U
    	-e                     @   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$ttks*n t|  tks:tt t} | t t  kr^ttksdn t| jtdfksvt| jtkst| j	dkstt
| tstt tt t } | ttt t kst|  ttt t kstt
| tst| jtdfkstt tt } |  | ks$tt tt t t } | jd jttttfksVt|  tttt t  ksxtt tt tt j } |  tttj tttj  tttj  tttj  kstt tt tt  } |  ttt ttt  kstt t tddt gddggks8t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stt t ||  tddgddggkstd S )Nr   r   r   ZN11   ZN12   ZN21   ZN22   ZM11ZM12ZM21   ZM22   F)deep         )r   r   r   AssertionErrorexpandr   shapekrowscols
isinstancer   r   m1r   r   r   argsr   Tr   Zdoitr	   jr   )exprx1Zx2 r8   m/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/stats/tests/test_symbolic_multivariate.pytest_multivariate_expectation)   sL    """ &**r:   c                  C   s^  t tdd  tt} | tt  kr2ttks8n t|  tttksNtttj	} | ttj	  krxttj	ks~n t|  tttksttt
} | tt
  krtt
ksn t| jttfkst| jtkst| jtkstt| tstttt
 } | ttt
 kst|  ttt
 tj	 ks<tt| tsLt| jttfks`tttt t
 } |  tt tt
 tj	 tj	 kstttt } |  | kstttt t t } | jd jttttfkst|  | kstttt
 tt  } |  dt tt
t tj	 ttt
 tj	  ttt tj	  ksZtd S )Nc                   S   s   t tS N)r   r   r8   r8   r8   r9   <lambda>Y       z,test_multivariate_variance.<locals>.<lambda>r   r   )r   r   r   r   r   r+   r,   r   r.   r4   r   r-   r/   r0   r1   r   r   r2   r   r   r   r3   r   r   r6   r8   r8   r9   test_multivariate_varianceX   s>    "
&" *r?   c                  C   s  t tdd  t tdd  ttjtj} | jdks8t|  t	ddksNtttt} | ttt  krxt
ttks~n t|  t	ttkst| jttfkst| jtkst| jtkstt| t
stttt t t} |  t	ttkstttt} t| t
st|  | ks$tttt} t| t
s>t|  ttksTtttt t} t| t
srt|  t
ttt
tt kstttt t} t| t
st|  tt
tt ksttttt } t| t
st|  t
tttj ks
tttt t tjt t } t| t
s6t|  tt
tt t ksVtttt tt  t tjt tjt  t } t| t
st|  tt
tt t tt
tt t  tt
tt t  tt
tt t  kstd S )Nc                   S   s   t ttjS r;   )r   r   r   r4   r8   r8   r8   r9   r<   ~   r=   z3test_multivariate_crosscovariance.<locals>.<lambda>c                   S   s
   t ttS r;   )r   r   r   r8   r8   r8   r9   r<      r=   )r   r   r   )r   r   r   r   r4   r   r-   r+   r,   r   r   r.   r/   r0   r1   r   r   r   r   r   r   r   r   r   r>   r8   r8   r9   !test_multivariate_crosscovariance}   sN    
&

" .(r@   N),Zsympy.statsr   r   r   r   Zsympy.testing.pytestr   Zsympy.core.symbolr   Zsympy.matrices.commonr   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   r5   r.   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r2   r:   r?   r@   r8   r8   r8   r9   <module>   s>   /%