
    #Ki             !       v   % 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J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  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$J%r%  S S
K&J'r'  S SKJ(r(J)r)J*r*J+r+J,r,  S SK-J.r.J/r/J0r0J1r1  S SK2J3r4  S SK5J6r6  \Rn                  Rp                  r8/ r9\:\;   \<S'   \Rz                  R|                  R~                  r? " S S\5      r@  GSS\S\R                  S\BS\B4S jjrC\" \C\R                  R                  SS9rE\" \C\R                  R                  S9rF\" \C\R                  R                  SS9rG\" \C\R                  R                  S9rIS\#S\JS\#4S jrK\%" \?R                  5      \1" S 5      \FS!\#S"\#4S# j5       5       5       rL\%" \?R                  5      \1" S 5      \FS!\#S"\#4S$ j5       5       5       rM\%" \?R                  5      \1" S 5      \FS!\#S\#S%\OS&\O4S' j5       5       5       rN\%" \?R                  5      \1" S 5      \FS(\#S)\OS*\OS+\OS,\BS-\#4S. j5       5       5       rP\%" \?R                  R                  /5      S/ 5       rS\%" \?R                  RF                  /5      S0\#4S1 j5       rT\%" \?R                  5      \1" 5       \FS2\#S\#4S3 j5       5       5       rU\%" \?R                  5      \1" S 5      \FS(\#S2\#4S4 j5       5       5       rV\%" \?R                  5      \1" S 5      S(\#S2\#S5\OS6\O4S7 j5       5       rW\%" \?R                  5      \1" 5       \FS2\#S\#4S8 j5       5       5       rX\%" \?R                  5      \1" 5       \FS(\#S2\#S\#4S9 j5       5       5       rY\%" \?R                  5      \1" S 5      S(\#S2\#S&\O4S: j5       5       rZ\%" \?R                  5      \1" S 5      \FS(\#S2\#S;\OS<\B4S= j5       5       5       r[\%" \?R                  5      \1" S 5      \FGSS>\#S2\#S?\;4S@ jj5       5       5       r\\%" \?R                  5      \FS(\#SA\#4SB j5       5       r]\%" \?R                  5      \1" 5       \FS2\#S\#4SC j5       5       5       r^\%" \?R                  5      \1" S 5      \FS(\#S2\#S\#4SD j5       5       5       r_\%" \?R                  5      S2\#SE\#S\#4SF j5       r`\%" \?R                  5      S(\#S2\#SE\#S\b\#\#4   4SG j5       ra\%" \?R                  5      \1" 5       \FS(\#S2\#SH\#SI\OSJ\OSK\BS<\BS\#4SL j5       5       5       rc\%" \?R                  5      \1" S 5      \FS(\#S2\#SM\#S\#4SN j5       5       5       rdSO\#SP\J4SQ jreSR\R                  4SS jrg\%" \?R                  5      \1" 5       \F\@R                  R                  4S2\#ST\#SP\JS\#4SU jj5       5       5       rh\%" \?R                  5      \1" S 5      \FS(\#SA\#ST\#SP\J4SV j5       5       5       rk\%" \?R                  5      GSSW j5       rm\%" \?R                  5      \1" 5       \F\@R                  R                  SX4S2\#ST\#SP\JS%\O4SY jj5       5       5       rn\%" \?R                  R                  5      \FS(\#S2\#ST\#SP\JS%\O4
SZ j5       5       ro\%" \?R                  R                  5      \FS(\#S2\#ST\#SP\JS%\OS \#4S[ j5       5       rr\%" \?R                  R                  5      \FS(\#S2\#ST\#SP\JS\\O4
S] j5       5       rs\%" \?R                  R                  5      \FS(\#S2\#ST\#SP\JS\\OS \#4S^ j5       5       ruS(\#S2\#ST\#SE\\#   SP\JS_\JS`\#S\#4Sa jrv\%" \?R                  5      \1" S 5      \FS(\#S2\#S\JS\#4Sb j5       5       5       rw\%" \?R                  5      \1" S 5      S(\#S2\#ST\#SE\\#   SP\JS_\JS`\#S\#4Sc j5       5       rx\%" \?R                  5      \1" S 5      S(\#S2\#ST\#SE\\#   SP\JS_\JS`\#S\#4Sd j5       5       ry\%" \?R                  5      \1" 5       \FS\@R                  R                  4S2\#ST\#SE\\#   SP\JS\#4
Se jj5       5       5       rz\%" \?R                  5      \1" S 5      \FS\@R                  R                  4S(\#S2\#ST\#SE\\#   SP\JS\#4Sf jj5       5       5       r{\%" \?R                  5      \1" 5       \F\@R                  R                  4SA\#ST\#SP\JS\#4Sg jj5       5       5       r|\%" \?R                  5      \1" S 5      \F\@R                  R                  4S(\#S2\#ST\#SP\JS\#4
