o
    i                     @   s  d dl mZ d dlZd dlZd dlmZmZ d dlm	Z
 d dlmZmZmZmZ ejdg dejdg ddd	 Zejdg dejd
g ddd Zejdg dejdg dejd
g ddd Zeg dg dg dg dg dddddejgg dddddejgg dg dg d g d!g d"g d#d$ddd%ejggZejjejd&edddd'f  d(d) Zejd*e d+d, Zejd-eeg d.d/d0gg d1d2d3 Zejd*g d d d ej d4fd d d/ej d4fd5d6d7d8d9d:d;d<d=d>d?d@ddAejfdBdCdDd@ddEejfdFdGdHdIdJd$d@dKdLejfdMdNdOdPdQdRdSdTdUdVdWdX ZdS )Y    )productN)assert_equalassert_allclose)log_wright_besselloggammargammawright_bessela)r   ư>皙?      ?   
   bc                 C   s2   t t| |dt| tt| |dt|  dS )zTest at x = 0.        N)r   r   r   r   r   r   )r	   r    r   `/home/kim/smarthome/.venv/lib/python3.10/site-packages/scipy/special/tests/test_wright_bessel.pytest_wright_bessel_zero   s   r   x)r   r
   r   r   r   c                 C   sX   |dkr*| d }t d|d |d d }tt|d || t||ddd dS dS )	zTest relation of wright_bessel and modified bessel function iv.

    iv(z) = (1/2*z)**v * Phi(1, v+1; 1/4*z**2).
    See https://dlmf.nist.gov/10.46.E2
    r   r      g      @g       @dy=rtolZatolN)r   r   nppowerscZiv)r   r   vwbr   r   r   test_wright_bessel_iv%   s   

r   )r   gjt?r      r   )r   r
   r   r   r   r   r   d   c                 C   sH   t t| |d || | t| ||  | |d t| ||  ddd dS )a=  Test functional relation of wright_bessel.

    Phi(a, b-1, z) = a*z*Phi(a, b+a, z) + (b-1)*Phi(a, b, z)

    Note that d/dx Phi(a, b, x) = Phi(a, b-1, x)
    See Eq. (22) of
    B. Stankovic, On the Function of E. M. Wright,
    Publ. de l' Institut Mathematique, Beograd,
    Nouvelle S`er. 10 (1970), 113-124.
    r   :0yE>r   Nr   r   r	   r   r   r   r   r   test_wright_functional7   s   
r$   )r         Y@9B.@gS
[.Gg:0yU>)r         $@r&   gUqZ+YIgv(x>)r   r'        @@g]a(aaHMr!   )r   r%   r(   g	5U4'g+i)+p>)      ?      4@     j@g+^%np~=r)   r%   r+   g
+eD)d     ?r*   r+   g'^%nr,   r-   gc+eD)      ?r        @@guc&Br,   )r.   g      =r/   gsc&Br,   )r.   g|=r/   gB&Br,   )r.   h㈵>r/   g]%Br,   )r.   r   r/   gKӨwqBgdy=)r.   r*   r+   g@IgA:)>r.   gmxi%%za, b, x, phi   c                 C   s   t t| |||dd dS )zDTest cases of test_data that do not reach relative accuracy of 1e-11r   r   Nr"   )r	   r   r   phir   r   r   test_wright_data_grid_failuresb   s   r4   za, b, x, phi, accuracyc                 C   >   t |rt t| ||sJ dS tt| ||||d dS )z}Test cases of test_data that do not reach relative accuracy of 1e-11

    Here we test for reduced accuracy or even nan.
    r2   N)r   isnanr   r   r	   r   r   r3   Zaccuracyr   r   r   #test_wright_data_grid_less_accuratek   s   
r8   za, b, x)r   r   r   r.   r   r   r   r   )MbP?r   r.   r   r   c                 C   s(   t t| ||tt| ||dd dS )z8Test that log_wright_bessel equals log of wright_bessel.r!   r2   N)r   r   r   logr   r#   r   r   r   ,test_log_wright_bessel_same_as_wright_bessely   s
   

r;   r   )r   r   Gz?r<   r   )r   r   d~QJr=   r   )r0   r   i  gujXV@r   )r0   r   r(   gF4@r   )r0   r    r(   g(@r   )r9   r   g     @g?@r   )r9   r   r+   g.x"S@r   )r9   r   g    .AgwV.Ar   )r9   r   r+   gZ<P@r   )r9   2   r+   gړD@r9   r9   r    grlqw4@)r   r   r+   gś 8ԯ@r   )r   r       cAgh{j@r   r   g&,@)r   r    r?   gDvu*@r   )r   r   r+   ge6Ѓ@r   )r   r       חAghՈ@r   )r.   r   r+   g}h@r   )r.   r   r@   gP2aI@r   r@   gSe@)r   r   r+   gtї#@r   )r   r   r@   gPw8@@r   )r   r      mBg/ft/c@r   )r   r    r+   gD%rvr   )r   r    rA   g8pK<ug-C6?)r   r    @xDg~8@g>)r    r   r+   g2ur   )r    r   rB   g?3Qsr   )r    r    r+   b%rvr   )r    r    rB   rC   r   c                 C   r5   )z6Test for log_wright_bessel, in particular for large x.r2   N)r   r6   r   r   r7   r   r   r   test_log_wright_bessel   s   
'rD   )	itertoolsr   Zpytestnumpyr   Znumpy.testingr   r   Zscipy.specialZspecialr   r   r   r   r   markZparametrizer   r   r$   arraynanZgrid_a_b_x_value_accZxfailtolistr4   r8   listr;   infrD   r   r   r   r   <module>   s   

$	
 %