a
    lh                     @   s|  d dl mZmZmZmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZ d dlmZ d dlmZ d dlmZ d d	lmZmZmZ ed
\ZZedeeZedeeZedeeZedeeZededZededZedddZedddZ ededZ!ededZ"ededZ#ededZ$edeeZ%edddZ&edd dZ'edeeddd ge'd ggZ(dd Z)dd  Z*d!d" Z+d#S )$    )ExpectationNormalVariance
Covariance)raises)symbols)
ShapeError)Matrix)MatrixSymbol)
ZeroMatrix)RandomMatrixSymbol)ExpectationMatrixVarianceMatrixCrossCovarianceMatrixzj,kABCDa   bA2   B2XYZWRX2normalZnormal2c                  C   s  t t} | t t  kr$ttks*n J |  tks:J t t} | t t  kr^ttksdn J | jtdfksvJ | jtksJ | jdksJ t	| tsJ t t
t t } | tt
t t ksJ |  t
tt t ksJ t	| tsJ | jtdfksJ t tt } |  | ks$J t tt t t } | jd jttttfksVJ |  tttt t  ksxJ t tt tt j } |  tttj tttj  tttj  tttj  ksJ t t
t tt  } |  t
tt ttt  ksJ t t tddt gddggks8J ttdddtdddgtdd	dtd
ddgg}ttdddtdddgtdddtdddgg}t t || jddt|| ksJ t t ||  tddgddggksJ d S )Nr   r   r   ZN11   ZN12   ZN21   ZN22   ZM11ZM12ZM21   ZM22   F)deep         )r   r   r   expandr   shapekrowscols
isinstancer   r   m1r   r   r   argsr   Tr   Zdoitr	   jr   )exprx1Zx2 r7   Z/var/www/auris/lib/python3.9/site-packages/sympy/stats/tests/test_symbolic_multivariate.pytest_multivariate_expectation)   sL    """ &**r9   c                  C   s^  t tdd  tt} | tt  kr2ttks8n J |  tttksNJ ttj} | ttj  krxttjks~n J |  tttksJ tt	} | tt	  krtt	ksn J | j
ttfksJ | jtksJ | jtksJ t| tsJ ttt	 } | ttt	 ksJ |  ttt	 tj ks<J t| tsLJ | j
ttfks`J ttt t	 } |  tt tt	 tj tj ksJ ttt } |  | ksJ ttt t t } | jd jttttfksJ |  | ksJ ttt	 tt  } |  dt tt	t tj ttt	 tj  ttt tj  ksZJ d S )Nc                   S   s   t tS N)r   r   r7   r7   r7   r8   <lambda>Y       z,test_multivariate_variance.<locals>.<lambda>r   r   )r   r   r   r   r   r+   r   r-   r3   r   r,   r.   r/   r0   r   r   r1   r   r   r   r2   r   r   r5   r7   r7   r8   test_multivariate_varianceX   s>    "
&" *r>   c                  C   s  t tdd  t tdd  ttjtj} | jdks8J |  tddksNJ ttt} | ttt  krxt	ttks~n J |  tt
t
ksJ | jt
t
fksJ | jt
ksJ | jt
ksJ t| t	sJ ttt t t} |  tt
t
ksJ ttt} t| t	sJ |  | ks$J ttt} t| t	s>J |  ttksTJ ttt t} t| t	srJ |  t	ttt	tt ksJ ttt t} t| t	sJ |  tt	tt ksJ tttt } t| t	sJ |  t	tttj ks
J ttt t tjt t } t| t	s6J |  tt	tt t ksVJ ttt tt  t tjt tjt  t } t| t	sJ |  tt	tt t tt	tt t  tt	tt t  tt	tt t  ksJ d S )Nc                   S   s   t ttjS r:   )r   r   r   r3   r7   r7   r7   r8   r;   ~   r<   z3test_multivariate_crosscovariance.<locals>.<lambda>c                   S   s
   t ttS r:   )r   r   r   r7   r7   r7   r8   r;      r<   )r   r   r   )r   r   r   r   r3   r   r,   r+   r   r   r-   r.   r/   r0   r   r   r   r   r   r   r   r   r   r=   r7   r7   r8   !test_multivariate_crosscovariance}   sN    
&

" .(r?   N),Zsympy.statsr   r   r   r   Zsympy.testing.pytestr   Zsympy.core.symbolr   Zsympy.matrices.exceptionsr   Zsympy.matrices.denser	   Z"sympy.matrices.expressions.matexprr
   Z"sympy.matrices.expressions.specialr   Zsympy.stats.rvr   Z-sympy.stats.symbolic_multivariate_probabilityr   r   r   r4   r-   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r1   r9   r>   r?   r7   r7   r7   r8   <module>   s>   /%