   r   r   r#  r   r0   tracer   )rM   r   PsinuZprobr  sigZlogdetXZ	logdetPsir   r  r=   r=   r>   test_logpdf_4x4r  s4    




zTestInvwishart.test_logpdf_4x4N)r   r   r   r  r"  r%  r'  r,  r=   r=   r=   r>   r    s
    !.r  c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestSpecialOrthoGroupc                 C   sf   t jd td}t g dg dg dg}t|| t jjdd}tjd|d}t|| d S )N  rD   )g(fg^A.g*B?)g:d?g2ugi}?)gR#xlF?g^`D?g?r   r   )r6   rz   r   r   r   r   r   r  )rM   rS   r  r   r=   r=   r>   test_reproducibility  s    


z*TestSpecialOrthoGroup.test_reproducibilityc                 C   s<   t ttjd  t ttjd t ttjd t ttjd d S Nr*  r	   r   )r   rH   r   r   rM   r=   r=   r>   test_invalid_dim  s    z&TestSpecialOrthoGroup.test_invalid_dimc                 C   s4   d}t |}|jdd}t j|dd}t|| d S )NrX   r   r   )r   r   r   )rM   r   rz  r{  r|  r=   r=   r>   test_frozen_matrix  s
    z(TestSpecialOrthoGroup.test_frozen_matrixc                 C   sd   dd t ddD }dd |D }t|dgd dd	 |D ]$}tt||jt|jd
  q:d S )Nc                 S   s$   g | ]}t d D ]}t|qqS rX  )r   r   r   .0r   r   r=   r=   r>   
<listcomp>  s   z<TestSpecialOrthoGroup.test_det_and_ortho.<locals>.<listcomp>rC   r  c                 S   s   g | ]}t j|qS r=   r6   r   r   r5  rS   r=   r=   r>   r6        r      vIh%<=r   r   )r   r   r   r6   r   r   rK   r8   )rM   r  detsrS   r=   r=   r>   test_det_and_ortho  s    z(TestSpecialOrthoGroup.test_det_and_orthoc                    sx   d}d}d}t jd tj||dd fdd D  fd	d
 D }fdd
|D }t|gt| | d S )NrU   r  皙?r.  ro   r  r  )r	   rW   rD  c                    s.   i | ]&\  ft  fd dD qS )c                    s   g | ]}|   qS r=   r=   r8  ecZerr=   r>   r6    r9  z>TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>sortedr5  r  r@  r>   
<dictcomp>  r9  z3TestSpecialOrthoGroup.test_haar.<locals>.<dictcomp>c                    s&   g | ]} D ]}||kr||fqqS r=   r=   r5  Ze0e1elsr=   r>   r6    r9  z3TestSpecialOrthoGroup.test_haar.<locals>.<listcomp>c                    s&   g | ]\}}t  |  | d  qS r  r   r5  p0p1projr=   r>   r6    r9  )r6   rz   r   r   r   r   r   rM   r   ra  Zks_probpairsZks_testsr=   rJ  rP  r  r>   	test_haar  s    
zTestSpecialOrthoGroup.test_haarN)r   r   r   r/  r2  r3  r=  rT  r=   r=   r=   r>   r-    s
   	r-  c                   @   s^   e Zd Zdd Zdd Zdd Zdd Zej	d	g d
dd Z
dd Zejjdd ZdS )TestOrthoGroupc                 C   sn   d}t j| td}tjd|d}tt j|d t g dg dg dg}t	|| t	|| d S )Nr.  rD   r   rY   )gm?gӠh"gEo?)g~7ݲC?g>Ŀg0J_ٿ)gݱ&ǿg 6qrg`X|[)
r6   rz   r   r   r   r   r   r   r   r   )rM   r   rS   r   r  r=   r=   r>   r/    s    


z#TestOrthoGroup.test_reproducibilityc                 C   s<   t ttjd  t ttjd t ttjd t ttjd d S r0  )r   rH   r   r   r1  r=   r=   r>   r2    s    zTestOrthoGroup.test_invalid_dimc                 C   sV   d}t |}t |dd}|jdd}t j|dd}|jdd}t|| t|| d S )NrX   r   r   r   r	   ro   )r   r   r   rM   r   rz  frozen_seedr{  r|  rvs3r=   r=   r>   r3    s    
z!TestOrthoGroup.test_frozen_matrixc                 C   s|   dd t ddD }tdd |D }tt|t|jdd |D ].}|D ]$}tt||j	t
|jd  qPqHd S )	Nc                    s"   g | ]  fd dt dD qS )c                    s   g | ]}t  qS r=   )r   r   r5  r   r   r=   r>   r6    s   @TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>.<listcomp>r   )r   rD  r=   rZ  r>   r6    s   
z5TestOrthoGroup.test_det_and_ortho.<locals>.<listcomp>rC   r  c                 S   s   g | ]}d d |D qS )c                 S   s   g | ]}t j|qS r=   r7  r8  r=   r=   r>   r6    r9  r[  r=   )r5  xxr=   r=   r>   r6    r9  r;  r   r   )r   r6   r   r   fabsrJ   r8   r   r   r   rK   )rM   r  r<  r\  rS   r=   r=   r>   r=    s    z!TestOrthoGroup.test_det_and_orthor   )rC   rU   r   r!  c                 C   s   t jd}t|d}|jd|d}tj|}t |dk}t	|}t
||}|jdd\}	}
|	d  k rv|
k s|n J d S )	Nl   <`Lr rZ  r1  r   r   gffffff?)Zconfidence_levelr   )r6   rz   r{   r   r   r   r   r   r~   r   r,   Z	binomtestZproportion_ci)rM   r   r   r   r   r<  r   r   r9   lowhighr=   r=   r>   test_det_distribution_gh18272   s    
z,TestOrthoGroup.test_det_distribution_gh18272c                    sx   d}d}d}t jd tj||dd fdd D  fd	d
 D }fdd
|D }t|gt| | d S )NrU   r  r>  i  ro   r?  c                    s.   i | ]&\  ft  fd dD qS )c                    s   g | ]}|   qS r=   r=   r8  r@  r=   r>   r6  #  r9  z7TestOrthoGroup.test_haar.<locals>.<dictcomp>.<listcomp>rB  rD  rE  r@  r>   rF  #  r9  z,TestOrthoGroup.test_haar.<locals>.<dictcomp>c                    s&   g | ]} D ]}||kr||fqqS r=   r=   rG  rI  r=   r>   r6  $  r9  z,TestOrthoGroup.test_haar.<locals>.<listcomp>c                    s&   g | ]\}}t  |  | d  qS r  rK  rL  rO  r=   r>   r6  %  r9  )r6   rz   r   r   r   r   r   rQ  r=   rS  r>   rT    s    
zTestOrthoGroup.test_haarc                    sh   t jd dd }tddD ]D d fdd		}||}|tjjj}tj||\}}t	d
| qd S )Nr.  c                 S   s,   t jt jj| | fd\}}}t ||S Nro   )r6   r   r   rz   r   r   )r   r   Z_sr   r=   r=   r>   random_ortho-  s     z<TestOrthoGroup.test_pairwise_distances.<locals>.random_orthorC   rV   r  r"  c                    s<   t  fddt|D }|t jj| ||jd7 }|S )Nc                    s*   g | ]"}t  d  d  d qS )rZ  rC   )r6   r~   )r5  r   )r   r   r=   r>   r6  3  s   z\TestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statistics.<locals>.<listcomp>ro   )r6   r   r   rz   r   r8   )r   r.  Zepsr,   rZ  )r   r>   generate_test_statistics2  s
    zHTestOrthoGroup.test_pairwise_distances.<locals>.generate_test_statisticsr>  )r  r"  )
r6   rz   r   r   r   r,   r   r   r   r   )rM   rb  rc  r  r   Z_Dr  r=   rZ  r>   test_pairwise_distances(  s    	z&TestOrthoGroup.test_pairwise_distancesN)r   r   r   r/  r2  r3  r=  rG   r   r   r`  rT  Zslowrd  r=   r=   r=   r>   rU    s   
rU  c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestRandomCorrelationc                 C   sb   t jd d}t|}tj|dd}t g dg dg dg dg}t|| t|| d S )Nr.  r   r  r   r   r   )r   ѓ2ǿA?Ϳ)rg  r   4($?R}%?)rh  rj  r   qTnƿ)ri  rk  rl  r   )r6   rz   r   r   r   r   r   )rM   r5  rS   r   r  r=   r=   r>   r/  D  s    