Sh jj5       5       5       r}\%" \?R                  5      \1" 5       GSSA\#Si\#Sj\O4Sk jj5       5       r~\%" \?R                  5      \1" 5       Sl\#Sm\#S\#4Sn j5       5       r\%" \?GR                   5      \1" 5       S(\#So\:\J   S\JSp\JSq\JSr\J4Ss j5       5       r\%" \?GR                  RF                  5          GSS2\#S\JSp\\J   Sq\\J   Sr\J4
Su jj5       rS\#S\JSp\\J   Sq\\J   S\b\J\J4   4
Sv jr\%" \?GR                  5      \1" 5           GSSA\#Sw\#S\JSp\\J   Sq\\J   Sr\J4Sx jj5       5       r\%" \?GR
                  5      \1" 5       S(\#So\:\J   S\JSy\J4Sz j5       5       r\%" \?GR                  5      \1" 5       S(\#So\:\J   S{\JS|\JS}\J4
S~ j5       5       rS(\#S \#S\R                  4S jr\%" \?GR                  5      \1" S 5      \ES(\#S\#S\JS\R                  4S j5       5       5       r\%" \?GR                  5      \1" 5       \ES(\#S\#S\JS\R                  4S j5       5       5       rS r\%" \?GR                  5      \1" 5       SA\#S\:\J   S\:\J   S\:\J   S\:\J   S\#4S j5       5       r\%" \?GR                  5      \1" 5       \FSA\#S\:\J   S\:\J   S\:\J   S\:\J   S\:\J   S\#4S j5       5       5       r\%" \?GR                  5      \1" 5       S(\#S\#S*\O4S j5       5       r\%" \?GR                  5      \1" 5       S>\#S\:\J   S\JS\JSr\JS\#4S j5       5       r\%" \?GR                  R                  5      \F GSS(\#S2\#S\\O   S\#4S jj5       5       r\%" \?GR                   5      \?GR                   R                  GR#                  \8GR$                  5      \?GR                   R                  GR#                  \8GR&                  5      SA\#Sj\OS\\B   4S j5       5       5       r\%" \?GR(                  5      \1" SS5      SA\#Sj\OS\\B   4S j5       5       r\%" \?GR*                  5      \1" 5       S\#S\JS\B4S j5       5       r\%" \?GR,                  5      \1" SS9S\#S\JS\B4S j5       5       r\%" \?GR.                  5      \1" 5          GSSE\#S\#S\JS\BS\BS\#4S jj5       5       r\%" \?GR0                  5      \1" 5       S(\#S\#S\JS\JS\B4
S j5       5       rS\:\J   4S jrS\:\#   S\JS\JS\:\#   4S jrS\:\#   4S jrS\:\#   S\J4S jrS\:\#   S\JS\J4S jr\%" \?GR<                  R                  \?GR<                  R                  /5       GSS\:\#   S\JS\JS\\#   S\#4
S jj5       r\%" \?GR>                  R                  \?GR>                  R                  /5        GSS2\#S\:\J   S\JS\\:\#      S\\:\#      4
S jj5       r\%" \?GR@                  RF                  5      GSSA\#S\JS\JS\b\#S4   4S jj5       r\%" \?GRB                  R                  5       GSSA\#S\:\J   S\JS\b\#S4   4S jj5       r\%" \?GRD                  RF                  5      GSS2\#S\JS\JS\b\#S4   4S jj5       r\?GRF                  GRH                  GR#                  \8GR$                  5       GSS2\#S\#S\JS\b\#S4   4S jj5       r\%" \?GRL                  5      \1" SS9\FGSS2\#S\#S\#S%\JS)\J4
S jj5       5       5       r\%" \?GRN                  5      \1" 5       \F   GSS2\#S\#S\#S%\JS)\JS\B4S jj5       5       5       r\%" \?GRP                  5      \1" SS9\FGSS2\#S\#S\#S%\JS)\J4
S jj5       5       5       r\%" \?GRR                  R                  5      \FS(\#SA\#S\#S\#S\\#   S\JS\JS\JS\JS\:\B   S\b\\#   \\#   \\#   4   4S j5       5       r\%" \?GRR                  R                  5      S(\#SA\#S\#S\#S\\#   S\JS\JS\JS\JS\:\B   S\RF                  S\RF                  S\RF                  S\b\\#   \\#   \\#   4   4S j5       rS\\#   S\\#   4S jr\%" \?GRX                  R                  5      S\#SA\#S\:\J   S\#S\#SE\\#   S\\#   S\:\B   S\b\\#   \\#   \\#   4   4S j5       r\%" \?GRX                  R                  5      S\#SA\#S\:\J   S\#S\#SE\\#   S\\#   S\:\B   S\RF                  S\RF                  S\RF                  S\b\\#   \\#   \\#   4   4S j5       r\%" \?GR\                  R                  5      SA\#S\:\J   SE\\#   S\\O   S\b\#\#4   4
