
    [Th=             !       t   % S SK r S SKrS SKrS SKrS SKrS SKJr  S SKJr  S SK J	r	J
r
  S SKJrJr  S SKJrJrJrJrJr  S SKrS SKrS SKJr  S SKJr  S SKJs  Jr  S SKJrJ r J!r!  S SK"J#r#  S S	K$J%r%  S S
KJ&r&J'r'J(r(J)r)J*r*  S SK+J,r,J-r-J.r.J/r/  S SK0J1r2  S SK3J4r4  \Rj                  Rl                  r6/ r7\8\9   \:S'   \Rv                  Rx                  Rz                  r= " S S\5      r> GSS\S\R~                  S\@4S jjrA\	" \A\R~                  R                  SS9rC\	" \A\R~                  R                  S9rD\	" \A\R~                  R                  S9rFS\!S\GS\!4S jrH\#" \=R                  5      \/" S5      \DS\!S\!4S  j5       5       5       rI\#" \=R                  5      \/" S5      \DS\!S\!4S! j5       5       5       rJ\#" \=R                  5      \/" S5      \DS\!S\!S"\LS#\L4S$ j5       5       5       rK\#" \=R                  5      \/" S5      \DS%\!S&\LS'\LS(\LS)\@S*\!4S+ j5       5       5       rM\#" \=R                  R                  /5      S, 5       rP\#" \=R                  RB                  /5      S-\!4S. j5       rQ\#" \=R                  5      \/" 5       \DS/\!S\!4S0 j5       5       5       rR\#" \=R                  5      \/" S5      \DS%\!S/\!4S1 j5       5       5       rS\#" \=R                  5      \/" S5      S%\!S/\!S2\LS3\L4S4 j5       5       rT\#" \=R                  5      \/" 5       \DS/\!S\!4S5 j5       5       5       rU\#" \=R                  5      \/" 5       \DS%\!S/\!S\!4S6 j5       5       5       rV\#" \=R                  5      \/" S5      S%\!S/\!S#\L4S7 j5       5       rW\#" \=R                  5      \/" S5      \DS%\!S/\!S8\LS9\@4S: j5       5       5       rX\#" \=R                  5      \/" S5      \DGSS;\!S/\!S<\94S= jj5       5       5       rY\#" \=R                  5      \DS%\!S>\!4S? j5       5       rZ\#" \=R                  5      \/" 5       \DS/\!S\!4S@ j5       5       5       r[\#" \=R                  5      \/" S5      \DS%\!S/\!S\!4SA j5       5       5       r\\#" \=R                  5      S/\!SB\!S\!4SC j5       r]\#" \=R                  5      S%\!S/\!SB\!S\_\!\!4   4SD j5       r^\#" \=R                  5      \/" 5       \DS%\!S/\!SE\!SF\LSG\LSH\@S9\@S\!4SI j5       5       5       r`\#" \=R                  5      \/" S5      \DS%\!S/\!SJ\!S\!4SK j5       5       5       raSL\!SM\G4SN jrbSO\R                  4SP jrd\#" \=R                  5      \/" 5       \D\>R                  R                  4S/\!SQ\!SM\GS\!4SR jj5       5       5       re\#" \=R                  5      \/" S5      \DS%\!S>\!SQ\!SM\G4SS j5       5       5       rh\#" \=R                  5      GSST j5       rj\#" \=R                  5      \/" 5       \D\>R                  R                  SU4S/\!SQ\!SM\GS"\L4SV jj5       5       5       rk\#" \=R                  R                  5      \DS%\!S/\!SQ\!SM\GS"\L4
SW j5       5       rl\#" \=R                  R                  5      \DS%\!S/\!SQ\!SM\GS"\LS\!4SX j5       5       ro\#" \=R                  R                  5      \DS%\!S/\!SQ\!SM\GSY\L4
SZ j5       5       rp\#" \=R                  R                  5      \DS%\!S/\!SQ\!SM\GSY\LS\!4S[ j5       5       rrS%\!S/\!SQ\!SB\\!   SM\GS\\GS]\!S\!4S^ jrs\#" \=R                  5      \/" S5      \DS%\!S/\!S\GS\!4S_ j5       5       5       rt\#" \=R                  5      \/" S5      S%\!S/\!SQ\!SB\\!   SM\GS\\GS]\!S\!4S` j5       5       ru\#" \=R                  5      \/" S5      S%\!S/\!SQ\!SB\\!   SM\GS\\GS]\!S\!4Sa j5       5       rv\#" \=R                  5      \/" 5       \DS\>R                  R                  4S/\!SQ\!SB\\!   SM\GS\!4
Sb jj5       5       5       rw\#" \=R                  5      \/" S5      \DS\>R                  R                  4S%\!S/\!SQ\!SB\\!   SM\GS\!4Sc jj5       5       5       rx\#" \=R                  5      \/" 5       \D\>R                  R                  4S>\!SQ\!SM\GS\!4Sd jj5       5       5       ry\#" \=R                  5      \/" S5      \D\>R                  R                  4S%\!S/\!SQ\!SM\GS\!4
Se jj5       5       5       rz\#" \=R                  5      \/" 5       GSS>\!Sf\!Sg\L4Sh jj5       5       r{\#" \=R                  5      \/" 5       Si\!Sj\!S\!4Sk j5       5       r|\#" \=R                  5      \/" 5       S%\!Sl\8\G   S\GSm\GSn\GSo\G4Sp j5       5       r}\#" \=R                  RB                  5          GSS/\!S\GSm\\G   Sn\\G   So\G4
Sr jj5       rS\!S\GSm\\G   Sn\\G   S\_\G\G4   4
Ss jr\#" \=GR                  5      \/" 5           GSS>\!St\!S\GSm\\G   Sn\\G   So\G4Su jj5       5       r\#" \=GR                  5      \/" 5       S%\!Sl\8\G   S\GSv\G4Sw j5       5       r\#" \=GR                  5      \/" 5       S%\!Sl\8\G   Sx\GSy\GSz\G4
S{ j5       5       rS%\!S\!S|\R                  4S} jr\#" \=GR
                  5      \/" S5      \CS%\!S~\!S\GS|\R                  4S j5       5       5       r\#" \=GR                  5      \/" 5       \CS%\!S~\!S\GS|\R                  4S j5       5       5       rS r\#" \=GR                  5      \/" 5       S>\!S\8\G   S\8\G   S\8\G   S\8\G   S\!4S j5       5       r\#" \=GR                  5      \/" 5       \DS>\!S\8\G   S\8\G   S\8\G   S\8\G   S\8\G   S\!4S j5       5       5       r\#" \=GR                  5      \/" 5       S%\!S\!S'\L4S j5       5       r\#" \=GR                  5      \/" 5       S;\!S\8\G   S\GS\GSo\GS\!4S j5       5       r\#" \=GR                  R                  5      \D GSS%\!S/\!S\\L   S\!4S jj5       5       r\#" \=GR                  5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      S>\!Sg\LS\\@   4S j5       5       5       r\#" \=GR"                  5      \/" SS5      S>\!Sg\LS\\@   4S j5       5       r\#" \=GR$                  5      \/" 5       S\!S\GS\@4S j5       5       r\#" \=GR&                  5      \/" SS9S\!S\GS\@4S j5       5       r\#" \=GR(                  5      \/" 5          GSSB\!S\!S\GS\@S\@S\!4S jj5       5       r\#" \=GR*                  5      \/" 5       S%\!S\!S\GS\GS\@4
S j5       5       rS\8\G   4S jrS\8\!   S\GS\GS\8\!   4S jrS\8\!   4S jrS\8\!   S\G4S jrS\8\!   S\GS\G4S jr\#" \=GR6                  R                  \=GR6                  R                  /5       GSS\8\!   S\GS\GS\\!   S\!4
S jj5       r\#" \=GR8                  R                  \=GR8                  R                  /5        GSS/\!S\8\G   S\GS\\8\!      S\\8\!      4
S jj5       r\#" \=GR:                  RB                  5      GSS>\!S\GS\GS\_\!S4   4S jj5       r\#" \=GR<                  R                  5       GSS>\!S\8\G   S\GS\_\!S4   4S jj5       r\#" \=GR>                  RB                  5      GSS/\!S\GS\GS\_\!S4   4S jj5       r\=GR@                  GRB                  GR                  \6GR                  5       GSS/\!S\!S\GS\_\!S4   4S jj5       r\#" \=GRF                  5      \/" SS9\DGSS/\!S\!S\!S"\GS&\G4
S jj5       5       5       r\#" \=GRH                  5      \/" 5       \D   GSS/\!S\!S\!S"\GS&\GS\@4S jj5       5       5       r\#" \=GRJ                  5      \/" 5       \DGSS/\!S\!S\!S"\GS&\G4
S jj5       5       5       r\#" \=GRL                  R                  5      \DS%\!S>\!S\!S\!S\\!   S\GS\GS\GS\GS\8\@   S\_\\!   \\!   \\!   4   4S j5       5       r\#" \=GRL                  R                  5      S%\!S>\!S\!S\!S\\!   S\GS\GS\GS\GS\8\@   S\RB                  S\RB                  S\RB                  S\_\\!   \\!   \\!   4   4S j5       rS\\!   S\\!   4S jr\#" \=GRR                  R                  5      S\!S>\!S\8\G   S\!S\!SB\\!   S\\!   S\8\@   S\_\\!   \\!   \\!   4   4S j5       r\#" \=GRR                  R                  5      S\!S>\!S\8\G   S\!S\!SB\\!   S\\!   S\8\@   S\RB                  S\RB                  S\RB                  S\_\\!   \\!   \\!   4   4S j5       rS>\!SB\\!   S\\!   S\\!   S\\!   SH\@S\LS\LS\@S\_\!\!\!\\!   \\!   4   4S jr\#" \=GRX                  5      \/" SSS5      S>\!SB\\!   S\\!   S\\!   S\\!   SH\@S\LS\LS\_\!\!\!4   4S j5       5       r\=GRX                  R                  GR                  \6GR                   5      \=GRX                  R                  GR                  \6GR                  5      S>\!SB\\!   S\\!   S\\!   S\\!   SH\@S\LS\LS\_\!\!\!4   4S j5       5       r\=GR\                  R                  GR                  \6GR                  5      GSS\8\!   4S jj5       r\#" \=GR`                  R                  5      S>\!SB\\!   S\\!   S\!S\!S\LS\LS\_\!\!\!4   4S j5       r\#" \=GRb                  R                  5      S>\!SB\\!   S\\!   S\!S\!SH\@S\LS\LS\_\!\!\!4   4S j5       r\#" \=GRb                  GRd                  5      S>\!SB\\!   S\\!   SH\@S\LS\LS\_\!\!\!4   4S j5       r\#" \=GRh                  R                  5      S>\!SB\\!   S\\!   S\!S\!SH\@S\LS\LS\_\!\!\!\!\!4   4S j5       rS>\!SB\\!   S\\!   S\!S\!S\LSH\@S\!4S jr\#" \=GRl                  R                  5      S>\!SB\\!   S\\!   S\!S\!S\LS\LS\_\!\!\!\!4   4S j5       r\#" \=GRn                  R                  5      S>\!SB\\!   S\\!   S\!S\!S\LS\LS\_\!\!\!\!\!\!4   4S j5       r\#" \=GRp                  R                  5      S>\!SB\\!   S\\!   S\!S\!S\LS\LS\_\!\!\!\!4   4S j5       r\#" \=GRr                  5      \/" SS5      \DGSS j5       5       5       r\#" \=GRv                  5      \/" 5       SSSSSSS.S\\!\'4   SO\\R                     S\\GRx                     S\@S\@S\\GRz                     4S jj5       5       r\#" \=GR|                  \=GR~                  \=GR                  /5      \/" 5       S 5       5       r\=GR                  R                  GR                  \6GR                   5      \#" \=GR                  5      \/" SSSS5      S>\!SB\!S\\!   S\\!   S\\!   SH\@S\LS\L4S j5       5       5       rS r\#" \=GR                  R                  5      S\!S>\!SB\\!   S\\!   S\\!   S\\!   S\\!   S\@S\LS\8\@   S\!S\_\!\\!   \\!   4   4S j5       r\#" \=GR                  R                  5      S\!S>\!SB\\!   S\\!   S\\!   S\\!   S\\!   S\@S\LS\8\@   S\_\!\\!   \\!   4   4S j5       r\#" \=GR                  R                  5      S\!S>\!SB\\!   S\\!   S\\!   S\\!   S\\!   S\@S\LS\8\@   S\RB                  S\RB                  S\RB                  S\_\!\\!   \\!   4   4S j5       r\#" \=GR                  5      \/" SSS5      S>\!S%\!SB\!S\\!   S\\!   S\\!   S\\!   S\L4S j5       5       r\#" \=GR                  5      \/" SSS5      S>\!S%\!SB\!S\\!   S\\!   S\\!   S\\!   S\LS\!4S j5       5       r\#" \=GR                  5      \/" 5       \DS>\!S\_\G\G4   4S j5       5       5       rS/\)S\)S\8\G   S\G4S jr\#" \=GR                  5      \/" 5       S/\)S\)S\8\G   4S j5       5       r\#" \=GR                  5      \/" 5       S>\)S\)S\8\G   S\8\G   S\8\G   4
S j5       5       r\#" \=GR                  5      SqS.S\)S\GSv\)S\)S&\'4
S jj5       r\#" \=GR                  5      \/" 5       SqS.S\)S\GSv\)S\)S&\'4
S jj5       5       rSqS.S\)S\GSv\)S\)S\@S&\'4S jjr\#" \=GR                  R                  5      \=GR                  R                  GR                  \6GR                  5      GSS j5       5       r\#" \=GR                  5      S\)S\GSv\)S\)4S j5       r\#" \=GR                  5      \/" 5       S\)S\GSv\)S\)4S j5       5       rS\)S\GSv\)S\)S\@4
S jr\#" \=GR                  5      \/" S~SJ5      \DS/\!S\_\!\!4   4GS  j5       5       5       r\#" \=GR                  5      \/" 5          GSS\!GS\\@\G\L4   GS\\@\G\L4   GS\\GR                     4GS jj5       5       r\#" \=GR                  5      GSGS j5       rGS rGS r\#" \=GR                  GR                  5      \#" \=GR                  GR                  5      \#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      S>\!S\\8\G      GS\\8\L      S\!4GS	 j5       5       5       5       5       5       5       5       5       r\#" \=GR                  GR                  5      \#" \=GR                  GR                  5      \#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      S>\!S\\8\G      GS\\8\L      S\!4GS
 j5       5       5       5       5       5       5       5       5       rGSGS jr\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9 GSS>\!S\8\G   GS\\L   S\!4GS jj5       5       5       5       r\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9 GSS>\!S\8\G   GS\\L   S\!4GS jj5       5       5       5       r\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9  GSS>\!S\8\G   GS\\L   GS\\L   S\!4
GS jj5       5       5       5       r\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9  GSS>\!S\8\G   GS\\L   GS\\L   S\!4
GS jj5       5       5       5       r\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9   GSS>\!S\8\G   GS\\L   GS\\L   GS\\L   S\!4GS jj5       5       5       5       r\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" SSGS9   GSS>\!S\8\G   GS\\L   GS\\L   GS\\L   S\!4GS jj5       5       5       5       r\D GSS>\!S\8\G   GS\8\\L      GS\@S\!4
GS jj5       rGS rGS rGS rGS r GSGS jrGS rGS rGSGS  jrGSGS! jrGS" r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS# 5       5       5       r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS$ 5       5       5       r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS% 5       5       5       r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS& 5       5       5       rGS' rGSGS( jrGSGS) jrGS* r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS+ 5       5       5       r\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS, 5       5       5       rGS- Gr GS. Gr\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS/ 5       5       5       Gr\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS0 5       5       5       Gr\#" \=GR
                  GR                  5      \=GR
                  GR                  GR                  \6GR                  5      \=GR
                  GR                  GR                  \6GR                   5      GS1 5       5       5       Gr\#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS2 5       5       5       Gr\#" \=GR                  GR                  5      \#" \=GR                  GR                  5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      \=GR                  GR                  GR                  \6GR                  5      \=GR                  GR                  GR                  \6GR                   5      GS3 5       5       5       5       5       5       5       5       Gr\#" \=GR                  R                  \=GR                  R                  /5      \/" 5        GSS>\!S\8\G   GS4\@GS\\L   S\!4
GS5 jj5       5       Gr\#" \=GR                  R                  \=GR                  R                  /5      \=GR                  R                  GR                  \6GR                   5      \/" 5         GSS>\!S\8\G   GS4\@GS\\L   GS\\L   S\!4GS6 jj5       5       5       Gr	\#" \=GR                  R                  \=GR                  R                  /5      \/" 5          GSS>\!S\8\G   GS4\@GS\\L   GS\\L   GS\\L   S\!4GS7 jj5       5       Gr
GSGS8 jGrGS9 GrSt\\!   GS:\\!   GS;\!S\!4GS< jGrGS:\*S\!4GS= jGr\DS>\!S\8\G   GS4\@GS\8\\L      S\!4
GS> j5       Gr\#" \=GR$                  R                  5      GS?\!GS@\!S\@4GSA j5       Gr\#" \=GR&                  \=GR(                  /5      \/" 5       GSB 5       5       Gr\#" \=GR*                  /5      GSC 5       Gr\#" \=GR,                  /5      GSGSD j5       Gr\#" \=GR.                  /5      GSE 5       Gr\#" \=GR0                  /5      GSF 5       GrS/\!SQ\!SB\\!   SM\GS\\GS\_\!\!4   4GSG jGr\#" \=GR4                  5      \/" S~S]5      S/\!SQ\!SB\\!   SM\GS\\GS\_\!\!4   4GSH j5       5       Gr\#" \=GR6                  5      \/" S~S]5      S/\!SQ\!SB\\!   SM\GS\\GS\_\!\!4   4GSI j5       5       GrS\!GSJ\LS\!4GSK jGrS\!GSJ\LS\!4GSL jGrGSM\!S\*4GSN jGrGSO\*GSP\!S\!4GSQ jGrGSP\\!   S\!4GSR jGr GSS\GGS4\@SO\R                  S\GRx                  4GST jGr!GSU\!GSV\GGSW\GGS4\@4GSX jGr"GSU\!GSY\GGSV\GGSW\GGS4\@4
GSZ jGr#GSU\!S\8\G   GS4\@4GS[ jGr$GSU\!S\8\G   GS4\@4GS\ jGr%\#" \=GRL                  5      \/" 5       \DGSU\!S\8\G   GS4\@4GS] j5       5       5       Gr&    GSGS?\!GS^\!GS_\GGS`\GGS4\@GSa\@S\!4GSb jjGr'\#" \=GRP                  5      \/" 5       \D   GSGS?\!GS^\!GS_\GGS`\GGS4\@S\!4GSc jj5       5       5       Gr(\#" \=GRR                  5      \/" 5       \DGSd 5       5       5       Gr)\#" \=GRT                  5      \/" 5       SS\>R                  R                  4GSe j5       5       Gr*GSf\RB                  GSg\RB                  GSh\@S\@4GSi jGr+\=GRX                  R                  GR                  \6GR                  5      \=GRX                  R                  GR                  \6GR                  5      \/" SGSj9SGSk.GSl j5       5       5       Gr,\#" \=GRZ                  R                  \=GRZ                  R                  /5      \=GRZ                  R                  GR                  \6GR                   5      \/" 5       \D  GSS>\!S\_\G\G4   GS4\@GSm\\L   GSn\\L   S\!4GSo jj5       5       5       5       Gr.\#" \=GRZ                  GR                  5      \=GRZ                  GR                  GR                  \6GR                  5      \=GRZ                  GR                  GR                  \6GR                   5      \/" 5       \D GSGS?\!S\\_\G\G4      GS4\@GS\\_\L\L4      S\!4
GSp jj5       5       5       5       5       Gr/\#" \=GR`                  5      \#" \=GRb                  5      \#" \=GRd                  5      \D\/" 5       GS?\!S\_\GS4   S\!4GSq j5       5       5       5       5       Gr3\#" \=GRh                  5      \#" \=GRj                  5      \#" \=GRl                  5      \D\/" 5       GS?\!S\_\GS4   S\!4GSr j5       5       5       5       5       Gr7GS?\!S\_\GS4   GSs\\G\G\G/\!4   S\!4GSt jGr8\#" \=GRr                  5      \#" \=GRt                  5      \#" \=GRv                  5      \/" S5      GSu 5       5       5       5       Gr<\#" \=GRz                  5      \/" GSvGSw5      SSGSx.GSy j5       5       Gr=\#" \=GR|                  5      \/" 5       GSSGSz.GS{ jj5       5       Gr>\#" \=GR~                  R                  \=GR~                  R                  /5      \/" 5       S\GR                  SSGS|.Sn\'SO\\R                     GS}\GR                  S\\GRx                     S\@4
GS~ jj5       5       GrB\#" \=GR~                  GR                  /5      S\GR                  SSGS|.Sm\'Sn\'SO\\R                     GS}\GR                  S\\GRx                     S\@4GS jj5       GrD\#" \%5      GS 5       GrE\#" \=GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" 5       SqSqS\>R                  R                  4S>\!SQ\!Sg\'GS\'SB\\!   SM\GS\!4GS jj5       5       5       GrF\#" \=GR                  5      \=GR                  R                  GR                  \6GR                   5      \/" S~GS5      S>\!SQ\!SM\GS\_\!\!4   4GS j5       5       5       GrG\#" \=GR                  R                  5        GSSSGS.GS\!GS\!S-\!GS\LGS\@GS\\!   S'\\L   S\_\!\!4   4GS jjj5       GrIGS GrJ\#" \=GR                  /5      \/" 5       \DGSGS j5       5       5       GrK\#" \=GR                  5      \/" 5       GS 5       5       GrL\#" \=GR                  5      GS 5       GrM\#" \=GR                  R                  \=GR                  R                  /5      SSGS.S/\!SO\\R                     S\\!   S\!4GS jj5       GrO\#" \=GR                  R                  \=GR                  GR                  /5      GSS/\!S\\G   4GS jj5       GrR\#" \Rx                  Rz                  GR                  5      GSGS j5       GrS\#" \=GR                  5      \/" 5       SSGS.GS j5       5       GrT\#" \=GR                  R                  5      SGS.S/\RB                  GS\\GR                     S\RB                  4GS jj5       GrUSGS.GS jGrVSSGS.GS jGrW\#" \=GR                  5      \/" 5       GS 5       5       GrX\#" \=GR                  5      GSGS j5       GrYG\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GRF                  5        G\J" \=GR                  \=GRJ                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=R                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=R                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=R                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                   \=GR                  5        G\J" \=GR                  \=GR                  5        G\J" \=GR                  \=R                  5        g(      N)Iterable)Enum)partialreduce)chainproduct)AnyCallablecastOptionalUnion)	sym_floatsym_intTensorregister_decomposition)	out_dtype)IntLike
NumberTypesuggest_memory_format
TensorLikeTensorSequenceType)_maybe_convert_to_dtype_maybe_resize_out_safe_copy_outout_wrapper)_pytree)tree_map__all__c                        \ rS rSrSrSrSrSrg)	Reduction0   r          N)__name__
__module____qualname____firstlineno__NONEMEANSUM__static_attributes__r%       T/var/www/auris/envauris/lib/python3.13/site-packages/torch/_decomp/decompositions.pyr!   r!   0   s    DD
Cr.   r!   Fftype_promotioncompute_dtype_onlyc                 N   ^ ^^ [         R                  " T 5      UU U4S j5       nU$ )Nc                  2  >^^ [         R                  " U 0 UD6 Vs/ s H  n[        U[        5      (       d  M  UPM     nn[        R
                  " UST06u  mmU4S jnU4S jnT
" [        X@5      0 [        XA5      D6nT	(       a  U$ [        XV5      $ s  snf )Ntype_promotion_kindc                 T   > [        U [        5      (       a  U R                  T5      $ U $ N
isinstancer   to)xcomputation_dtypes    r/   increase_prec0type_casts.<locals>.inner.<locals>.increase_precH   s%    !V$$tt-..r.   c                 T   > [        U [        5      (       a  U R                  T5      $ U $ r7   r8   )r;   result_dtypes    r/   decrease_prec0type_casts.<locals>.inner.<locals>.decrease_precN   s$    !V$$ttL))r.   )pytreearg_tree_leavesr9   r   utilselementwise_dtypesr   )argskwargsr;   	flat_argsr=   rA   rr<   r@   r2   r0   r1   s          @@r/   innertype_casts.<locals>.inner>   s     --t>v>
>!*QPVBWA> 	 
 +0*B*B+
,:+
'<
		 x,P0OPHM--1
s
   BB)	functoolswraps)r0   r1   r2   rK   s   ``` r/   
type_castsrO   9   s'    
 __Q. .6 Lr.   T)r1   r2   )r1   r;   dimreturnc                 l    [        XR                  5       -
  5       H  nU R                  S5      n M     U $ N)rangerP   	unsqueeze)r;   rP   _s      r/   _unsqueeze_to_dimrX   k   s+    3=!KKO "Hr.   
grad_inputout_gradyc                 2    U SX-  -
  R                  5       -  $ Nr#   conj_physicalrZ   r[   s     r/   tanh_backwardra   q   s     q15y//111r.   c                 2    XSU-
  -  R                  5       -  $ r]   r^   r`   s     r/   sigmoid_backwardrc   x   s     AE{11333r.   beta	thresholdc                 p    X-  R                  5       n[        R                  " X-  U:  X U-  US-   -  5      $ N      ?)exptorchwhere)rZ   r;   rd   re   zs        r/   softplus_backwardrm      s7     
A;;I-xAS9QRRr.   grad_outputalphascaleinput_scale	is_resultself_or_resultc                     X-  nUnUnU(       a$  [         R                  " US:*  X-  XV-   -  X-  5      $ [         R                  " US:*  X-  U-  [         R                  " XX-  5      -  X-  5      $ Nr   )rj   rk   ri   )	rn   ro   rp   rq   rr   rs   negcoefposcoef
negiptcoefs	            r/   elu_backwardry      s     mGGJ{{a$(@A!
 	