z*TestRandomCorrelation.test_reproducibilityc                 C   s|   t ttjd  t ttjd t ttjd t ttjdg t ttjddgddgg t ttjddg t ttjg d d S )	Ntestr   r	   rC   rD   rW   g      )r	   rC   r   )r   rH   r   r   r1  r=   r=   r>   test_invalid_eigsP  s    z'TestRandomCorrelation.test_invalid_eigsc                 C   sR   d}t |}t |dd}t j|dd}|jdd}| }t|| t|| d S )Nrf  r.  r   r   )r   r   r   )rM   r5  rz  rW  r{  r|  rX  r=   r=   r>   r3  Y  s    
z(TestRandomCorrelation.test_frozen_matrixc           
         s   dd  t jd  fddtddD }|g d d	d |D }d
d |D }dd |D }dd |D }t||ddd dd |D }t||D ]\}}t||dd q|D ]}	t|	|	jdd qd S )Nc                 S   s   | | t | S r5   )r~   )r   r  r=   r=   r>   r   m  s    z3TestRandomCorrelation.test_definition.<locals>.normr  c                    s    g | ]} |t jj|d qS )ro   )r6   rz   r   rY  r   r=   r>   r6  r  r9  z9TestRandomCorrelation.test_definition.<locals>.<listcomp>rC   rV   )rW   r   r   r   c                 S   s   g | ]}d gt | qS )r   )r   r5  r  r=   r=   r>   r6  u  r9  c                 S   s   g | ]}t |qS r=   )r   r   rp  r=   r=   r>   r6  v  r9  c                 S   s   g | ]}t t j|qS r=   )r6   r]  r   r   r8  r=   r=   r>   r6  |  r9  c                 S   s   g | ]}t |qS r=   )r6   prodrp  r=   r=   r>   r6  }  r9  r;  r  c                 S   s   g | ]}t |qS r=   )r6   r`   r8  r=   r=   r>   r6    r9  r   )r6   rz   r   r   r  r   zipr   )
rM   r5  rJ   r  r<  Z
dets_knownZdiagsr?  r@  rS   r=   ro  r>   test_definitione  s    z%TestRandomCorrelation.test_definitionc                 C   s|  t jddgddggtd}t|}t|t ddgddgg t jdd t ddgddgg}t jddgdt ddggtd}t| }t||j	
|
| t jd	dgdd
ggtd}t| }t||j	
|
| W d    n1 s0    Y  t jddgddggtd}t| }t|d d t jddgddggtd}t| }t|d d d S )Nr   r   r	   r   ignore)ZoverrY   gu <7~r   r  rC   r  gMk   @)r6   r   r   r   Z_to_corrr   errstate	nextaftercopyr   r   )rM   rh  gZm0r=   r=   r>   test_to_corr  s"    
"8z"TestRandomCorrelation.test_to_corrN)r   r   r   r/  rn  r3  rs  ry  r=   r=   r=   r>   re  C  s
   	$re  c                   @   st   e Zd Zejdddgejdg ddd Zejdg dd	d
 Zdd Zejdg ddd Z	dS )TestUniformDirectionr   r	   rD   rp   Nr	   rU   )rU   rW   c           
      C   sv   t jd}t||d}||}t |t | }}|j|||dj}|j|ksXJ t j	j
|dd}	t|	d d S )N   Sid)_i4 r   ro   rY   rs   r   )r6   rz   r{   r&   r   r   rK   r   r8   r   r   r   )
rM   r   rp   r   Zuniform_direction_distra  r   r   expected_shapenormsr=   r=   r>   r    s    
z!TestUniformDirection.test_samples)Nr   r*  r   c                 C   s@   d}t jt|d t| W d    n1 s20    Y  d S )NzMDimension of vector must be specified, and must be an integer greater than 0.rA   )rG   r   rH   r&   r   )rM   r   rN   r=   r=   r>   r2    s    z%TestUniformDirection.test_invalid_dimc                 C   sR   d}t |}t |dd}|jdd}t j|dd}| }t|| t|| d S )NrU   r.  r   r   )r&   r   r   rV  r=   r=   r>   test_frozen_distribution  s    
z-TestUniformDirection.test_frozen_distribution)rC   rU   r  c                 C   s   t jd}t||d}|jdd\}}||| | 8 }|t j| }t|| ddd |jdd}|| }|| }t ||}	|	t j	7 }	|	dt j	  }	t
 }
t|	|
j}|jd	ksJ d S )
Nl   @9Y sr   rC   ro   r   r  r#  '  r>  )r6   rz   r{   r&   r   r   r   r   arctan2r4  r   r   r   pvalue)rM   r   r   Zspherical_distv1v2ra  s1s2anglesZuniform_distZkstest_resultr=   r=   r>   test_uniform  s    
z!TestUniformDirection.test_uniformN)
r   r   r   rG   r   r   r  r2  r  r  r=   r=   r=   r>   rz    s   
rz  c                   @   s4   e Zd Zdd Zdd Zdd Zdd Zd	d
 ZdS )TestUnitaryGroupc                 C   sX   t jd td}tjddd}t g dg dg dg}t|| t|| d S )Nr.  rD   r   )y~p?yZ?y뉦?ĭ?y8Z?&4?)yEHξr?8i?ye??+ݓݿyu=ٿB۽'?)yqXQÿ?yN6ҿzܷy! 8l?2W'?)r6   rz   r   r   r   r   r   )rM   rS   r   r  r=   r=   r>   r/    s    

