ó
    ƒ(ph©  ã                   óf   • S r SSKr SSKrSSKJr  S rS r	\
S:X  a  \	" 5         gg! \ a     Nf = f)zŠCompute a Pade approximation for the principal branch of the
Lambert W function around 0 and compare it to various other
approximations.

é    Nc            	      óÀ   • [        S5       V s/ s H'  n [        R                  " [        R                  SU S9PM)     nn [        R                  " USS5      u  p#X#4$ s  sn f )Né   r   )Úné   é   )ÚrangeÚmpmathÚdiffÚlambertwÚpade)r   ÚderivsÚpÚqs       ÚU/var/www/html/venv/lib/python3.13/site-packages/scipy/special/_precompute/lambertw.pyÚlambertw_pader      sL   € Ü<AÀ!¼HÓEºH°qŒfkŠkœ&Ÿ/™/¨1°Ô2¹H€FÐEÜ;Š;v˜q !Ó$D€AØˆ4€Kùò Fs   Ž.Ac                  óB  • [        [        5        [        R                  " S5         [	        5       u  pU S S S2   US S S2   p[        SU  35        [        SU 35        S S S 5        [
        R                  " SSS5      [
        R                  " SSS5      p2[
        R                  " X#5      u  p#USU-  -   n/ nUR                  5        H1  nUR                  [        [        R                  " U5      5      5        M3     [
        R                  " U5      R                  UR                  5      n[        R                   " S	S
S9u  px[
        R                  " W  V	s/ s H  n	[#        U	5      PM     sn	5      n [
        R                  " W V
s/ s H  n
[#        U
5      PM     sn
5      n[
        R$                  " X5      [
        R$                  " X5      -  n['        Xµ-
  5      nUS   R)                  X#U5        [
        R*                  " U5      [
        R*                  " [
        R*                  " U5      5      -
  n['        XÕ-
  5      nUS
   R)                  X#U5        [
        R,                  " S[
        R.                  " S
5      U-  S
-   -  5      n SU -   U S-  S	-  -
  n['        Xõ-
  5      nUS   R)                  X#U5      nUR1                  UUR3                  5       R5                  5       S9  [        R6                  " 5         [        R                   " S
S
S9u  nnXÎ:  nUR)                  X#U5      n[
        R                  " SS5      nUR9                  S['        U5      -  S-
  US5        UR1                  UUS9  [        R6                  " 5         g ! , (       d  f       GN.= fs  sn	f s  sn
f )Né2   éÿÿÿÿzp = zq = g      ø¿g      ø?éK   y              ð?r   é   )ÚnrowsÚncolsr   r   )Úaxg333333Ó¿g333333Ó?g      Àgš™™™™™É?Úr)ÚprintÚ__doc__r	   Úworkdpsr   ÚnpÚlinspaceÚmeshgridÚflattenÚappendÚcomplexr   ÚarrayÚreshapeÚshapeÚpltÚsubplotsÚfloatÚpolyvalÚabsÚ
pcolormeshÚlogÚsqrtÚexpÚcolorbarÚravelÚtolistÚshowÚplot)r   r   ÚxÚyÚzÚlambertw_stdÚz0ÚfigÚaxesÚp0Úq0Úpade_approxÚpade_errÚ
asy_approxÚasy_errÚseries_approxÚ
series_errÚimr   Úpade_betterÚts                        r   ÚmainrG      sÁ  € Ü	Œ'„NÜ	Š˜Õ	Ü‹‰ˆØ‘2‰w˜™$˜B˜$™ˆ1ÜQCˆjÔÜQCˆjÔ÷	 
ô ;Š;t˜S "Ó%¤r§{¢{°4¸¸bÓ'A€qÜ;Š;qÓD€AØ	ˆBˆq‰D‰€AØ€LØi‰iŽkˆØ×ÑœG¤F§O¢O°BÓ$7Ó8Ö9ñ ä—8’8˜LÓ)×1Ñ1°!·'±'Ó:€Lä—’ 1¨AÑ.I€Cä
Š¡aÓ(¢a ”%˜–)¡aÑ(Ó)€AÜ
Š¡aÓ(¢a ”%˜–)¡aÑ(Ó)€AÜ—*’*˜QÓ"¤2§:¢:¨aÓ#3Ñ3€KÜ;Ñ-Ó.€HØˆG×Ñq˜XÔ&ä—’˜“œRŸVšV¤B§F¢F¨1£IÓ.Ñ.€JÜ*Ñ+Ó,€GØˆG×Ñq˜WÔ%ô 	Š”2—6’6˜!“9˜Q‘; ‘?Ñ#Ó$€AØ˜‘F˜Q ™T !™V‘O€MÜ]Ñ1Ó2€JØ	ˆa‰×	Ñ	˜A *Ó	-€Bà‡LL˜Ÿ
™
›×+Ñ+Ó-€LÑ.Ü‡H‚H„JälŠl ¨!Ñ,G€CˆØÑ$€KØ	‰q˜[Ó	)€BÜ
ŠD˜#Ó€AØ‡GGˆD”Q“‰K˜#Ñ˜q #Ô&Ø‡LL˜€LÑÜ‡H‚H…J÷S 
Ö	üò  )ùÚ(s   ¦8NÅNÆNÎ
NÚ__main__)r   Únumpyr   r	   Úmatplotlib.pyplotÚpyplotr'   ÚImportErrorr   rG   Ú__name__© ó    r   Ú<module>rP      sN   ðñó
 ð	ÛÝ#ò
ò+ð\ ˆzÓÙ…Fð øðq ó 	Ùð	ús   ˆ
' §0¯0