+
    0i                        ^ RI Ht ^ RIt^ RIt^ RIHtHt ^ RIH	t
 ^ RIHtHtHtHt ]P                  P!                  R. R!O4      ]P                  P!                  R. R!O4      R 4       4       t]P                  P!                  R. R!O4      ]P                  P!                  R	. R"O4      R
 4       4       t]P                  P!                  R. R!O4      ]P                  P!                  R. R#O4      ]P                  P!                  R	. R$O4      R 4       4       4       t]P(                  ! . R%O. R&O. R'O. R(O. R)ORRRR]P*                  .. R*ORRRR]P*                  .. R+O. R,O. R-O. R.O. R/O. R0ORRRR]P*                  ..4      t]P                  P.                  ]P                  P!                  R]R1,          P1                  4       4      R 4       4       t]P                  P!                  R]P1                  4       4      R 4       t]P                  P!                  R]! ]! . R2O^^.. R3O4      4      4      R 4       t]P                  P!                  R. ^ ^ ^ ]P:                  ) R3N^ ^ ^]P:                  ) R3NR4NR5NR6NR7NR8NR9NR:NR;NR<NR=NR^dRR]P*                  3NR>NR?NR^dRR]P*                  3NR@NRANRBNRCNRDNR^dRR]P*                  3NRENRFNRGNRHNRINRJNRKNRLNRMNRNN4      R  4       tR# )O    )productN)assert_equalassert_allclose)log_wright_besselloggammargammawright_bessela      ?bc                    \        \        WR4      \        V4      4       \        \	        WR4      \        V4      ) 4       R# )zTest at x = 0.        N)r   r	   r   r   r   r   )r
   r   s   &&d/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/special/tests/test_wright_bessel.pytest_wright_bessel_zeror      s1     qR(&)4%aB/(1+>    xc                    V^ 8w  dt   V ^,
          p\        ^V^,           V^,          R,          4      p\        \        P                  ! VR,          V4      V,          \        P
                  ! W!4      RRR7       R# R# )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
g      @g       @dy=rtolatolN)r	   r   nppowersciv)r   r   vwbs   &&  r   test_wright_bessel_ivr   %   sc     	AvE1a!eQTBY/ 	R+b0a"	0 r   MbP?c           
         \        \        W^,
          V4      W,          \        WV ,           V4      ,          V^,
          \        WV4      ,          ,           RRR7       R# )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.
:0yE>r   Nr   r	   r
   r   r   s   &&&r   test_wright_functionalr$   7   sK     M!UA.EM!UA661uaA 667D*r         Y@      ?     j@g
+eDd     ?gc+eD      ?gmxi%%za, b, x, phic                6    \        \        WV4      VRR7       R# )zDTest cases of test_data that do not reach relative accuracy of 1e-11r   r   Nr"   )r
   r   r   phis   &&&&r   test_wright_data_grid_failuresr-   b   s     M!*Ce<r   za, b, x, phi, accuracyc                    \         P                  ! V4      '       d+   \         P                  ! \        WV4      4      '       g   Q hR# \        \        WV4      W4R7       R# )zuTest 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   r,   accuracys   &&&&&r   #test_wright_data_grid_less_accurater2   k   s@     
xxxxaA.////aA.Cr   za, b, xc           
     r    \        \        WV4      \        P                  ! \	        WV4      4      RR7       R# )z8Test that log_wright_bessel equals log of wright_bessel.r!   r+   N)r   r   r   logr	   r#   s   &&&r   ,test_log_wright_bessel_same_as_wright_besselr5   y   s,     !"
}Q1%&r   r   grlqw4@g&,@    חAgSe@c                    \         P                  ! V4      '       d+   \         P                  ! \        WV4      4      '       g   Q hR# \        \        WV4      W4R7       R# )z6Test for log_wright_bessel, in particular for large x.r+   N)r   r/   r   r   r0   s   &&&&&r   test_log_wright_besselr8      sC    N 
xxxx)!23333)!2CGr   )r   ư>皙?r      
   )r   r9   r:   r   r;   )r;   gjt?      r<   )r   r9   r:   r   r;   r>   r<   d   )r:   r%   9B.@gS
[.Gg:0yU>)r         $@r@   gUqZ+YIgv(x>)r   rA        @@g]a(aaHMr!   )r   r%   rB   g	5U4'g+i)+p>)r&         4@r'   g+^%np~=)r(   rC   r'   g'^%nrD   )r)   r        @@guc&BrD   )r)   g      =rE   gsc&BrD   )r)   g|=rE   gB&BrD   )r)   h㈵>rE   g]%BrD   )r)   r:   rE   gKӨwqBgdy=)r)   rC   r'   g@IgA:)>):NNN:N   N)r   r:   r   r)   r>   r<   )r   r;   r)   r>   r<   )r   r;   Gz?rH   r   )r   r;   d~QJrI   r   )rF   r   i  gujXV@r   )rF   r   rB   gF4@r   )rF   r?   rB   g(@r   )r   r   g     @g?@r   )r   r   r'   g.x"S@r   )r   r   g    .AgwV.Ar   )r   r<   r'   gZ<P@r   )r   2   r'   gړD@r   )r   r   r'   gś 8ԯ@r   )r   r       cAgh{j@r   )r   r?   rK   gDvu*@r   )r;   r   r'   ge6Ѓ@r   )r;   r   r6   ghՈ@r   )r)   r   r'   g}h@r   )r)   r   r6   gP2aI@r   )r>   r   r'   gtї#@r   )r>   r   r6   gPw8@@r   )r>   r      mBg/ft/c@r   )r>   r?   r'   gD%rvr   )r>   r?   rL   g8pK<ug-C6?)r>   r?   @xDg~8@g>)r?   r   r'   g2ur   )r?   r   rM   g?3Qsr   )r?   r?   r'   b%rvr   )r?   r?   rM   rN   r   )	itertoolsr   pytestnumpyr   numpy.testingr   r   scipy.specialspecialr   r   r   r   r	   markparametrizer   r   r$   arraynangrid_a_b_x_value_accxfailtolistr-   r2   listr5   infr8    r   r   <module>r_      s  &    7  L L 8989? : :? 89450 6 :0  8956@A* B 7 :** xx@?479%1266:H*@"&&I0B22/5%1266:!  & &&(*=* =
 !#D#D )Aq63HIH !	
Aq266'5!!	
Aq266'5!! 	"! 	"	!
 	1! 	2! 	3! 	2! 	2! 	2! 	2! 	2! 
sC+RVV4! 	1! 	1!  
c3*BFF3!!" 	3#!$ 	/%!& 	/'!( 	1)!* 	0+!, 
c3*BFF3-!. 	//!0 	/1!2 	03!4 	25!6 	27!8 	19!: 	2;!< 	3=!> 	3?!@ 	4A!$JHK$JHr   