o
    Ö­j  ã                   @   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	„ ƒƒZej dg d¢¡ej d
g d¢¡dd„ ƒƒZej dg d¢¡ej dg d¢¡ej d
g d¢¡dd„ ƒƒƒ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$ddd%ejgg¡Zejjej d&edd…dd'…f  ¡ ¡d(d)„ ƒƒZej d*e ¡ ¡d+d,„ ƒZej d-eeg d.¢d/d0gg d1¢ƒƒ¡d2d3„ ƒZej d*g d d d ej d4f‘d d d/ej d4f‘d5‘d6‘d7‘d8‘d9‘d:‘d;‘d<‘d=‘d>‘d?d@ddAejf‘dB‘dC‘dDd@ddEejf‘dF‘dG‘dH‘dI‘dJ‘d$d@dKdLejf‘dM‘dN‘dO‘dP‘dQ‘dR‘dS‘dT‘dU‘dV‘¡dWdX„ ƒZdS )Yé    )ÚproductN)Úassert_equalÚassert_allclose)Úlog_wright_besselÚloggammaÚrgammaÚwright_besselÚa)r   ç�íµ ÷Æ°>çš™™™™™¹?ç      à?é   é
   Úbc                 C   s2   t t| |dƒt|ƒƒ tt| |dƒt|ƒ ƒ dS )zTest at x = 0.ç        N)r   r   r   r   r   r   )r	   r   © r   úc/var/www/html/CropPilot/venv/lib/python3.10/site-packages/scipy/special/tests/test_wright_bessel.pyÚtest_wright_bessel_zero   s   r   Úx)r   r
   r   r   r   c                 C   sX   |dkr*| d }t d|d |d d ƒ}tt |d |¡| t ||¡ddd� dS dS )	zœTest 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   é   g      @g       @ç•dyáý¥=©ÚrtolÚatolN)r   r   ÚnpÚpowerÚscÚiv)r   r   ÚvÚwbr   r   r   Útest_wright_bessel_iv%   s   

þûr    )r   gj¼t“ð?r   é   r   )r   r
   r   r   r   r!   r   éd   c                 C   sH   t t| |d |ƒ| | t| ||  |ƒ |d t| ||ƒ  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   ç:Œ0âŽyE>r   N©r   r   ©r	   r   r   r   r   r   Útest_wright_functional7   s   ÿ
ýr&   )r   ç      Y@çð9úþB.†@gªS
[˜ê.Gg:Œ0âŽyU>)r   ç      $@r(   g¢UqZ+YýIgÁ�v¾À(x>)r   r)   ç     @�@g]a(aaHMr#   )r   r'   r*   gü	¾5U4Á'g+i¤)+p>)ç      ð?ç      4@ç     jø@g +^%³nçpé~À=r+   r'   r-   gá
ð+�e�D)çd     ð?r,   r-   gÕ'^%³nr.   r/   gÕcí+�e�D)ç      ø?r   ç     @@g€uc•&Br.   )r0   g      =r1   g¤sc•&Br.   )r0   g»½×Ùß|Û=r1   gÂB•&Br.   )r0   çñhãˆµøä>r1   g]¬ª¯Ï%Br.   )r0   r   r1   gKÓ¨wÓqBg•dyáýµ=)r0   r,   r-   g¼Ò@ åIgßA:ÜÅ)>r0   gŸmxÀ˜i%%za, b, x, phié   c                 C   s   t t| ||ƒ|dd� dS )zDTest cases of test_data that do not reach relative accuracy of 1e-11r   ©r   Nr$   )r	   r   r   Úphir   r   r   Útest_wright_data_grid_failuresb   s   r6   za, b, x, phi, accuracyc                 C   ó>   t  |¡rt  t| ||ƒ¡sJ ‚dS tt| ||ƒ||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.
    r4   N)r   Úisnanr   r   ©r	   r   r   r5   Úaccuracyr   r   r   Ú#test_wright_data_grid_less_accuratek   s   
r;   za, b, x)r   r   r   r0   r!   r   r   r   )çü©ñÒMbP?r   r0   r!   r   c                 C   s(   t t| ||ƒt t| ||ƒ¡dd� dS )z8Test that log_wright_bessel equals log of wright_bessel.r#   r4   N)r   r   r   Úlogr   r%   r   r   r   Ú,test_log_wright_bessel_same_as_wright_bessely   s
   

ýr>   r   )r   r   ç®Gáz®ó?r?   r   )r   r   çšd~ÅQJr@   r   )r2   r   i¼  g€ujXV¸…@r   )r2   r   r*   gÖÐÌF4�@r   )r2   r"   r*   g(þíïŽ„@r   )r<   r   g     ˆÃ@g?»‰œ�Ã@r   )r<   r   r-   g.x"»žSø@r   )r<   r   g    €„.Ag®¬w�V.Ar   )r<   r   r-   gZ<¢·Pø@r   )r<   é2   r-   gžìÑÚ“Dø@r<   r<   r"   grÎlqw4ø@)r   r   r-   gÅ› õ8Ô¯@r   )r   r   ç    ÐcAghÒ{ÕÈjõ@r   r   gÚÝ&É,ª@)r   r"   rB   gDvuÂ�*õ@r   )r   r   r-   geî6�ŠÐƒ@r   )r   r   ç    „×—Agh†¦¼ÕˆÓ@r   )r0   r   r-   g¡}ž‘ h@r   )r0   r   rC   gP2aŽùI¨@r   rC   géSÈe¢@)r!   r   r-   gtÑ—òÌË#@r   )r!   r   rC   gPˆw8Ò@@r   )r!   r   ç   ¢”mBg/f�t/±c@r   )r!   r"   r-   gD«%rvÀr   )r!   r"   rD   g8póK<uÀg-Cëâ6?)r!   r"   ç@Œµx¯DgáÚç†~8¤@g�íµ ÷ÆÀ>)r"   r   r-   g2Ãð¹uÀr   )r"   r   rE   g?3ïQ‘sÀr   )r"   r"   r-   çb”‡´%rvÀr   )r"   r"   rE   rF   r   c                 C   r7   )z6Test for log_wright_bessel, in particular for large x.r4   N)r   r8   r   r   r9   r   r   r   Útest_log_wright_bessel£   s   
'rG   )Ú	itertoolsr   ÚpytestÚnumpyr   Únumpy.testingr   r   Úscipy.specialÚspecialr   r   r   r   r   ÚmarkÚparametrizer   r    r&   ÚarrayÚnanÚgrid_a_b_x_value_accÚxfailÚtolistr6   r;   Úlistr>   ÚinfrG   r   r   r   r   Ú<module>   sð   ñþþ
ÿþ
$ÿþýüûúùø	÷
öõôóòñðïîíìëêéèçæåäãâá àþ%