S j5       r\%" \?GR^                  R                  5      S\#SA\#S\:\J   S\#SE\\#   S\:\B   S\b\\#   \\#   4   4S j5       rSA\#SE\\#   S\\#   S\\#   S\\#   SK\BS\OS\OS\BS\b\#\#\#\\#   \\#   4   4S jr\%" \?GRb                  5      \1" SSS5      SA\#SE\\#   S\\#   S\\#   S\\#   SK\BS\OS\OS\b\#\#\#4   4S j5       5       r\?GRb                  R                  GR#                  \8GR&                  5      \?GRb                  R                  GR#                  \8GR$                  5      SA\#SE\\#   S\\#   S\\#   S\\#   SK\BS\OS\OS\b\#\#\#4   4S j5       5       r\?GRf                  R                  GR#                  \8GR$                  5      GSS\:\#   4S jj5       r\%" \?GRj                  R                  5      SA\#SE\\#   S\\#   S\#S\#S\OS\OS\b\#\#\#4   4S j5       r\%" \?GRl                  R                  5      SA\#SE\\#   S\\#   S\#S\#SK\BS\OS\OS\b\#\#\#4   4S j5       r\%" \?GRl                  GRn                  5      SA\#SE\\#   S\\#   SK\BS\OS\OS\b\#\#\#4   4S j5       r\%" \?GRr                  R                  5      SA\#SE\\#   S\\#   S\#S\#SK\BS\OS\OS\b\#\#\#\#\#4   4S j5       rSA\#SE\\#   S\\#   S\#S\#S\OSK\BS\#4S jr\%" \?GRv                  R                  5      SA\#SE\\#   S\\#   S\#S\#S\OS\OS\b\#\#\#\#4   4S j5       r\%" \?GRx                  R                  5      SA\#SE\\#   S\\#   S\#S\#S\OS\OS\b\#\#\#\#\#\#4   4S j5       r\%" \?GRz                  R                  5      SA\#SE\\#   S\\#   S\#S\#S\OS\OS\b\#\#\#\#4   4S j5       r\%" \?GR|                  5      \1" SS5      \FGSS j5       5       5       r\%" \?GR                  5      \1" 5       SSSSSSS.S\\#\)4   SR\\R                     S\\GR                     S\BS\BS\\GR                     4S jj5       5       r\%" \?GR                  \?GR                  \?GR                  /5      \1" 5       S 5       5       r\?GR                  R                  GR#                  \8GR&                  5      \%" \?GR                  5      \1" SSSS5      SA\#SE\#S\\#   S\\#   S\\#   SK\BS\OS\O4S j5       5       5       rS r\%" \?GR                  R                  5      S\#SA\#SE\\#   S\\#   S\\#   S\\#   S\\#   S\BS\OS\:\B   S\#S\b\#\\#   \\#   4   4S j5       r\%" \?GR                  R                  5      S\#SA\#SE\\#   S\\#   S\\#   S\\#   S\\#   S\BS\OS\:\B   S\b\#\\#   \\#   4   4S j5       r\%" \?GR                  R                  5      S\#SA\#SE\\#   S\\#   S\\#   S\\#   S\\#   S\BS\OS\:\B   S\RF                  S\RF                  S\RF                  S\b\#\\#   \\#   4   4S j5       r\%" \?GR                  5      \1" SSS5      SA\#S(\#SE\#S\\#   S\\#   S\\#   S\\#   S\O4S j5       5       r\%" \?GR                  5      \1" SSS5      SA\#S(\#SE\#S\\#   S\\#   S\\#   S\\#   S\OS\#4S j5       5       r\%" \?GR                  5      \1" 5       \FSA\#S\b\J\J4   4S j5       5       5       rS2\+S\+S\:\J   S\J4S jr\%" \?GR                  5      \1" 5       S2\+S\+S\:\J   4S j5       5       r\%" \?GR                  5      \1" 5       SA\+S\+S\:\J   S\:\J   S\:\J   4
S j5       5       r\%" \?GR                  5      StS.S\+S\JSy\+S\+S)\)4
S jj5       r\%" \?GR                  5      \1" 5       StS.S\+S\JSy\+S\+S)\)4
S jj5       5       rStS.S\+S\JSy\+S\+S\BS)\)4GS  jjr\%" \?GR                  R                  5      \?GR                  R                  GR#                  \8GR$                  5      GSGS j5       5       r\%" \?GR                  5      S\+S\JSy\+S\+4GS j5       r\%" \?GR                  5      \1" 5       S\+S\JSy\+S\+4GS j5       5       rS\+S\JSy\+S\+S\B4
GS jr\%" \?GR                  5      \1" SSM5      \FS2\#S\b\#\#4   4GS j5       5       5       r\%" \?GR                  5      \1" 5          GSS\#GS\\B\J\O4   GS\\B\J\O4   GS\\GR                     4GS	 jj5       5       r\%" \?GR                  5      GSGS
