a
    hZ                     @   s  d dl Z d dl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mZmZ d dlZ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 e jdg dd	d
 Z e jdddgdd Z!dd Z"dd Z#dd Z$dd Z%dd Z&dd Z'dd Z(dd Z)e jdej*e+e,fgd   d!d" Z-d#d$ Z.d%d& Z/d'd( Z0d)d* Z1d+d, Z2d-d. Z3d/d0 Z4e jd1g d2d3d4 Z5d5d6 Z6d7d8 Z7d9d: Z8d;d< Z9d=d> Z:G d?d@ d@Z;G dAdB dBZ<e jdCg dDg dEgdFdG Z=dHdI Z>G dJdK dKZ?G dLdM dMZ@dS )N    N)	betabinom
betanbinom	hypergeom
nhypergeom	bernoulli	boltzmannskellamzipfzipfianbinomnbinomnchypergeom_fishernchypergeom_walleniusrandint)assert_almost_equalassert_equalassert_allclosesuppress_warnings)r   )root_scalar)quadzk, M, n, N, expected, rtol))   
         g<<?V瞯<)k   '       g?r   )r   r   r   r   gS;绽|=c                 C   s"   t | |||}t|||d d S Nrtol)r   cdfr   kMnNexpectedr"   p r+   b/var/www/html/assistant/venv/lib/python3.9/site-packages/scipy/stats/tests/test_discrete_distns.pytest_hypergeom_cdf   s    r-   )   r   r   r   g?r   )}   r   r   r   g!:<r   c                 C   s"   t | |||}t|||d d S r    )r   sfr   r$   r+   r+   r,   test_hypergeom_sf"   s    r1   c            
      C   s   d} d}d}d}t | |||}t ||  ||| |}t ||  |||| }t | |||}t||dd t||dd t||dd d} d}d}d}t | |||}t| || }	t||	dd d S )Nr   2   r      )decimal      )r   Zlogpmfr   r   )
r%   r(   Kr'   Zlogpmf1Zlogpmf2Zlogpmf3Zlogpmf4Zhypergeom_logpmfZbernoulli_logpmfr+   r+   r,   test_hypergeom_logpmf,   s$    r8   c                  C   sh   d\} }}d}t || ||}t|| ||| d | | |d   | || d   }t||dd d S )N)-            r5   绽|=r!   )r   pmfr   r   )r&   r'   rr%   ZNHGZHGr+   r+   r,   test_nhypergeom_pmfF   s
    
8r@   c                  C   sb   d} d}d}t |d }t|| ||}t|| ||}t|g ddd t|g ddd d S )	Nr;   r   r   r5   )$I$I?g۶m۶m?m۶m?rB   vIh%<=r!   )rA   $I$I?g%I$I?      ?)nparanger   r>   r#   r   )r&   r'   r?   supportr>   r#   r+   r+   r,   test_nhypergeom_pmfcdfO   s    rI   c                  C   sF   d} d}d}t g dg dg| ||}t|g dg dgdd	 d S )
Nr   r   r   )r   r5      r   )r5   rJ   r   r   )r5   r   r   r5   )r   r   r5   r   rC   r!   )r   r>   r   )r&   r'   r?   r>   r+   r+   r,   test_nhypergeom_r0[   s
    rK   c                  C   s0   t jdg ddgdggdd} | jdks,J d S )N   )r6   r;   	   r3   r:   r   r5   rJ   r   size)r   rvsshape)xr+   r+   r,   test_nhypergeom_rvs_shaped   s    rT   c                  C   sV   t jd tjddddd} t jd t jjdd}t|ddd}t| | d S )Nr   rL   r6      d   rO   )rF   randomseedr   rQ   uniformppfr   )rS   r*   yr+   r+   r,   test_nhypergeom_accuracyl   s    r\   c                  C   s   t dd} d}t| d|}| dk}t|| t d}d}t| ||}g d}t||d	d
 t| ||}g d}t||d	d
 d S )Nr   r5   grh|?r   rJ   r   )r   r   r   $I$I?rD   g$I$I?r   r   rC   r!   )r   r   r   r^   g۶m۶m?r5   r5   r5   )rF   rG   r   r>   r   logr   r#   )r%   r(   r*   r)   Zlamcr+   r+   r,   test_boltzmann_upper_boundw   s    