 {{a$w.>;V1WW!
 	
r.   c                 .    [         R                  " X5      $ r7   )rj   	full_likeselfvalues     r/   fill_scalarr      s    ??4''r.   r~   c                    ^ [         R                  " TR                  5       S:H  U4S j5        [        R	                  U T5      $ )Nr   c                  ,   > ST R                  5        S3$ )Nz@fill only supports 0-dimension value tensor but got tensor with z dimensionsrP   )r~   s   r/   <lambda>fill_tensor.<locals>.<lambda>   s    RSXS\S\S^R__jkr.   )rj   _checkrP   atencopyr|   s    `r/   fill_tensorr      s3    	LL		qk 99T5!!r.   r}   c                 ^    [         R                  " [         R                  " U S-   SS9SS9S-  $ N   r   min   maxrj   clampr}   s    r/   hardsigmoidr      s)     ;;u{{4!83;a??r.   c                 J    [         R                  " US:  US:  -  U S-  S5      $ )Ng      g      @gUUUUUU?        rj   rk   rn   r}   s     r/   hardsigmoid_backwardr      s0     ;;	$y! r.   min_valmax_valc                 @    [         R                  " X:*  X:  -  SU 5      $ )Nr   r   )rn   r}   r   r   s       r/   hardtanh_backwardr      s     
 ;;DO<c;OOr.   c                 d    U [         R                  " [         R                  " U S-   SS9SS9-  S-  $ r   r   r   s    r/   	hardswishr      s.     %++ekk$(:BBQFFr.   c           
      z    [         R                  " US:  S[         R                  " US:*  XS-  S-   -  U 5      5      $ )Nr   r         ?r   r   s     r/   hardswish_backwardr      s?     ;;r	DAI{ax3.>?M r.   c                 6    [         R                  " X:*  SU 5      $ ru   r   )rn   r}   re   s      r/   threshold_backwardr      s     ;;t(![99r.   negative_slopeself_is_resultc                 <    [         R                  " US:  X U-  5      $ ru   r   )rn   r}   r   r   s       r/   leaky_relu_backwardr      s     ;;taxN.JKKr.   gradapproximatec                    SnSnSnUS:X  ab  X5-  S-  nSnX-  nX-  n	XaXy-  -   -  n
[         R                  " U
5      nSU-  nSU-   nSU-  nSX-  -
  nUSSU-  U-  -   -  nX-  U-  nXU-   -  $ UnXT-  S-  nSS[         R                  " UU-  5      -   -  nU[         R                  " X-  S	-  5      -  nU UUU-  -   -  $ )
Ng;f?g;f?gmBP?tanhr   gHm?r#   r   g      )rj   r   erfri   )r   r}   r   M_SQRT2	M_SQRT1_2
M_2_SQRTPIkBetakKappax_sqx_cuberK   
tanh_innerleftrightleft_derivativetanh_derivativeinner_derivativeright_derivativekAlphacdfpdfs                        r/   gelu_backwardr      s    %G&I'Jf$s*{/0ZZ&
TzJ+j55 AF
T(9$9:14DD)99::&,Q4&=112eiid 233sTCZ'((r.   inputc                     [         R                  " [        R                  " U5      5      n[         R                  " U5      nX-  SX"-  -
  -  nXU-   -  $ r]   )rj   r   Fsoftplussigmoid)rn   r   input_tanh_softplusinput_sigmoidouts        r/   mish_backwardr     sN      **QZZ%67MM%(M

1':'P#P
QC344r.   c                 4    U [         R                  " U 5      -  $ r7   )rj   r   r   s    r/   silur     s     %--%%%r.   c                 \    SS[         R                  " U* 5      -   -  nX-  SUSU-
  -  -   -  $ r]   )rj   ri   )rn   r}   r   s      r/   silu_backwardr     s:     1uyy$''(G AG(<$<==r.   weightc                 <    [         R                  " U S:  XU -  5      $ ru   r   )r}   r   s     r/   _prelu_kernelr   %  s    ;;tax}55r.   c                 |    [         R                  " US:  XU -  5      n[         R                  " US:  SX-  5      nX44$ )Nr   r   r   )rn   r}   r   
input_gradweight_grads        r/   _prelu_kernel_backwardr   *  s?     TAX{[4HIJ++dQhT-?@K$$r.   noiseloweruppertrainingc                 |    U(       a  XC-
  S:  a  U R                  U5      $ X4-   S-  n[        R                  XXv5      $ )Ngư>r$   )mulr   r   )rn   r}   r   r   r   r   r   r   s           r/   rrelu_with_noise_backwardr   5  sC     EMD(u%%-1,''~
 	
r.   bufferc                     US:  n[         R                  " USS5      n[         R                  " USS5      n[         R                  " [         R                  " U5      * 5      nXXVSU-   -  -  -
  -  $ )Nr   r#   rT   )rj   rk   ri   abs)rn   r}   r   in_negative	max_derivsignrl   s          r/   log_sigmoid_backwardr   J  sc     (KKA.I;;{Ar*D		599T?"#Ad1q5k&::;;r.   loss	reductionc                     U[         R                  R                  :X  a  [        R                  " U 5      $ U[         R
                  R                  :X  a  [        R                  " U 5      $ U $ r7   )r!   r+   r~   rj   meanr,   sum)r   r   s     r/   apply_loss_reductionr   W  sH    INN(((zz$	imm))	)yyr.   dtypec                     U [         R                  :X  a  [         R                  $ U [         R                  :X  a  [         R                  $ U [         R
                  :X  a  [         R                  $ g r7   )rj   	complex32float16	complex64float32
complex128float64r   s    r/   to_real_dtyper   `  sK    }}	%//	!}}	%""	"}} 
#r.   targetc                 &    X-
  S-  n[        X25      $ )Nr$   )r   )r}   r   r   r   s       r/   mse_lossr   o  s     MaD00r.   c                 |    U[         R                  R                  :X  a  SUR                  5       -  OSnXAU-
  -  U -  $ )N       @)r!   r+   r~   numel)rn   r   r   r   norms        r/   mse_loss_backwardr   y  s9     #,y~~/C/C"C3D6>"[00r.   c                     [         R                  " XUS9nU R                  [        S5      5      n[         R                  " XASS9n[         R
                  " U5      n[         R                  " XVU5      $ )N)rP   r   z-infTrP   keepdim)rj   softmaxeqfloatall
zeros_likerk   )r}   rP   r   r   maskedmasked_rowszeross          r/   safe_softmaxr    sU    
--U
3CWWU6]#F))FT:KS!E;;{3//r.   rh   c                     X-
  R                  5       n[        R                  " XC:  SUS-  -  U-  USU-  -
  5      n[        XB5      $ )Nr   r$   )r   rj   rk   r   )r}   r   r   rd   r   s        r/   smooth_l1_lossr    sI     M D;;t{C$'MD$8$t:KLD00r.   c                    U[         R                  R                  :X  a  SUR                  5       -  OSnX-
  n[        R
                  " U5      nXP-  n[        R                  " Xt:  X-  U-  U[        R                  " U5      -  5      $ rg   )r!   r+   r~   r   rj   r   rk   r   )	rn   r}   r   r   rd   r   r;   abs_x	norm_grads	            r/   smooth_l1_loss_backwardr    ss    
 "+inn.B.B!B3DAIIaLE"I;;EJJqM! r.   c                 Z    [        XX#U5      n[        XVR                  5        [        XeSS9$ NT	copy_fromcopy_toexact_dtype)r  r   shaper   )rn   r}   r   r   rd   rY   results          r/   smooth_l1_loss_backward_outr    s+     %[4PFj,,/FDQQr.   deltac           
          U[         R                  R                  :X  a  SUR                  5       -  OSnX-
  n[        R
                  " Xd* :  U* U -  U-  [        R
                  " Xd:  XP-  U-  XV-  U -  5      5      $ rg   )r!   r+   r~   r   rj   rk   )rn   r}   r   r   r  r   r;   s          r/   huber_loss_backwardr    sv    
 "+inn.B.B!B3DA;;	F
	e#AIt1E948k;QR r.   c                 Z    [        XX#U5      n[        XVR                  5        [        XeSS9$ r  )r  r   r  r   )rn   r}   r   r   r  rY   r  s          r/   huber_loss_backward_outr    s+     !FuMFj,,/FDQQr.   ignore_indextotal_weightc                    UR                  5       S:  a  SOSnU[        R                  R                  :X  a  X-  n UR	                  U5      n[
        R                  " X%:g  US5      n[
        R                  " U5      n	[
        R                  " XUS5      n	U	R                  5       U R                  5       s=:  a  S:  a  O  OU R	                  U5      n UbO  [        UR                  5       5       V
s/ s H  n
SPM     nn
UR                  S   X'   UR                  U5      nX-  n [
        R                  " X%:g  U S5      n X-  $ s  sn
f )Nr$   r   r#   g      )rP   r!   r+   r~   rV   rj   rk   r  scatterrU   r  reshape)rn   r}   r   r   r   r  r  channel_dimsafe_targetrY   rW   	new_shapes               r/   _nll_loss_backwardr#    s    xxzA~!1KINN(((!0k*F++f4fa@K!!$'JzTJJ~~+//+/a/!++K8 %dhhj 12 11Q 1	2!'a		*!*++f4k1EK## 3s   /Ec                    UR                  5       S:  d   S5       e[        R                  " UR                  5       U5      nUR                  U5      nUS-  S:X  d   SU SU 35       eUS-  nUR	                  USU5      nUR	                  X5U5      n[
        R                  " U5      nSU-
  U-  U-  U -  n	X-  n[
        R                  " X/US9$ )Nr   z*glu does not support 0-dimensional tensorsr$   z.Halving dimension must be even, but dimension z	 is size rh   r   )rP   rE   canonicalize_dimsizenarrowrj   r   cat)
rn   r}   rP   wrap_dimnIn	inputSize	firstHalf
secondHalfgradInputFirstHalfgradInputSecondHalfs
             r/   glu_backwardr0    s     88:>GGG>%%dhhj#6H
))H
C7a< 
8
)C5Q< qIHa3IX)<Jz2	!	!%77)CkQ  ,999(>HMMr.   c           	         SUR                  5       s=::  a  S::  d   S5       e   S5       eUR                  5       S::  d   S5       eUR                  5       S:H  =(       a    UR                  5       S:H  nU(       dB  UR                  S   UR                  S   :X  d"   SUR                   SUR                   S35       eUR                  5       S:X  d'   S	UR                   S
UR                  5        S345       eUb(  UR                  5       UR                  S   :X  d   S5       eU[        R                  R
                  :X  a  UR                  5       S:X  am  U R                  5       S:X  a   U R                  S   UR                  S   :X  d8   SUR                  S    SU R                  5        SU R                  S    35       eO<U R                  5       S::  a  U R                  5       S:X  d   SU R                   35       e[        XX#XEU5      $ )Nr   r$   input tensor should be 1D or 2Dr#   ;0D or 1D target tensor expected, multi-target not supportedsize mismatch (got input: 
, target: ):expected total_weight to be a single element tensor, got: z (z
 elements)rT   z<weight tensor should be defined either for all or no classesz7Expected a tensor of dimension 1 and tensor.size[0] == z but got: dimension z and tensor.size[0] == z7Expected a single element grad_output tensor, but got: )rP   r  r   r!   r*   r~   r#  )rn   r}   r   r   r   r  r  no_batch_dims           r/   nll_loss_backwardr9    s    
aB!BBB!BB::<1 E 88:?8vzz|q'8LDJJqMV\\!_< 
$TZZL
6<<.J= 1$ D
b!3!3!5 6jA' $
 >V\\^tzz"~= F= INN(((TXXZ1_ A%+*;*;A*>$**Q-*O 	
EdjjQRm_ U)oo/00GHYHYZ[H\G]_	
O*O
  A%+*;*;*=*B 	
EkFWFWEXY	
B 69L r.   c           	      D   UR                  5       S:X  d   SUR                  5        35       eUR                  5       S:X  d   SUR                  5        35       eUR                  S   UR                  S   :X  a@  UR                  S   UR                  S   :X  a   UR                  S   UR                  S   :X  d!   SUR                   S	UR                   35       eUR                  5       S:X  d&   S
UR                   SUR                  5        S35       e[        XX#XEU5      $ )N   zSonly batches of spatial inputs supported (4D tensors), but got input of dimension: r   zUonly batches of spatial targets supported (3D tensors) but got targets of dimension: r   r$   r#   r4  r5  r7  z ( z, elements))rP   r  r   r#  )rn   r}   r   r   r   r  r  s          r/   nll_loss2d_backwardr<  8  s:    88:? 
]^b^f^f^h]ij? ::<1 
_`f`j`j`l_mn
 	

1a(JJqMV\\!_,JJqMV\\!_,I 
$DJJ<z&,,H	I	-
 1$ 	""#3|'9'9';&<K	I$
 69L r.   c           	      (   US-
  [         R                  " [         R                  " U * 5      U R                  SS5      5      -  U[         R                  " [         R                  " U 5      U R                  SS5      5      -  -
  nUb  XB-  n[        XC5      $ )Nr#   r%   i)rj   maximumlog1pnew_fulllogr   )r}   r   r   r   r   s        r/   binary_cross_entropyrB  [  s~     QJ%--TEDMM"d3 uyyb$0GHHID }00r.   c                     SnXU-
  -  [         R                  " USU-
  -  US9-  nUb  Xc-  nU[        R                  R                  :X  a  XaR                  5       -  nU$ )Ng-q=r#   r   )rj   r   r!   r+   r~   r   )rn   r}   r   r   r   EPSILONr  s          r/   binary_cross_entropy_backwardrE  q  sa     G6M*U[[T9JPW-XXFINN(((**,&Mr.   c                 t    [         R                  " [         R                  " U * U-  5      5      n[        X25      $ r7   )rj   r?  ri   r   )r   r   r   r   s       r/   soft_margin_lossrG    s,     ;;uyy%&12D00r.   c                     X -  [         R                  " X!-  5      S-
  -  nU[        R                  R                  :X  a  XAR                  5       -  nU$ r]   )rj   r   r!   r+   r~   r   )rn   r}   r   r   rY   s        r/   soft_margin_loss_backwardrI    sG     %v})E)IJJINN(((**,.
r.   otherpc                 .    [         R                  X-
  US9$ )N)rK  )r   r   )r   rJ  rK  s      r/   distrM    s     99U]a9((r.   x1x2c                    U R                  S5      R                  SS5      n[        R                  " U[        R                  S9nUR                  S5      R                  SS5      n[        R                  " U[        R                  S9n[        R
                  " U R                  S5      X#/S5      n[        R
                  " XU/S5      nUR                  UR                  5      nUR                  S5      R                  5       $ )Nr$   rT   Tmemory_formatr   )powr   rj   	ones_likecontiguous_formatr(  r   matmulmT	clamp_minsqrt)	rN  rO  x1_normx1_padx2_normx2_padx1_x2_r  s	            r/   _euclidean_distra    s     ffQimmB%G__WE4K4KLFffQimmB%G__WE4K4KLF
))RVVBZ12
6C
))R)2
.CZZFA##%%r.   input_sizesstartendstepc                 T    U R                  U5      n[        R                  " X`X#XE5      $ r7   )	new_zerosrj   slice_scatter)rn   rb  rP   rc  rd  re  rY   s          r/   slice_backwardri    s)     &&{3JzCNNr.   r#   c                 Z   SSK JnJn  U R                  5       nUS:X  a  [	        S5      e[
        R                  " U R                  5       U5      n[        U R                  5       5      n[        U R                  5       5      n	US::  a  [	        S5      eUb  UOSn
Ub  UO[        R                  nU" U
S:  5      (       a  XU   -  n
U" US:  5      (       a  XU   -  nU" U
S:  5      (       a  Sn
OU" XU   :  5      (       a  X   n
U" X:  5      (       a  U
nO4U" U[        R                  :H  5      (       d  U" XU   :  5      (       a  X   nU R                  5       XU   -  -   nX-
  nX-   S-
  U-  X'   X==   U-  ss'   U R                  (       a  [        S5      eU R                  XU5      $ )Nr   )guard_size_obliviousstatically_known_truez,slice() cannot be applied to a 0-dim tensor.zslice step must be positiver#   z<Slice decomposition for quantized tensors aren't implemented)%torch.fx.experimental.symbolic_shapesrk  rl  rP   RuntimeErrorrE   r%  listr&  stridesysmaxsizestorage_offsetis_quantizedNotImplementedError
as_strided)r}   rP   rc  rd  re  rk  rl  ndimsizesstrides	start_valend_valrs  lens                 r/   slice_forwardr}    s   
 88:DqyIJJ

 
 S
1CE4;;=!Gqy899*I_c#++GIM**3Z	GaK((:IM**		i*4	5	5J	G/00	w#++5	6	6:N*; ; *((*Y-EEN

C*q.T)EJLDL!J
 	
 u~>>r.   c                 n   ^ U R                   U   mS[        4U4S jjnU" USTS5      nU" X2TT5      nX#4$ )zb
Normalize start and end such that both are in the range
[0, x.get_size()[dim]] and start <= end.
rQ   c                 N   > U c  U$ U S:  a  U T-   n [        [        X5      U5      $ ru   r   r   )valr   r   defaultdim_sizes       r/   
clamp_wrap(_normalize_start_end.<locals>.clamp_wrap  s.    ;N7.C3s?E**r.   r   )r  int)r;   rP   rc  rd  r  r  s        @r/   _normalize_start_endr    sF     wws|H+# + ua1-E
S8
4C:r.   srcc           	      h   [         R                  " U R                  U5      nU R                  U   n[	        XX45      u  p4[        U R                  5      nXC-
  US-
  -   U-  Xr'   UR                  U5      nUS:X  a  XF:X  a  US:X  a  UR                  5       $ S /U R                  5       -  n[        R                  " X`R                  S9n	X-
  U-  X'   [        R                  " X`R                  [        R                  S9n
US:w  a  [        R                  " XU:  5      n
XF:w  a  [        R                  " XU:  5      n
US:w  a  [        R                  " XU-
  U-  S:H  5      n
S/U R                  5       -  nSX'   U
R                  U5      n
[         R#                  U
[         R%                  XUS5      U 5      $ )Nr#   r   devicer  r   rT   )rE   r%  rw  r  r  ro  expandclonerP   rj   aranger  onesboollogical_andviewr   rk   _unsafe_masked_index)r   r  rP   rc  rd  re  r  src_sizeindicesidxmask
mask_shapes               r/   rh  rh    sr    
 
 S
1C{{3H%e%=JEEKK H[D1H-$6HM
**X
Czco$!)yy{fuyy{"G
,,x
5CKD(GL::h||5::FDz  e|4
  Sy1qy  et';q'@Auyy{"JJO99Z D::dD55c!LeTTr.   indexc                 R    U R                  U5      n[        R                  " X@X#5      $ r7   )rg  rj   select_scatter)rn   rb  rP   r  rY   s        r/   select_backwardr  :  s'     &&{3J
DDr.   offsetdim1dim2c                 T    U R                  U5      n[        R                  " XPX#U5      $ r7   )rg  rj   diagonal_scatter)rn   rb  r  r  r  rY   s         r/   diagonal_backwardr  A  s)    
 &&{3J!!*6NNr.   input_dtypec                 H    U R                   U:w  a  UR                  U5      nU$ r7   )r   r:   )rn   rY   r  s      r/   _cast_grad_to_input_dtyper  J  s&     K']];/
r.   outputc                 r    X-  nXA[         R                  " XBSS9-  -
  n[        XU5      R                  5       $ NTr   )rj   r   r  
contiguous)rn   r  rP   r  new_grad_outputrY   s         r/   _softmax_backward_datar  R  sC     "*O EII$- $ J %[kJUUWWr.   c                 x    U [         R                  " U5      [         R                  " XSS9-  -
  n[        XU5      $ r  )rj   ri   r   r  )rn   r  rP   r  rY   s        r/   _log_softmax_backward_datar  d  s=     uyy0599d4   J %[kJJr.   c                     XS-  -   X!S-
  -  -
  n[        [        R                  [        R                  US9nU" SXd5      R	                  S5      nU" SX-  U5      R	                  S5      n	X-   $ )z/Utility function to implement im2col and col2imr$   r#   r   r  r   rT   )r   rj   r  int64rV   )
input_dkernel_d
dilation_d	padding_dstride_dr  blocks_d	arange_kwblocks_d_indiceskernel_grids
             r/    _im2col_col2im_indices_along_dimr  p  su     Q&!|)DDHEKKGI !H7AA!D Ax4jAKKBOK ))r.   kernel_sizedilationpaddingrp  c           
      