z%TestUnitaryGroup.test_reproducibilityc                 C   s<   t ttjd  t ttjd t ttjd t ttjd d S r0  )r   rH   r   r   r1  r=   r=   r>   r2    s    z!TestUnitaryGroup.test_invalid_dimc                 C   sV   d}t |}t |dd}|jdd}t j|dd}|jdd}t|| t|| d S )NrX   r.  r   r   r	   ro   )r   r   r   rV  r=   r=   r>   r3    s    
z#TestUnitaryGroup.test_frozen_matrixc                 C   sJ   dd t ddD }|D ],}tt|| jt|jd dd qd S )Nc                 S   s$   g | ]}t d D ]}t|qqS rX  )r   r   r   r4  r=   r=   r>   r6  	  s   z3TestUnitaryGroup.test_unitarity.<locals>.<listcomp>rC   r  r   rS  r#  )r   r   r6   r   Zconjr   rK   r8   )rM   r  rS   r=   r=   r>   test_unitarity	  s
    zTestUnitaryGroup.test_unitarityc                 C   sx   d}d}t jd tj||d}t dd |D }t |j|j}t	|
 tt j dt j j}t|jdk d S )	NrU   r  r.  ro   c                 S   s   g | ]}t j|qS r=   )r   r   Zeigvalsr8  r=   r=   r>   r6  	  r9  z.TestUnitaryGroup.test_haar.<locals>.<listcomp>rC   r>  )r6   rz   r   r   r   r  r  imagrealr   Zravelr   r4  r   r   r  )rM   r   ra  r  r5  rS   r9   r=   r=   r>   rT  	  s     zTestUnitaryGroup.test_haarN)r   r   r   r/  r2  r3  r  rT  r=   r=   r=   r>   r    s
   	r  c                   @   s,  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d Zejdedd Zdd Z	dd Z
eddd Zdd  Zd!d" Zd#d$d%d&dgdd&ggd%ddgd&dgdd&ggdfd%d&dgdd&ggd&ddgd&dgdd&ggd&fd&d&gd%d%d&d&gddgddggdfd&d&gd%d&d&d&gddgddggd&fd&d&gd&dgdd&ggd%d&d&gd&dgdd&ggdfd&d&gd&dgdd&ggd&d&d&gd&dgdd&ggd&fgZejd'ed(d) Zd*ddd*gdggdfd*gdgdd*gdggdfed*gedgdd*gdggdfgZejd'ed+d, Zd-d. Zd/d0 Zd1d2 Zejd3d4d5gejd6g d7ejd8d9d:ejgd;d< Zd=d> Zejd6g d?d@dA Zejd6g dBdCdD ZdqdFdGZdHdI Zejd6g dJejdKg dLejdMdEdNgdOdP ZdQdR Z dSdT Z!dUdV Z"dWdX Z#ejd6dYdZd[ Z$d\d] Z%ejd8g d^d_d` Z&ejdadbe'dddcddfdeedfdgddbggdgdhfgdidj Z(ejdkg dldmdn Z)dodp Z*d%S )rTestMultivariateTr	   rC   rW   rD   rU   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?)rY   r	   2   )r   r   r  )r   r   r  )r  r  r   r  )gJ#R<g^<gL[<gN=<g`$<zx, loc, shape, df, ansc                 C   s(   t |||dd}||}t|| d S Nr   r   )r"   r   r   )rM   rS   r  r8   r  ansr   valr=   r=   r>   test_pdf_correctnessh	  s    
z&TestMultivariateT.test_pdf_correctnessc           	      C   s8   t |||dd}||}||}tt|| d S r  )r"   r   r   r   r6   r   )	rM   rS   r  r8   r  r  r   r  r  r=   r=   r>   test_logpdf_correctn	  s    

z%TestMultivariateT.test_logpdf_correctc                 C   s.   g d}t j|dd}t|}t|| d S )N)
r  rX   rW   r	   r  r   r  rY   rD   r	   r  )r"   r   r#   r   )rM   rS   r  r  r=   r=   r>   test_mvt_with_df_one_is_cauchyv	  s    
z0TestMultivariateT.test_mvt_with_df_one_is_cauchyc                 C   s   d}t ddddd}|jdd}t|\}}||ks8J t ddgd	d
gd
d	ggddd}|jdd}t|\}}||k sJ d S )Nr   r   r	   順 r  r   ro   r\   rD   r   rY   *   )r"   r   r$   r   )rM   Z	P_VAL_MINr   ra  r   r  r=   r=   r>   &test_mvt_with_high_df_is_approx_normal|	  s    z8TestMultivariateT.test_mvt_with_high_df_is_approx_normalz'scipy.stats.multivariate_normal._logpdfc                 C   s`   t ddtjdd}t|ts J t jdtjd |jdks>J t jdtjd |jdks\J d S )Nr   r	   rX   r  r  rC   )r"   r6   r   r   r   r   Z
call_countr   )rM   Zmockr   r=   r=   r>   !test_mvt_with_inf_df_calls_normal	  s    z3TestMultivariateT.test_mvt_with_inf_df_calls_normalc           	      C   s"  d}t |}t |}d}t |}t||||}t |sFJ t||||}t |sfJ d}t j||f}t||||}|j|fksJ t||||}|j|fksJ tt dt dd	 }t |sJ d}tt dt ddj	|d}|j|fksJ d S )NrW         @rX   r	   ro   )
r6   r   rK   r"   r   Zisscalarr   rz   r8   r   )	rM   r   r  r8   r  rS   r9   	n_samplesrp   r=   r=   r>   test_shape_correctness	  s(    


 z(TestMultivariateT.test_shape_correctnessc                 C   s6   t  }t|jdg t|jdgg |jdks2J d S )Nr   r	   r"   r   r  r8   r  )rM   r   r=   r=   r>   test_default_arguments	  s    z(TestMultivariateT.test_default_arguments)NNNr   r	   r	   )NNrX   r   r	   rX   NrX   z*loc, shape, df, loc_ans, shape_ans, df_ansc                 C   s8   t |||d}t|j| t|j| |j|ks4J d S )Nr  r8   r  r  rM   r  r8   r  Zloc_ansZ	shape_ansZdf_ansr   r=   r=   r>   test_default_args	  s    z#TestMultivariateT.test_default_argsrY   c                 C   s4   t |||}t|j| t|j| t|j| d S r5   r  r  r=   r=   r>   &test_scalar_list_and_ndarray_arguments	  s    z8TestMultivariateT.test_scalar_list_and_ndarray_argumentsc                 C   s   ddgg}t ttfi t|d ddgddgddgg}t ttfi t||d td}td}d}t ttfi t|||d d}t ttfi t|||d d S )	Nr	   )r  rC   rD   )r  r8   rY   r  r   )r   rH   r"   dictr6   r   rK   )rM   r  r8   r  r=   r=   r>   test_argument_error_handling	  s4    



z.TestMultivariateT.test_argument_error_handlingc                 C   sh   t jd}|jdd}t d}t||ddd}t||ddd}|jdd}|jdd}t|| d S )NrW   rD   ro   rC   r  r   )r6   rz   r  r   rK   r"   r   r   )rM   r   r  r8   r   Zdist2Zsamples1Zsamples2r=   r=   r>   r/  	  s    
z&TestMultivariateT.test_reproducibilityc                 C   s:   t ddgddgddggddd}ttjjtfi | d S )Nr   r	   F)r  r8   r  rQ   )r  r   r6   r   r  r"   )rM   r;   r=   r=   r>   test_allow_singular
  s     z%TestMultivariateT.test_allow_singularrp   )r   rD   )rU   rV   rW   rD   r   )rC   rD   rW   rU   r  r   r  c                 C   s<   t t|t||}|j|d}|j||f ks8J d S ra  )r"   r6   r   rK   r   r8   )rM   rp   r   r  r   r   r=   r=   r>   test_rvs
  s    zTestMultivariateT.test_rvsc                 C   s   t d}t d}d}g dg dg dg dg}g dg dg dg dg}t g d}tj|||||d}t||d	 |  d S )
NrD   r   r8  rZ   rG  rH  rI  r<  r   rJ  )rM   r   r   r  r@  r?  rK  r   r=   r=   r>   rL  
  s    