ra   c                  C   sJ   d} t | d }t| dd|}t d| d  | d }t|| d S )N   r5   )rF   rG   r   r>   repeatr   )r'   r%   r*   r)   r+   r+   r,   test_betabinom_a_and_b_unity   s
    rd   dtypesr   c                 C   sB   | \}}}|d|d|d  }}}t tj|||ddd d S )Nr   rJ   r   r%   Zmomentsgaa)r   r   stats)re   Zn_typea_typeb_typer'   abr+   r+   r,   -test_betabinom_stats_a_and_b_integers_gh18026   s    
rl   c                  C   sH   d} d}t d}td| ||}t| | |  |}t|| d S )Ngffffff@g)\(?rJ   r5   )rF   rG   r   r>   r   r   )rj   rk   r%   r*   r)   r+   r+   r,   test_betabinom_bernoulli   s    
rm   c                  C   s$   d\} }}t tj| ||dd d S )N)g?r   r5   Z
confidencer'   r*   r   r   )r   r   intervalalphar'   r*   r+   r+   r,   test_issue_10317   s    
rs   c                  C   s$   d\} }}t tj| ||dd d S )N)gffffff?r   r   rn   ro   )r   r   rp   rq   r+   r+   r,   test_issue_11134   s    
rt   c                   C   sT   t jd ttt jdddd ttdddd ttdddd d S )Nr   r         ?r5   )rF   rW   rX   r   r   rZ   randr+   r+   r+   r,   test_issue_7406   s    rx   c                  C   sv   d} t jjddd}d}t||| }t|d t ddd}t||| }t|d d}t||| }t|| d S )	Nr   rV   r   rO   rv   {Gz?gGz?r5   )rF   rW   r   r   rZ   r   linspace)r*   r'   rS   rZ   r+   r+   r,   test_issue_5122   s    