  ^^^^^^ [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        SS jnU" TS5        U" TS5        U" TS	S
S9  U" TS5        U R                  m[        T5      n[         R                  " US;   =(       a    [	        S TSS   5       5      U4S j5        [        S [        TSS  TTTT5       5       5      m[         R                  " [	        S T 5       5      UUUUUU4S j5        US:H  nU(       d  U R                  S5      n U R                  u  ppTu  pTu  pTu  nnTu  nn[        U
UUXU R                  5      n[        UUUXU R                  5      n[        R                  " XXU45      nUR                  S5      R                  S5      nUS S 2S S 2UU4   nUR                  SSSSSS5      nUR                  S5      nUR                  S5      nUR                  XU-  U-  UU-  5      nU(       d  UR                  S5      nU$ )Nr$   c                      g)Nz"im2col(): only 2D kernel supportedr%   r%   r.   r/   r   im2col.<locals>.<lambda>  s    0Tr.   c                      g)Nz$im2col(): only 2D dilation supportedr%   r%   r.   r/   r   r    s    -Sr.   c                      g)Nz#im2col(): only 2D padding supportedr%   r%   r.   r/   r   r    s    ,Qr.   c                      g)Nz"im2col(): only 2D stride supportedr%   r%   r.   r/   r   r    s    +Or.   c                     U(       a  [        S U  5       5      O[        S U  5       5      n[        R                  " US 5        g )Nc              3   *   #    U  H	  oS :  v   M     g7fr   Nr%   .0rK  s     r/   	<genexpr>1im2col.<locals>.check_positive.<locals>.<genexpr>       (%Qq5%   c              3   *   #    U  H	  oS :  v   M     g7fr  r%   r  s     r/   r  r         ;REqFEr  c                      g)Nz<{param_name} should be greater {'than' zero, but got {param}r%   r%   r.   r/   r   0im2col.<locals>.check_positive.<locals>.<lambda>  s    Xr.   r  rj   r   param
param_namestrictconds       r/   check_positiveim2col.<locals>.check_positive  s3    ,2s(%((;RE;R8RX	
r.   r  r  r  Fr  rp  r   r;  c              3   *   #    U  H	  oS :g  v   M     g7fr  r%   r  ds     r/   r  im2col.<locals>.<genexpr>       :z!Avzr  r   c                      > S[        T 5       3$ )NzmExpected 3D or 4D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: tupler  s   r/   r   r         --25\N<r.   c              3   \   #    U  H"  u  pp4nS USU-  -   X4S -
  -  -
  S -
  U-  -   v   M$     g7f)r#   r$   Nr%   )r  r   paddilkersts         r/   r  r    sD      '
"Cc 	
S1s7]S!G_,q0R77'
s   *,rS  c              3   *   #    U  H	  oS :  v   M     g7fr  r%   )r  cs     r/   r  r    s     ';aE;r  c                  F   > S[        TSS  5       ST ST  ST ST ST S3$ )	Nz!Given an input with spacial size rS  , kernel_size=, dilation=
, padding=	, stride=z9, the calculated shape of the array of sliding blocks is z*, but its components must be at least one.r  )r  r  output_sizer  r  rp  s   r/   r   r    sJ    3E%*4E3F G"m;xj 9)9VH -]D	Fr.   r;  r   rT   r#   r      T)rj   r   r|  r  r  r  ziprV   r  r  r   r  permuter&  r  squeeze)r   r  r  r  rp  r  rw  batched_input	batch_dimr   input_hinput_wstride_hstride_w	padding_h	padding_w
dilation_h
dilation_wkernel_hkernel_wblocks_row_indicesblocks_col_indicespadded_inputr  num_blocks_rownum_blocks_colr  r  s    ````                     @@r/   im2colr	    sl    
LL[!Q&(TU	LLX!#%ST	LLW"$QR	LLV!#OP
 ;.8Z(8Yu568$KKEu:D	LL:3:uRSz::	<
  &)"#J;'
 K 
LL';''	F 	F AIM"/4{{,IGH"I%J
$Hh9:yELL ::yELL 55I) LML+55b9CCBG!Q 24FFGF^^Aq!Q1-F',,Q/N',,Q/N^^)H4n~6UF "Mr.   r  c                   ^^^^^^!^" [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        SS jnU" TS	5        U" TS
5        U" TSSS9  U" TS5        U" TS5        U R                  m"[        T"5      n[         R                  " US;   =(       a    [	        S T"SS   5       5      U"4S j5        TS   TS   -  n[         R                  " T"S   U-  S:H  UU"4S j5        [        TTTTT5       V	V
VVVs/ s H   u  ppnSU	SU
-  -   XS-
  -  -
  S-
  U-  -   PM"     nnnn
n	nUS   US   -  m![         R                  " T"S   T!:H  U!UUUUU"U4S j5        [         R                  " T!S:  U!UUUUU"U4S j5        US:H  nU(       d  U R                  S5      n U R                  m"Tu  nnTu  nnTu  nnTu  nnTu  nnU R                  T"S   T"S   U-  /T-   U-   5      n U R                  SSSSSS5      n [        UUUUUU R                  5      n[        US5      n[        UUUUUU R                  5      n[        TT5       VVs/ s H  u  nnUSU-  -   PM     nnnU R                  T"S   T"S   [        T5      -  /U-   5      nS S UU4n [        R                  UU U SS9n[         R"                  " UU* U* U* U* 45      nU(       d  UR%                  S5      nU$ s  snnnn
n	f s  snnf )Nr$   c                      g)Nzonly 2D output_size supportedr%   r%   r.   r/   r   col2im.<locals>.<lambda>  s    0Or.   c                      g)Nzonly 2D kernel supportedr%   r%   r.   r/   r   r    s    0Jr.   c                      g)Nzonly 2D dilation supportedr%   r%   r.   r/   r   r    s    -Ir.   c                      g)Nzonly 2D padding supportedr%   r%   r.   r/   r   r    s    ,Gr.   c                      g)Nzonly 2D stride supportedr%   r%   r.   r/   r   r    s    +Er.   Tc                     U(       a  [        S U  5       5      O[        S U  5       5      n[        R                  " US 5        g )Nc              3   *   #    U  H	  oS :  v   M     g7fr  r%   r  s     r/   r  1col2im.<locals>.check_positive.<locals>.<genexpr>  r  r  c              3   *   #    U  H	  oS :  v   M     g7fr  r%   r  s     r/   r  r    r  r  c                      g)Nz9{param_name} should be greater than zero, but got {param}r%   r%   r.   r/   r   0col2im.<locals>.check_positive.<locals>.<lambda>  s    Ur.   r  r  s       r/   r  col2im.<locals>.check_positive  s3    ,2s(%((;RE;R8RU	
r.   r  r  r  Fr  rp  r  )r$   r   c              3   *   #    U  H	  oS :g  v   M     g7fr  r%   r  s     r/   r  col2im.<locals>.<genexpr>  r  r  rS  c                      > S[        T 5       3$ )NzmExpected 2D or 3D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: r  r  s   r/   r   r    r  r.   r   r#   c                     > STS    ST  3$ )Nz|Expected size of input's first non-batch dimension to be divisible by the product of kernel_size, but got input.shape[-2] = rS  z and kernel_size=r%   )r  r  s   r/   r   r    s!     ==B2YK H"m%r.   rT   c                  :   > ST ST ST ST ST ST  STS    S	3$ 
NzGiven output_size=r  r  r  r  z , expected input.size(-1) to be 	 but got rT   .r%   Lr  r  r  r  r  rp  s   r/   r   r  	  D    $[M} M:Zy	& B))*9U2YKqBr.   c                  :   > ST ST ST ST ST ST  STS    S	3$ r  r%   r   s   r/   r   r    r"  r.   r   r;  r  
accumulater  )rj   r   r|  r  r  r  rV   r  r  r  r  rX   rg  prodr   _unsafe_index_putr   r  r  )#r   r  r  r  r  rp  r  rw  prod_kernel_sizer   r  r  r  r  colr  out_hout_wr  r  r  r  r   r  r  r  indices_rowindices_colorK  output_padded_sizer  r  r!  r  s#    `````                           @@r/   col2imr0    s    
LL[!Q&(OP	LL[!Q&(JK	LLX!#%IJ	LLW"$GH	LLV!#EF
 ;.8Z(7Ie468$;.KKEu:D	LL:3:uRSz::	<
 #1~A6	LLb	$$)	% '*(K'
'
"Cc 	
S1s7]S!G_,q0R77'
   	AQA	LLb	Q	B 	B 
LL	A	B 	B AIM"KKELE5Hh"Iy%J
$Hh MM58U1X1A%AB[PSVVWEMM!Q1a+E2xY%,,K $K3K2xY%,,K 14K0IJ0I1!a!e)0IJ__	q58tK0014FFF {K
0C##FC4#HFUU6YJ
YJ
KLF"MkV Ks   'M$M-r  c                 t    XR                  U 5      U-  -  R                  [        R                  " U 5      S9nU$ NrQ  )type_asr  rE   r   )rn   r  rp   rJ   s       r/   native_dropout_backwardr4  8  s@     
[1E9	:AA11+> 	B 	A Hr.   
input_size	dimensionr&  c                    [        U5      S:X  a  [        R                  " U S5      $ [        R                  " [        U5      U5      n[        R
                  " X   U R                  [        R                  S9nUR                  SX45      R                  5       nU R                  SUS-   5      R                  XUS-   5      n U R                  U5      nSU-  U4-   n[        R                  XxU SS9R                  5       $ )Nr   r  rT   r#   r7   Tr$  )r|  rj   squeeze_copyrE   r%  r  r  int32unfoldflattenmovedimrg  r   r'  r  )	r   r5  r6  r&  re  rP   r  rY   r  s	            r/   unfold_backwardr=  G  s    
 :!!!$**

 
 Z)
<C
,,zt{{%++
NC
**Q
#
+
+
-C<<C!G$,,S':D 
+JcMSF"E!!*Td!KVVXXr.   epsc           
      0   Ub@  UnSU-
  n[         R                  " [         R                  " X:  X:*  5      XSU-
  -  -  S5      $ [         R                  " [         R                  " US:  US:*  5      XSU-
  -  -  UR                  S[	        S5      5      5      $ )Nrh   r   r%   nan)rj   rk   r  r@  r   )rn   r}   r>  lohis        r/   logit_backwardrC  Z  s    
 2X{{dj$*53:./
 	
 {{dck43;73:./MM"eEl+
 	
r.   trainc                 n    U(       a  US:w  a  [         R                  XU5      S   $ U R                  5       $ ru   )r   native_dropoutr  )r   rK  rD  s      r/   dropoutrG  o  s1     a""5U3A66{{}r.   out0out1c                    U(       a  US:w  a  US:X  a9  [         R                  " U 5      [         R                  " U [         R                  S94$ U R                  R                  (       d  [        S5      e[         R                  " U 5      U:  nX0-  [        SSU-
  -  5      -  nXC4$ U [         R                  " U [         R                  S94$ )Nr   r#   r   z?result type Float can't be cast to the desired output type Longrh   )	rj   r  r  r   is_floating_pointrn  	rand_liker   rU  )r   rK  rD  	bool_maskress        r/   rF  rF  y  s     a6$$U+U-=-=e5::-VWW{{,,Q  OOE*Q.	%sQw"88uuEJJ?@@r.   half_to_floatc                    U R                  5       n U(       a   U R                  [        R                  :X  d   e[        R
                  " U [        R                  R                  S9u  p4U R                  U5      n U R                  5       S:X  a  [        R                  " U 5      nO-[        R                  " XSS9n[        R                  " X-
  5      nU[        R                  " XQSS9-  nU(       d  UR                  U5      nU$ Nr5   r   T)r   )r  r   rj   halfrE   rF   ELEMENTWISE_TYPE_PROMOTION_KINDDEFAULTr:   r   ri   amaxr   )r;   rP   rO  r<   r@   unnormalizedx_maxr  s           r/   _softmaxrY    s    
 	
Aww%**$$$&+&>&>	uDDLL'# 	
AwwyA~yy|

140yy+EIIlFFF<(Mr.   )r  c                    U R                  5       n U(       a   U R                  [        R                  :X  d   e[        R
                  " U [        R                  R                  S9u  p4U R                  U5      n U R                  5       S:X  a  U nO[        R                  " XSS9nX-
  n[        R                  " [        R                  " [        R                  " U5      USS95      nXW-
  nU(       d  UR                  U5      nU$ rQ  )r  r   rj   rS  rE   rF   rT  rU  r:   r   rV  rA  r   ri   )	r;   rP   rO  r<   r@   shiftedrX  shifted_logsumexpr  s	            r/   _log_softmaxr]    s    
 	
Aww%**$$$&+&>&>	uDDLL'# 	
AwwyA~

140)		%))EIIg,>T"RS(F<(Mr.   r  padding_idxscale_grad_by_freqsparsec                     U R                  5       S:X  d   S5       eUR                  S::  a5  U R                  SU5      nUR                  S:X  a  UR                  S5      nU$ X   $ )Nr$   z'weight' must be 2-Dr#   r   )rP   rw  index_selectr  )r   r  r^  r_  r`  r   s         r/   	embeddingrc    sb     ::<1444||q!!!W-<<1++a.C
r.   num_weightsc                 d   [         R                  " U [         R                  R                  S9u  pVU R	                  U5      n [        U[        R                  5      nU(       aU  UR                  U45      n[        R                  " U5      n[        R                  Xq/USS9nXq   n	X	R                  S5      -  n [        X:H  U R                  5      n
U R                  U
S5      nU R                  U4U R                   UR                  S  -   5      n[        R                  X/USS9R	                  U5      $ )NrR  Tr$  rT   r   )rE   rF   rT  rU  r:   r   rj   longrg  rU  r   r'  rV   rX   rw  masked_fillr  )rn   r  rd  r^  r_  r<   r@   countsr  grad_weights_scaler  r   grad_weights                r/   embedding_dense_backwardrk    s    ',&>&>)N)N)V)V'# ..!23K%guzz:G""K>2w'''	4D'Q#_!$@$@$DDW3[5E5EFD""4+D''	**7<<>::K !!+y$4!PSS r.   c                 $    SnU  H  nX-  nM	     U$ r]   r%   )r;   rJ   is      r/   r&  r&    s    	A	 Hr.   tensors
num_chunksc                 Z   / nU  H  nUR                  5       nXQ   U-   S-
  U-  U-  nXeU   :w  a9  S/S-  UR                  U-
  S-
  -  SXeU   -
  /-   n[        R                  XGS5      nUS U [        R
                  " US/5      -   nUR                  UR                  U5      5        M     U$ )Nr#   r   r$   rT   )r&  rw  r   constant_pad_ndrj   Sizeappendr  )	rn  rP   ro  padded_tensorstensortensor_sizepad_along_dimr  	view_sizes	            r/   
_pad_chunkry    s    
 Nkkm$)J6:zIJV,,#'V[[3.23C 007 C ))&q9F%

J3C(DD	fkk)45  r.   c                 X    U S   R                   nU  H  nUR                   U:w  d  M    g   g)Nr   FTrw  )rn  rw  ru  s      r/   have_same_ndimsr|  	  s-    1:??D;;$  r.   c                     U S   R                  5       S U nU  H/  n[        R                  " UR                  5       S U U:H  S 5        M1     g )Nr   c                      g)NzG_chunk_cat expects same sizes of 0,...,dim-1 dimensions for all tensorsr%   r%   r.   r/   r   +leading_dimension_matches.<locals>.<lambda>  s    ]r.   )r&  rj   r   )rn  rP   leading_dim_sizesru  s       r/   leading_dimension_matchesr    sI    
)$3/KKM$3#44]	
 r.   c                    [         R                  " US:  S 5        [         R                  " [        U 5      S:  S 5        U S   R                  nU S   R                  nU  Hv  n[         R                  " UR                  5       S:  S 5        [         R                  " UR                  U:H  S 5        [         R                  " UR                  U:H  S 5        Mx     [        U 5      (       a)  [        R                  " U S   R                  5       U5      nOH[         R                  " US:  S 5        U  H'  n[         R                  " XR                  :  S	 5        M)     [        X5        U$ )
Nr#   c                      g)Nz&_chunk_cat expects positive num_chunksr%   r%   r.   r/   r   ._preprocess_chunk_cat_inputs.<locals>.<lambda>  s    *Rr.   r   c                      g)Nz0_chunk_cat expects a non-empty input tensor listr%   r%   r.   r/   r   r  !  s    "Tr.   c                      g)Nz#_chunk_cat expects non-empty tensorr%   r%   r.   r/   r   r  &  s    1Vr.   c                      g)Nz8_chunk_cat expects all input tensors with the same dtyper%   r%   r.   r/   r   r  )      Nr.   c                      g)Nz8_chunk_cat expects all inputs tensors on the same devicer%   r%   r.   r/   r   r  -  r  r.   c                      g)NzK_chunk_cat expects non-negative dim when input tensors have different ndimsr%   r%   r.   r/   r   r  4  s    ar.   c                      g)Nz3_chunk_cat expects dim < ndim for all input tensorsr%   r%   r.   r/   r   r  9      Mr.   )rj   r   r|  r   r  r   r|  rE   r%  rP   rw  r  )rn  rP   ro  expected_dtypeexpected_deviceru  s         r/   _preprocess_chunk_cat_inputsr    s"   
 
LLq"RS	LLGqT QZ%%Naj''OV\\^a')VWLLN*N	
 	MM_,N	
  w$$WQZ^^%5s;1Ha	
 FLLkk!M 
 g+Jr.   r   c                     [        XU5      n[        XU5      nUc  [        R                  " XAS-   5      $ [        R                  " XAS-   US9  U$ )Nr#   )r   )r  ry  rj   r(  )rn  rP   ro  r   rt  s        r/   
_chunk_catr  ?  sK     'wZ
@Cj9N
{yyq11		.'s3
r.   split_sizesc                     [         R                  XUS9nUc-  U Vs/ s H  oUR                  [        R                  S9PM!     sn$ [        X45       H$  u  pg[        XgR                  5        [        XvSS9  M&     g s  snf )Nr   rQ  Tr  )	r   split_with_sizesr  rj   rV  r  r   r  r   )r}   r  rP   r   splitssr  splits           r/   split_with_sizes_copyr  P  st     ""4#">F
{HNO1e&=&=>OO -MFfkk2UM .  Ps   &A9
split_size.c                 B    [         R                  R                  XU5      $ r7   )r   r  r   )r   r  rP   s      r/   unsafe_splitr  c  s    ::U44r.   c                 B    [         R                  R                  XU5      $ r7   )r   r  r  )r   r  rP   s      r/   unsafe_split_with_sizesr  h  s       ((SAAr.   c                    U R                   nX2   nUS:X  a  US:X  d   eU R                  5       4$ XA-   S-
  U-  nSSKJn  U" U5      n[	        U5       Vs/ s H  oqPM     nnXU-  U-
  -
  US'   [
        R                  " XU5      $ s  snf )Nr   r#   )	guard_intrT   )r  detachrm  r  rU   rj   r  )	r}   r  rP   rb  r  chunksr  rm  r  s	            r/   r  r  o  s    **KHQ1}}#a'J6F @vF',V}5}!:}K5 $7($BCKO;;t#.. 6s   Btensor_indices_or_sectionsc                   ^ UR                   R                  S:X  d   eUR                  [        R                  :X  d   eUR                  5       m[        R                  " TS:H  =(       d    TS:H  U4S j5        TS:X  a8  UR                  5       n[        U[        5      (       d   eU R                  X25      $ U Vs/ s H  oDR                  5       PM     nnU R                  XR5      $ s  snf )Ncpur#   r   c                     > ST  S3$ )Nz{tensor_split expected tensor_indices_or_sections to be a zero-dimensional or one-dimensional tensor, but got a tensor with z dimsr%   )	split_dims   r/   r   Atensor_split_tensor_indices_or_sections_py_impl.<locals>.<lambda>  s     <<E;eMr.   )r  typer   rj   r  rP   r   itemr9   r   tensor_split)r}   r  rP   sectionsrm  r  r  s         @r/   /tensor_split_tensor_indices_or_sections_py_implr    s     &,,11U:::%++u{{:::*..0I	LLQ()q.	M
 A~-224(G,,,,  //%?@%?668%?@   .. As   :C&mat1mat2c                     U R                  5       (       d+  U R                  5       (       d  [        U5      n[        U5      nU[        R                  " X5      -  nUS:X  a  U$ XSU -  -   $ ru   )rK  
is_complexr  rj   mm)r}   r  r  rd   ro   r   s         r/   addmmr    s_     !!##DOO,=,=4yE

%((4&
&Cqy
 r.   use_geluc                     [        XX#U5      nU(       a:  U R                  (       a  [        R                  USS9$ [        R                  U5      $ [        R	                  U5      $ )Nr   )r   )r  is_cudar   gelurelu)r}   r  r  rd   ro   r  r   s          r/   _addmm_activationr    sK     D
.C<<99Sf95599S>!99S>r.   vecc                    U R                  5       (       d+  U R                  5       (       d  [        U5      n[        U5      nU[        R                  " X5      -  nUS:X  a  U$ UR                  5       S:X  a  X0-  $ XSU -  -   $ ru   )rK  r  r  rj   mvr   )r}   r  r  rd   ro   r   s         r/   addmvr    ss     !!##DOO,=,=4yE

%((4%
%Cqy

yy{a{r.   r   rstdgammaNCHxWgroupoutput_maskc
           	      h  ^^^^^^ [         R                  " XTUSS9  [         R                  " XSS9  [         R                  " TUSS9  [        R                  " UR                  5       TT-  T-  :H  UUU4S j5        [        R                  " TR                  TT4:H  UUU4S j5        [        R                  " TS L =(       d    TR                  5       T:H  UU4S j5        [        TT5      u  p[        R                  " US:H  UU4S j5        [        R                  " X5      R                  TTT5      R                  S/S	9nU R                  TTT5      R                  S/S	9nS nS nS nU	S   (       Ga/  S
TU
-  -  nTb  [        R                  " UTR                  S5      5      R                  TTU
5      R                  S5      n[        R                  " UTR                  S5      5      R                  TTU
5      R                  S5      n[        R                  " UR                  S5      TR                  STU
5      5      nOUR                  TTU
5      R                  S5      nUR                  TTU
5      R                  S5      n[        R                  " UR                  S5      [        R                  " STU
4UR                  S95      nUT-  U-
  U-  U-  U-  U-  nU* T-  UU-  U-  -
  nUR                  S5      n[        US5      n[        US5      n[        R                  " U R                  TTU
T5      U5      [        R                  " UR                  TTU
T5      U5      -   U-   nUR                  UR                  5      R!                  UR"                  5      nU	S   (       ah  UR                  TTU
5      UR                  TTU
5      TR                  S5      -  -
  UR                  S5      -  R                  S/S	9R                  T5      nU	S   (       a  UR                  S/S	9nXU4$ )NF)allow_cpu_scalar_tensorsc                     > STT -  T-   S3$ )NzExpect input to have z	 elementsr%   )r  r  r  s   r/   r   ,native_group_norm_backward.<locals>.<lambda>  s    'A}I>r.   c                  .   > ST  ST STR                    3$ )NzExpect mean to have shape (, z
, but got r  )r  r  r   s   r/   r   r    s    -aS5'DJJ<Pr.   c                  >   > ST  STb  TR                  5        3$ S 3$ )NzExpect gamma to have z elements but got rT   )r   )r  r  s   r/   r   r    s)    's*<eN_U[[]<hieg<hir.   r   c                     > ST  ST 3$ )NzExpect number of channels z, to be evenly-divisible by number of groups r%   )r  r  s   r/   r   r    s    ,QC/[\a[bcr.   r$   r   rh   rT   r#   r  r;  )rE   check_same_devicecheck_same_shaperj   r   r   r  divmodr   r  r   rV   r  r  r  rX   r:   r   )rn   r   r   r  r  r  r  r  r  r  cpg_remdsdbd_inputd_gammad_biasr  ds_valdb_valc1c2c3s     ` `````              r/   native_group_norm_backwardr    s    
D$ 
5N	4F	LLQ$> 
LL

q%j P 
LL+!+i
 q% IC	LL	c 
;	&	+	+Aq#	6	:	:s	:	CB			!Q	$	(	(aS	(	1B $G $G#F1~~39YYr5??1#56>>q%MQQRSTFYYr5??1#56>>q%MQQRSTFr"a,B
 ZZ5#.2215FZZ5#.2215Fr"