z TestMultivariateT.test_cdf_signs)r	   rC   rU   r   c                 C   s   |  | d S r5   cdf_against_mvn_testrM   r   r=   r=   r>   $test_cdf_against_multivariate_normal
  s    z6TestMultivariateT.test_cdf_against_multivariate_normal)rD   rV   r  c                 C   s   |  dd d S )NrD   Tr  r  r=   r=   r>   -test_cdf_against_multivariate_normal_singular 
  s    z?TestMultivariateT.test_cdf_against_multivariate_normal_singularFc              	   C   s   t jd}d}d|jdd|d }t||||}d|jdd|d t |j|d }d|jdd||fd  | }d|jdd||fd | }	tjj	|	||d	|d
|d}
tj
j	|	||d
|d}t|
|dd d S )N   ]J>?a rD   r   r\   r	   ro   rY   rC   r  T)r  r=  rQ   r   )rQ   r=  Mb@?r#  )r6   rz   r{   r   r   signr   r,   r"   r   r   r   )rM   r   rq   r   r   r  r   r   r?  r@  r9   r:   r=   r=   r>   r  %
  s    &z&TestMultivariateT.cdf_against_mvn_testc           	      C   s   t jd}d}d}|jdt |d}d}tjj||||t j |d}tj	|||t |}tj
||t |}t||dd	 t t || d
ksJ d S )Nr  rC   r   r   )rp   r   rD   )r=  r   r  r#  r   )r6   rz   r{   r   sqrtr,   r"   r   r   tr   r   r   r   )	rM   r   r   r   rS   r  r9   r:   Z	incorrectr=   r=   r>   test_cdf_against_univariate_t7
  s    z/TestMultivariateT.test_cdf_against_univariate_t)rC   rD   rU   r   r   )   no l   m, l   sO l   U iOfYl   O_ rq   Tc              	   C   s^  |r|dkrt d tj|}d|jdd|d }t||||}||}|| }||}	| d }
tjj	|	|||
|dd	}tj
d
d0 td|
|tj| |	| |d }W d    n1 s0    Y  t||ddd tjj	|	|||
||dd}tj
d
d. td|
||| |	| |d }W d    n1 s@0    Y  t||ddd d S )Nr  z4Agreement with qsimvtv is not great in singular caser   r\   rC   ro   rU   T)r   rQ   rt  )invalidr&  r   g-C6*?r   r  r   )r=  r   rQ   rE  )rG   rv   r6   rz   r{   r   r   r,   r"   r   ru  r3   r   r   )rM   r   r   rq   r   r  r   r   r?  r@  r  r9   r:   r=   r=   r>   test_cdf_against_qsimvtvF
  s*    


>>z*TestMultivariateT.test_cdf_against_qsimvtvc           	   	      s  d}t jd}d|jdd|d }t|||dd |||| }||}| d	 tjj| ||d
} fdd}t|||tj	j
||dd}t||jdd  fdd}t||d |d |d |d |d |d }t||d dd d S )NrD   l   	!y r   rY   r	   ro   T)rq   rU   )r   r=  c                    s   t j| j S r5   )r,   r"   r   r   rR   r   r  r   r=   r>   	integrandq
  s    zITestMultivariateT.test_cdf_against_generic_integrators.<locals>.integrand)r   r   )Zqrngr   r   c                     s   t j| d d d  S )NrY   )r,   r"   r   )Zzyxr  r=   r>   r  w
  s    r   rC   )r6   rz   r{   r   r   r,   r"   r   r.   ZqmcZHaltonr   Zintegralr/   )	rM   r   r   r  r?  r@  r9   r  r:   r=   r  r>   $test_cdf_against_generic_integratorsc
  s"    

,z6TestMultivariateT.test_cdf_against_generic_integratorsc                 C   sb   t jd}t g dg dg dg}d}tj||d}|jg d|d}d	}t||d
d d S )Nl   Ja )go!@S<?^Ss@)r  gRP=@jT0@)r  r  gk`-3@gWK?r8   r  rZ   r   g1%?r   r   )r6   rz   r{   r   r,   r"   r   r   )rM   r   r   r  r   r9   r:   r=   r=   r>   test_against_matlab}
  s    
z%TestMultivariateT.test_against_matlabc                 C   s   d}t j|}|jdd}|jdd| }t d}| }|||f}t j|}t j|}	tj|d|i}
t|
|tj|g|R d|	i d S )Nl   2m rD   ro   r   r   )	r6   rz   r{   r   rK   r,   r"   r   r   )rM   r   r   r  rS   r8   r  r;   Z
rng_frozenZrng_unfrozenr   r=   r=   r>   r  
  s    


zTestMultivariateT.test_frozenc                    s   d}d}t jdj||fd}||j  |||f } d tjj| d} fdd}t |d	|}t||d
dd d S )NrW   rD  r  ro   rU   r   c                    s"   t d tj |  |  d S )Nr  r   )r3   r6   r   rR   r   r  r   r   r=   r>   _cdf_1d
  s    z2TestMultivariateT.test_vectorized.<locals>._cdf_1drY   rE  r   r  )	r6   rz   r{   r   r,   r"   r   Zapply_along_axisr   )rM   r   r   rf   rS   r9   r  r:   r=   r  r>   test_vectorized
  s    

z!TestMultivariateT.test_vectorizedr  c                 C   sd   t jd}tjjdgdg|d   d}tj|djdg| |d}d|d  }t	||dd	 d S )
Nr  r	   r   )r  )r8   r   r   g-C6
?r   )
r6   rz   r{   r   r   Ztoeplitzr,   r"   r   r   )rM   r   r   rf   r9   r:   r=   r=   r>   test_against_analytical
  s
    z)TestMultivariateT.test_against_analyticalc                 C   s@   t dd}t j}tjj||d}tjd |}||ks<J d S )NrD   r  )r6   rK   r   r,   r"   r   r   )rM   r   r  mvt_entropyZmvn_entropyr=   r=   r>   test_entropy_inf_df
  s
    z%TestMultivariateT.test_entropy_inf_df)r	   r   r   c                 C   s0   t jjd|d}t jj|d}t||dd d S )Nr   r  r  r;  r   )r,   r"   r   r  r   )rM   r  r  Z	t_entropyr=   r=   r>   test_entropy_1d
  s    z!TestMultivariateT.test_entropy_1dzdf, cov, ref, tolr   g}M@r  r   r   gNfh@r`  c                 C   s.   t d}t|||}t| ||d d S )Nr  r   )r6   r   r,   r"   r   r   )rM   r  r   r:   tolr  mvtr=   r=   r>   %test_entropy_vs_numerical_integration
  s    
z7TestMultivariateT.test_entropy_vs_numerical_integrationzdf, dim, ref, tol))r   r	   gDdVW?rS  )r   r	   gU?r;  )r  r	   g/+?r  )@xDr	   Z_2?rS  )}Ô%ITr	   r  rS  )r   r   gzg#.@rS  )r  r   gD:f,@r;  )r  r   1>`,@rS  )r  r   r  rS  )r   r   g8d?b@rS  )r  r   g-YҺa@r  )r  r   ZGra@rS  )r  r   r  rS  c                 C   s*   t jt||d}t| ||d d S )Nr  r   )r,   r"   r6   rK   r   r   )rM   r  r   r:   r  r  r=   r=   r>   test_extreme_entropy
  s    #z&TestMultivariateT.test_extreme_entropyc           
      C   s   t g dg dg dg dg dg}||j }d}tjj||d}td |d }t||d	d
 d}d}tjj||d}tjj||d}	t||	d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  rS  r   i  i   r  )r6   r   r   r,   r"   r   r   r   )
rM   Z_Ar   r  Zmul_t_entropyZmul_norm_entropyZdf1Zdf2Z	_entropy1Z	_entropy2r=   r=   r>   test_entropy_with_covariance  s"    
z.TestMultivariateT.test_entropy_with_covariance)F)+r   r   r   Z	PDF_TESTSrG   r   r   r  r  r  r  r4   r  r  r  ZDEFAULT_ARGS_TESTSr  r6   r   ZARGS_SHAPES_TESTSr  r  r/  r  r   r  rL  r  r  r  r  r  r  r  r  r  r  r  r  rK   r  r  r  r=   r=   r=   r>   r  	  s   
(B