 j5       rGS rGS r\%" \?GR                  GR                  5      \%" \?GR                  GR                  5      \%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      SA\#S\\:\J      GS\\:\O      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#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      SA\#S\\:\J      GS\\:\O      S\#4GS j5       5       5       5       5       5       5       5       5       rGSGS jr\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9 GSSA\#S\:\J   GS\\O   S\#4GS jj5       5       5       5       r\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9 GSSA\#S\:\J   GS\\O   S\#4GS jj5       5       5       5       r\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9  GSSA\#S\:\J   GS\\O   GS\\O   S\#4
GS jj5       5       5       5       r\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9  GSSA\#S\:\J   GS\\O   GS\\O   S\#4
GS jj5       5       5       5       r\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9   GSSA\#S\:\J   GS\\O   GS\\O   GS\\O   S\#4GS jj5       5       5       5       r\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR$                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SSGS9   GSSA\#S\:\J   GS\\O   GS\\O   GS\\O   S\#4GS jj5       5       5       5       r\F GSSA\#S\:\J   GS\:\\O      GS\BS\#4
GS jj5       rGS rGS rGS  rGS! r GSGS" jrGS# rGS$ rGSGS% jrGSGS& jrGS' r\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS( 5       5       5       r\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS) 5       5       5       r\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS* 5       5       5       r\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS+ 5       5       5       rGS, rGSGS- jrGSGS. jGr GS/ Gr\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS0 5       5       5       Gr\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS1 5       5       5       GrGS2 GrGS3 Gr\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS4 5       5       5       Gr\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS5 5       5       5       Gr	\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS6 5       5       5       Gr\%" \?GR                  GR                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS7 5       5       5       Gr\%" \?GR                  GR                  5      \%" \?GR                  GR                  5      \?GR                   GR                  GR#                  \8GR$                  5      \?GR                   GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      \?GR                  GR                  GR#                  \8GR$                  5      \?GR                  GR                  GR#                  \8GR&                  5      GS8 5       5       5       5       5       5       5       5       Gr\%" \?GR                   R                  \?GR                   R                  /5      \1" 5        GSSA\#S\:\J   GS9\BGS\\O   S\#4
GS: jj5       5       Gr\%" \?GR                  R                  \?GR                  R                  /5      \?GR                  R                  GR#                  \8GR&                  5      \1" 5         GSSA\#S\:\J   GS9\BGS\\O   GS\\O   S\#4GS; jj5       5       5       Gr\%" \?GR                  R                  \?GR                  R                  /5      \1" 5          GSSA\#S\:\J   GS9\BGS\\O   GS\\O   GS\\O   S\#4GS< jj5       5       GrGSGS= jGrGS> GrSw\\#   GS?\\#   GS@\#S\#4GSA jGrGS?\,S\#4GSB jGr\FSA\#S\:\J   GS9\BGS\:\\O      S\#4
GSC j5       Gr\%" \?GR.                  R                  5      GSD\#GSE\#S\B4GSF j5       Gr\%" \?GR0                  \?GR2                  /5      \1" 5       GSG 5       5       Gr\%" \?GR4                  /5      GSH 5       Gr\%" \?GR6                  /5      GSGSI j5       Gr\%" \?GR8                  /5      GSJ 5       Gr\%" \?GR:                  /5      GSK 5       GrS2\#ST\#SE\\#   SP\JS_\JS\b\#\#4   4GSL jGr\%" \?GR>                  5      \1" SS`5      S2\#ST\#SE\\#   SP\JS_\JS\b\#\#4   4GSM j5       5       Gr\%" \?GR@                  5      \1" SS`5      S2\#ST\#SE\\#   SP\JS_\JS\b\#\#4   4GSN j5       5       Gr S\#GSO\OS\#4GSP jGr!S\#GSO\OS\#4GSQ jGr"GSR\#S\,4GSS jGr#GST\,GSU\#S\#4GSV jGr$GSU\\#   S\#4GSW jGr%GSX\JGS9\BSR\R                  S\GR                  4GSY jGr&GSZ\#GS[\JGS\\JGS9\B4GS] jGr'GSZ\#GS^\JGS[\JGS\\JGS9\B4