Auc?4;;?B tmf$,t3d:Q>S4Z&4-!++\\"r1%r1%IIk))!UC=rBiiaS92>? 	
 //%++.11%++>1~ E3'"''!UC*@4>>RTCU*UU..$% SaSS\WQZ 	 1~QCf%%r.   out2c
                    [        XX#XEXgX5
      nXU4n[        U5       H0  u  nnUc  M  [        X   UR                  5        [	        UX   SS9  M2     U$ r  )r  	enumerater   r  r   )rn   r   r   r  r  r  r  r  r  r  rH  rI  r  r  rY   rm  rJ   s                    r/   native_group_norm_backward_outr  4  sc    " (D!%F d#J&!1=jmQWW5Q
4P "
 r.   c                 .    U b  U R                  U5      $ U $ r7   r:   )r;   r   s     r/   _maybe_castr  Q  s    }ttE{Hr.   grad_outnormalized_shapebiasc                   ^" UR                   nUR                  5       n	[        R                  " UR                  5      m"U"4S jXXV4 5       u  ppU
c   eU	[        U5      -
  nXS  nUS U n/ n/ n[        U	5       H-  nUU:  a  UR                  U5        M  UR                  U5        M/     [        U5      n[        U5      nSSK	J
n  U" US:*  5      (       d  U" US:*  5      (       a[  US   (       a  UR                  U5      OS US   (       a  UR                  XS  5      OS US   (       a  UR                  XS  5      4$ S 4$ [        X;R                  5       5      n[        XKR                  5       5      nX-
  U-  nUb  X-  nOU
nUU-  n[        R                  " UUS5      n[        R                  " UU5      n[        R                  " UUS5      n[        R                  " UU5      nUU-
  U-
  nS nS n S n!US   (       a  UU-  U-  nUS   (       a3  Ub0  [        U5      S:  a  [        R                  " U
U-  US5      n OU
U-  n US   (       a;  Ub8  [        U5      S:  a  [        R                  " U
US5      n!OU
R!                  5       n![#        UUR                  5      [#        U UR                  5      [#        U!UR                  5      4$ )Nc              3   j   >#    U  H(  nUb  UR                  T[        R                  S9OUv   M*     g 7fr2  )r:   rj   rV  r  r;   r<   s     r/   r  -native_layer_norm_backward.<locals>.<genexpr>f  s?      9 1A = 	
e.E.EF	 1s   03r   rk  r#   r$   TF)r  rP   rE   get_computation_dtyper   r|  rU   rs  r&  rm  rk  rg  rX   rj   r   r   r  r  )#r  r   r  r   r  r   r  r  input_shape
input_ndimgrad_out_cast
input_castweight_cast	bias_castaxis
inner_dims
outer_dimsinner_dim_indicesouter_dim_indicesrm  r  Mrk  x_hat
grad_x_hatabr  r  r  rK   r  d_weightr  r<   s#                                     @r/   native_layer_norm_backwardr  X  s    ++KJ33EKK@9 60	95M{ $$$,--DU#JUd#J#%#%:9$$Q'$$Q'	  	ZAZAJAF##';AF'C'C,7NEOOK(3>q>EOOK./t3>q>EOOK./
 	
 HL
 	

 T>>#34DT>>#34D$&E"0
"
QA		*/6A	:u	%B	2($	/B	5"	BEBJE $G!%H#F1~!8u$1~+1 !A%yy!68I5QH$u,H1~)/ !A%YY}.?GF"((*F 	GU[[)Hekk*FEKK( r.   c          
          [        XX#XEXg5      nXU
4n[        U5       H/  u  pUc  M
  [        X   UR                  5        [	        XU   SS9  M1     U$ r  )r  r  r   r  r   )r  r   r  r   r  r   r  r  rH  rI  r  r  rY   rm  rJ   s                  r/   native_layer_norm_backward_outr    s`     ()tF d#J&!=jmQWW5Q14P "
 r.   running_meanrunning_varmomentum
functionalc	                 .   S/[        [        SU R                  5       5      5      -   n	[        R                  " U R
                  5      n
UnUnU(       Ga'  [        R                  " U R
                  5      n
U R                  U
S9n[        R                  " XSSS9u  p[        R                  " X-   5      nX-
  U-  n[        R                  " X5      n[        R                  " UU	5      nUb&  UU-  SU-
  U-  -   nU(       d  UR                  U5        Ubg  U R                  5       U R                  S   -  n[        R                  " X5      nUUUS-
  -  -  nUU-  SU-
  U-  -   nU(       d  UR                  U5        OUb  Uc   eUR                  U
SS9nUnUR                  U
SS9nUnUnS[        R                  " XG-   5      -  nU R                  R                   S:w  a  UnUnO"U R#                  S	5      nU R#                  S	5      n[%        XR                  5       S-
  5      n[%        UU R                  5       S-
  5      nX-
  U-  nUb1  UR'                  5       n[%        XR                  5       S-
  5      nUU-  nUb1  UR'                  5       n[%        X R                  5       S-
  5      nUU-   nU R                  R                   S:X  a2  UR                  U R
                  S9nUR                  U R
                  S9nUR                  U R
                  S9UUUU4$ )
Nr   r$   r   T)rP   
correctionr   r#   )r   r   r  r   )ro  rU   rP   rE   r  r   r:   rj   var_meanrsqrtr  copy_r   r  rZ  r  r  rg  rX   r;  )r   r   r  r   r  r   r  r>  r  reduction_dimsr<   new_running_meannew_running_var	input_acc
biased_varr   r  r  	save_mean	save_rstdnsqueezed_varunbiased_varinvstds                           r/   native_batch_norm_helperr    s    S4a 566N33EKK@#!O!77DHH#4H5	 >>a

 {{:+,,$&MM$7	MM$7	#')3q8||6SS""#34"A.A !==DL'1A;7L&5X8TTO!!/2'K,CCC#->TJ'!nn+<4nH%ejj!234<<%$II-I-I yy{Q7"6599;?;,&(!"699;?;&||~ yy{Q7$||E!LLu{{L3	LLu{{L3				$ r.   r  save_invstdc                 2    [        XX#XEXgS5	      u  pn
  nXU
4$ NFr  r   r   r  r   r  r   r  r>  r  r  r  rW   s               r/   native_batch_normr    s1     *Bt;(QV*&Fy!Q i''r.   c           
          Uc  Uc  [         R                  XX%Xg5      $ Uc  [        S5      eUc  [        S5      eU(       a  [         R                  XX#XEXg5      $ [         R                  XX#XFU5      $ )Nz`running_mean is None, but running_var is provided. They should both be None or both be provided.z`running_var is None, but running_mean is provided. They should both be None or both be provided.)r   _native_batch_norm_legitrn  $_native_batch_norm_legit_no_training)r   r   r  r   r  r   r  r>  s           r/   native_batch_norm_decompositionr  4  s      3,,48
 	
 <
 	
 <
 	
 ,,4{h
 	
 884{c
 	
r.   c                 j   U R                  U5      nX1-   S-
  U-  nUS:X  aZ  US:X  aT  U Vs/ s H  oTPM     nnXDU-  U-
  -
  XaS-
  '   [        R                  R                  R                  R                  XU5      $ [        R                  R                  R                  R                  XU5      $ s  snf Nr#   r   )r&  rj   opsr   r  r  r  r   )ru  r  rP   r  r  rW   r  s          r/   unsafe_chunk_py_implr#  Y  s    {{3H#a'F2JQ8q=+126az62",V0Ch0N"OQJyy~~55==fSVWW99>>&&--f#FF 3s   B0c           
      N    [         R                  R                  U UUUUSUU5      $ r  )r   r  r  )r   r   r  r   r  r  r>  s          r/   r  r  e  s5     ((00	 	r.   c                 2    [        XX#XEXgS5	      u  pn
  nXU
4$ r  r  r  s               r/   r  r  {  s1     *Bt;(QV*&Fy!Q i''r.   c                 6    [        XUS S X4US5	      u  pgn  n	XgU4$ r  r  )
r   r   r  r   r  r>  r  r  r  rW   s
             r/   !_native_batch_norm_legit_no_statsr'    s4     *BtT4S%*&Fy!Q i''r.   c                 ^    [        XX#XEXgS5	      u  nn	n
nnUc   S5       eUc   S5       eXXU4$ )NT#new_running_mean should not be None"new_running_var should not be Noner  )r   r   r  r   r  r   r  r>  r  r  r  r  r  s                r/   #_native_batch_norm_legit_functionalr+    s_    " 	!t;(QU	 'N)NN'&L(LL&i?JJr.   c           	      L   [         R                  R                  XX#USU5      nSnU[         R                  R                  R                  :X  a  [         R                  R                  X5      n[         R                  " U[         R                  U R                  U R                  S9$ )a  
Return a reserve tensor for batch norm, used only by cudnn to pass forward state to the
backward pass. This is needed for `_batch_norm_with_update` and `_batch_norm_no_update`,
which support a variety of backends including cudnn. We create this tensor here to get
the correct shape in the traced graph if we detect that will call the cudnn kernel,
and rely on DCE to avoid materializing this tensor.
Tr   )r   layoutr  )
rj   _C_select_batch_norm_backend_BatchNormBackendCudnn(_get_cudnn_batch_norm_reserve_space_sizeemptyuint8r-  r  )	r   r   r  r   r  r>  r   backendreserve_sizes	            r/   _get_batch_norm_reserve_tensorr7    s      hh11t;cG L%((,,222xxHH
 ;;EKKU\\ r.   c                 R    [        U UUUUSUUS5	      u  pxn	  n
[        XX#XFSS9nXxX4$ )NTFr   r  r7  r   r   r  r   r  r  r>  r  r  r  rW   reserves               r/   _batch_norm_with_updater=    sU     *B
*&Fy!Q -t;dG i00r.   c                 x    [        XX#USXVS5	      u  nnn	n
n[        XX#XFSS9nU
c   S5       eUc   S5       eXxXX4$ )NTr9  r)  r*  r:  )r   r   r  r   r  r  r>  r  r  r  new_rmnew_rvr<  s                r/   "_batch_norm_with_update_functionalrA    su      	!t;hT	 -t;dG DDDCCCy6BBr.   c                 R    [        U UUUUSUUS5	      u  pxn	  n
[        XX#XFSS9nXxX4$ )NFr9  r:  r;  s               r/   _batch_norm_no_updaterC    sU     *B
*&Fy!Q -t;eG i00r.   c                     Ub   e[         R                  " U 5      U:  R                  [         R                  S9nUR	                  U 5      U -  SU-  -  nXC4$ )Nr   rh   )rj   rL  r:   r4  r3  )r   rK  	generatorr  rN  s        r/   _fused_dropout_decompositionrF  "  sY     OOE"Q&***=D
,,u

%q
1C;r.   )r   r-  r  
pin_memorynon_blockingrR  r  rG  rH  rR  c                
   U(       a  U[         R                  :X  d   S5       eU(       a   S5       e[        U [         R                  [        [
        [        [        45      (       d   eUc7  Uc4  Uc1  [        U [         R                  5      (       a  U R                  5       $ U $ Sn[        U [         R                  5      (       a  U nO[         R                  " U 5      nUbc  X8R                  :w  aT  Ub1  UR                  S:X  a!  [         R                  R                  X5      nSn[         R                  R                  XU5      nUb(  U(       d!  [         R                  R                  X5      nSnUb  [         R                  " XS9$ U$ )NTODOFr  TrQ  )rj   stridedr9   r   r  r   r  complexr  scalar_tensorr  r  _primsconvert_element_type
device_put)	r;   r   r-  r  rG  rH  rR  dtype_convertedx_tensors	            r/   _to_copyrS  ,  s1    5==08&80!6!>a%,,UD'BCCCC~%-M,Aa&&779HO!U\\""&&q)f7!5||88IH"O<<**8\J<<44XE {{8AAOr.   c                 ,    [         R                  U 5      $ r7   )r   alias)r;   s    r/   nop_decompositionrV  Z  s     ::a=r.   out3exponential_average_factorepsilonc           
         [         R                  U UUUUUUU5      u  pn
U(       a   XXR                  S[        R                  S94$ UUR                  S5      UR                  S5      U R                  S[        R                  S94$ )Nr  r   )r   r  rg  rj   r4  )r   r   r  r   r  r   rX  rY  r  r  r  s              r/   cudnn_batch_normr[  b  s     $$"	GA! aU[[ABB	EKK0	 r.   c                     [        U5       HB  u  p#US:X  d  M  X R                  :  a  U R                  U   U:X  a  M1  U R                  U5      n MD     U $ r]   )r  rw  r  rV   )r;   broadcast_maskr  r  s       r/   _broadcast_batch_norm_backwardr^    sF    /
19dVVm0ED!A 0 Hr.   r<  c                 *    [        U UUUUUUUUU	5
      $ r7   )native_batch_norm_backward)r  r   r   r   r  r  r  rD  r>  r  r<  s              r/   batch_norm_backwardra    s/     & r.   c
                 .  ^& UR                   n
Ub  UR                   nOU
n[        R                  " UR                   5      m&U&4S jU UUUUUU4 5       u  nnnnnnnUR                  nUR	                  5       nUS:  d   S5       eSn[        [        U5      5      UU   -  nUnUnU(       a	  Ub  Uc   eO#Ub  Uc   eUn[        R                  " UU-   5      nS/U-  nUU   UU'   / n[        U5       H  nUU:w  d  M  UR                  U5        M     [        UU5      nSU-  n[        R                  " UU5      n[        R                  " XU-
  -  U5      n[        UU-  U5      n[        [        R                  " UU-  UU-  5      U5      n Uc  [        UU5      S-  n!O[        UU-  U5      n!U(       a  UU-
  U -  n"UU"-
  U-
  U!-  n#OUU!-  n#U	S   (       a  UU-  n$OS n$U	S   (       a  Un%OS n%U#R                  U
5      [        U$U5      [        U%U5      4$ )Nc              3   P   >#    U  H  nUb  UR                  T5      OUv   M     g 7fr7   r  r  s     r/   r  -native_batch_norm_backward.<locals>.<genexpr>  s/      	
A $%=a7
s   #&r$   z$rank of the input must be at least 2r#   rh   )r   rE   r  r  rP   r&  ro  rj   r  rU   rs  r^  r   r   r:   r  )'r  r   r   r   r  r  r  rD  r>  r  r  weight_dtyper  r  r  running_mean_castrunning_var_castsave_mean_castsave_invstd_castr  
input_rankr  num_featuresr   r  r]  reduction_axesrm  r   grad_output_sumdot_p	grad_mean
proj_scale
grad_scaleprojrY   rj  	grad_biasr<   s'                                         @r/   r`  r`    st    ++K||"33EKK@	 
	 ++KJ?BBB?D[)*[->>LDFF$666$6 !,1A1MMM -34!"j 0N&t,N4 "N:9!!!$  *$?DDii~>OIImD'89>JE./E~VI/		%$,0J
 3FNKcQ
3[ .

 T!Z/$t+y8JF
"Z/
1~fn1~#		 	k"K.I|, r.   c
                    [        U UUUUUUUUU	5
      nXU4n[        U5       H0  u  nnUc  M  [        X   UR                  5        [	        UX   SS9  M2     U$ r  )r`  r  r   r  r   )r  r   r   r   r  r  r  rD  r>  r  rH  rI  r  r  rY   rm  rJ   s                    r/   native_batch_norm_backward_outru  	  sv    " (F d#J&!1=jmQWW5Q
4P "
 r.   save_varc                 B    [         R                  UU UUUUUSU/ SQ5
      $ NT)TTTr   r`  )r   rn   r   r   r  r  rv  rY  s           r/   miopen_batch_norm_backwardrz  6	  s5     ** r.   reserveSpacec	                 B    [         R                  UU UUUUUSU/ SQ5
      $ rx  ry  )	r   rn   r   r   r  r  rv  rY  r{  s	            r/   cudnn_batch_norm_backwardr}  P	  s5     ** r.   c                   ^^^^^ U R                   mU R                  m[        T5      m[        R                  " TS;   U4S j5        U R                  SS   H!  n[        R                  " US:g  U4S j5        M#     TS   US   -  S:X  aw  TS   US   -  S:X  ah  [        S [        TSS  U5       5       5      n[        S [        TSS  X5       5       5      n[        R                  R                  R                  XU5      $ S	 mS
 mUUU4S jnU" TS   US   5      u  pgpU" TS   US   5      u  ppU S[        US5      U
4   nU	(       d  U(       d  [        R                  " USS9$ S nU" XXSS9u  pU" XXSS9u  pS n[        [        UR                  S   5      [        UR                  S   5      5       H$  u  nnUc  USUS S 2U4   nM  UUSUS S 2U4   -   nM&     UX{-  -  $ )Nr  c                     > ST  3$ )Nz9adaptive_avg_pool2d(): Expected 3D or 4D tensor, but got r%   r{  s   r/   r   %adaptive_avg_pool2d.<locals>.<lambda>u	  s    KD6Rr.   rS  r   c                  "   > S[        T 5       S3$ )Nzjadaptive_avg_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has shape r  r  r  s   r/   r   r  z	  s     99>uaIr.   rT   c              3   .   #    U  H  u  pX-  v   M     g 7fr7   r%   )r  rm  r.  s      r/   r  &adaptive_avg_pool2d.<locals>.<genexpr>	  s     G*F$!qv*F   c              3   <   #    U  H  u  po1US -
  U-  -
  v   M     g7fr#   Nr%   )r  rm  r.  r  s       r/   r  r  	  s"      
+OaQ!O+Os   c                 2    [         R                  " X-  USS9$ )Ntruncrounding_moderj   divr  r  r  s      r/   start_index(adaptive_avg_pool2d.<locals>.start_index	  s    yy99r.   c                 F    [         R                  " U S-   U-  U-   S-
  USS9$ )Nr#   r  r  r  r  s      r/   	end_index&adaptive_avg_pool2d.<locals>.end_index	  s&    yy!a%1q1,awGGr.   c                    > [         R                  " UT[         R                  S9nT" X!U 5      nX-  S-   nX-  nUS:H  =(       d    X-  S:H  (       + nU(       a  US-  nOUS:X  a  US-  n[         R                  " UT[         R                  S9nUR                  S5      U-   nU(       aQ  [         R                  " U S-
  UR
                  UR                  S9n	[         R                  " X5      nT" X!U 5      n
X-
  nOUnXXv4$ )Nr  r#   r   rT   r  )rj   r  r  rV   rM  r   r  minimum)in_sizeout_sizeorangei0	maxlengthin_size_modadaptive	range_maxr  maxvali1lengthr  r  r  s               r/   compute_idx(adaptive_avg_pool2d.<locals>.compute_idx	  s    hvU[[I73 '!+	(#q(GH,Ba,GHNIANILL6M	ll2* ((!399SZZF --,C 6W5BWFFI//r.   .r;  )r   rT   r   c                     [        U[        5      (       a  X4$ US:  d   eX!R                  S5      :  nUS:X  a  [        US5      n[        R
                  " XS5      n [        X* 5      nX4$ )Nr   rT   rS  r;  r   )r9   r   rV   rX   rj   rg  )valsr  r  r  rP   r  s         r/   
maybe_mask'adaptive_avg_pool2d.<locals>.maybe_mask	  sp    fg&&< 7N7 0 0 44Dby(q1$$T5D&vt4F<r.   )r  rP   r   )r  r  r|  rj   r   r  r  nnr  
avg_pool2drX   r   r   rU   )r   r  r  rp  kernelr  idxhlength_hrange_max_h
adaptive_hidxwlength_wrange_max_w
adaptive_wr  r  retrm  jr  r  rw  r  r  s                      @@@@@r/   adaptive_avg_pool2dr  k	  s   
 \\FKKEu:D	LLR [[FI	
  Ry;r?"a'E"IB,G1,LG#eBCj+*FGG 
+.uRSz;+O
 
 xx""--eVDD:H0@ /:%)[QS_.U+DK.9%)[QS_.U+DK'a0$67Djzz$H--   bND  bND
 Cdjjn-uTZZ^/DE1;sAq!|$CS!Q\**C	 F
 (%&&r.   c                    [         R                  " SU S35        [        [        R                  U R
                  S U*  5      n[        [        R                  U5      nS/U R                  -  nU R
                  S U*  US U* & U[        R                  X@R                  S9R                  U5      U-  -   R                  S5      nU R                  [        U R
                  S U*  5      [        U5      -   5      n[        R                  UR                  S5      U/U R                  S5      SS9R                  UR
                  5      $ )Nmax_unpoolingd_forward_outr#   r  rT   Fr$  )rE   alert_not_deterministicr   operatorr   r  rw  r   r  r  r  r  rg  ro  r'  )	r}   r  r  rP   nchwindices_nc_shapeindices_flatr  s	            r/   _max_unpoolndr  	  s    
!!M#m"DE	djj3$/	0B	k	*BsTYY"jj3$/Usd$++b+5::;KLrQQgbk  ^^DEcT!23d;6GGHF!!r\NDLL,< " 
d6<<r.   c                 ,  ^ ^^^ [         R                  " TR                  [         R                  :H  U4S j5        [         R                  " [	        T5      S:H  U4S j5        [         R                  " T R
                  S;   U 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [        ST R
                  5       H1  m[         R                  " T R                  T5      S:  UU 4S	 j5        M3     [        T TTS5      $ )
Nc                  "   > ST R                    3$ )Nz2elements in indices should be type int64 but got: r   )r  s   r/   r   max_unpool2d.<locals>.<lambda>	  s    DW]]OTr.   r$   c                  "   > S[        T 5       S3$ )NzMThere should be exactly two elements (height, width) in output_size, but got 
 elements.r|  r  s   r/   r   r  	      ;'(
4r.   r  c                  $   > ST R                    S3$ )NzLInput to max_unpooling2d should be a 3d or 4d Tensor, but got a tensor with  dimensions.r{  r   s   r/   r   r  
  s    %%)YYK|=r.   c                  <   > STR                    ST R                    3$ NzBExpected shape of indices to be same as that of the input tensor (z%) but got indices tensor with shape: r  )r  r}   s   r/   r   r  
  s'    PQUQ[Q[P\ ]229--Br.   r#   r   c                  *   > STR                    ST  S3$ )NzZmax_unpooling2d(): Expected input to have non-zero size for non-batch dimensions, but got  with dimension  being empty.r  )rm  r}   s   r/   r   r  
  s     ::,&6qcHr.   )
rj   r   r   r  r|  rw  r  rU   r&  r  )r}   r  r  rm  s   ```@r/   max_unpool2dr  	  s     
LL$T 
LLKA	
 