 **""..
$








r  c                   @   s  e Zd Zejdddgddgddfddgddgdej fd	dgddgdej fddgd
dgdejfddgddggddgd
dggddgejejgfd	dgd
dgdejfddgddgdejfddgddgdejfddgddgdejfddgddgdej fg
dd Z	dd Z
dd Zdd Zejdg ddfg ddfddgdfdgdffdd  Zejddgdgddfddgddgdd!fddgdd"ggdd#gddgggddgd"d"gd"dggd$d%gdd&ggfejg ed'ejg ed'dg fddgddgddfg d(g d)d*d+fgd,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d0d1gfdgdgggdgdggddgd0d1ggfdgdggdggggddgd0d1gggfgd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJS )KTestMultivariateHypergeomzx, m, n, expectedrD   rW   rU   r   rX   gr   r  r	   rC   r^   iir  r  rY   ic                 C   s    t |||}t||dd d S )Ngư>r   )r   r  r   rM   rS   rh  r   r  valsr=   r=   r>   r  !  s    z%TestMultivariateHypergeom.test_logpmfc                 C   st   t jddgddgdd}tjddddd}t||d	d
 t jddgddgdd}tjddddd}t||d	d
 d S )NrD   r	   r   rU   rW   )rS   rh  r      )r   r   r   r.  r`  r   rX      )r   r  r!   r   r  r=   r=   r>   test_reduces_hypergeom?  s    z0TestMultivariateHypergeom.test_reduces_hypergeomc                 C   s:   t ddgdd}|jddd}t|d| d	d
 d S )NrD   rU   rW   rh  r   r  r  r   r   r  r   r   r   r   r   rM   r   r   r=   r=   r>   r  J  s    z"TestMultivariateHypergeom.test_rvsc                 C   sF   t ddgddggddgd}|jddd	}t|d
| dd d S )NrD   rU   r   rW   r  r  r  rC   r  r   r   r  r   r  r  r=   r=   r>   test_rvs_broadcastingQ  s    z/TestMultivariateHypergeom.test_rvs_broadcastingzm, n)r   r   r!  r   r   )r   r   r   r   r   c                 C   s8   t ||}t|}| }|||dk< t|| d S )Nr   )r   r   r6   r7   rw  r   )rM   rh  r   r9   Zres_exr=   r=   r>   test_rvs_gh16171V  s
    
z*TestMultivariateHypergeom.test_rvs_gh16171g zl?r  r  gQ?gE|?g
y?r   r  )rU   rV   rX   rV   gzp?c                 C   s    t |||}t||dd d S Nr  r   r   r  r   r  r=   r=   r>   r  a  s    z"TestMultivariateHypergeom.test_pmfr  g ?r   r   c                 C   s    t |||}t||dd d S r  r  r  r=   r=   r>   r  u  s    
z/TestMultivariateHypergeom.test_pmf_broadcastingc                 C   s:   t jg ddd}g dg dg dg}t||dd d S )	N)rD   rX   r   r  r  )gf_?&BUп疈Cx@ؿ)r  ggs>d?ZsK)r  r  g35?r`  r   r   r   r   )rM   r  r'  r=   r=   r>   r    s    z"TestMultivariateHypergeom.test_covc                 C   s   t jddgddggddgd}dd	gd	dggd
dgdd
ggg}t||dd t jdgdggddgd}dggdggg}t||dd t jddgddgd}dd	gd	dggddgddggg}t||dd d S )NrX   r  r   r  r  r  r  g?gg(\?g(\r`  r   rW   rU   r   g333333?g333333r  r  r=   r=   r>   r    s    z/TestMultivariateHypergeom.test_cov_broadcastingc                 C   s4   t jddgdd}tjdddd}t||dd d S )	Nr   rU   rW   r  r  r   r   r.  r`  r   )r   r  r!   r   )rM   var0var1r=   r=   r>   test_var  s    z"TestMultivariateHypergeom.test_varc                 C   s   t jddgddgd}t jddgdd}t jddgdd}t|d |dd t|d	 |dd t jddgdd
ggddgd}ddgddgg}t||dd t jdgdggddgd}dgdgg}t||dd d S )Nr   rU   rW   r  r  r   r`  r   r	   r  g̍3eY?gI{?r   )r   r  r   )rM   r  r  var2var3Zvar4Zvar5Zvar6r=   r=   r>   test_var_broadcasting  s    z/TestMultivariateHypergeom.test_var_broadcastingc                 C   s`   t jddgdd}tjdddd}t|d |dd	 t jd
dgdd}ddg}t||dd	 d S )Nr   rU   rW   r  r  r  r   r`  r   r  r  g      @r  )r   r   r!   r   rM   mean0r  r&  Zmean3r=   r=   r>   r    s    z#TestMultivariateHypergeom.test_meanc                 C   s@   t jddgddggddgd}ddgd	d
gg}t||dd d S )NrD   rU   r   rW   r  r  r   r   gUUUUUU@gUUUUUU@r`  r   )r   r   r   )rM   r  r  r=   r=   r>   r    s    z0TestMultivariateHypergeom.test_mean_broadcastingc                 C   s   t jg ddd}t|g d t jg ddd}t|tjtjtjg t jg dg dgdd}t|tjtjtjgg dgd	d
 t jtjg tddd}t|g  t|j	dk d S )NrZ   r   r  r   r   r   r	   r   r   rC   rG  )r   r   r   FFg<r   r   r   )
r   r   r   r6   r  r   r   intr   r8   r  r=   r=   r>   test_mean_edge_cases  s    
z.TestMultivariateHypergeom.test_mean_edge_casesc                 C   s   t jg ddd}t|g ddd t jg ddd}t|tjtjtjg t jg dg d	gdd}t|tjtjtjgg dgd
d t jtjg tddd}t|g  t|j	dk d S )NrZ   r   r  r  gؗҜ<r   r  rC   rG  r  r   r  )
r   r  r   r   r6   r  r   r  r   r8   )rM   r  r  r  r  r=   r=   r>   test_var_edge_cases  s    
z-TestMultivariateHypergeom.test_var_edge_casesc                 C   s   t jg ddd}g dg dg dg}t||dd t jg ddd}g dg dg dg}t|| t jtjg td	dd}tjg tjd	dd}t||dd t	|j
d
k d S )Nr  r	   r  r  r  r   rZ   r   r   r  )r   r   r   r   r6   r   r  r   r  r   r8   )rM   Zcov0r  r  r	  r
  r  r=   r=   r>   test_cov_edge_cases  s    
z-TestMultivariateHypergeom.test_cov_edge_casesc                 C   s   t jd d}g d}g dg dg dg dg dg}t j|td	}t||}t||t||| t||t||| t|	 t	|| t|
 t
|| d S )
Nr   r  )rX   r  r     r  r  r  r  r  r   )r6   rz   r   r7   r  r   r   r  r  r  r   )rM   r   rh  rS   Z
mhg_frozenr=   r=   r>   r    s     


z%TestMultivariateHypergeom.test_frozenc                 C   s   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 )	NrU   r   rW   g      @r  r  g      %@g      /@)r   rH   r   r  	TypeErrorr1  r=   r=   r>   test_invalid_params  s    z-TestMultivariateHypergeom.test_invalid_paramsN)r   r   r   rG   r   r   r6   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     sv   


"&&	

r  c                   @   s0  e Zd Zdd Zdd Zejdddd Zd	d
 Z	ejddejdddd Z
ejdddd Zdd Zejdddd Zejdddd Zejdddd Zejddejdg dgfejdg dgfd d! Zejd"d#d$d% Zd&d' Zejddd(d) Zd*S )+TestRandomTablec                 C   s   t jdS )Nl   OfE)r6   rz   r{   r1  r=   r=   r>   get_rng  s    zTestRandomTable.get_rngc                 C   s>  d}t jt|d$ tddggddg W d    n1 s<0    Y  d}t jt|d$ tddgddgg W d    n1 s0    Y  d}t jt|d" tddgddg W d    n1 s0    Y  d}t jt|d" tddgdd	g W d    n1 s0    Y  d
}t jt|d" tddgddg W d    n1 sR0    Y  d}t jt|d" tddgg d W d    n1 s0    Y  d}t jt|d" tddgg d W d    n1 s0    Y  ddg}g d}tddgg d\}}}t|| t|| |t|ks:J d S )Nz`row` must be one-dimensionalrA   r	   rC   z`col` must be one-dimensionalz*each element of `row` must be non-negativerY   z*each element of `col` must be non-negativer\   z'sums over `row` and `col` must be equalr   z(each element of `row` must be an integer @)r	   r	   rC   z(each element of `col` must be an integer)r  r  r	   rD   rC   r	   r	   )rG   r   rH   r%   Z_process_parametersr   r6   r~   )rM   rN   rowcolr   r  r   r=   r=   r>   test_process_parameters  s6    2202222

