o
    GZhw                     @   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sJ e;e9dsJ e;e9e9d rJ dd Z<dd Z=d d! Z>d"d# Z?d$d% Z@d&d' ZAd(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+   Q/var/www/auris/lib/python3.10/site-packages/sympy/stats/tests/test_compound_rv.py<lambda>   s    r-   c                  G   s   t ttt| dkS )N   )lensetmapflat)ar+   r+   r,   r-      s    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s3J t|dks;J t	|dktdd ksIJ t	|dk tdd t
tdd d  kscJ t|t| d	 ksoJ d S )
NXr.         
   (            )r   r   r%   simplifyr
   r	   r   r   r   r   r   r   )r4   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s<J t| | | ksHJ d S )Nzk t yTZpositiverealGr   r.   )r   r   r   r   r<   r   r   )ktyrA   Dr+   r+   r,   test_poisson_CompoundDist/   s
   
NrF   c                  C   sR  t ddd} td| }t|jtdd tdd dksJ t|tt|d  kr5tdd ks8J  J t|tdd ksDJ t	|tdd ddksSJ tdtdd }td	|}t|jtdd tdd dksuJ t|d
ktdd ksJ t
ddd} td| }t|tdd ksJ tt|dt|ksJ d S )Nr4   r.   r5   r=      )r   r.   	   r3   bg      ?r   )r   r   r   dictr   r   r   r   r   r   r   )r4   r=   r3   rI   r+   r+   r,   test_bernoulli_CompoundDist8   s   
(2
(
rK   c            
      C   sL  t dd} tdd| }d}tt|t|sJ d}tt tt|ddt	|s-J W d    n1 s7w   Y  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sJ tdd	d}tddd}td||}	d}tt|	ddt|sJ d S )NRr6   r4   rG   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   Nr5   MrE   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#   UserWarningr   Zrewriter   r   r   r	   r   r   )
rL   r4   ZansZexprer=   rO   ZexprdrQ   rR   rE   r+   r+   r,   test_unevaluated_CompoundDistL   s0   




<rU   c            	         s
  t ddd} t| d}t|}|jsJ |jtt tksJ |jtdd	 t
td  d td  tdd  d	tt  ksCJ tttdd
trOJ 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szJ |jddhksJ 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sJ tdddd\}}}td||}t|} t| }|jsJ |jtjksJ |j|dd	 || |d | |   t||  t|t|d   ksJ d S )Nr4   r5   r6   TrM   @   r;   r.      rG   c                      s   t  S )N)r   r+   rR   r+   r,   r-   x   s    z,test_Compound_Distribution.<locals>.<lambda>r   rD   F)negativeinteger   <   )r   Tzk t zr?   rA   )r   r   r   Zis_Continuousr0   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   )	r4   rQ   CBrD   rB   rC   zrA   r+   rX   r,   test_Compound_Distributionm   s>   

H
, 

,rb   c                     s  t ddd} t ddd}t|jtrJ tdd}td}tddd	}td
|}td|}td|}t|tr9J t|tr@J t|trGJ tddgddgddgg tt	 fdd t d| d}t|jtskJ |jj
tt| dksxJ |jjjtt tksJ d S )Nr4   r5   r6   r=   rG      r.   g?r   rQ   rE   r`   c                      s
   t d S )NrR   )r   r+   rX   r+   r,   r-      s   
 z&test_compound_pspace.<locals>.<lambda>)r   r]   Zpspacer   r   r    r!   r$   r"   
ValueErrordistributionr   domainr0   r   r   )r4   r=   rQ   rE   r`   Zpspace1Zpspace2Zpspace3r+   rX   r,   test_compound_pspace   s$   



rg   N)BZ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%   r2   rS   r>   rF   rK   rU   rb   rg   r+   r+   r+   r,   <module>   sB    8	! 