LL		V	
 
LL

gmm#	
 1dii IIaL1	
 ! wQ77r.   c                 D  ^ ^^^^^ [         R                  " TR                  [         R                  :H  S 5        [         R                  " T R                  S;   U 4S j5        [         R                  " [        T5      S:H  U4S j5        [         R                  " [        T5      S:H  U4S j5        [         R                  " [        T5      S:H  U4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        [        S	T R                  5       H1  m[         R                  " T R                  T5      S
:  UU 4S j5        M3     [         R                  " TS
   S
:  =(       a    TS	   S
:  =(       a    TS   S
:  U4S j5        [        T TTS5      $ )Nc                      g)Nz(elements in indices should be type int64r%   r%   r.   r/   r   max_unpool3d.<locals>.<lambda>%
  s    .Xr.   r;  r  c                  $   > ST R                    S3$ )NzLInput to max_unpooling3d should be a 4d or 5d Tensor, but got a tensor with r  r{  r   s   r/   r   r  )
  s    ^_d_i_i^jjvwr.   r   c                  "   > S[        T 5       S3$ )NzVThere should be exactly three elements (depth, height, width) in output_size, but got r  r  r  s   r/   r   r  -
  r  r.   c                  "   > S[        T 5       S3$ )NzRThere should be exactly three elements (depth, height, width) in stride, but got: r  r  rp  s   r/   r   r  4
  s    dehioepdqq{|r.   c                  "   > S[        T 5       S3$ )NzSThere should be exactly three elements (depth, height, width) in padding, but got: r  r  )r  s   r/   r   r  8
  s    efijqfress}~r.   c                  <   > STR                    ST R                    3$ r  r  )r  r   s   r/   r   r  <
  s'    PQVQ\Q\P] ^229--Br.   r#   r   c                  *   > STR                    ST  S3$ )NzZmax_unpooling3d(): Expected input to have non-zero size for non-batch dimensions, but got r  r  r  )rm  r   s   r/   r   r  E
  s      ;;-'7s-Ir.   r$   c                     > ST  3$ )Nz5strides should be greater than zero, but got stride: r%   r  s   r/   r   r  N
  s    GxPr.   )
rj   r   r   r  rw  r|  r  rU   r&  r  )r   r  r  rp  r  rm  s   `````@r/   max_unpool3dr  
  s?    
LL$&X 
LL

fw 
LLKA	
 
LLFq| 
LLG~ 
LLw}}$	
 1ejj!JJqMA	
 " 
LLq	A9&)a-9F1IMP
 a88r.   )ro   ru  c          	          [        XX#SUS9$ )NTinplacero   
_index_addr;   rP   r  ru  ro   s        r/   
index_add_r  T
  s     aeTGGr.   c          	          [        XX#SUS9$ )NFr  r  r  s        r/   	index_addr  `
  s     aeU%HHr.   r  c                z  ^^^^^^ [         R                  " U R                  T5      m[        R                  " TR                  S:*  U4S j5        TR                  S:X  a  TR                  S5      OSmUR                  S:  a  UR                  T5      OSm[        R                  " TT:H  UUU4S j5        TS:w  ao  [         R                  " U R                  5      m[        R                  " T[        :H  =(       d     [         R                  " [        T5      T5      UU4S j5        UT-  nU R                  S:H  nU(       a  U R                  S5      OU nST-  T4-   nU(       a  [        R                  O[        R                  n	U	" XxUSS9n
U(       a  U $ U(       a  U
R                  S5      $ U
R!                  5       $ )	Nr#   c                  $   > ST R                    S3$ Nz(Index should have dimension 1 or 0 (got r6  r{  r  s   r/   r   _index_add.<locals>.<lambda>y
      :5::,aHr.   r   c                     > ST ST ST < 3$ )NzNumber of indices (z') should be equal to tensor.size(dim) (z), for dim=r%   )rP   
index_sizerv  s   r/   r   r  
  s    %j\1XYdXeeqmplrsr.   c                  (   > S[        T 5       ST S3$ )Nzalpha argument of type z cannot be safely cast to type !)r  )ro   python_types   r/   r   r  
  s    -d5k]:YZeYffghr.   r7   Tr$  )rE   canonicalize_dimsrw  rj   r   r&  dtype_to_typer   r  is_weakly_lesser_typer  rV   r   
index_put_	index_putr  r  )r;   rP   r  ru  r  ro   zero_dimrN  r  r  r   r  r  rv  s    ``  `     @@@r/   r  r  m
  sK    
!
!!&&#
.C	LL

aH #(**/AqJ&,kkAo&++c"1K	LLz!s z))!''24 E**4;Dh	

 %vv{H#QB
C-5(
"C#*I
BV
5C!)s{{1~?s~~/??r.   c           
      
   [         R                  " [        U 5      S:  S 5        [        U 5      nU S   R                  5       nUSS  n[	        S U  5       5      nU(       a  X64nOXc4nXu-   nU S   R                  Xr5      nS[        U5      -  n	[        U5       Hf  n
X
   n[        R                  XSXkR                  S5      -
  4-   U5      nU(       a  [        R                  XSU
S9nMQ  [        R                  XSU
S9nMh     U$ )Nr   c                      g)Nz#received an empty list of sequencesr%   r%   r.   r/   r   pad_sequence.<locals>.<lambda>
  s    -Rr.   r#   c              3   B   #    U  H  oR                  S 5      v   M     g7fr  r&  )r  r;   s     r/   r  pad_sequence.<locals>.<genexpr>
  s     /Y&&))Ys   )r   r   rP   r  )
rj   r   r|  r&  r   r@  rU   r   rq  r  )	sequencesbatch_firstpadding_valuesequences_sizemax_sizetrailing_dimsmax_lenout_dimsr   dim_paddingsrm  currseqrows                r/   pad_sequencer  
  s
    
LLY!#%RS^N|  "HQRLM/Y//G",,'H
A,


8CC..L>",""Q,,q/(A$BBM
 %%cAQ%?C%%cAQ%?C # Jr.   c                     [        XX#SS9$ )NTr  _index_copyr;   rP   r  ru  s       r/   index_copy_r  
  s    qud;;r.   c                     [        XX#SS9$ )NFr
  r  r  s       r/   
index_copyr  
  s     que<<r.   c                  ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        U R                  S:H  nU(       a  U R                  S5      OU nTR                  S:X  a  TR                  S5      OTmSU-  T4-   nU(       a  [        R                  O[        R                  nU" XgU5      n	U(       a  U $ U(       a  U	R                  S5      $ U	R                  5       $ )Nr#   c                  $   > ST R                    S3$ r  r{  r  s   r/   r   _index_copy.<locals>.<lambda>
  r  r.   r   r7   )rE   r  rw  rj   r   rV   r   r  r  r  r  )
r;   rP   r  ru  r  r  rN  r  r  r   s
     `       r/   r  r  
  s     
!
!!&&#
.C	LL

aH
 vv{H#QB"'**/EOOAuE
C-5(
"C#*I
BV
$C!)s{{1~?s~~/??r.   c                 F   [         R                  " U R                  S5      U 5      n[         R                  " [         R                  " U 5      * 5      nU R
                  (       d  U R                  (       a  U R                  S5      nOUnU[         R                  " U5      -
  U4$ )Nr%   r  )rj   r  rg  ri   r   r  is_xpur?  )r}   r   rl   r   s       r/   log_sigmoid_forwardr  
  sn     --r*D
1C		599T?"#A||t{{%Q''r.   lowhighrE  c           	          [         R                  " U R                  [        U5      [        U5      U R                  U R
                  US9$ )N)r  r  r   r  rE  )prims_uniform_helperr  r   r   r  )r;   r  r  rE  s       r/   uniformr  
  s=       	cNt_ggxx r.   c                 8    U R                  [        XX#5      5      $ r7   )r	  r  )r}   r  r  rE  s       r/   uniform_r  
  s    ::gd9::r.   c                 2   [        U 5      S-
  nUb@  [        R                  " US L S 5        [        R                  " [        U5      U:H  S 5        U$ Ub  [        R                  " US L S 5        [        R                  " [        U5      U:H  S 5        / n[        U5       HZ  u  pE[	        U5      U:X  a$  UR                  XS-      [	        U5      -  5        M8  UR                  [        XS-      U-  5      5        M\     U$ [        R                  " SS 5        g )Nr$   c                      gNz9Must specify exactly one of output_size and scale_factorsr%   r%   r.   r/   r   .upsample_compute_output_size.<locals>.<lambda>
      Or.   c                      gN r%   r%   r.   r/   r   r"  
  s    Rr.   c                      gr!  r%   r%   r.   r/   r   r"    r#  r.   c                      gr%  r%   r%   r.   r/   r   r"    s    rr.   Fc                      gr!  r%   r%   r.   r/   r   r"    s    Rr.   )r|  rj   r   r  r  rs  r   )r5  r  scale_factorsspatial_dimensionsrm  r  s         r/   upsample_compute_output_sizer,  
  s    Z1,T!O	
 	S%);;ZH 4O	
 	S'+==zJm,DA1v{"":!e#4s1v#=>""7:!e+<q+@#AB	 -
 	LLRr.   c                     U c  g X   $ r7   r%   )scalesr  s     r/   get_scale_valuer/    s    ~;r.   r*  c                 ~    [        U R                  5       X5      nU(       a  UOS /[        U5      -  n[        XU5      $ r7   r,  r&  r|  _upsample_nearestr   r  r*  osizer.  s        r/   _upsample_nearest_vecr5    s<     ){RE&TFSZ,?  U622r.   c                 |    [        U R                  5       X5      nU(       a  UOS /[        U5      -  n[        XUSS9$ NTexactr1  r3  s        r/   _upsample_nearest_exact_vecr:  -  s>     ){RE&TFSZ,?  U6>>r.   c                    / n[        U5      nU(       a  SOSn[        U5       H  nX   nU R                  U* U-      n	X'   b	  XX'   -  -  OX-  n
[        R                  " U[        R
                  U R                  S9nX-   U
-  R                  [        R                  5      n[        US-
  U-
  5       H  nUR                  S5      nM     UR                  U5        M     U$ )Nr   r   r  r#   rT   )r|  rU   r  rj   r  r   r  r:   r  rV   rs  )r   r  r.  r9  r  num_spatial_dimsr  r  r4  isizerp   output_indicesinput_indicesrW   s                 r/   !_compute_upsample_nearest_indicesr@  B  s     G;'SsF#$ --12/5y/D*+%-e5==V(1U:>>u{{K'!+a/0A)33B7M 1}%+ %, Nr.   )preserve_memory_formatr  r.  c                     [        XU/5      $ r7   r2  r   r  r.  s      r/   upsample_nearest1drE  b  s     U&::r.   c                     [        XU/SS9$ r7  rC  rD  s      r/   upsample_nearest_exact1drG  n  s     U&FFr.   scales_hscales_wc                     [        XX#/5      $ r7   rC  r   r  rH  rI  s       r/   upsample_nearest2drL  |  s     U(1EFFr.   c                     [        XX#/SS9$ r7  rC  rK  s       r/   _upsample_nearest_exact2drN    s     U(1ETRRr.   scales_dc                     [        XX#U/5      $ r7   rC  r   r  rO  rH  rI  s        r/   upsample_nearest3drR    s     U(h1OPPr.   c                     [        XX#U/SS9$ r7  rC  rQ  s        r/   _upsample_nearest_exact3drT    s     X:$ r.   r9  c                 :   [        XX#S9nS S /U-   n[        R                  X5      nUR                  S:X  ad  [        R
                  " U 5      nU R                  S   nU R                  R                  S:X  a  US:  a  [        R                  nUR                  US9nU$ )Nr8  r;  r#   cudarQ  )r@  r   _unsafe_indexrw  rE   r   r  r  r  rj   rV  r  )	r   r  r.  r9  spatial_indicesr  r  rR  
n_channelss	            r/   r2  r2    s     8FO Tl_,G/F{{a33E: [[^
<<&:>!33M"""?Mr.   c           	         U(       a
  U(       a  SnOU(       a  SnOU(       a  SnOSn[        U 5      U-  S:X  d   [        U 5      5       e[        S[        U 5      U5       Vs/ s H  n[        XXC-    5      PM     sn$ s  snf )Nr  r;  r   r$   r   )r|  rU   r  )params
has_biaseshas_projections
group_sizerm  s        r/   gather_paramsr_    s|    o
	
	

v;#q(5#f+5(38CK3T3Taf()3T  s   "A>c                 x    U(       a%  U SU-     USU-     pTU SU-  S-      USU-  S-      pvOX   X   pTSu  pgXEXg4$ )Nr$   r#   NNr%   )r[  hiddensrm  bidirectional
cur_params
cur_hiddenbidir_paramsbidir_hiddens           r/   params_hiddensrh    s[    !'AAJ%+AEAI%6A	8Jl!'GJJ%/"<==r.   c                 ~    X:  d   eUR                  U R                  SX!U-
  5      5        U R                  SSU5      $ ru   )rs  r'  )re  last_batch_size
batch_sizerb  s       r/   update_hidden_for_packedrl    sA    '''NN:$$Q
j4PQRQ:..r.   c           	      t    X:X  a  U $ X:  d   e[         R                  " U UR                  SXU-
  5      45      $ ru   )rj   concatr'  )re  rj  rk  
inp_hiddens       r/    update_hidden_for_packed_reverserp    sJ     $'''<<a2NO	
 r.   c           	         US   nUS   nU(       a  US   OS n	U(       a  US   OS n
/ n/ nU(       a  US   OUS   nUR                  SSU5      n[        R                  " U [        U5      5      nU(       a  US S S2   nU HX  n U R                  S   nUU:X  a  O"U(       a  [        XUU5      nO[        XUU5      nU" XXyX5      nUnUR                  U5        MZ     U(       a  UR                  5         O!UR                  U5        UR                  5         [        R                  " US5      nU(       d  [        R                  " US5      OUnUU4$ )Nr   r#   r$   r   rT   )
r'  rj   r  ro  r  rp  rl  rs  reverser(  )inphiddenr[  r\  	hidden_fnbatch_sizesrr  	ih_weight	hh_weightih_biashh_biasstep_outputrb  rj  re  	split_inprm  r   
hidden_outs                      r/   one_layer_rnn_datar~    sC    q	Iq	I%fQi4G%fQi4GK"$G)0k"ok!nOq!_5JCk!23IddO	IIaLa9QJ 2QJ s	IW
:&# & z"
))K
#C.57A&:J
?r.   c                    ^  U 4S jnU$ )Nc                 D   > T" [         R                  " XU5      U -   5      $ r7   r   linearrm  re  rw  ry  rx  rz  nonlinearitys         r/   rK   rnn_cell.<locals>.inner1  s    AHHZGDqHIIr.   r%   r  rK   s   ` r/   rnn_cellr  0  s    J Lr.   c                    ^  U 4S jnU$ )Nc                 r   > [         R                  " XU5      n T" [         R                  " XU5      U -   5      $ r7   r  r  s         r/   rK   rnn_cell_data.<locals>.inner8  s.    HHQ7+AHHZGDqHIIr.   r%   r  s   ` r/   rnn_cell_datar  7  s    J Lr.   c           	         US   nUS   nU(       a  US   OS nU(       a  US   OS n	[         R                  " XU5      n
U(       a  U
R                  S5      OU
n
UR                  S5      n/ nU
 H  nU" XXhXy5      nUR	                  U5        M      U(       a  UR                  5         [        R                  " US5      nXR                  S5      4$ )Nr   r#   r$   r   )	r   r  fliprV   rs  rr  rj   r(  r  )rs  rt  r[  r\  ru  rr  rw  rx  ry  rz  precomputed_inputre  r{  rm  r   s                  r/   one_layer_rnnr  ?  s    q	Iq	I%fQi4G%fQi4G95<)..q1BS!!!$JKqi)U
:&  
))K
#C""1%%%r.   c                    US   nUS   nU(       a  US   nUS   nOH[         R                  " UR                  5       5      n[         R                  " UR                  5       5      nUS   R                  S5      n	US   R                  S5      n
/ nSnU	R                  S5      nSnSnSnSnU R	                  5       n U	R	                  5       n	U
R	                  5       n
[         R
                  R                  R                  R                  U UUUUU	U
UUUUUUUUU5      nUS   US   US   nnnUUR                  S5      UR                  S5      44$ )Nr   r#   r$   r   F)
rj   r  r&  rV   r  r"  r   mkldnn_rnn_layerr  r  )rs  rt  r[  r\  rr  w0w1w2w3hxcxrv  modehidden_size
num_layersrc  r  rD  outputsr[   hycys                         r/   mkldnn_one_layer_lstmr  U  sS   	B	BAYAY[[#[[#			Q	B			Q	BKD''!*KJ MKE ..
C	B	Biinn--55





!G$ 
GAJ
2rArzz!}bjjm,,,r.   c
           	      (   U(       a  U R                  SS5      OU n / n
[        U5       H  n[        X!X5      u  ppU(       a
  XKS-
  :  a  UOSnU	" XX5      u  nnU
R                  U5        U(       a  U	" XXSS9u  nnU
R                  U5        U(       a+  [        R
                  " UW/UR                  5       S-
  5      n OUn US:w  d  M  U(       d  M  XS-
  :  d  M  [        R                  " XSS9n M     U(       a  U R                  SS5      OU n X
4$ )Nr   r#   r   T)rr  )rD  )	transposerU   rh  rs  rj   r(  rP   rG  )r   rt  r[  r\  r  rG  rD  rc  r  layer_fnfinal_hiddensrm  rd  re  rf  rg  fwd_inp
fwd_hiddenbwd_inp
bwd_hiddens                       r/   _rnn_helperr    s    &1EOOAq!eEM:=KA>
:
 $
U(:'&u*QZ("*\t#GZ   ,IIw0'++-!2CDEEa<EEaq.&8MM%=E) , &1EOOAq!eEr.   c	                     UR                  S5      n	[        X#S5      n[        U U	UUUUUUU[        [        [        [        R                  5      S95
      u  pU
[        R                  " US5      4$ Nr   Fru  )	unbindr_  r  r   r  r  rj   r   stackr   r  r[  r\  r  rG  rD  rc  r  rt  r   r  s               r/   rnn_tanh_inputr    p     YYq\F6u5F$%**)=>C M1---r.   c	                     UR                  S5      n	[        X#S5      n[        U U	UUUUUUU[        [        [        [        R                  5      S95
      u  pU
[        R                  " US5      4$ r  )	r  r_  r  r   r  r  rj   r  r  r  s               r/   rnn_relu_inputr    r  r.   c	                     UR                  S5      n	[        X4S5      n[        U U	UUUUUUS[        [        U[        [        R                  5      S95
      u  pU
[        R                  " US5      4$ Nr   Frv  ru  )	r  r_  r  r   r~  r  rj   r  r  datarv  r  r[  r\  r  rG  rD  rc  rt  r   r  s               r/   rnn_relu_datar    w     YYq\F6u5F$##EJJ/	
C  M1---r.   c	                     UR                  S5      n	[        X4S5      n[        U U	UUUUUUS[        [        U[        [        R                  5      S95
      u  pU
[        R                  " US5      4$ r  )	r  r_  r  r   r~  r  rj   r   r  r  s               r/   rnn_tanh_datar    r  r.   c                 f   [         R                  " XU5      U -   nUR                  SU5      nUS   R                  5       n	US   R                  5       n
US   R	                  5       nUS   R                  5       nX-  X-  -   nXR	                  5       -  nUc  UO[         R                  " XS 5      nX4$ )Nr;  r   r#   r$   r   r   r  chunkr   r   )rs  r  r  rx  rz  	hr_weight	chunk_dimgateschunked_gatesin_gateforget_gate	cell_gateout_gater  r  s                  r/   	lstm_cellr  4  s    HHRG,s2EKK9-MA&&(G"**,Ka %%'IQ'')H		W0	1B	GGI	B ahhrd&CB6Mr.   c                 J   US   nUS   nU(       a  US   OS nU(       a  US   OS n[        U5      S:X  a  US   O[        U5      S:X  a  US   OS n	US   R                  S5      n
US   R                  S5      n[        R                  " XU5      nU(       a  UR	                  S5      OUn/ nU H"  n [        X
XXSS9u  pUR                  U
5        M$     U(       a  UR                  5         [        R                  " US5      nXR                  S5      UR                  S5      44$ )Nr   r#   r$   r   r  r;  r  )r|  rV   r   r  r  r  rs  rr  rj   r(  r  )rs  rt  r[  r\  rr  rw  rx  ry  rz  r  r  r  r  r{  r   s                  r/   one_layer_lstmr  B  s   q	Iq	I%fQi4G%fQi4G[A%q	Fq8H6!9d  
		Q	B			Q	B95<)..q1BSK 3B7QRS2 ! 
))K
#CA

1...r.   c                    US   nUS   nU(       a  US   OS nU(       a  US   OS n	[        U5      S:X  a  US   O[        U5      S:X  a  US   OS n
/ n/ nU(       a  US   OUS   n[        R                  " U [        U5      5      nU(       a  US S S2   nUS   nUS   nUR	                  SSU5      UR	                  SSU5      nnU GH  n U R
                  S   n[        R                  " XU5      n UU:  aa  UR                  UR	                  SUUU-
  5      UR	                  SUUU-
  5      45        UR	                  SSU5      UR	                  SSU5      nnUU:  aZ  [        R                  " UUR	                  SUUU-
  5      4S5      n[        R                  " UUR	                  SUUU-
  5      4S5      n[        U UUXyU
SS9u  nnUnUR                  U5        GM     U(       a  UR                  5         UU4nO\UR                  UU45        UR                  5         [        U6 u  nn[        R                  " US5      [        R                  " US5      4n[        R                  " US5      nUU4$ )	Nr   r#   r$   r   r  r;  rT   r  )r|  rj   r  ro  r'  r  r   r  rs  rn  r  rr  r  r(  )rs  rt  r[  r\  rv  rr  rw  rx  ry  rz  r  r{  rb  rj  r|  orig_hxorig_cxr  r  rm  r}  hidden0hidden1r   s                           r/   one_layer_lstm_datar  ]  sp   q	Iq	I%fQi4G%fQi4G[A%q	Fq8H6!9d  KG)0k"ok!nOCk!23IddO	QiGQiGq!_-q!_- 	B
 IIaLhhsw/ NNIIaOa$78IIaOa$78 YYq!Q'1a);B W^^AO8KLMqB W^^AO8KLMqB 3B	IQRSB23 6 "X
Bx =YYw*EIIgq,AA

))K
#C
?r.   c                 <    S nU" XU5      (       a  [         $ [        $ )a  Check whether we could use decompose lstm with mkldnn_rnn_layer.
All the below conditions need to be met:
    * ``torch._C._get_mkldnn_enabled()`` returns ``True``.
    * All the input args are on CPU.
    * The dtypes of args are either torch.float or torch.bfloat16.
    * Inference.
    * ``has_projections`` returns ``False``.