r{   c                   C   s"   t tdtdddd d S )N  r]   iry   r   )r   r   rF   logspacerZ   r+   r+   r+   r,   test_issue_1603   s    r~   c                  C   s2   d} t ddd}tt|d| | ddd d S )Nru   r      r3   rJ   ry   )atol)rF   r}   r   r   r#   )r*   rS   r+   r+   r,   test_issue_5503   s    r   zx, n, p, cdf_desired)	)i,  r|   333333?g24?)r   r   r   gU7i(?)i0u  i r   gέ̑?)i i@B r   g8@
?)i- 逖 r   gf(G?)i r   gwtg ?)ir   r   gV}ֈ?)ipr   r   gz̍?)i0 r   r   gnC:c                 C   s   t t| ||| d S Nr   r   r#   )rS   r'   r*   Zcdf_desiredr+   r+   r,   test_issue_5503pt2   s    r   c                   C   s   t tdddd d S )NrJ   l    J)g-q=gB.+n?r   r+   r+   r+   r,   test_issue_5503pt3   s    r   c                   C   s   t tdddd d S )N   r2   gAA?g_[Cˮi8)r   r   r0   r+   r+   r+   r,   test_issue_6682   s    r   c                  C   s.   t g ddd} dtj dg}t| | d S )N)r   rv   r5   r   ru   gG޿g1D&+)r   logcdfrF   infr   )result	referencer+   r+   r,   test_issue_19747   s    r   c                  C   s$   d} d}d}t t|| |d d S )Nr|   ry   i          )r   r   r>   )r'   r*   r%   r+   r+   r,   %test_boost_divide_by_zero_issue_15101   s    r   c                  C   s,   g d} t d| | }g d}t|| d S )N)	r5   r   rV   r|     i  i  i  ip  r   )	g>l?gzo?gVrRs?g$?gVWCW?g4yB?g4.?g.Lr?gD?)r   r#   r   )mur#   Zcdf_expectedr+   r+   r,   test_skellam_gh11474   s    r   c                   @   st   e Zd Zdd Zdd Zdd Zejd e	e
dd	d
ejddd
fjZejdedd Zdd ZdS )TestZipfianc                 C   s   d}d}t dd}tt|||t|| tt|||t|| tt|||t|| ttj||ddtj|dd d S )Ng      @r   r5      msvkrf   )	rF   rG   r   r
   r>   r	   r#   r0   rg   )selfrj   r(   r%   r+   r+   r,   test_zipfian_asymptotic  s    z#TestZipfian.test_zipfian_asymptoticc                 C   s   d\}}d}t d|d }tt|||t|||dd tt|||t|||dd tt|||t|||dd ttj||ddtj||dddd d S )N)gG?g1  ?   r5   gƠ>r!   r   rf   )rF   rG   r   r
   r>   r#   r0   rg   )r   Zalt1Zagt1r(   r%   r+   r+   r,   test_zipfian_continuity  s    z#TestZipfian.test_zipfian_continuityc                 C   s   t jd t jjdddd}t jdd d }t jjdddd}g d}g d}tt|||dd  |dd  d	d
 tt|||dd  |dd  dd
 d S )Nr   r5   rb   r   rO   rV   )
gĹԨ?gءk>	]x[?g>g	W4?g
-?g$fhn=g9[.>g`֔>gnm?)
gaj?gZk=?r   g?g90?gɸU?rE   gJ_9?g2h2-?gB0?ư>r!   g-C6
?)	rF   rW   rX   r   rw   r   r
   r>   r#   )r   r%   rj   r'   r>   r#   r+   r+   r,   test_zipfian_R(  s    (zTestZipfian.test_zipfian_Rr   r5   r   rJ   (   za, nc                    s   t jdd  t j fdd}t |d }||||}t |}t j||d}t j|| d |d}|d }	t j|| |	 d	 |d}
t j|| |	 d
 |dd	 }tt|||| tt|||| ttj	||dd|||
|g d S )Nc                 S   s   dt d| d |   S )z$Naive implementation of harmonic sumr5   )rF   rG   sum)r'   sr+   r+   r,   HnsH  s    z+TestZipfian.test_zipfian_naive.<locals>.Hnsc                    s.   | dk s| |krdS d| |   || S dS )z#Naive implementation of zipfian pmfr5   r   Nr+   )r%   rj   r'   r   r+   r,   pzipM  s    z,TestZipfian.test_zipfian_naive.<locals>.pzipr5   )weightsrJ   ru   r   r   Zmvskrf   )
rF   	vectorizerG   ZcumsumZaverager   r
   r>   r#   rg   )r   rj   r'   r   r%   r>   r#   meanvarZstdZskewZkurtosisr+   r   r,   test_zipfian_naiveD  s"    


zTestZipfian.test_zipfian_naivec                 C   sD   t dd}|t j}tdd}||}||}t|| d S )Nr   r|   o   rL   )rF   rG   astypeint32r
   r>   r   r   r%   Zk_int32distr>   Zpmf_k_int32r+   r+   r,   test_pmf_integer_kb  s    


