U
    	-ew                     @   s  d dl mZ d dl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 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 m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z) d dl*m+Z+m,Z, d dl-m.Z. d dl/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5 d dl6m7Z7 d dl8m9Z9 dd Z:dd Z;e;e9e9s`t<e;e9dspt<e;e9e9d rt<dd Z=dd Z>d d! Z?d"d# Z@d$d% ZAd&d' ZBd(S ))    )Sum)oopi)Eq)S)symbols)	factorial)exp)sqrt)	Piecewise)beta)erf)gamma)Integral)Interval)NormalPEdensityGammaPoissonRayleighvariance	BernoulliBetaUniformcdf)CompoundDistributionCompoundPSpace)NormalDistribution)PoissonDistribution)BernoulliDistribution)raisesignore_warnings)MultivariateNormalDistribution)xc                 C   s   d t|  S )N )joinstrsplit)s r+   c/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/stats/tests/test_compound_rv.py<lambda>       r-   c                  G   s   t ttt| dkS )N   )lensetmapflat)ar+   r+   r,   r-      r.   r%   r/   c                  C   s   t ddd} t d| d}t|t tdttd  d td  tdd   dtt  ksftt	|dksvtt
|dktdd kstt
|dk tdd ttdd d  kstt|t| d	 kstd S )
NXr/         
   (            )r   r   r%   simplifyr
   r	   r   r   AssertionErrorr   r   r   r   )r5   Yr+   r+   r,   test_normal_CompoundDist#   s    N4r@   c                  C   s   t dddd\} }}td| |}td|}t|| || |d |  |   t| |  t| t|d   ksxtt| | | kstd S )Nzk t yTZpositiverealGr   r/   )r   r   r   r   r=   r   r>   r   )ktyrC   Dr+   r+   r,   test_poisson_CompoundDist/   s
    
NrH   c                  C   sV  t ddd} td| }t|jtdd tdd dks>tt|tt|d  krhtdd ksnn tt	|tdd kstt
|tdd ddksttdtdd }td	|}t|jtdd tdd dkstt|d
ktdd ksttddd} td| }t|tdd ks6ttt|dt|ksRtd S )Nr5   r/   r6   r?      )r   r/   	   r4   bg      ?r   )r   r   r   dictr   r>   r   r   r   r   r   r   )r5   r?   r4   rK   r+   r+   r,   test_bernoulli_CompoundDist8   s    
(0
(
rM   c            
   	   C   s:  t dd} tdd| }d}tt|t|s0td}tt" tt|dd	t
|sZtW 5 Q R X tdd	}td
|}td|}tt| |t  ttdt|  ||  t|t|  |dtf tt |dtf}t|t|ksttdd	d}tddd}td||}	d}tt|	ddt|s6td S )NRr7   r5   rI   z
        Piecewise(((-sqrt(pi)*sinh(x/4 - 3/4) + sqrt(pi)*cosh(x/4 - 3/4))/(
        8*sqrt(pi)), Abs(arg(x - 3)) <= pi/4), (Integral(sqrt(2)*exp(-(x - 3)
        **2/(2*R**2))*exp(-R**2/32)/(32*sqrt(pi)), (R, 0, oo)), True))zw
        Integral(X*Integral(sqrt(2)*exp(-(X-3)**2/(2*R**2))*exp(-R**2/32)/(32*
        sqrt(pi)),(R,0,oo)),(X,-oo,oo))Fevaluater/   r?   Zr   Nr6   MrG   z
        Integral(sqrt(2)*exp(-(N-1)**2/8)*Integral(exp(-(x-M)**2/(2*N**2))*exp
        (-(M-3)**2/32)/(8*pi*N),(M,-oo,oo))/(4*sqrt(pi)),(N,-oo,oo)))r   r   streqr   r%   r>   r#   UserWarningr   Zrewriter   r   r   r	   r   r   )
rN   r5   ZansZexprer?   rQ   ZexprdrS   rT   rG   r+   r+   r,   test_unevaluated_CompoundDistL   s.    

&


<rW   c            	         s  t ddd} t| d}t|}|js(t|jtt tks>t|jt	dd
 tt	d  d t	d  tdd  d	tt  ksttttdd
trttddgddgddgg tt fdd tddd} t| dd}t|}|jst|jddhksttdddd}|j|ddttddtdd  t|dftddtdd  t|dfdksnttdddd\}}}td||}t|} t| }|jst|jtjkst|j|dd
 || |d | |   t||  t|t|d   kstd S )Nr5   r6   r7   TrO   @   r<   r/      rI   c                      s   t  S )N)r   r+   rT   r+   r,   r-   x   r.   z,test_Compound_Distribution.<locals>.<lambda>r   rF   F)negativeinteger   <   )r   Tzk t zrA   rC   )r   r   r   Zis_Continuousr>   r1   r   r   Zpdfr%   r=   r	   r   r
   r   
isinstancer$   r"   NotImplementedErrorr   r!   Z	is_Finiter   r   r   r   r   r    Zis_DiscreteZ	Naturals0r   )	r5   rS   CBrF   rD   rE   zrC   r+   rZ   r,   test_Compound_Distributionm   s@    

H
, ,rd   c                     s  t ddd} t ddd}t|jtr(ttdd}td}tddd	}td
|}td|}td|}t|trrtt|trtt|trttddgddgddgg t	t
 fdd t d| d}t|jtst|jjtt| dkst|jjjtt tkstd S )Nr5   r6   r7   r?   rI      r/   g?r   rS   rG   rb   c                      s
   t d S )NrT   )r   r+   rZ   r+   r,   r-      r.   z&test_compound_pspace.<locals>.<lambda>)r   r_   Zpspacer   r>   r   r    r!   r$   r"   
ValueErrordistributionr   domainr1   r   r   )r5   r?   rS   rG   rb   Zpspace1Zpspace2Zpspace3r+   rZ   r,   test_compound_pspace   s$    



ri   N)CZsympy.concrete.summationsr   Zsympy.core.numbersr   r   Zsympy.core.relationalr   Zsympy.core.singletonr   Zsympy.core.symbolr   Z(sympy.functions.combinatorial.factorialsr   Z&sympy.functions.elementary.exponentialr	   Z(sympy.functions.elementary.miscellaneousr
   Z$sympy.functions.elementary.piecewiser   Z&sympy.functions.special.beta_functionsr   Z'sympy.functions.special.error_functionsr   Z'sympy.functions.special.gamma_functionsr   Zsympy.integrals.integralsr   Zsympy.sets.setsr   Zsympy.statsr   r   r   r   r   r   r   r   r   r   r   r   Zsympy.stats.compound_rvr   r   Zsympy.stats.crv_typesr   Zsympy.stats.drv_typesr    Zsympy.stats.frv_typesr!   Zsympy.testing.pytestr"   r#   Zsympy.stats.joint_rv_typesr$   Z	sympy.abcr%   r3   rU   r>   r@   rH   rM   rW   rd   ri   r+   r+   r+   r,   <module>   s@   8	! 