Args:
    * input: the input sequence to LSTM
    * hx: a tuple of the input hidden state and cell state ``(h_0, c_0)`` to LSTM
    * params: the weight and bias tensors of LSTM
c                    [         R                  R                  5       (       d  gU /[        U5      -   [        [        R
                  " U5      5      -   nU Vs1 s H  oDR                  iM     nn[        U5      S:w  a  gUR                  5       nU[         R                  " S5      :w  a  gU Vs1 s H  oDR                  iM     nnU H)  nU[         R                  [         R                  4;  d  M)    g   U R                  (       a  gUS   R                  S5      US   R                  S5      :g  n	U	(       a  ggs  snf s  snf )NFr#   r  r   r$   T)rj   r.  _get_mkldnn_enabledro  r   from_iterabler  r|  popr   r   bfloat16requires_gradr&  )
r   r  r[  rn  tdevicesr  dtypesr   r]  s
             r/   
use_mkldnn2select_one_layer_lstm_function.<locals>.use_mkldnn  s    xx++--'DH$tE,?,?,G'HH%,-W88W-w<1U\\%((#*+7a''7+EU[[%..99  Q%**Q-2a5::a=8) . ,s   D8.D=)r  r  )r   r  r[  r  s       r/   select_one_layer_lstm_functionr    s"    : %V$$$$r.   c	                    [        U5      S:X  d   S5       e[        X#US   R                  S5      US   R                  S5      :g  5      n[        [	        US   US   5      5      n	[        XU5      n
[        U U	UUUUUUUU
5
      u  p[        [	        U6 5      nU[        R                  " US   S5      [        R                  " US   S5      4$ )Nr$   lstm expects two hidden statesr   r#   )	r|  r_  r&  ro  r  r  r  rj   r  )r   r  r[  r\  r  rG  rD  rc  r  rt  r  r   r  s                r/   	lstm_implr    s     r7a<999<6r!uzz!}1

1/MNF#beRU#$F-e@H$C m,-MM!,a0%++mA>NPQ2RRRr.   c	                    [        U5      S:X  d   S5       e[        X4US   R                  S5      US   R                  S5      :g  5      n[        [	        US   US   5      5      n	[        U U	UUUUUUS[        [        US95
      u  p[        [	        U6 5      nU
[        R                  " US   S5      [        R                  " US   S5      4$ )Nr$   r  r   r#   F)rv  )
r|  r_  r&  ro  r  r  r   r  rj   r  r  s               r/   lstm_data_implr    s     r7a<999<6r!uzz!}1

1/MNF#beRU#$F$#=C m,-MM!,a0%++mA>NPQ2RRRr.   c                 $   U R                  SS5      n[        R                  " XU5      R                  SS5      nUS   US   -   R                  5       nUS   US   -   R                  5       n	US   US   U-  -   R	                  5       n
X-
  U	-  U
-   $ )Nr   r#   r$   r   )r  r   r  r   r   rs  re  rw  ry  rx  rz  chunked_igateschunked_hgates
reset_gate
input_gatenew_gates              r/   gru_cellr    s    YYq!_NXXjW=CCAqIN #nQ&77@@BJ #nQ&77@@BJq!^A%6%CDJJLH!Z/(::r.   c                 N   [         R                  " XU5      R                  SS5      n[         R                  " XU5      R                  SS5      nUS   US   -   R                  5       nUS   US   -   R                  5       n	US   US   U-  -   R	                  5       n
X-
  U	-  U
-   $ )Nr   r#   r   r$   r  r  s              r/   gru_cell_datar    s    XXcg6<<QBNXXjW=CCAqIN #nQ&77@@BJ #nQ&77@@BJq!^A%6%CDJJLH!Z/(::r.   c	                     [        X4S5      n[        U UR                  S5      UUUUUUS[        [        U[
        S95
      u  pU	[        R                  " U
S5      4$ )NFr   r  )r_  r  r  r   r~  r  rj   r  )r  rv  r  r[  r\  r  rG  rD  rc  r   r  s              r/   gru_impl_datar  $  se     6u5F$
		!"}UC M1---r.   c	                     [        X#S5      n[        U UR                  S5      UUUUUUU[        [        [
        S95
      u  pU	[        R                  " U
S5      4$ )NFr   r  )r_  r  r  r   r  r  rj   r  )r   r  r[  r\  r  rG  rD  rc  r  r   r  s              r/   gru_implr  B  sb     6u5F$
		!2C M1---r.   c                     [        U R                  5       X5      n[        US5      n[        US5      n[        R                  R
                  R                  XX%U5      $ Nr   r#   )r,  r&  r/  rj   r"  r   _upsample_bilinear2d_aar   r  align_cornersr*  r4  scale_hscale_ws          r/   upsample_bilinear2d_aa_vecr  `  sP     ){REmQ/GmQ/G99>>11mg r.   c                     [        U R                  5       X5      n[        US5      n[        US5      n[        R                  R
                  R                  XX%U5      $ r  )r,  r&  r/  rj   r"  r   _upsample_bicubic2d_aar  s          r/   upsample_bicubic2d_aa_vecr  l  sP     ){REmQ/GmQ/G99>>00mg r.   c                 ~    [        U R                  5       X5      nU(       a  UOS /[        U5      -  n[        XX%5      $ r7   )r,  r&  r|  _upsample_linear)r   r  r  r*  r4  r.  s         r/   _upsample_linear_vecr  x  s7     ){RE+]$#e*1DFE-@@r.   r  c                     [        XX#/5      $ r7   r  )r   r  r  rI  s       r/   upsample_linear1dr     s     EzJJr.   c                     [        XX#U/5      $ r7   r  )r   r  r  rH  rI  s        r/   upsample_bilinear2dr    s     E(?STTr.   c                     [        XX#XE/5      $ r7   r  )r   r  r  rO  rH  rI  s         r/   upsample_trilinear3dr    s     Mh+I r.   c                 Z    U(       a  US:  a  U S-
  US-
  -  $ S$ Ub  US:  a  SU-  $ X-  $ )Nr#   rh   r   r%   )r  r  r  rp   s       r/   _compute_scaler    s@    5=\#(S.1HqH#/EAIsU{U7CUUr.   c                 ,    U(       a  X-  $ XS-   -  S-
  $ Nr   r%   )rp   	dst_indexr  s      r/   _compute_source_indexr
    s       C(3..r.   weightsweights_precisionc                     [        S [        X5       5       5      SUS-
  -  -   nX2-	  n[        R                  " USS5      R	                  [        R
                  5      $ )Nc              3      #    U  HF  u  pUR                  [        R                  5      UR                  [        R                  5      -  v   MH     g 7fr7   )r:   rj   r9  )r  r  r  s      r/   r  %_sum_tensors_uint8.<locals>.<genexpr>  s5      :K$!U[[ADD--:Ks   AAr#   r      )_sum_tensorsr  rj   r   r:   r4  )r  r  r  r  s       r/   _sum_tensors_uint8r    s_      :=c:K 	
 1$	%'F (F;;vq#&))%++66r.   c                     [         R                  " U 5      R                  5       nSn[         R                  " X!R                  S9nSUSUS-   -  -  -   nUS:  nX%R                  5       -
  $ )N   r  r   r#   i   )rj   r  r   r  r  r   )r  
max_weightmax_weight_precision
precisionsvaluesr  s         r/   _compute_weight_precisionr    se    W%))+J2;L;LMJ:zA~!677FgD((*,,r.   c                   ^ ^^ T R                   S   nT R                   SS  n[        U5      n[        R                  " T [        R                  R
                  S9u  nmUUU 4S jn[        [        XQU5      5       V	V
VVs/ s H  u  n	u  pnU" XX6S-
  U	-
  5      PM     nnn
n	n[        [        U6 5      u  pn/ n[        SS//U-  6  Hh  nS S /[        U5       Vs/ s H  nUU   S:X  a  UU   OUU   PM     sn-   n[        R                  T U5      n[        UT5      nUR                  U5        Mj     [        [        U5      5       Hs  n	X   X   -
  R!                  SS5      R#                  T5      n[        US S S2   USS S2   5       VVs/ s H#  u  nnU[$        R&                  " UU-
  U5      -   PM%     nnnMu     [        U5      S:X  d   eUS   n[        R(                  " T 5      nT R*                  R,                  S:X  a  US	:  a  [$        R.                  n[1        U[$        R2                  5      (       d   eUR5                  US
9nT R7                  5       (       d  UR9                  5       nU$ s  snnn
n	f s  snf s  snnf )Nr#   r$   rR  c                 `  > [        XT	U5      n[        R                  " UTR                  S9R	                  T
S9n[        XET	5      R                  SS9nUR                  " UR                  S   /S/U-  Q76 nUR	                  [        R                  5      nUS-   R                  U S-
  S9nXgU4$ )Nr  r   r   r   r   r#   r   )
r  rj   r  r  r:   r
  r   r  r  r  )inp_sizer  r.  nsqueezescale_factorrm  x_f32r;   xp1r  r   r   s            r/   
get_values$_upsample_linear.<locals>.get_values  s    %h-P LL%,,7:::G%l}EKKPSKTekk!n@sh/?@HHU[[!1umm1m-}r.   r   r   rh   rV     rQ  )r  r|  rE   rF   rT  INT_TO_FLOATr  r  ro  r   rU   r   rW  r   rs  reversedr   r:   rj   r   r   r  r  rV  r9   r   r  rK  round)r   r  r  r.  rY  	inp_sizesn_dimsrW   r!  rm  r  r  r  xs_f32xsxp1svsr  kr  vxscalev1v2r  rR  r   s   ` `                       @r/   r  r    sv    QJABI^F''!AANNHAu
 09	/0
0
+A+F 	8vzA~>0
   CL)F	B1vh'(TluV}U}!qtqybed1g=}UUuc*#Au-
		!	 ) eFm$)be#**3477> b1gr!$Q$x0
 1B 27F++0 	 
 % r7a<<UF //6M ||F"zB//fell++++];F""$$MQ V
s   ?I1
I9*I>r  r  c                 4    U R                   UR                   :H  $ r7   r  )r  r  s     r/   is_same_sizer3    s    77aggr.   c                 ,    [         R                  X5      $ r7   )r   r  )r;   r  rG   s      r/   _reshape_aliasr5  !  s     99Qr.   c                 ,    [         R                  X5      $ r7   )r   r  )r;   r  s     r/   rW  rW  '  s    ::a!!r.   c                 .    [         R                  XX#5      $ r7   )r   r  )r;   r  r~   r%  s       r/   r'  r'  ,  s    >>!e88r.   c                    U HK  nUc  M  [         R                  " UR                  [         R                  [         R                  4;   S 5        MM     [         R                  " UR                  [         R
                  :H  S 5        SSKJn  U" U R                  5       S:H  5      (       a;  [         R                  R                  X5      nU R                  UR                  U5      $ [        [        U5      5       H0  nX'   nUc  M  UR                  SU R!                  U5      S-
  S9X''   M2     ["        R%                  X5      R'                  U) U5      $ )Nc                      gNz3tensors used as indices must be long or int tensorsr%   r%   r.   r/   r   &_unsafe_masked_index.<locals>.<lambda>7  r  r.   c                      gNz*tensors used as masks must be bool tensorsr%   r%   r.   r/   r   r;  <      <r.   r   r  r#   r  )rj   r   r   rf  r  r  rm  rk  r   _meta_registrationsmeta_index_Tensorr@  r  rU   r|  r   r&  r   rW  rg  )r;   r  r  fillr  rk  meta_resultrm  s           r/   r  r  1  s   LL

EII66M  
LL

ejj <
 KAGGIN++//AA!Mzz+++T223w< 
q	A>GJ !
 a)55teTBBr.   c                 R   U HK  nUc  M  [         R                  " UR                  [         R                  [         R                  4;   S 5        MM     [         R                  " UR                  [         R
                  :H  S 5        U R                  5       S:X  a  U R                  5       $ [        [        U5      5       H@  nX%   nUc  M  UR                  U R                  U5      * U R                  U5      S-
  S9X%'   MB     UR                  U) S5      n[        R                  XUSS9$ )Nc                      gr:  r%   r%   r.   r/   r   5_unsafe_masked_index_put_accumulate.<locals>.<lambda>S  r  r.   c                      gr=  r%   r%   r.   r/   r   rE  X  r>  r.   r   r#   r  Tr$  )rj   r   r   rf  r  r  r   r  rU   r|  r   r&  rg  r   r'  )r;   r  r  r  r  rm  masked_values          r/   #_unsafe_masked_index_put_accumulaterH  M  s    LL

EII66M  
LL

ejj <
 	wwyA~wwy3w< 
!&&)QGGJ !
 %%teQ/L!!!lt!LLr.   c                    U R                  5       nSnUS:  a  SnUb5  US:  a)  S/U-  nUR                  S   Xv'   UR                  U5      nOUnX-  n [        R                  " X:g  US5      n	U	R                  U5      n
[        R                  " XU
5      R                  U5      * n[        R                  " X:g  US5      nU[        R                  R                  :X  a  US:  a  U R                  SS5      nX4$ Ubl  WR                  U R                  5      n[        R                  " XU
5      R                  U5      n[        R                  " X:g  US5      nUR                  5       nO!X:g  R                  5       R                  U 5      nU[        R                  R                  :X  a  UR                  5       nX4$ U[        R                   R                  :X  a  UR                  5       U-  nX4$ )Nr#   r$   r   r%   r   )rP   r  r  rj   rk   rV   gatherr  r!   r*   r~   r@  r  r   r:   r,   r+   )r}   r   r   r   r  r(  r   r  wr!  safe_target_r  r  wsums                 r/   _nll_loss_forwardrN  g  s    XXZFKzA:E "(aEE"AAx++f4fa@K((5L ll4l;CCKPPF[[/;FINN(((VaZ}}R-##HHTZZ ||AL9AA+N{{614;xxz.33588>IMM'''  
inn**	*,r.   c                 >   U R                  5       S:  a  U R                  5       S::  d   S5       eUR                  5       S::  d   S5       eU R                  5       S:H  =(       a    UR                  5       S:H  nU(       dB  U R                  S   UR                  S   :X  d"   SU R                   SUR                   S35       eU R                  S	   nUb?  UR                  5       S:X  a  UR                  5       U:X  d   S
U SUR                   35       e[        XX#U5      $ )Nr   r$   r2  r#   r3  r4  r5  r6  rT   z/weight tensor should be defined either for all z7 classes or no classes but got weight tensor of shape: )rP   r  r   rN  )r}   r   r   r   r  r8  	n_classess          r/   nll_loss_forwardrQ    s    88:>dhhjAoP/PP-::<1 E 88:?8vzz|q'8LDJJqMV\\!_< 
$TZZL
6<<.J= 

2I>fjjla/FLLNi4O 
9) E++1<<.	:P
 T6lKKr.   c                     [        XX#U5      $ r7   )rN  )r}   r   r   r   r  s        r/   nll_loss2d_forwardrS    s     T6lKKr.   Ac                 0    US-   U -  US-   -
  U -  U -  S-   $ )Nr$   r   r#   r%   r;   rT  s     r/   _upsample_cubic_convolution1rW    s(    UaK1q5!Q&*Q..r.   c                 :    X-  SU-  -
  U -  SU-  -   U -  SU-  -
  $ )Nr     r;  r%   rV  s     r/   _upsample_cubic_convolution2rZ    s.    UQU]a!a%'1,q1u44r.   r  c                    SnU R                   [        R                   " S5      :X  a  [        R                  " U SU -
  /SS9n[        R                  " U S-   SU -
  /SS9n[        X15      n[	        X!5      n[        R
                  " USS9u  pg[        R
                  " USS9u  pXhX4$ [        U S-   U5      [	        X5      [	        SU -
  U5      [        SU -
  U5      4$ )Ng      r  rh   r   r   r   )r  rj   r  rZ  rW  r  )
r  rT  tt1tt2w03w12r  r  r  r  s
             r/    _upsample_get_cubic_coefficientsr`    s    Axx5<<&&kk1cAg,A.kk1s7C!G,!4*32*32cq)cq)r~ )S!4(.(q!4(q!4	
 	
r.   coeffstsc                 N    [        U5      n[        S [        X5       5       5      $ )Nc              3   .   #    U  H  u  pX-  v   M     g 7fr7   r%   r  r  r  s      r/   r  +_upsample_cubic_interp1d.<locals>.<genexpr>  s     E0DHR0Dr  )r`  r  r  )ra  rb  coeffs2s      r/   _upsample_cubic_interp1drh    s"    .r2GEF0DEEEr.   c                 6    [        [        R                  U 5      $ r7   )r   rj   add)rb  s    r/   r  r    s    %))R  r.   	num_stepsc                     U S::  a  [         R                  " SX2S9$ U(       d  U S-
  U -  OSn[         R                  " U* X@X2S9$ )Nr#   r   r  )stepsr  r   )rj   ru  linspace)rk  r  r   r  r  s        r/   _linspace_from_neg_onero    sC     A~||Af::-:)a-9	$A>>1"aMMr.   thetahrK  c                    U R                   nU R                  n[        X#XE5      R                  SUS5      n[        XXE5      R                  USS5      n[        R
                  " SXES9n[        R                  R                  R                  USSSS9n[        R                  R                  R                  USSSS9n[        R                  R                  R                  US	SSS9nXg-   U-   $ )
Nr#   )r#   r#   r#   r  )r   r$   constantr   r  r  r~   r#   r#   )r$   r   	r   r  ro  r  rj   r  r  r  r  )	rp  rq  rK  r  r   r  grid_xgrid_ygrid_ones	            r/   _make_base_grid_4drz    s    KKE\\F $AeDII!QPQRF#AeDII!QPQRFzz)5@H XX  $$VjPQ$RFXX  $$VjPQ$RFxx""&&xV*TU&VH?X%%r.   r  c                 t   U R                   nU R                  n[        X4XV5      R                  SSUS5      n[        X$XV5      R                  SUSS5      n[        XXV5      R                  USSS5      n	[        R
                  " SXVS9n
[        R                  R                  R                  USSSS9n[        R                  R                  R                  USSSS9n[        R                  R                  R                  U	S	SSS9n	[        R                  R                  R                  U
S
SSS9n
Xx-   U	-   U
-   $ )Nr#   )r#   r#   r#   r#   r  )r   r   rs  r   rt  )r#   r$   )r$   r#   )r   r   rv  )rp  r  rq  rK  r  r   r  rw  rx  grid_zry  s              r/   _make_base_grid_5dr}    s%   KKE\\F#AeDII!QPQSTUF#AeDII!QPQSTUF#AeDII!QPQSTUFzz,eCH XX  $$VjPQ$RFXX  $$VjPQ$RFXX  $$VjPQ$RFxx""&&xV*TU&VH?V#h..r.   c                     Uu  p4pV[        XXbS9nUR                  SSS5      U R                  R                  S5      -  R	                  S5      nUR                  X5US5      $ )Nr  rT   r   r#   rS  r$   )rz  r  rX  rV   r   )	rp  r&  r  r  rW   rq  rK  	base_gridgrids	            r/   _affine_grid_generator_4dr    s]    JA!"5QLI NN2q!$uxx'9'9!'<<AA"ED99Q1a  r.   c                     Uu  p4pVn[        XXgUS9nUR                  SSS5      U R                  R                  S5      -  R	                  S5      n	U	R                  X5XgS5      $ )Nr  rT   r;  r#   rS  r   )r}  r  rX  rV   r   )
rp  r&  r  r  rW   r  rq  rK  r  r  s
             r/   _affine_grid_generator_5dr  #  sa    MA!"5QOI NN2q!$uxx'9'9!'<<AA"ED99Q1##r.   c                     [         R                  " [        U5      S;   S 5        [        U5      S:X  a
  [        XUS9$ [	        XUS9$ )Nr  c                      g)NzCaffine_grid_generator needs 4d (spatial) or 5d (volumetric) inputs.r%   r%   r.   r/   r   'affine_grid_generator.<locals>.<lambda>3  s    Ur.   r;  r  )rj   r   r|  r  r  )rp  r&  r  s      r/   affine_grid_generatorr  -  sF     
LLD	VU 4yA~(MRR(MRRr.   r  interpolation_modepadding_mode_expand_gridc           	        ^ ^^^^^^^^^^ ^!^"^#^$^%^&^'^(^)^*^+^,^- [         R                  " TS;   U4S j5        [         R                  " TS;   U4S j5        S[        S[        S[        4U4S jjm-S[        S[        S	[        S[        4S
 jm+S[        S[        S[        4UUU+4S jjm S[        S[        S[        4U U-4S jjnT R                  u  mmm$m%UR                  u  nm)m*nUS:X  d   eT(       a(  UR                  TST)T*U5      R                  TTT)T*S5      nS[        S[        S[        4U$U%4S jjm&[         R                  " TT R                  S9R                  TSSS5      m[         R                  " TT R                  S9R                  STSS5      mS[        S[        S[        S[        4UUUU&U)U*4S jjmS[        S[        S[        4UUU U4S jjm"US   n	US   n
TS:X  a  U" U	T%5      nU" U
T$5      nUR                  5       UR                  5       sm'm(T'S-   T(pT'T(S-   nnUUnnUU-
  UU-
  -  nX-
  UU-
  -  nX-
  X-
  -  nUT'-
  UT(-
  -  n[        U"4S jT'T(U4XU4UUU4UUU44 5       5      $ TS:X  a<  U" U	T%5      nU" U
T$5      nUR                  5       nUR                  5       nT"" UUS5      $ T-" U	T%5      nT-" U
T$5      nUR                  5       m'UR                  5       m(UT'-
  m,UT(-
  nT(       d"  T,R                  S5      m,UR                  S5      nS[        S[        S[        4U U"U$U%4S jjm#S[        S[        4U#U'U(U,4S jjm![        U!4S j[        S 5       5       5      n[!        UU5      $ )!N)r   r#   r$   c                     > ST  3$ )NzInvalid interpolation mode r%   )r  s   r/   r   "_grid_sampler_2d.<locals>.<lambda>L  s    -.@-ABr.   c                     > ST  3$ )NzInvalid padding mode r%   )r  s   r/   r   r  O  s    -B<.+Qr.   coordsr&  rQ   c                 J   > T(       a  US-  S-
  OUS-  nUS-  S-
  nX-  U-   $ r  r%   )r  r&  r   ofsr  s       r/   unnormalize%_grid_sampler_2d.<locals>.unnormalizeR  s6     %2tczCs
Sj3|c!!r.   	twice_low
twice_highc                 D   X:X  a  [         R                  " U 5      $ US-  nX!-
  S-  nX-
  R                  5       n[         R                  " XT5      nXT-  R	                  5       R                  [         R                  S9n[         R                  " US-  S:H  Xc-   XC-   U-
  5      $ )Nr$   r   r#   r   )rj   r  r   fmodfloorr:   int8rk   )r  r  r  
coords_mincoords_spancoords2extraflipss           r/   reflect_coordinates-_grid_sampler_2d.<locals>.reflect_coordinates]  s    "##F++]
!-2&++-