zTestZipfian.test_pmf_integer_kN)__name__
__module____qualname__r   r   r   rF   rW   rX   Zvstackr}   r   TZnaive_testspytestmarkparametrizer   r   r+   r+   r+   r,   r     s   
r   c                   @   s   e Zd Zejd dZdZejjdeedZ	ejjdeedZ
e	e
 ZejdeejdZedee
 Zeee	ZejeeejdZejjej d Zejddd	gd
d Zdd Zdd Zdd Zejddd	gdd ZdS )TestNCHrJ   rJ   r   r   rV   r5   rO   r   	dist_namer   r   c                 C   sX   t td}|| }| j| j| j| jf\}}}}t|j||||ddt|||| d S )Nr   r   r5   )odds)	r   r   rS   r(   m1r'   r   r>   r   )r   r   distsr   rS   r(   r   r'   r+   r+   r,   test_nch_hypergeomy  s    zTestNCH.test_nch_hypergeomc           
      C   s   | j | j| j| j| jf\}}}}}tjdd }||||||\}}}	tt	|||||| ttj
||||dd| ttj
||||dd|	 d S )Nc                    s   | t d t fdd  fdd}|d}|d}|d} | | }	|| }
|| || d  }|	|
|fS )Nr   c                    s(   t  | }t |  }|| |   S r   )special_binom)rS   t1t2r   m2r'   wr+   r,   f  s    
zFTestNCH.test_nchypergeom_fisher_naive.<locals>.pmf_mean_var.<locals>.fc                    s"   t  fddtd D S )Nc                 3   s   | ]} ||  V  qd S r   r+   ).0r[   )r   r%   r+   r,   	<genexpr>      zYTestNCH.test_nchypergeom_fisher_naive.<locals>.pmf_mean_var.<locals>.P.<locals>.<genexpr>r5   )r   ranger%   )r   xlxur   r,   P  s    zFTestNCH.test_nchypergeom_fisher_naive.<locals>.pmf_mean_var.<locals>.Pr5   rJ   rF   maximumminimum)rS   r(   r   r'   r   r   ZP0ZP1ZP2r>   r   r   r+   )r   r   r   r'   r   r   r   r,   pmf_mean_var  s    z;TestNCH.test_nchypergeom_fisher_naive.<locals>.pmf_mean_varmrf   v)rS   r(   r   r'   r   rF   r   r   r   r>   rg   )
r   rS   r(   r   r'   r   r   r>   r   r   r+   r+   r,   test_nchypergeom_fisher_naive  s    "
z%TestNCH.test_nchypergeom_fisher_naivec              	      s  t jd d}d}t jjd||d}t jjd||d}|| }tjd||jd}t d|| }t ||}tj|||jd}	t jj|	j d }
dd t j	fd	d
 t
 B}|jtdd tt||||
 ||||
dd W d    n1 s0    Y  t j	 fdd}t
 F}|jtdd ttj||||
dd|||||
dd W d    n1 sj0    Y  t j	fdd}||	||||
}t|	||||
}d\}}t || ||t |  k }| t |d ksJ t||  ||  ||  |
|  D ]r\}}}}
|| }||||
\}}t ||d }	||	||||
 dk sfJ tt|	||||
 d qd S )NrJ   r   rV   r5   rO   r   c                 S   s,   | | }t d|| }t ||}||fS )Nr   r   )r(   r   r'   r   r   r   r   r+   r+   r,   rH     s    z9TestNCH.test_nchypergeom_wallenius_naive.<locals>.supportc                    s>   |   |  \}} fdd}t |||fdjS )Nc                    s    |   d|      d S Nr5   r+   )ur   r+   r,   fun  s    zCTestNCH.test_nchypergeom_wallenius_naive.<locals>.mean.<locals>.fun)Zbracket)r   root)r(   r   r'   r   r   r   r   rH   r   r,   r     s    z6TestNCH.test_nchypergeom_wallenius_naive.<locals>.meanz!invalid value encountered in mean)messageg{Gz?r!   c                    sZ   | | } | |||}|||  }|| || |  }| | | | d || ||    S r   r+   )r(   r   r'   r   r   r   rj   rk   )r   r+   r,   variance  s
    z:TestNCH.test_nchypergeom_wallenius_naive.<locals>.variancer   rf   g?c                    sH   | |\}}fdd  fdd}|S )Nc                    sH         }d| |    d| d|      }|S r   r+   )tDres)r   r   r'   r   rS   r+   r,   	integrand  s    ,zHTestNCH.test_nchypergeom_wallenius_naive.<locals>.pmf.<locals>.integrandc                    s:   t | }t |  }t ddddd}|| |d  S )Nr   r5   gؗҜ<)ZepsrelZepsabs)r   r   )rS   r   r   Zthe_integral)r   r   r   r'   r+   r,   r     s    
z@TestNCH.test_nchypergeom_wallenius_naive.<locals>.pmf.<locals>.fr+   )rS   r(   r   r'   r   r   r   r   r   )r   r   r   r'   r   rS   r,   r>     s
    z5TestNCH.test_nchypergeom_wallenius_naive.<locals>.pmf)r   r   ru   )rF   rW   rX   r   rQ   rR   r   r   rw   r   r   filterRuntimeWarningr   r   r   rg   r>   absr   prodziprG   )r   rR   max_mr   r   r(   r'   r   r   rS   r   supr   r>   Zpmf0Zpmf1r   r"   ir+   )r   rH   r,    test_nchypergeom_wallenius_naive  sZ    	$& 2z(TestNCH.test_nchypergeom_wallenius_naivec           	      C   s   d}d}d}d}t d}t g d}d}d}tt||||||d	d	d
 tt|||||d	d tt|||||dd d S )Nr2   r   rb   g      @r   )g9T;gr<gD,P=g4 V=g'	,=gCG>gyztj>gt>g+k?g MeGD?gqNZVɒo?gc2n?g~ZN?gE}?Y?g?g·aQ?g]??gr)?gp{?g39	y?g m>?gJ򕴝-@gih@rC   )r"   r   r!   gdy=)rF   rG   arrayr   r   r>   r   r   )	r   r&   r'   r(   r   r   r>   r   r   r+   r+   r,   test_wallenius_against_mpmath  s"    
z%TestNCH.test_wallenius_against_mpmathc                 C   sD   t td}|| }|jdddgdggg ddd}|jdks@J d S )	Nr   r2   r   r   rb   )ru   rE   g       @rN   rO   )r   r   rQ   rR   )r   r   r   r   rS   r+   r+   r,   test_rvs_shape-  s     zTestNCH.test_rvs_shapeN)r   r   r   rF   rW   rX   rR   r   r   r   r   r(   rQ   r'   r   r   r   r   rS   rw   r   r   r   r   r   r   r   r   r   r+   r+   r+   r,   r   k  s,   