GS_ jGr(GSZ\#S\:\J   GS9\B4GS` jGr)GSZ\#S\:\J   GS9\B4GSa jGr*\%" \?GRV                  5      \1" 5       \FGSZ\#S\:\J   GS9\B4GSb j5       5       5       Gr+    GSGSD\#GSc\#GSd\JGSe\JGS9\BGSf\BS\#4GSg jjGr,\%" \?GRZ                  5      \1" 5       \F   GSGSD\#GSc\#GSd\JGSe\JGS9\BS\#4GSh jj5       5       5       Gr-\%" \?GR\                  5      \1" SS9\FGSi 5       5       5       Gr.\%" \?GR^                  5      \1" 5       SS\@R                  R                  4GSj j5       5       Gr/GSk\RF                  GSl\RF                  GSm\BS\B4GSn jGr0\?GRb                  R                  GR#                  \8GR$                  5      \?GRb                  R                  GR#                  \8GR$                  5      \1" SGSo9SGSp.GSq j5       5       5       Gr1\%" \?GRd                  R                  \?GRd                  R                  /5      \?GRd                  R                  GR#                  \8GR&                  5      \1" 5       \F  GSSA\#S\b\J\J4   GS9\BGSr\\O   GSs\\O   S\#4GSt jj5       5       5       5       Gr3\%" \?GRd                  GR                  5      \?GRd                  GR                  GR#                  \8GR$                  5      \?GRd                  GR                  GR#                  \8GR&                  5      \1" 5       \F GSGSD\#S\\b\J\J4      GS9\BGS\\b\O\O4      S\#4
GSu jj5       5       5       5       5       Gr4\%" \?GRj                  5      \%" \?GRl                  5      \%" \?GRn                  5      \F\1" 5       GSD\#S\b\JS4   S\#4GSv j5       5       5       5       5       Gr8\%" \?GRr                  5      \%" \?GRt                  5      \%" \?GRv                  5      \F\1" 5       GSD\#S\b\JS4   S\#4GSw j5       5       5       5       5       Gr<GSD\#S\b\JS4   GSx\\J\J\J/\#4   S\#4GSy jGr=\%" \?GR|                  5      \%" \?GR~                  5      \%" \?GR                  5      \1" S 5      GSz 5       5       5       5       GrA\%" \?GR                  5      \1" GS{GS|5      SSGS}.GS~ j5       5       GrB\%" \?GR                  5      \1" 5       GSSGS.GS jj5       5       GrC\%" \?GR                  R                  \?GR                  R                  /5      \1" 5       S\GR                  SSGS.Sq\)SR\\R                     GS\GR                  S\\GR                     S\B4
GS jj5       5       GrG\%" \?GR                  GR                  /5      S\GR                  SSGS.Sp\)Sq\)SR\\R                     GS\GR                  S\\GR                     S\B4GS jj5       GrI\%" \'5      GS 5       GrJ\%" \?GR                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" 5       StStS\@R                  R                  4SA\#ST\#Sj\)GS\)SE\\#   SP\JS\#4GS jj5       5       5       GrK\%" \?GR                  5      \?GR                  R                  GR#                  \8GR&                  5      \1" SGS5      SA\#ST\#SP\JS\b\#\#4   4GS j5       5       5       GrL\%" \?GR                  R                  5        GSSSGS.GS\#GS\#S0\#GS\OGS\BGS\\#   S*\\O   S\b\#\#4   4GS jjj5       GrNGS GrO\%" \?GR                  /5      \1" SS9\FGSGS j5       5       5       GrP\%" \?GR                  5      \1" 5       GS 5       5       GrQ\%" \?GR                  5      GS 5       GrR\%" \?GR                  R                  \?GR                  R                  /5      SSGS.S2\#SR\\R                     S\\#   S\#4GS jj5       GrT\%" \?GR                  R                  \?GR                  GR                  /5      