70&--/222D{{AINE.0H50P
 	
r.   c                    > TS:X  a  U $ TS:X  a  [         R                  " U SUS-
  5      $ T(       a  T" U SSUS-
  -  5      nOT" U SSU-  S-
  5      n[         R                  " USUS-
  5      $ )Nr   r#   r$   rT   r   )r  r&  coords_reflectedr  r  r  s      r/   compute_coordinates-_grid_sampler_2d.<locals>.compute_coordinatesi  sx    1MQ;;vq$(33#6vq!tax.#Q #6vr1t8a<#P ;;/D1H==r.   c                 $   > T" X5      nT" X!5      $ r7   r%   )r  r&  	coords_unr  r  s      r/   compute_source_index._grid_sampler_2d.<locals>.compute_source_indexu  s    -	"933r.   r$   r#   r*  ysc                    > [         R                  " SU :*  [         R                  " U T:  [         R                  " SU:*  UT:  5      5      5      $ ru   rj   r  )r*  r  iHiWs     r/   in_bounds_cond(_grid_sampler_2d.<locals>.in_bounds_cond  sF      GU&&rBw0A0A!r'2PR70ST
 	
r.   r  wsc                    >^^ T" X5      mT(       a  TOSm[        UUUU	U
4S jU R                  [        R                  S9UR                  [        R                  S9U4 5       5      $ )Nr#   c              3   x   >#    U  H/  n[         R                  " TUS 5      R                  TTTT5      v   M1     g7fr  )rj   rk   r  )r  r  r  r  r  oHoWs     r/   r  1_grid_sampler_2d.<locals>.clip.<locals>.<genexpr>  s9      
M KKa#((Ar266Ms   7:r   )r  r:   rj   r  )r*  r  r  r  r  r  r  r  r  r  r  s      @@r/   clip_grid_sampler_2d.<locals>.clip  s\    b%
 A1 
 
ee%++e.EKK0H"M
 
 	
r.   ixiyc                 2   > T	" XU5      u  p4nTTTXC4   U-  $ r7   r%   )
r  r  rK  idx_xidx_yw_C_idxN_idxr  r  s
         r/   get_summand%_grid_sampler_2d.<locals>.get_summand  s*    ?bu+,r11r.   ).r   ).r#   r   c              3   <   >#    U  H  u  pnT" XU5      v   M     g 7fr7   r%   )r  r  r  rK  r  s       r/   r  #_grid_sampler_2d.<locals>.<genexpr>  s*      
  "" s   c                 :   > T" U T5      nT" UT5      nT" X#S5      $ r]   r%   )r  r  r;   r[   r  r  r  r  s       r/   get_value_bounded+_grid_sampler_2d.<locals>.get_value_bounded  s(    #B+A#B+AqQ''r.   r  c                    > TU S-
  -   nT" TS-
  U5      T" TU5      T" TS-   U5      T" TS-   U5      4n[        UT5      $ )Nr#   r$   )rh  )r  iy_ofscsr  ix_nwiy_nwtxs      r/   	get_coeff#_grid_sampler_2d.<locals>.get_coeff  s[    cAg&F!%!)V4!%0!%!)V4!%!)V4	B ,B33r.   c              3   4   >#    U  H  nT" U5      v   M     g 7fr7   r%   )r  r  r  s     r/   r  r    s     :#y~~   r;  )rj   r   r   r  r  r  r  r  r  r   r  r  r&  rV   r  rU   rh  ).r  r  r  r  r  r  r  rW   twor;   r[   r  r  ix_neiy_neix_swiy_swix_seiy_sew_nww_new_sww_se
ix_nearest
iy_nearesttyra  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  s.   ` ````                     @@@@@@@@@@@@@@@@@@@r/   _grid_sampler_2dr  ;  s    
LLi'B 
LL	!#Q"F "# "& "

F 

s 

 

PV 


>F 
># 
>& 
> 
>4V 43 46 4 4 77LAq"bZZNAr2s!8O8 yyAr2s+221aRC
6 
v 
& 
 

 LL188,11!Q1=ELL188,11!Q1=E

 

V 

 

4F 

 

2 2F 2& 2 2
 	VAVAQ!!R(!!R(xxz288:uqy%ueaiueu
urz*
urz*
rz*U
rEz* 
 t$t$t$t$	 
 
 	
 
q	 !!R(!!R(XXZ
XXZ
:z155BB

%Z%ZaBaB	(& 	(f 	( 	( 	(
	43 	46 	4 	4 :q::'33r.   c                     [        U UUUUS9$ )N)r  r  r  r  )r  )r  r  r  r  r  s        r/   grid_sampler_2dr    s      	-!# r.   c                 2  ^ ^ [         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  U U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T T-  R	                  SS9$ )Nr$   r#   c                  L   > ST R                  5        STR                  5        3$ )Nzmatrix @ vector expected, got r  r   r}   r  s   r/   r   mv.<locals>.<lambda>  s    0BswwykJr.   r   c                  v   > ST R                  S5       ST R                  S5       STR                  S5       S3$ )Nzsize mismatch, got input (r   r;   r#   z), vec (r6  r  r  s   r/   r   r    s:    ,TYYq\N!DIIaL>RURZRZ[\R]Q^^_`r.   r   )rj   r   rP   r&  r   r  s   ``r/   r  r    ss     
LL
a*CGGINJ 
LL		!#` 3J""r.   c                     Ub.  US-
  U-  S-   nSU-
  U -  U[         R                  " U 5      -  -
  nOSU-
  U -  [         R                  " U 5      -
  nUb  Xb-  n[        Xd5      $ r]   )r   
logsigmoidr   )r}   r   r   
pos_weightr   
log_weightr   s          r/    binary_cross_entropy_with_logitsr    sr    
  1n.2
F
d"j1<<3E&EFF
d"Q\\$%77}00r.   tensor1tensor2is_outc                    ^	 U R                   UR                   :  a  X4OX4u  p4SSKJm	  UR                   S:  a  UR                   S::  d  gUR                  (       a  U(       d  gU R                   S:X  a  gT	" UR	                  5       S:H  5      (       a  gUR
                  nUR                  5       nS/n[        USS  5       H  nUR                  XS   -  5        M     [        U	4S	 j[        U[        [        U5      5      U5       5       5      $ )
Nr   r  r   r$   FTr#   rT   c              3   V   >#    U  H  u  pnT" US :H  5      =(       d    X:H  v   M      g7fr  r%   )r  r   r   r&  rk  s       r/   r  should_fold.<locals>.<genexpr>-  s4      "
D 	TQY'84=8"
s   &))rw  rm  rk  r  r   r  rp  r%  rs  r  r  ro  )
r  r  r  t1t2t1_shape	t1_strideexpected_strider&  rk  s
            @r/   should_foldr    s     $+<<7<<#?ggEWFBJGGqLRWW\	||qBHHJ!O,,xxH		I
 cO!"&tb&99: ' !$tH_56"
  r.   )pass_is_out)r  c                	   U R                  5       nUR                  5       nUS:w  a  US:w  d   eUS:X  a  US:X  a  [        R                  " X5      $ US:X  a  US:X  a  [        R                  " X5      $ US:X  aG  US:X  aA  [        R                  " [        R
                  " [        R                  " U S5      U5      S5      $ US:X  a  US:X  a  [        R
                  " X5      $ [        XU5      (       GaV  XC:  nU(       a  UR                  OU nU(       d  UOUS:X  a  U R                  5       OU nUR                  n[        US S 5      n	[        [        R                  U	5      n
UR                  5       S:H  nU(       a  U	R                  UR                  S   5        UR!                  XS   5      nU(       a\  [        R"                  R$                  R'                  UR                  U5      U	5      nU(       a  UR                  R)                  5       $ U$ [        R"                  R$                  R'                  UR                  U5      U	5      $ US:  Ga}  US:  Gav  US:  a  U R+                  S5      OSnU R+                  S5      nU R                  S S nUS:  a  UR+                  S5      OUR+                  S5      nUS:  a  UR+                  S5      OSn/ n[-        US-
  5       H#  nUR                  UR+                  U5      5        M%     US:X  a{  US:X  au  US   US   :w  ai  US   S:X  a,  U R.                  (       a  [1        U R	                  S5      U5      $ US   S:X  a+  UR.                  (       a  [1        XR	                  S5      5      $ [        [        R2                  " UU5      5      nUX/-   n[5        U5      nU R7                  U5      R!                  UX5      nUS:H  nU(       a7  UU/-   nUR7                  U5      R!                  UU5      R                  S5      nO)UUU/-   nUR7                  U5      R!                  UUU5      nUn	US:  a  U	R                  U5        US:  a  U	R                  U5        U(       a/  UR9                  U5      R	                  S5      R;                  U	5      $ UR9                  U5      R;                  U	5      $ [        R<                  " SS 5        g )	Nr   r#   r$   rT   rS  r   Fc                      g)Nz/both arguments to matmul need to be at least 1Dr%   r%   r.   r/   r   matmul.<locals>.<lambda>  s    $Ur.   )rP   rj   dotr  r  r  rV   r  rX  r  r  ro  r   r  r   rs  r  r"  r   _unsafe_viewr  r&  rU   r  rW  broadcast_shapesr&  r  bmmr  r   )r  r  r  dim_tensor1dim_tensor2r  r  r  sizes_1output_shapefolded_dim1t2_is_matrix	t1_foldedr  r  m1batch_tensor1m2rK  batch_tensor2rm  expand_batch_portiontensor1_expand_sizeexpand_batch_producttensor1_expanded
vector_rhstensor2_expand_sizetensor2_expandeds                               r/   rW  rW  5  sG    ++-K++-K!q 000aK1,yy**		kQ.xx))		kQ.}}UXXeoogq&A7KQOO		kQ.xx))	Wv	.	.  -	$WZZ'$G+:J799;PW 	 ((GCRL)X\\<8 vvx1}, JJ{BK8	 YY^^00b1A<PF-6699'')BFB99>>..y||B/?NN		kQ. !,aGLLQ\\"cr*!,qW\\"gll26F +aGLLQ#%{Q'A  a1 ( 1q a M!$44Q1$)>)>gooa0'::Q1$)>)>gq'9::  $""=-@ 
 3aW<#$89 #>>*=>FF !
 !A%
"6""=23-r21  #7"a"@&~~.ABJJ$b!  ,?"?"#''(89AA"EJJ<XX#''(89>>|LLUUVr.   r  r  c                 J  ^ ^^^^^^^ T R                   u    nmm[        TUS   X#5      n[        TUS   X$5      n[        R                  " T [        R                  R
                  S9u  pX[        R                  " US   T R                  S9R                  US9n	[        R                  " US   T R                  S9R                  US9n
[        XzU5      n[        XiU5      nUR                  S5      nUR                  5       nUR                  5       nX-
  R                  SS5      nX-
  R                  SS5      nUR                  [        R                  5      nUR                  [        R                  5      nUS-
  XS-   US	-   4nUS-
  XS-   US	-   4m[        U5      m[        U5      nS
u  mnT R                   [        R"                  :X  a  [%        T5      m[%        U5      nT Vs/ s HB  nUST-  -  [        R&                  " U5      S-  -   R                  [        R(                  5      PMD     snmU Vs/ s HB  nUSU-  -  [        R&                  " U5      S-  -   R                  [        R(                  5      PMD     nnUUU 4S jmU UUUU4S jm[+        U4S jU 5       5      nT R                   [        R"                  :X  a  Uc   e[-        UUU5      nO[/        S [1        UU5       5       5      n[        R2                  " T 5      nUR5                  US9nU$ s  snf s  snf )Nr   r#   rR  r  r   rT   r   rh   r$   ra  r   c                    > [         R                  " U STS-
  5      n[         R                  " USTS-
  5      n[        R                  TS S X#/5      nU$ r  )rj   r   r   rW  )r  r*  y_idxx_idxr.  in_hin_wr   s        r/   load_bounded0upsample_bicubic2d_default.<locals>.load_bounded  sM    B4!8,B4!8,utT5&@Ar.   c                    >^  [        UU 4S jT 5       5      nTR                  [        R                  :X  a  Tc   e[	        UTT5      $ [        S [        UT5       5       5      $ )Nc              3   6   >#    U  H  nT" TU5      v   M     g 7fr7   r%   )r  x_ofsr  r[   s     r/   r  Cupsample_bicubic2d_default.<locals>.get_x_interp.<locals>.<genexpr>  s     B'l1e,,'s   c              3   .   #    U  H  u  pX-  v   M     g 7fr7   r%   re  s      r/   r  r    s     J4IBG4Ir  )r  r   rj   r4  r  r  r  )r[   src_xr   ixs_ofsr  weights_precision_x	weights_xs   ` r/   get_x_interp0upsample_bicubic2d_default.<locals>.get_x_interp  sW    B'BB;;%++%&222%eY8KLLJCy4IJJJr.   c              3   4   >#    U  H  nT" U5      v   M     g 7fr7   r%   )r  y_ofsr$  s     r/   r  -upsample_bicubic2d_default.<locals>.<genexpr>  s     ;7%,u%%7r  c              3   .   #    U  H  u  pX-  v   M     g 7fr7   r%   re  s      r/   r  r(    s     L6K(2bg6Kr  rQ  )r  r  rE   rF   rT  r$  rj   r  r  r:   r
  rV   r  r   r  r`  r   r4  r  r   int16r  r  r  r  r   r  )r   r  r  r  r  rW   h_scale_factorw_scale_factorr   rm  r  x_floaty_floatr;   r[   yscaler/  iys_ofs	weights_yweights_precision_yrK  src_yr  rR  r$  r  r  r!  r  r"  r#  s   `                       @@@@@@@r/   upsample_bicubic2d_defaultr4    s    {{Aq$ $D+a.-QN#D+a.-QN''5#H#H#U#UHA 	[^ELL9<<5<IA[^ELL9<<5<IA#N}EG#N}EG#GAA k  c*Fk  c*F	U[[A	U[[A1uaQA&G1uaQA&G08I08I/9,,{{ekk!7	B7	B 
 !**+ejjmc.AAEEekkR
	 
 !**+ejjmc.AAEEekkR 	 

K K ;7;;E{{ekk!"...#E96IJLc%6KLL //6M];FMA

s   %A	L5A	L c                 .   [         R                  " [        U5      [        U5      -   S:H  S 5        UcI  Uc   e[        [        [
        [
        4   [	        S [        U R                  SS  U5       5       5      5      nU(       a  UOSu  pE[        XX$U5      $ )Nr#   c                      g)Nz:Must specify exactly one of output_size and scale_factors.r%   r%   r.   r/   r   (upsample_bicubic2d_vec.<locals>.<lambda>  s    Lr.   c              3   T   #    U  H  u  p[        [        U5      U-  5      v   M      g 7fr7   )r   r   )r  rK  rp   s      r/   r  )upsample_bicubic2d_vec.<locals>.<genexpr>  s*       ?HA 	!u,-- ?s   &(r$   ra  )	rj   r   r  r   r  r  r  r  r4  )r  r  r  r*  r  r  s         r/   upsample_bicubic2d_vecr:    s     
LL[D//14L (((#s(O  #AGGABK ? 
 )6}<G%amgVVr.   c                 *   ^  U 4S jn[        T UU5      $ )Nc                    > [         R                  " U * X-   TR                  S9nUS-
  US-
  UR                  5       -
  R                  5       -
  $ )Nr  r#   )rj   r  r  r   r   middler   dim_idxr  s       r/   r  _reflection_pad.<locals>.idx(  sD    ,,ufnQXXFzVaZ'++-7<<>>>r.   _reflection_or_replication_padr  r  r  s   `  r/   _reflection_padrD  "  s     ? *	 r.   c                 *   ^  U 4S jn[        T UU5      $ )Nc                    > [         R                  " U * X-   TR                  S9n[         R                  " USUS-
  5      $ )Nr  r   r#   )rj   r  r  r   r=  s       r/   r  _replication_pad.<locals>.idx9  s4    ,,ufnQXXF{{7Avz22r.   rA  rC  s   `  r/   _replication_padrH  3  s     3 *	 r.   idx_fnc                 r  ^ [        U5      S-  m[        R                  " U R                  5       TS-   TS-   4;   U4S j5        U R                  T* S  nU R                  5       T-
  n[        T5       Vs/ s H  oQSTS-
  U-
  -     PM     nn[        T5       Vs/ s H  oQSTS-
  U-
  -  S-      PM     nnU n[        T5       HA  nS /UR                  5       -  n	U" Xe   X5   Xu   5      XU-   '   [        R                  X5      nMC     [        R                  " U5      n
UR                  U
S9nU$ s  snf s  snf )Nr$   r#   c                  (   > ST  ST S-    ST S-    S3$ )Nreflection_padzd requires r#   zD or r$   zD inputr%   r   s   r/   r   0_reflection_or_replication_pad.<locals>.<lambda>L  s"    .[q	sQwiwOr.   rQ  )r|  rj   r   rP   r  rU   r   rW  rE   r   r  )r  r  rI  	inp_shapenc_dimrm  padding_leftpadding_rightr  r  rR  rP   s              @r/   rB  rB  D  s7   
 g,!
C	LL	C!GS1W%%O IUUWs]F8=c
C
1Aq1-.
LC=B3ZHZQ#'A+.23ZMHF3Z&**,. ),@PQJ##F0  //7M];FM DHs   4D/D4c           
      2  ^ ^^^ [        U5      S-  mUR                  T* S   Vs/ s H  o3S-
  PM	     nn[        T5       Vs/ s H  oRSTS-
  U-
  -     PM     nn[        T5       Vs/ s H  oRSTS-
  U-
  -  S-      PM     nn/ n[        UR                  5       Ha  nS/UR                  -  n	SX'   UR	                  [
        R                  " UR                  U   UR                  S9R                  U	5      5        Mc     US T*  mUT* S  n
S m[        T5       Vs/ s H  oZU   Xe   -   PM     nn[        T5       Vs/ s H  oVU   X   -
  PM     nn[        T5       Vs/ s H  nSXE   -  Xe   -   X   -
  PM     nn[        T5       Vs/ s H  o[U   SXE   Xe   -   Xu   -   4PM     nn[        R                  " [        R                  [        T5       Vs/ s H  nT" X   5      PM     sn5      n[        R                  T UTU-   S5      nUUU U4S jn[        R                  " [        T5       Vs/ s H  n/ S	QPM	     sn6  H  nU[!        S/T-  5      :X  a  M  / n/ n[        T5       Hn  nUU   S:X  a	  X   nX   nO7UU   S:X  a  X   nX   SXe   4nO UU   S:X  a  X   nX   XE   Xu   -
  XE   S-
  4nUR	                  W5        UR	                  W5        Mp     U" UUU5      nM     U$ s  snf s  snf s  snf s  snf s  snf s  snf s  snf s  snf s  snf )
Nr$   r#   rT   r  c                 B    U u  pn[         R                  " X:  X:*  5      $ r7   r  )index_rangerm  lbubs       r/   index_range_condition7_reflection_pad_backward.<locals>.index_range_conditionu  s"    	r  !'22r.   r   r   c           	      J  > [        T	5       H4  nX#   S   X#   S   :  n[        U[        5      (       d  M)  U(       d  M2  U s  $    [        R                  " [
        R                  U Vs/ s H  nT" U5      PM     sn5      n[
        R                  T
UTU-   S5      nX-   $ s  snf )Nr$   r#   r   )rU   r9   r  rM   r   r   r  r  )r   r   index_rangesrm  upper_less_than_lowerrT  r  gr  rP   rn   rW  s           r/   r%  ,_reflection_pad_backward.<locals>.accumulate  s     sA$0OA$69K$K!/66;P;P 
 COP<K";/<P
 %%k4S#Fx Qs   (B 
)rT   r   r#   )r|  r  rU   rw  rs  rj   r  r  r  rM   r   r   r  r  	itertoolsr   r  )rn   r;   r  rq  dhwrm  rP  rQ  r  
view_shapexyzcenterleft_reflectright_reflectrange_cr  r   r%  rW   areaoutsrZ  r   rT  r  rP   rW  s   `                       @@@r/   _reflection_pad_backwardrh  `  s1   
 g,!
C''3$%.
).Qq5.C
)8=c
C
1Aq1-.
LC=B3ZHZQ#'A+.23ZMHG166]S166\

u||AGGAJqxx@EEjQR 
 	#A
3$%.C3 16c
;
1!f|&
F;6;CjAjOcf,jLADI#JOJqQZ,/1CF:JMO
 NSSVZMWAsv/-2BBCZ   eCjQj0<jQD $$[$F
CHD  !!c
#C
1J
#CD5!s##sAAw!|i%jaB"o"vq,/:aA#&"vsv0@'@#&1*MKK,  $l3- E0 Kc *CH2 <AO R& $Ds5   K,K1(K6K;>L  L
L
L
1Lr   r   r   c                \    [         R                  " XUS9n[         R                  " XUS9nX44$ )Nr   )rj   aminrV  )r}   rP   r   rj  rV  s        r/   aminmaxrk    s,     ::dW5D::dW5D:r.   r   c                    [         R                  [        R                  " [        R                  " U 5      SU 5      XUS9$ )Nr   r   )r   r   rj   rk   isnan)r}   rP   r   r   s       r/   nansumrn    s0     88EKKD 11d;SQV8WWr.   r   r-  r  rG  r-  c          
      D    [         R                  R                  SU SXX4S9$ )Nr   r#   ro  r   r  
start_step)rd  r   r-  r  rG  s        r/   arange_defaultrs    s+     ;;!!	3f "  r.   c          
      B    [         R                  R                  XSX#XES9$ )Nr#   ro  rq  )rc  rd  r   r-  r  rG  s         r/   arange_startru    s)     ;;!!AU& "  r.   c                      SSK Jn  U" U 0 UD6$ )Nr   )out_dtype_dense)!torch._higher_order_ops.out_dtyperw  )rG   rH   rw  s      r/   out_dtype_decompry    s    AD+F++r.   marginc                   ^ ^^^	^
 [         R                  " T 5      m [         R                  " T5      mT R                  S   m
T R                  S   m	[         R                  " US:H  =(       d    US:H  S 5        [         R                  " T R
                  S:H  =(       a    T	S:g  U 4S j5        [         R                  " TR
                  S:H  =(       a    TR                  5       T
:H  U
U4S j5        TbY  [         R                  " T5      m[         R                  " TR
                  S:H  =(       a    TR                  5       T	:H  U	U4S j5        TR                  S5      m[         R                  " T STS9nX6-
  T -   nUR                  S5      nUS:X  a  UOXw-  nTb  UTT   -  n[         R                  " T	T R                  S	9n[         R                  " UT:g  US5      nU[        R                  R                  :X  a  UR!                  5       $ U[        R"                  R                  :X  a   UR%                  5       UR                  S   -  $ UR!                  SS
9$ )Nr   r#   r$   c                      g)Nz only p == 1 and p == 2 supportedr%   r%   r.   r/   r   #multi_margin_loss.<locals>.<lambda>  s    +Mr.   c                  "   > ST R                    3$ NzMExpected non-empty vector or matrix with optional 0-dim batch size, but got: r  r  s   r/   r   r}     s    _`e`k`k_lmr.   c                  (   > ST  STR                    3$ )Nz#inconsistent target size, expected r  r  )nframer   s   r/   r   r}    s    5fXYv||nUr.   c                  (   > ST  STR                    3$ )Nz#inconsistent weight size, expected r  r  )rP   r   s   r/   r   r}  
  s    9#i~Vr.   r  r  r   )rj   
atleast_2d
atleast_1dr  r   rw  r   rV   rJ  rY  r  r  rk   r!   r+   r~   r   r,   r   )r   r   rK  rz  r   r   url   r  rP   r  s   ``  `    @@r/   multi_margin_lossr    s    U#Ef%F[[^F
++a.C	LLa!16#MN	LL