z'TestRandomTable.test_process_parameterszscale,method))r	   boyett)r   	patefieldc                 C   sZ   t ddg| }t g d| }t}|j|||dd}|j||d dd}t|| d S )Nr	   rD   r  methodr   )r6   r   r%   r   r   )rM   r   r  r  r   ctr  gotr=   r=   r>   test_process_rvs_method_on_None,  s    z/TestRandomTable.test_process_rvs_method_on_Nonec                 C   sV   ddg}g d}d}t jt|d  tj||dd W d    n1 sH0    Y  d S )Nr	   rD   r  z$'foo' not recognized, must be one ofrA   Zfoor  )rG   r   rH   r%   r   )rM   r  r   rN   r=   r=   r>   $test_process_rvs_method_bad_argument8  s
    z4TestRandomTable.test_process_rvs_method_bad_argumentrz  )TFr   c                    sR  |   }ddgg d tj dd|d}|r:t nt}t||rJdnd|sh fd	d
|rxfddn}tj|ddd\}}||}	t|	t| |dd |t|d }
t	|
|	d  |
d|jdd   }||}	|	jdksJ t|	jd D ]F}t|	jd D ]0}|	||f }|||f }||}t	|| qqg dg dg}t	tj|dd ||}	|	dksJ g dg dg}t	tj|dd  ||}	|	dksJ d}tjt|d |dg W d    n1 s0    Y  d}tjt|d |dgg W d    n1 s80    Y  d}tjt|d |tjgg W d    n1 sz0    Y  d}tjt|d |dgg W d    n1 s0    Y  d }tjt|d |g d!g W d    n1 s0    Y  d"}tjt|d$ |ddgd#d$gg W d    n1 sD0    Y  d S )%NrC   rV   r	   rD   rW   r  r  rp   r  r   r  r  c                    s   |  S r5   r=   rR   )r   original_methodr  r=   r>   r  R  s    z/TestRandomTable.test_pmf_logpmf.<locals>.methodc                    s   t  | S r5   )r6   r   rR   r	  r=   r>   rT   T  r9  z1TestRandomTable.test_pmf_logpmf.<locals>.<lambda>r   Trt   Zreturn_countsr   r   )r   r   r	   )r   r	   r	   )rC   r	   rD   rY   rs   r   )r	   rC   rC   r\   z$`x` must be at least two-dimensionalrA   z%`x` must contain only integral valuesr  z)`x` must contain only non-negative valuesz"shape of `x` must agree with `row`rF   z"shape of `x` must agree with `col`rD   rW   )r  r%   r   ra   r6   uniquer   r   r   r   r  r8   r   r~   rG   r   rH   r  )rM   rz  r   r   r   objr  
unique_rvscountsr  p2Zrvs_ndr   r   ZpijZrvijZqijrS   rN   r=   )r   r  r  r  r>   test_pmf_logpmfA  sl    
*,.,.zTestRandomTable.test_pmf_logpmfr  )r  r  c                 C   s   |   }ddg}g d}tj||d||d}t||}tt|t| t|d|dd t|jd	d
t|d t|jdd
t|d d S )NrC   rV   r  r  r  r   r>  r#  rY   rs   r  r\   )r  rD   )	r  r%   r   r   r   r6   r~   r   Zbroadcast_to)rM   r  r   r  r   r   r   r=   r=   r>   test_rvs_mean  s    zTestRandomTable.test_rvs_meanc                 C   sn   |   }ddg}g d}tj||dd|d}tj||dd|d}tj|dd	}tj|dd	}t||d
d d S )NrC   rV   r  r  r  r  r  r   rs   {Gz?r#  )r  r%   r   r6   r  r   )rM   r   r  r   r{  r|  r  r'  r=   r=   r>   test_rvs_cov  s    zTestRandomTable.test_rvs_covc           
      C   s  ddg}g d}t j||||  d}|jdks4J t j||d||  d}|jdksZJ t||d	  t j||d	||  d}|jd
ksJ t j||d||  d}|jdksJ t j||d||  d}|jdksJ t|ddd|dd d}	tjt	|	d( t j||d||  d W d    n1 s40    Y  tjt	|	d* t j||t
j||  d W d    n1 s~0    Y  d S )NrC   rV   r  r  rD  r	   r  rF   r   )r   rC   rD   r!  )r!  rC   rD   )rW   rU   )rW   rU   rC   rD   rD   rS  r   z/`size` must be a non-negative integer or `None`rA   rY   )r%   r   r  r8   r   r   r  rG   r   rH   r6   r  )
rM   r  r  r   r   Zrv2Zrv3Zrv4Zrv5rN   r=   r=   r>   test_rvs_size  sB    
&zTestRandomTable.test_rvs_sizec           	      C   sh   ddg}g d}t }|j||d||  d}tj|ddd\}}||||}t|t| |d	d
 d S )NrC   rV   r  r  r  r   Tr  r  r   )r%   r   r  r6   r  r  r   r   )	rM   r  r  r   r  r   r  r  r  r=   r=   r>   test_rvs_method  s    zTestRandomTable.test_rvs_methodc                 C   sn   g d}g d}t ||}|jd||  d}tdt|t|f}g dg dg dg|d< t|| d S )NrH  )r	   r   r   r   r  r  )r   r   r   r   .r%   r   r  r6   r   r   r   rM   r  r  r   r   r   r  r=   r=   r>   test_rvs_with_zeros_in_col_row  s    
z.TestRandomTable.test_rvs_with_zeros_in_col_row)Nr  r  r   r   r  c                 C   sD   t ||}|jd||  d}tdt|t|f}t|| d S )Nr   r  r  r  r=   r=   r>   test_rvs_with_edge_cases  s    
z(TestRandomTable.test_rvs_with_edge_casesr   r  c                 C   s   dd l m  m} tjddgtjd}tjg dtjd}t|d| }t|}||||d|  }|j	dt
|t
|fksJ t||ksJ d S )Nr   r	   rD   r   r  Z	rvs_rcont)Zscipy.stats._rcontr,   _rcontr6   r   Zint64ra   r~   r  r8   r   )rM   r   r  r  r   r   Zntotresultr=   r=   r>   test_rvs_rcont  s    
zTestRandomTable.test_rvs_rcontc                 C   s   ddg}g d}t |||  d}| }t ||}t||  t |||}t||| t |||}t||| d S )NrC   rV   r  r   )r%   r  r   r   r   r  r  )rM   r  r   r   r,  r  r=   r=   r>   r    s    zTestRandomTable.test_frozenc                 C   sV   ddg}g d}t |||  d}t j||d||  d}|jd|d}t|| d S )NrC   rV   r  r   r   r  )rp   r  )r%   r  r   r   )rM   r  r  r   r   r  r  r=   r=   r>   test_rvs_frozen#  s    zTestRandomTable.test_rvs_frozenN)r   r   r   r  r  rG   r   r   r  r
  r  r  r  r  r  r  r  r   r  r!  r=   r=   r=   r>   r    s8   $