"\*r   zmu, q, expected)r   x   g@	#)i  r   g"qVUc                 C   s.   d}||||    }}t t|||| d S )Nrb   )r   r   r   )r   qr)   rP   r'   r*   r+   r+   r,   test_nbinom_11465:  s    r   c                  C   s`   t ddd} d}t|| }| d dk}t|d | t|d d|  t||  d d S )Nr   r5   rU   g?rv   )rF   rz   r   r>   r   r   )rS   r*   r>   r   r+   r+   r,   test_gh_17146G  s    r   c                   @   s\   e Zd Zejdg dg dg dgdd Zejdg dg d	g d
gdd ZdS )TestBetaNBinomzx, n, a, b, ref)r   g    SAr   rb   g:[Y))rV   r2   r   rb   g dg?)r   r|   r   rb   gL&[>c                 C   s   t t|||||dd d S )Nr=   r!   )r   r   r>   )r   rS   r'   rj   rk   refr+   r+   r,   test_betanbinom_pmfT  s    z"TestBetaNBinom.test_betanbinom_pmfzn, a, b, ref)r   r   r2   g:o?)r   rM   rM   g>["@)rV   r|   r   g >[?c                 C   s    t tj|||dd|dd d S )Nr%   rf   g [n<r!   )r   r   rg   )r   r'   rj   rk   r   r+   r+   r,   test_betanbinom_kurtosisg  s    z'TestBetaNBinom.test_betanbinom_kurtosisN)r   r   r   r   r   r   r   r   r+   r+   r+   r,   r   S  s   
r   c                   @   s   e Zd Zdd ZdS )TestZipfc                 C   sB   t dd}|t j}td}||}||}t|| d S )Nr   r|   rM   )rF   rG   r   r   r	   r>   r   r   r+   r+   r,   test_gh20692  s    

zTestZipf.test_gh20692N)r   r   r   r   r+   r+   r+   r,   r     s   r   )Ar   	itertoolsZscipy.statsr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   numpyrF   Znumpy.testingr   r   r   r   Zscipy.specialr   Zscipy.optimizer   Zscipy.integrater   r   r   r-   r1   r8   r@   rI   rK   rT   r\   ra   rd   productintfloatrl   rm   rs   rt   rx   r{   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r+   r+   r+   r,   <module>   sj   @

		


	
^ P

-