GSS2\#S\\J   4GS jj5       GrW\%" \R|                  R~                  GR                  5      GSGS j5       GrX\%" \?GR                  5      \1" 5       SSGS.GS j5       5       GrY\%" \?GR                  R                  5      SGS.S2\RF                  GS\\GR                     S\RF                  4GS jj5       GrZSGS.GS jGr[SSGS.GS jGr\\%" \?GR                  5      \1" 5       GS 5       5       Gr]\%" \?GR                  5      GSGS j5       Gr^G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GRL                  5        G\O" \?GR                  \?GRP                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?R                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?R                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?R                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                   5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR
                  \?GR                  5        G\O" \?GR                  \?GR                  5        G\O" \?GR                  \?R                  5        g(      N)CallableIterable)nullcontext)Enum)partialreduce)chainproduct)Any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)	Reduction1   r          N)__name__
__module____qualname____firstlineno__NONEMEANSUM__static_attributes__r&       ^/var/www/html/dynamic-report/venv/lib/python3.13/site-packages/torch/_decomp/decompositions.pyr"   r"   1   s    DD
Cr/   r"   Fftype_promotioncompute_dtype_onlyinclude_non_tensor_argsc                 R   ^ ^^^ [         R                  " T 5      UU UU4S j5       nU$ )Nc                    >^^	 T(       a   [         [        R                  R                  4O[         4n[        R
                  " U 0 UD6 Vs/ s H  n[        X25      (       d  M  UPM     nn[        R                  " UST06u  mm	U4S jnU	4S jnT" [        XP5      0 [        XQ5      D6nT
(       a  U$ [        Xg5      $ s  snf )Ntype_promotion_kindc                 T   > [        U [        5      (       a  U R                  T5      $ U $ N
isinstancer   to)xcomputation_dtypes    r0   increase_prec0type_casts.<locals>.inner.<locals>.increase_precO   s%    !V$$tt-..r/   c                 T   > [        U [        5      (       a  U R                  T5      $ U $ r9   r:   )r=   result_dtypes    r0   decrease_prec0type_casts.<locals>.inner.<locals>.decrease_precU   s$    !V$$ttL))r/   )
r   torchtypes_Numberpytreearg_tree_leavesr;   utilselementwise_dtypesr   )argskwargsallowed_typesr=   	flat_argsr?   rC   rr>   rB   r3   r1   r4   r2   s           @@r0   innertype_casts.<locals>.inner@   s     .EVU[[(()6) 	
 ++T<V<
<!+ < 	 

 +0*B*B+
,:+
'<
		 x,P0OPHM--5
s   
B="B=)	functoolswraps)r1   r2   r3   r4   rQ   s   ```` r0   
type_castsrU   :   s(     __Q. .@ Lr/   T)r2   r3   )r2   )r2   r4   r=   dimreturnc                 l    [        XR                  5       -
  5       H  nU R                  S5      n M     U $ N)rangerV   	unsqueeze)r=   rV   _s      r0   _unsqueeze_to_dimr^   w   s+    3=!KKO "Hr/   
grad_inputout_gradyc                 2    U SX-  -
  R                  5       -  $ Nr$   conj_physicalr`   ra   s     r0   tanh_backwardrg   }   s     q15y//111r/   c                 2    XSU-
  -  R                  5       -  $ rc   rd   rf   s     r0   sigmoid_backwardri      s     AE{11333r/   beta	thresholdc                 p    X-  R                  5       n[        R                  " X-  U:  X U-  US-   -  5      $ N      ?)exprE   where)r`   r=   rj   rk   zs        r0   softplus_backwardrr      s7     
A;;I-xAS9QRRr/   grad_outputalphascaleinput_scale	is_resultself_or_resultc                     X-  nUnUnU(       a$  [         R                  " US:*  X-  XV-   -  X-  5      $ [         R                  " US:*  X-  U-  [         R                  " XX-  5      -  X-  5      $ Nr   )rE   rp   ro   )	rs   rt   ru   rv   rw   rx   negcoefposcoef
negiptcoefs	            r0   elu_backwardr~      s     mGGJ{{a$(@A!
