o
    g                     @   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normalnormal2c                  C   s  t t} | t t  krttksJ  J |  tksJ t t} | t t  kr1ttks4J  J | jtdfks=J | jtksDJ | jdksKJ t	| tsRJ t t
t t } | tt
t t ksfJ |  t
tt t kstJ t	| ts{J | jtdfksJ t tt } |  | ksJ t tt t t } | jd jttttfksJ |  tttt t  ksJ 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sJ 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sbJ t t ||  tddgddggksyJ d S )Nr   r   r   N11   N12   N21   N22   M11M12M21   M22   F)deep         )r   r   r   expandr   shapekrowscols
isinstancer   r   m1r   r   r   argsr   Tr   doitr	   jr   )exprx1x2 rB   c/var/www/visachat/venv/lib/python3.10/site-packages/sympy/stats/tests/test_symbolic_multivariate.pytest_multivariate_expectation)   sL   $$  
&**2rD   c                  C   sT  t tdd  tt} | tt  krttksJ  J |  tttks(J ttj} | ttj  kr>ttjksAJ  J |  tttksLJ tt	} | tt	  kr_tt	ksbJ  J | j
ttfkskJ | jtksrJ | jtksyJ t| tsJ ttt	 } | ttt	 ksJ |  ttt	 tj ksJ t| tsJ | j
ttfksJ 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s(J d S )Nc                   S   s   t tS N)r   r   rB   rB   rB   rC   <lambda>Y   s    z,test_multivariate_variance.<locals>.<lambda>r   r   )r   r   r   r   r   r4   r   r6   r<   r   r5   r7   r8   r9   r   r   r:   r   r   r   r;   r   r   r?   rB   rB   rC   test_multivariate_varianceX   s>   $
($(rH   c                  C   s  t tdd  t tdd  ttjtj} | jdksJ |  tddks'J ttt} | ttt  kr=t	ttks@J  J |  tt
t
ksKJ | jt
t
fksTJ | jt
ks[J | jt
ksbJ t| t	siJ ttt t t} |  tt
t
ks}J ttt} t| t	sJ |  | ksJ ttt} t| t	sJ |  ttksJ ttt t} t| t	sJ |  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sJ ttt t tjt t } t| t	sJ |  tt	tt t ks"J ttt tt  t tjt tjt  t } t| t	sAJ |  tt	tt t tt	tt t  tt	tt t  tt	tt t  kslJ d S )Nc                   S   s   t ttjS rE   )r   r   r   r<   rB   rB   rB   rC   rF   ~   s    z3test_multivariate_crosscovariance.<locals>.<lambda>c                   S   s
   t ttS rE   )r   r   r   rB   rB   rB   rC   rF      s   
 )r   r   r   )r   r   r   r   r<   r   r5   r4   r   r   r6   r7   r8   r9   r   r   r   r   r   r   r   r   r   rG   rB   rB   rC   !test_multivariate_crosscovariance}   sN   
(

  .(rI   N),sympy.statsr   r   r   r   sympy.testing.pytestr   sympy.core.symbolr   sympy.matrices.exceptionsr   sympy.matrices.denser	   "sympy.matrices.expressions.matexprr
   "sympy.matrices.expressions.specialr   sympy.stats.rvr   -sympy.stats.symbolic_multivariate_probabilityr   r   r   r>   r6   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r:   rD   rH   rI   rB   rB   rB   rC   <module>   s@    /%