a$C1Hm 
LLq5V\\^v5U !!&)KK163!6V	
 a FU0A
UA	AA!VAv
,,s5<<
0CC6M1a(AINN(((vvx	imm))	)uuw##vv!v}r.   	is_targetc                   ^^ U R                   mUR                   m[        R                  " U 5      n [        R                  " U5      nU R                   S   n[        R                  " [	        T5      S:*  =(       a    US:g  U4S j5        [        R                  " [	        T5      S:*  =(       a    TT:H  UU4S j5        [        R
                  " X1R                  S9nUS:H  n[        R                  " [        R                  " XTU5      SSS	9nXF:  n[        R                  " XqS5      n[        R                  " U SUS
9n	[        R                  " XqS5      n
[        R                  " XJR                  SS9:H  SS9nSU	R                  R                  SS9-
  U -   nUR                  S5      nX-  n[        R                  " USU5      nU[        R                  R                   :X  a  UR#                  SS9R%                  5       nO>U[        R&                  R                   :X  a  UR#                  5       nOUR#                  SS9nUR)                  U R*                  5      R-                  T5      nX4$ )Nr#   r$   r   c                     > ST  3$ r  r%   )orig_input_shapes   r/   r   0multilabel_margin_loss_forward.<locals>.<lambda>,  s    _`p_qrr.   c                     > ST ST  3$ )Nzinconsistent target size: z for input of size: r%   )r  orig_target_shapes   r/   r   r  0  s    ,->,??STdSefr.   r  rT   Tr   r  r   rh   )r   rT   )r  rj   r  r   r|  r  r  rj  rk   rJ  anyrV   TrY  r!   r+   r~   r   r   r,   r:   r   r  )r   r   r   rP   r  is_endend_idxtarget_masktidx0r  tidx1r  rl   r  r  s                @@r/   multilabel_margin_loss_forwardr    s    {{U#Ef%F
++a.C	LL"/saxr 
LL!#M(9=M(Mf
 ,,s==
1Cr\FjjV#6BMG-KKKQ/EU%0AKKR0E		#R!88a@Iaccmmm##e+A	AA	AIq!$AINN(((EEgE##%	imm))	)EEGEEgEU[[)112CDI<r.   )	attn_maskrp   querykey	dropout_p	is_causalr  c                  ^ ^^^ [         R                  " [         R                  " T 5      U 4S j5        [         R                  " T R                  5       S:H  =(       a-    TR                  5       S:H  =(       a    TR                  5       S:H  UU U4S j5        [         R                  " TS:H  U4S j5        [         R                  " T R                  S   TR                  S   :H  =(       a    TR                  S   TR                  S   :H  S 5        [
        R                  R                  T TTUTUS US9u  pxUR                  S	S
SS5      R                  [         R                  S9R                  SS	S
S5      nXx4$ )Nc                  "   > ST R                    3$ )Nz-query must be FP32, FP64, BF16, FP16 but got r   )r  s   r/   r   <scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>i  s    ?}Mr.   r;  c                  n   > STR                  5        ST R                  5        STR                  5        3$ )Nz,q, k, v must be a 4 dimensional tensor, got r  r   )r  r  r~   s   r/   r   r  m  s1    >uyy{m2cggi[XZ[`[d[d[fZghr.   r   c                     > ST  3$ )Nz&dropout probability must be zero, got r%   )r  s   r/   r   r  p  s    $J9+"Vr.   r   c                      g)Nz&q, k, v should have the same head sizer%   r%   r.   r/   r   r  t  s    8r.   )r  r  r  dropout_maskrp   r$   r   r#   rQ  )rj   r   rK  rP   r  r   "_scaled_dot_product_attention_mathr  r  r  rV  )	r  r  r~   r  r  r  rp   r  attns	   ````     r/   *scaled_dot_product_flash_attention_for_cpur  \  s:    
LL&M 
LL		q@SWWY!^@		q0@h 
LLSV 
LLA%++a.(KSYYq\U[[^-K8
 ::BB C 	LFD 	q!Q"	%"9"9	:	Aq!	 
 <r.   c                 0   ^ [        U 5      U4S j5       nU$ )Nc                  <   > T" U 0 UD6nU S   R                  U5      $ ru   )r	  )rG   rH   r   outplace_ops      r/   
inplace_op$register_inplace.<locals>.inplace_op  s%    4*6*Aw}}S!!r.   r   )aten_opr  r  s    ` r/   register_inplacer    s"    G$" %" r.   c                 j   U R                  5       (       d+  U R                  5       (       d  [        U5      n[        U5      n[        R                  " X5      n[        U[        R                  5      (       a  US:w  a  XT-  nUS:X  a  U$ [        U[        R                  5      (       a  US:w  a  X-  n X-   $ r!  )rK  r  r  rj   r   r9   numbersNumber)r}   batch1batch2rd   ro   r  s         r/   baddbmmr    s     !!##DOO,=,=4yE
YYv&FeW^^,,
qydGNN++tqy{=r.   c                 ,    [         R                  " XSS9$ )Nr  r  r  )r}   rJ  s     r/   floor_divider    s     99T88r.   c                 b    [         R                  " [        R                  U R                  S5      $ r]   )rM   r   r  r   r  )r  s    r/   	sym_numelr    s    HLL!''155r.   r   r   c                    Uc  [         R                  R                  U / US9$ [         R                  R                  U / XS9$ )Nr   r  )r   r   dim_IntListIntList_out)r}   r   r   s      r/   sum_defaultr    sA     {xx##D"E#::xx##D"E#CCr.   c           	      
   [        U [        R                  5      (       d  U $ Uc@  [        R                  R                  U [        [        U R                  5       5      5      5      $ [        R                  R                  X/5      $ r7   )	r9   rj   r   r   r  dimsro  rU   rP   )r}   rP   s     r/   squeeze_defaultr    s]     dELL))
{||  tE$((*,='>??||  u--r.   c                 .  ^ [        U4S j[        [        U R                  5      5       5       5      nUR                  [
        R                  :X  a  [
        R                  OS nU R                  SUSUS9nXUR                  UR                  5      -  -  U4$ )Nc              3   6   >#    U  H  oT:w  d  M
  Uv   M     g 7fr7   r%   )r  rm  rP   s     r/   r  )_weight_norm_interface.<locals>.<genexpr>  s     @ 31CxQQ 3s   		r$   T)r   r   )
r  rU   r|  r  r   rj   r  r   r   r:   )r.  r\  rP   keep_dim
norm_dtyper   s     `   r/   _weight_norm_interfacer    sr     @c!''l 3@@H !5>> 9tJ66!Xt:6>DDGGAGG$$%t++r.   assume_uniqueinvertc                   [        U [        R                  5      (       d  [        R                  " XR                  S9n [        U[        R                  5      (       d3  U(       a  [        R
                  " X5      $ [        R                  " X5      $ UR                  5       S[        U R                  5       S5      -  :  a
  [        XUS9$ [        XX#S9$ )Nr  g      $@g(\?r  r  )r9   rj   r   ru  r  ner   r   rT  isin_defaultisin_sorting)elementstest_elementsr  r  s       r/   isinr    s     h--<<1E1EFmU\\2288H4488H44tc(..*:E&BBBHFCC=
 	
r.   )rE  c                :   Uc=  [         R                  " U R                  5       [         R                  U R                  S9nO=[         R                  " U R                  5       U[         R                  U R                  S9nX :  R                  U R                  5      nU$ )Nr  )rE  r   r  )rj   randr&  r   r  r:   r   )r}   rE  raw_prK  s       r/   	bernoullir    so     

499;emmDKKP

IIK--;;	
 
$**%AHr.   r  c                H   U R                  5       S:X  a#  [        R                  " U [        R                  S9$ U R                  " / U R
                  QSUR                  -  Q76 n[        [        SUR                  * S-
  S5      5      nX1:H  R                  US9nU(       a  U) $ U$ )Nr   r   )r#   rT   r#   r   )
r   rj   
empty_liker  r  r  rw  r  rU   r  )r  r  r  r;   rP   rN  s         r/   r  r    s    ~~1

;;Dx~~D0B0B)BDA
b=---126
7C
"
"s
"
+CC4"s"r.   c                   U R                  5       nUR                  5       nU(       a  [        R                  " XE/5      n[        R                  " USS9u  pxUSS  US S :H  n	[        R                  " U	SS/S5      n	U(       a  U	R                  5       n	[        R                  " U	5      n
U
R                  SX5      n
U
SU R                  5        $ [        R                  " U5      u  p[        R                  " X5      n[        R                  " XR                  5       :  US5      nX   U:H  nU(       a  UR                  5       OUnUR                  U R                  5      $ )NT)stabler#   rT   r   F)r;  rj   r(  sortrq  logical_notr  r  r   searchsortedrk   r  r  )r  r  r  r  elements_flattest_elements_flatall_elementssorted_elementssorted_orderduplicate_maskr  sorted_test_elementsrW   r  test_idxcmps                   r/   r  r    s/   $$&M&..0 yy-!DE(-

<(M%(,0DD..~1vuM+779N/q,?A())"'**-?"@  !5E;;s%?%?%AA3J",=#)coos{{8>>**r.   c                 ,    U R                  S5      nX!   $ rS   )r  )r}   r  	flatteneds      r/   taker  5  s     R Ir.   c                     Uc  [         R                  nU[         R                  :X  a  [        U5      n[        R                  XR                  US9$ r2  )rj   rV  preserve_formatr   r   resizer  )r}   rJ  rR  s      r/   	resize_asr  <  sB    //----e4;;t[[;FFr.   )F)noner7   )r$   )r   NNr#   )rT   FFr  r  ru  )r#   r#   F)Fr   )r   rh   N)r   r#   Nra  )NNN)r   r   FT)r   r   Fr  )r   F(  rM   r^  r  r  rq  collections.abcr   enumr   r   r   r   r   typingr	   r
   r   r   r   rj   torch._meta_registrationstorch._primsrN  r  torch._prims_common_prims_commonrE   torch.nn.functionalr  r  r   r   r   r   torch._decompr   rx  r   r   r   r   r   r   torch._prims_common.wrappersr   r   r   r   torch.utilsr   rC   torch.utils._pytreer   r.  DispatchKeyr   ro  str__annotations___opsr"  r   r!   rT  r  rO   rU  compute_only_pw_cast_for_opmathpw_cast_for_opmathr$  pw_cast_for_int_to_realr  rX   ra   rc   rm   r   ry   rA  Scalarr   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r   r   r   r   r   r+   r~   r   _safe_softmaxr  r  r  r  rY   r  r  r   r  r#  r0  r9  r<  rB  rE  rG  rI  rM  ra  ri  slicer}  r  rh  r  r  r  r  r  r  r	  r0  r4  r=  rC  rG  py_implCompositeImplicitAutogradAutogradrF  rY  r]  rc  rk  r&  ry  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  unsafe_chunkr#  r  r  no_statsr'  r+  r7  r=  rA  rC  _fused_dropoutrF  rS  r  rR  r  lift
lift_freshrV  r[  r^  ra  r`  ru  rz  r}  _adaptive_avg_pool2dr  r  r  r  r  r  r  r  r  r  r  r  r  	Generatorr  r,  r/  rE  r  rL  rR  r5  _upsample_nearest_exact1drN  rT  r:  r@  rG  r2  r_  rh  rl  rp  r~  r  r  r  r  r  rnn_tanhr   r  rnn_relur  r  r  r  r  r  r  r  lstmr  r  r  r  grur  r  r  r  r  r  r  r  r   r  r  r
  r  r  r  r3  r5  r  rW  r'  r  rH  rN  rQ  rS  rW  rZ  r`  rh  r  ro  rz  r}  r  r  r  r  r  r  r  r  rW  upsample_bicubic2dr4  r:  reflection_pad1dreflection_pad2dreflection_pad3drD  replication_pad1dreplication_pad2dreplication_pad3drH  rB  reflection_pad1d_backwardreflection_pad2d_backwardreflection_pad3d_backwardrh  rk  rn  r  rK  r-  rs  rc  ru  ry  r  r  +_scaled_dot_product_flash_attention_for_cpur  r  r  r  r  r   r  r  rP   r  r  r  r  r  r  r  r  addbmm_addbmmaddmm_addmv_baddbmm_fill_gelu_r  
hardswish_	hardtanh_hardtanhhardsigmoid___iand____and____ilshift__
__lshift__r  r  index_reduce_index_reduce__ior____or____irshift__
__rshift____ixor____xor__leaky_relu_
leaky_relulogit_logitrelu_r  renorm_renormround_r&  scatter_r  scatter_add_scatter_addscatter_reduce_scatter_reducesilu_r%   r.   r/   <module>r@     sM       
 $  % $ 7 7     #   , , 0 7   * ( hh"" c zz~~   %!!99! !H #*88@@# 
 uDDLL  "uDDQQ  c f  **+\2F 2v 2   ,2 --.\4v 4& 4   /4 ../\S S6 S S5 S   0S
 ))*\


 
 	

 
 
   +
2 ))*+( ,( ))*+"V " ," (()@f @ @   *@ 112\f F    3 ../\PP%P05P@EP  0P 'GF Gv G   (G //0F & V    1 //0\:F :& :U :  1: 001\LL%L7<LNRL   2L **+\) )f )3 )   ,)< **+5v 5f 5  ,5 		"&v && &   #& **+\>v >V > >   ,>
 **+6 6 66 6 ,6 334%%
% % 66>	% 5% 667



 
 	

 
 
 
 
   8
$ 112\<f <F <F <v <   3<v #   &3<>>3G3G1
1 1-011   '1 ../\11 &1061CF1   01 **+0 ,0 ++, ^^))	1
11 1 	1   -1 44<<=%/5BEMR  > 44??@
R
R

R 
R 	
R
 
R 
R  A
R 00889		%	/5	BE	NS	  :	 00445
R
R

R 
R 	
R
 
R 
R  6
R$$
$ $ V	$
 $ $ $ $@ ))*\Nf NF N N N   +N$ ../\''
' ' V	'
 ' ' ' '  0'T 001\
  V	
      2B 112  $^^))	1
11 V1 	1
 1   31& ::;\
  $^^))
  V	
     <  --. ^^))111 1 	1   /1 667\
 ^^))			
	 	 		
 	   8	 		") )v )% )  #) ,,-& &F &v &  .& ++,	O	Oc	O 
	O 		O
 
	O 	O  -	O 

))* 6?
6? 
6? C=	6?
 
#6? 6? +6?r (4<SM
38_. **+ $U$U	$U 
$U C=	$U
 
#$U $U  ,$UN ,,-E Ed3i Ec ERU E  .E
 ../OO&*3iO9<ODGOORO  0O%+:?++ 334\ XX!'X.1X@EX !  5X 778 KK!'K.1K@EK !  9K*& $MMcM 3iM #Y	M
 IM M  %M` $]]c] c] 3i	]
 #Y] I] ]   %]@ 445
 
v 
e 
  6
 ,,-Y
Y"3iY47Y?BYJMYY  .Y" ++334>B

%
,4UO

  5
& %kCCDk2236 e HTN  4 E & ++,VVA& AU A8D> A  -A & S    '* ))*F  T   +, ' $  	
    (& 556  	
   7:DI &\	  
&\	*T&\ 
tF| 
# 
"&\"	" "J 00$//2E2EFG
 !	&\	  
&		
  H  	'')C)C)G)GH "&	
c 
 
$v,		
 d6l  ))0015 5C 5c 5%PSBT 5 25 44<<=67BB $S	B03B
63;B >B 

))*/ /C /c /%:L / +/" --55)) /
/ &/ 
/ 63;	//@ 

# f F # #    $" ../
 

  	
     0" 

#	 	f 	6 	 	 	   $	 77??@S&S&S& S& 	S&
 FS& S& S& 
S& S& dS& 8FXf-x/??@S&  AS&n 77;;<  	
 F   
  d ,, ,, ,, 8FXf-x/??@ =88F# x/?  77??@NNN 3iN 	N
 N VN 6
N dN 8FXf-x/??@N ANd 77;;< 3i 	
  V 6
 d ,, ,, ,, 8FXf-x/??@ =4OOVO 6
O 6"	O
 &!O O O 
O O 6668F#3Xf5EEFOd ../UK/((V( 6
( 6"	(
 &!( ( ( 
( 666!"( 0 0(4 ''(<(<=''(M(MN 
 
V 
 6
 
 6"	 

 &! 
  
  
 
 
 666!" 
 O > 
F "";#H#HIG4< G JG AAIIJV 6
 	
   
 666!" K* 55==>((V( 6
( 	(
 ( ( ( 
( 666!"( ?(  55>>?((V( 6
( 	(
 ( 
( 666!"( @( @@HHIKKVK 6
K 	K
 K K K 
K 6666612K JK0V 6
 	
  
  : 44<<=11V1 6
1 	1
 1 1 
1 6666)*1 >14 ??GGHCCVC 6
C 	C
 C C 
C 6666669:C IC4 22::;11V1 6
1 	1
 1 1 
1 6666)*1 <14 ++,VV   - & $(%)37&VZ & EKK &
 U\\"& & & E//0&  '&X diiAB  C &&{';';<--.VVVV, 6
 6"	
 &!  !&  - / => 00889 V 6"	
 &!  &!  
 d  68F#Xf%556 :6 77??@ddd Vd 6"	d
 &!d d &!d d 
d dd 68F#Xf%556d AdP 77;;<""" V" 6"	"
 &!" " &!" " 
" d" ,," ,," ,," 68F#Xf%556" ="J 778VVV$  6"	
 &!  v  % 90 667VVV$  6"	
 &!  v   % 82 112c'v c'E#s(O c'   3c'L
)8<S	HK0 ))**8
*8*8 c*8  +*8Z ))*494949 c49 I	49
 #Y49  +49n ( HH	H H 	H H )H ' II	I I 	I I  (I$ %@%@	%@ %@ 	%@ %@ %@P ))112"";#H#HI J 32 (()<: <C <
 <J < *< (=* =3 =z =: =  )=@@@$.@8B@PT@, 001Xx (f (vv~)> (  ! 2( % $'$'+/		tS%	  c5 
! (	  &  &; ';
8 //334//334//334$$[%J%JK$$[%9%9:$$[%J%JK$$[%9%9:$$[%J%JK$$[%9%9:	3	3$s)$	3 DK(	3 		3 ; L ; L ; L 5 5 5	3 66::;66::;66::;##++K,Q,QR##++K,@,@A##++K,Q,QR##++K,@,@A##++K,Q,QR##++K,@,@A	?	?$s)$	? DK(	? 		? B S B S B S < < <	?@ 0088$:Q:Q:U:UVW  (()N)NO  (()=)=>Dd; #;;c; UO; 	; < ? P X; 	##++T-K-K-O-OP ''//0U0UV''//0D0DEDd; #GGcG UOG 	G < F WG 0088$:Q:Q:U:UVW  (()N)NO  (()=)=>Dd; !% $	GGcG uoG uo	G
 G < ? P XG 	##++T-K-K-O-OP ''//0U0UV''//0D0DEDd; !% $	SScS uoS uo	S
 S < F WS 0088$:Q:Q:U:UVW  (()N)NO  (()=)=>Dd; !% $ $QQcQ uoQ uo	Q
 uoQ Q < ? P XQ 	##++T-K-K-O-OP ''//0U0UV''//0D0DEDd; !% $ $		c	 uo	 uo		
 uo	 	 < F W	 
 	c %! 	
  4 >/ FK+\&,/-d& R ++,[BBC[112. 3 D -.8 ++,[BBC[112. 3 D -.8 **+KAABK001. 2 C ,.@ **+KAABK001. 2 C ,.@/6=@/d 		(>>?--.S / @ )S> 		'==>,,-S . ? (S<;; &{<<={++,. - > '.6 '==>,,-. . ? (.6 44889!!))+*O*OP!!))+*>*>? @ Q : 33778  (()N)NO  (()=)=> ? P 9 0044511556##K$I$IJ##K$8$89%%k&K&KL%%k&:&:;&&{'L'LM&&{';';<A = N < M : K 7 6A //779O9O9S9STU
 !%	KKcK K uo	K
 K  VK 	%%t'?'?'C'CD !!))+*>*>?
 !% $UUcU U uo	U
 uoU U  @
U 	&&(A(A(E(EF 
 !% $ $

c
 
 uo	

 uo
 uo
 
 
V/7	&	7$,V$47IO77-'9 -f - EEcE E %!	E
 E ER ))112F v $  3 ,,d.?.?@A  B ++,-" ." //019 29 2234C 5C6 AABCM DM22 
2 2  V2  	2 
 2  66>2 j --.X~&L
LL VL 	L
 L 66>L ' /L6 //0X~&L
LL VL 	L
 L 66>L ' 1L/F /u / /5F 5u 5 5
 
3E 
(F%7 FV F F!Xf% !& !NN#'N05NEJ\\N&f & & &T &"/f / / / /T /"!V !49 !T !$V $49 $T $ 223S StCy S S   4S  c4c4
c4 c4 	c4
 c4 c4 c4L ,,-  
  	
     .   	#   !	# ==>$)..:N:N1  ?1  d t B [BBC>>?', tW  @ DtWn 0088$:Q:Q:U:UVW  (()=)=>
  $#PPsCxP P e_	P
 e_P P   ? XPf //334$$[%J%JK$$[%9%9:
 48	WW%S/*W W E%,/0	W
 W   ; L 5
W. --.--.--.	v 	c3h 	F 	   / / /
	 ../../../	 	sCx 	V 	   0 0 0
	38_ c3_f,- 	8 667667667\T  8 8 8Tn %UEu   & $X4 X  %X ,,dkkoo>? $( ==%)
	
 EKK 
 LL	

 U\\"
 
  @
 **+,
 $( ==%)	 EKK 	
 LL U\\"  - 	", #, ../''(<(<= #^^))))) ) 	)
 V) ) )  > 0)X ;;<$$,,44[5I5IJX{#--- - 66>	- $ K =-x HHPPQ
 @ #'!@@	@ @ 	@
 @ @ E?@ 66>@ R@F '   ( ))*9  +9 '6 (6 ))488<<89 $( 		D
	D EKK 	D 
&			D
 	D :	D --t||/?/?@A.& .x} . B. 		==>, ?, 		"38 
  #
$ ../ ,0
,, ( \\	 0$ 5: # # <A + +: 		"  #
 'G (G t{{ + djj ) djj )  - TYY ' TYY ' $.. 1  / ""D$4$4 5  - !!4?? 3 $.. 1 ##T%6%6 7 t{{ + !!4?? 3  - !!4?? 3 djj ) TYY ' t{{ + djj )  - ""D$4$4 5 %%t':': ; TYY 'r.   