 	
 {{a$w.>;V1WW!
 	
r/   c                 .    [         R                  " X5      $ r9   )rE   	full_likeselfvalues     r0   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rV   )r   s   r0   <lambda>fill_tensor.<locals>.<lambda>   s    RSXS\S\S^R__jkr/   )rE   _checkrV   atencopyr   s    `r0   fill_tensorr      s3    	LL		qk 99T5!!r/   r   c                 ^    [         R                  " [         R                  " U S-   SS9SS9S-  $ N   r   min   maxrE   clampr   s    r0   hardsigmoidr      s)     ;;u{{4!83;a??r/   c                 J    [         R                  " US:  US:  -  U S-  S5      $ )Ng      g      @gUUUUUU?        rE   rp   rs   r   s     r0   hardsigmoid_backwardr      s0     ;;	$y! r/   min_valmax_valc                 @    [         R                  " X:*  X:  -  SU 5      $ )Nr   r   )rs   r   r   r   s       r0   hardtanh_backwardr      s     
 ;;DO<c;OOr/   c                 d    U [         R                  " [         R                  " U S-   SS9SS9-  S-  $ r   r   r   s    r0   	hardswishr      s.     %++ekk$(:BBQFFr/   c           
      z    [         R                  " US:*  S[         R                  " US:  XS-  S-   -  U 5      5      $ )Nr   r         ?r   r   s     r0   hardswish_backwardr      s?     ;;
D1HkQh#-=>L r/   c                 6    [         R                  " X:*  SU 5      $ rz   r   )rs   r   rk   s      r0   threshold_backwardr      s     ;;t(![99r/   negative_slopeself_is_resultc                 <    [         R                  " US:  X U-  5      $ rz   r   )rs   r   r   r   s       r0   leaky_relu_backwardr      s     ;;taxN.JKKr/   gradapproximatec                    SnSnSnUS:X  ab  X5-  S-  nSnX-  nX-  n	XaXy-  -   -  n
[         R                  " U
5      nSU-  nSU-   nSU-  nSX-  -
  nUSSU-  U-  -   -  nX-  U-  nXU-   -  $ 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      )rE   r   erfro   )r   r   r   M_SQRT2	M_SQRT1_2
M_2_SQRTPIkBetakKappax_sqx_cuberQ   
tanh_innerleftrightleft_derivativetanh_derivativeinner_derivativeright_derivativekAlphacdfpdfs                        r0   gelu_backwardr      s    %G&I'Jf$s*{/0ZZ&
TzJ+j55 AF
T(9$9:14DD)99::&,Q4&=112eiid 233sTCZ'((r/   inputc                     [         R                  " [        R                  " U5      5      n[         R                  " U5      nX-  SX"-  -
  -  nXU-   -  $ rc   )rE   r   Fsoftplussigmoid)rs   r   input_tanh_softplusinput_sigmoidouts        r0   mish_backwardr     sN      **QZZ%67MM%(M

1':'P#P
QC344r/   c                 4    U [         R                  " U 5      -  $ r9   )rE   r   r   s    r0   silur   "  s     %--%%%r/   c                 \    SS[         R                  " U* 5      -   -  nX-  SUSU-
  -  -   -  $ rc   )rE   ro   )rs   r   r   s      r0   silu_backwardr   )  s:     1uyy$''(G AG(<$<==r/   weightc                 <    [         R                  " U S:  XU -  5      $ rz   r   )r   r   s     r0   _prelu_kernelr   1  s    ;;tax}55r/   c                 |    [         R                  " US:  XU -  5      n[         R                  " US:  SX-  5      nX44$ )Nr   r   r   )rs   r   r   
input_gradweight_grads        r0   _prelu_kernel_backwardr   6  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   )rs   r   r   r   r   r   r   r   s           r0   rrelu_with_noise_backwardr   A  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-   -  -  -
