o
    h;                     @   s  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
 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dS ),    N)assert_equalassert_allclose)rgammawright_bessela)r   ư>皙?      ?   
   bc                 C   s   t t| |dt| dS )zTest at x = 0.        N)r   r   r   )r   r    r   a/var/www/html/scripts/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=rtolatolN)r   r   nppowersc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_functional4   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,   gh㈵>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_failures_   s   r1   za, b, x, phi, accuracyc                 C   s>   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.
    r/   N)r   isnanr   r   )r   r   r   r0   accuracyr   r   r   #test_wright_data_grid_less_accurateh   s   
r4   )pytestnumpyr   numpy.testingr   r   scipy.specialspecialr   r   r   markparametrizer   r   r"   arraynangrid_a_b_x_value_accxfailtolistr1   r4   r   r   r   r   <module>   sV   