	N

)


r  c                 C   sd   | j }d| _ | j|ddi t| }| j|ddi}t|}|j|ddi}t|| || _ d S )Nr   rp   r  )r   r   pickledumpsloadsr   )distfnr;   r  r   Zr0Z	unpickledr1r=   r=   r>   check_pickling/  s    


r'  c                  C   s   t d} d| d< d| d< tdgtt 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|| qfd S )NrD   r   r   r  r=   r   r   rU   r  r  )r6   rK   r   r   r   r   r   r   r   r   r2   r'  )r   distsr%  r;   r=   r=   r>   test_random_state_propertyC  s    


	
r)  c                   @   s  e Zd Zejdg dejdg ddd Zejdddgejd	g d
dd Zdd Zdd Z	dd Z
ejd	ddgdd Zejd	ddgdd Zejdejejgdd Zejdejejgdd Zejd eg d!eg d!d"d#feg d$eg d%d"d&feg d!eg d!d'd(feg d$eg d%d'd)feg d!eed*ed+dgd,d-feg d$eg d!d,d.feg d/eg d/d,d0feg d/eed*ed+dddgd,d1feg d/eed2ed3dddgd,d4fg	d5d6 Zejd eg d!eg d!d"d7feg d$eg d%d"d8feg d!eg d!d'd9feg d$eg d%d'd:feg d!eed*ed+dgd,d;feg d$eg d!d,d<feg d/eg d/d,d=feg d/eed*ed+dddgd,d>feg d/eed2ed3dddgd,d?fg	d@dA ZejdBg dCdDdE ZejdejejgdFdG ZdHdI Zejdg dJejdKg dLdMdN ZdOdP ZdQdR ZdSdT ZdUS )VTestVonMises_Fisherr   )rC   rD   rW   rV   rp   r{  c                 C   s   t jd}t |fdt | }t|d|d}||}t |t | }}|j	|||dj
}	|j
|	ksrJ t jj|dd}
t|
d d S )Nr|  r	   r   ro   rY   rs   r   )r6   rz   r{   r  r  r'   r   r   rK   r   r8   r   r   r   )rM   r   rp   r   r   vmf_distra  r   r   r}  r~  r=   r=   r>   r  V  s    
z TestVonMises_Fisher.test_samplesrU   r  kappa)g  4&kCr  gꌠ9Y>)Fc                 C   s@   t jd}t |fdt | }t|||d}|d d S )Nr|  r	   r   r   )r6   rz   r{   r  r  r'   r   )rM   r   r,  r   r   r+  r=   r=   r>    test_sampling_high_concentrationd  s    z4TestVonMises_Fisher.test_sampling_high_concentrationc                 C   sJ   t d}d}tjt|d t|d W d    n1 s<0    Y  d S )Nr*  z%'mu' must have one-dimensional shape.rA   r	   r6   rJ   rG   r   rH   r'   rM   r   r  r=   r=   r>   test_two_dimensional_mum  s    
z+TestVonMises_Fisher.test_two_dimensional_muc                 C   sJ   t d}d}tjt|d t|d W d    n1 s<0    Y  d S )Nr  z%'mu' must be a unit vector of norm 1.rA   r	   r.  r/  r=   r=   r>   test_wrong_norm_mus  s    
z&TestVonMises_Fisher.test_wrong_norm_muc                 C   sJ   t d}d}tjt|d t|d W d    n1 s<0    Y  d S )Nr  z$'mu' must have at least two entries.rA   r	   r.  r/  r=   r=   r>   test_one_entry_muy  s    
z%TestVonMises_Fisher.test_one_entry_murY   )rU   rD   c                 C   sD   d}t jt|d tddg| W d    n1 s60    Y  d S )Nz"'kappa' must be a positive scalar.rA   r	   r   rG   r   rH   r'   rM   r,  r  r=   r=   r>   test_kappa_validation  s    z)TestVonMises_Fisher.test_kappa_validationr   r   c                 C   sD   d}t jt|d tddg| W d    n1 s60    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.rA   r	   r   r3  r4  r=   r=   r>   test_kappa_zero  s    z#TestVonMises_Fisher.test_kappa_zeror  c                 C   sT   t g d}d}tjt|d  ||ddgd W d    n1 sF0    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.rA   r	   r   r6   r   rG   r   rH   rM   r  rS   r  r=   r=   r>   test_invalid_shapes_pdf_logpdf  s    z2TestVonMises_Fisher.test_invalid_shapes_pdf_logpdfc                 C   sT   t ddg}d}tjt|d  ||ddgd W d    n1 sF0    Y  d S )Nr   r   8'x' must be unit vectors of norm 1 along last dimension.rA   r	   r   r8  r9  r=   r=   r>   test_unnormalized_input  s    z+TestVonMises_Fisher.test_unnormalized_inputzx, mu, kappa, reference)r   r   r   rE  g0_?r7  )r   r   r   g7m0_?r   gLI/@gFK:h*7g\(\?r  i  g3pB>g7Ks@)r   r   r   r   r   go齿@gW+x\(?r  r   gS-c                 C   s"   t |||}t||dd d S )Nr;  r   )r'   r   r   )rM   rS   r   r,  	referencer   r=   r=   r>   test_pdf_accuracy  s    z%TestVonMises_Fisher.test_pdf_accuracyg[d6U?g1*?gJ8j#@g=fNXg][,g1VV@g|'@gmF&!gehc                 C   s"   t |||}t||dd d S )Nr  r   )r'   r   r   )rM   rS   r   r,  r=  r   r=   r=   r>   test_logpdf_accuracy  s    z(TestVonMises_Fisher.test_logpdf_accuracyzdim, kappa, reference))rD   rE  g?@)rD   r   gp&F)rU   r1  gT;ӷ&)r  r	   goZ@c                 C   s8   t |fdt | }t|| }t||dd d S )Nr	   g+=r   )r6   r  r  r'   r   r   )rM   r   r,  r=  r   r   r=   r=   r>   test_entropy_accuracy  s    z)TestVonMises_Fisher.test_entropy_accuracyc                 C   s   d}t jd}tdj||d}t ddt d }d}||||}|j|ksVJ t|d D ]F}t|d D ]4}	||||	d d f ||}
t	|
|||	f d	d
 qrqbd S )Nr*  r|  rD   r   rX  r	   rU   r   rS  r   )
r6   rz   r{   r&   r   r  r  r8   r   r   )rM   r  Z	testshaper   rS   r   r,  Z
result_allr   r   Zcurrent_valr=   r=   r>   r     s    z%TestVonMises_Fisher.test_broadcastingc           	      C   s   t jd}t ddg}t |d |d }d}t||}t||d}tdjd|d}t |d d df |d d df }t	|
 |
  t	|||| t	|||| d S )	Nr|  r   r	   r!  )r  r,  rC   r   r   )r6   rz   r{   r   r  r'   r)   r&   r   r   r   r   r   )	rM   r   r   Zmu_angler,  ZvmfZvonmises_distZvectorsr  r=   r=   r>   test_vs_vonmises_2d  s    
$z'TestVonMises_Fisher.test_vs_vonmises_2d)rC   rD   rV   zkappa, mu_tol, kappa_tol))r	   r>  r>  )r   r  r  )r   {Gzt?r  )r  r   r  c                 C   s   t |fdt | }t||}t jd}d}|j||d}	t|	\}
}t |	|
}t
|d|dd t
|||d d S )	Nr	   r|  r  r   r   r   r  r   )r6   r  r  r'   rz   r{   r   rO  Zarccosr   r   )rM   r   r,  Zmu_tolZ	kappa_tolr   r+  r   r  ra  Zmu_fitZ	kappa_fitZangular_errorr=   r=   r>   test_fit_accuracy+  s    
z%TestVonMises_Fisher.test_fit_accuracyc                 C   sJ   t d}d}tjt|d t| W d    n1 s<0    Y  d S )NrX  z'x' must be two dimensional.rA   )r6   r   rG   r   rH   r'   rO  rM   rS   r  r=   r=   r>   #test_fit_error_one_dimensional_data<  s    
z7TestVonMises_Fisher.test_fit_error_one_dimensional_datac                 C   sJ   t d}d}tjt|d t| W d    n1 s<0    Y  d S )NrC  r;  rA   )r6   rJ   rG   r   rH   r'   rO  rD  r=   r=   r>    test_fit_error_unnormalized_dataB  s    
z4TestVonMises_Fisher.test_fit_error_unnormalized_datac                 C   sf   t g d}d}t||}t||dd}|jdd}tj||dd}| }t|| t|| d S )N)r   r   r	   rU   r.  r   r   )r6   r   r'   r   r   )rM   r   r,  rz  rW  r{  r|  rX  r=   r=   r>   r  H  s    

z,TestVonMises_Fisher.test_frozen_distributionN)r   r   r   rG   r   r   r  r-  r0  r1  r2  r5  r6  r'   r   r   r:  r<  r6   r   r  r>  r?  r@  r   rA  rC  rE  rF  r  r=   r=   r=   r>   r*  U  s   

	





r*  c                   @   s   e Zd Zedd Zdd Zdd Zdd Zd	d
 Ze	j
dddgdd Ze	j
dddgdd Zdd Zdd Ze	j
dddgdd Ze	j
dg ddd ZdS )TestDirichletMultinomialc                 C   sJ   t jd}|jdddd}|jdd|dfd}|jdd	}|||||fS )
N   t7)r   r   rC   ro   r	   r!  rY   rs   )r6   rz   r{   r   integersr~   )rM   rh  r   r9  rS   r   r=   r=   r>   
get_paramsW  s
    z#TestDirichletMultinomial.get_paramsc                 C   s   t jd}|ddd}|ddd}t j|dd}t||}t||t||| t|	|t	||| t|
 t
|| t| t|| t| t|| d S )NrH  r   r   r   rY   rs   )r6   rz   r{   r   rI  r~   r(   r   r  r  r   r  r   )rM   r   r9  rS   r   r   r=   r=   r>   r  _  s    
z$TestDirichletMultinomial.test_frozenc                 C   s   t g d}t |}t g d}t|||}t|||}d}t|| t|t | |j|j  krxdks~n J t j	
d}|ddd}|ddd}t j|d	d
}t|||}t|||}d}t|| t|t | d S )NrF   rD   rW   rU   gp.U.?r=   rH  r   r   r   rY   rs   g+T<)r6   r   r~   r(   r  r  r   r   r8   rz   r{   r   rI  )rM   rS   r   r9  r9   Zlogresr:   r   r=   r=   r>   test_pmf_logpmf_against_Rm  s$    


z2TestDirichletMultinomial.test_pmf_logpmf_against_Rc                 C   s  |  d\}}}}}|d7 }tt|||d tt|||tj  |  d\}}}}}|jdddk}t|| d ||< tt|||| d tt|||| tj  t	t||||  dksJ t	t||||  tj ksJ d S )Nr	   r   r   ro   r   rC   )
rJ  r   r(   r  r  r6   r   rz   roundr   )rM   r   rh  r9  r   rS   r   r=   r=   r>   test_pmf_logpmf_support  s    $z0TestDirichletMultinomial.test_pmf_logpmf_supportc                 C   s   d}dg}t |g}t||}t||d t||d d t||d t||d t j  t| | t| d t|	 d d S )NrV   r   r	   r   )
r6   r7   r(   r   r  r  r   r   r  r   )rM   r   r9  rS   r   r=   r=   r>   test_dimensionality_one  s    
z0TestDirichletMultinomial.test_dimensionality_onemethod_namer  r  c                 C   sb   |  d\}}}}}tt|||}ttj|g|jR  |}||}	||jd }
t|	|
 d S Nr   r   rJ  ra   r(   r,   Z	betabinomr   r   rM   rP  r   rh  r9  r   rS   r  Z
ref_methodr9   r:   r=   r=   r>   test_against_betabinom_pmf  s    z3TestDirichletMultinomial.test_against_betabinom_pmfr   r  c                 C   sd   |  d\}}}}}tt|||}ttj|g|jR  |}| d d df }	| }
t|	|
 d S rQ  rR  rS  r=   r=   r>   test_against_betabinom_moments  s    z7TestDirichletMultinomial.test_against_betabinom_momentsc                 C   sB  d}t tjt dk r"tj|d tjd}d}|dd}|j|dd	 }t||}d
}|j	||d}|j
|||d}	t| tj|	dddd t| tj|	dddd | j| j  kr|fksn J | }
|
j||fksJ t|
t|	jdd tt|
|  ttj|
d dks>J d S )Nz/Needs NumPy 1.22.0 for multinomial broadcastingz1.22.0)reasonrH  rU   r	   r   ro   r   r  r   rs   rB  r   r  r  )r1   r6   __version__rG   rv   rz   r{   rI  r(   r   r   r   r   r  r8   r   r   r   r`   r   r   r   r   )rM   rN   r   r   r   r9  r   rh  r  rS   r   r=   r=   r>   r    s&    
(z%TestDirichletMultinomial.test_momentsc                 C   s  t g d}t |}t g d}d}tt|d" tg d|| W d    n1 s^0    Y  tt|d" tg d|| W d    n1 s0    Y  d}tt|d" t|g d| W d    n1 s0    Y  tt|d" t|g d	| W d    n1 s0    Y  d
}tt|d t||d W d    n1 s^0    Y  tt|d t||d W d    n1 s0    Y  t g d}t g d}d}tt|d" t|||  W d    n1 s0    Y  d S )NrF   rK  z,`x` must contain only non-negative integers.rA   )r	   rY   rD   )r	   r  rD   z*`alpha` must contain only positive values.)rD   r   rW   )rD   rY   rW   z`n` must be a positive integer.ǧH@r   )r	   rC   rD   rW   z&`x` and `alpha` must be broadcastable.)r6   r   r~   r   rH   r(   r  )rM   Zx0Zn0Zalpha0textrS   r9  r=   r=   r>   rO     s.    
0002..z.TestDirichletMultinomial.test_input_validationr  c                 C   s   t g dg dg dg dg}t dgdgdgg}t g dg d	gd
}tt|}||||}|jdksxJ tt|D ]d}tt|D ]R}tt|D ]@}||||f }	|||  ||  ||  }
t	|	|
 qqqd S )NrK  r  rU   rU   rX   r  r  r   rV   rX   r  rF   )rC   rC   rD   )rC   r	   r	   rD   )rC   rD   rW   )
r6   r   r  ra   r(   r8   r   r   r   r   )rM   r  r9  r   rS   r9   r   r   r   res_ijkr:   r=   r=   r>   test_broadcasting_pmf  s    "
$z.TestDirichletMultinomial.test_broadcasting_pmf)r   r  r   c           
      C   s   t g dg dg dg dg}t dgdgdgg}tt|}|||}|dkr`|jd	kshnd
shJ tt|D ]F}tt|D ]4}|||f }|||  ||  }	t||	 qqtd S )NrK  r  rY  rZ  rV   rX   r  r   )rD   rW   rD   )rD   rW   rD   rD   )	r6   r   ra   r(   r8   r   r   r   r   )
rM   rP  r9  r   r  r9   r   r   r[  r:   r=   r=   r>   test_broadcasting_moments  s    "

z2TestDirichletMultinomial.test_broadcasting_momentsN)r   r   r   classmethodrJ  r  rL  rN  rO  rG   r   r   rT  rU  r  rO   r\  r]  r=   r=   r=   r>   rG  V  s    





rG  )F)[__doc__r"  Znumpy.testingr   r   r   r   r   r   rG   r   r   Ztest_continuous_basicr
   r2  r6   Zscipy.linalgr   Zscipy.stats._multivariater   r   r   Zscipy.statsr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   Zscipy.integrater-   r.   r/   Zscipy.specialr0   Zscipy._lib._pep440r1   Zcommon_testsr2   Z	data._mvtr3   Zunittest.mockr4   r?   r@   r   r   r   rl  r  r  r  r  r  r-  rU  re  rz  r  r  r  r  r'  r)  r*  rG  r=   r=   r=   r>   <module>   sz    x	 a
      L J l - %Frg9<     e  -  