  -  $ )Nr   r$   rZ   )rE   rp   ro   abs)rs   r   r   in_negative	max_derivsignrq   s          r0   log_sigmoid_backwardr   V  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 $ r9   )r"   r,   r   rE   meanr-   sum)r   r   s     r0   apply_loss_reductionr   c  sH    INN(((zz$	imm))	)yyr/   dtypec                     U [         R                  :X  a  [         R                  $ U [         R                  :X  a  [         R                  $ U [         R
                  :X  a  [         R                  $ g r9   )rE   	complex32float16	complex64float32
complex128float64r   s    r0   to_real_dtyper   l  sK    }}	%//	!}}	%""	"}} 
#r/   targetc                 &    X-
  S-  n[        X25      $ )Nr%   )r   )r   r   r   r   s       r0   mse_lossr   {  s     MaD00r/   c                 |    U[         R                  R                  :X  a  SUR                  5       -  OSnXAU-
  -  U -  $ )N       @)r"   r,   r   numel)rs   r   r   r   norms        r0   mse_loss_backwardr     s9     #,y~~/C/C"C3D6>"[00r/   c                     [         R                  " XUS9nU R                  [        S5      5      n[         R                  " XASS9n[         R
                  " U5      n[         R                  " XVU5      $ )N)rV   r   z-infTrV   keepdim)rE   softmaxeqfloatall
zeros_likerp   )r   rV   r   r   maskedmasked_rowszeross          r0   safe_softmaxr    sU    
--U
3CWWU6]#F))FT:KS!E;;{3//r/   rn   c                     X-
  R                  5       n[        R                  " XC:  SUS-  -  U-  USU-  -
  5      n[        XB5      $ )Nr   r%   )r   rE   rp   r   )r   r   r   rj   r   s        r0   smooth_l1_lossr    sI     M D;;t{C$'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      $ rm   )r"   r,   r   r   rE   r   rp   r   )	rs   r   r   r   rj   r   r=   abs_x	norm_grads	            r0   smooth_l1_loss_backwardr    ss    
 "+inn.B.B!B3DAIIaLE"I;;EJJqM! r/   c                 Z    [        XX#U5      n[        XVR                  5        [        XeSS9$ NT	copy_fromcopy_toexact_dtype)r  r   shaper   )rs   r   r   r   rj   r_   results          r0   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      $ rm   )r"   r,   r   r   rE   rp   )rs   r   r   r   r  r   r=   s          r0   huber_loss_backwardr    sv    
 "+inn.B.B!B3DA;;	F
	e#AIt1E948k;QR r/   c                 Z    [        XX#U5      n[        XVR                  5        [        XeSS9$ r  )r  r   r  r   )rs   r   r   r   r  r_   r  s          r0   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      )rV   r"   r,   r   r\   rE   rp   r  scatterr[   r  reshape)rs   r   r   r   r   r   r!  channel_dimsafe_targetr_   r]   	new_shapes               r0   _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 rn   r   )rV   rJ   canonicalize_dimsizenarrowrE   r   cat)
rs   r   rV   wrap_dimnIn	inputSize	firstHalf
secondHalfgradInputFirstHalfgradInputSecondHalfs
             r0   glu_backwardr5    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)rZ   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: )rV   r  r   r"   r+   r   r(  )rs   r   r   r   r   r   r!  no_batch_dims           r0   nll_loss_backwardr>    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$   r9  r:  r<  z ( z, elements))rV   r  r   r(  )rs   r   r   r   r   r   r!  s          r0   nll_loss2d_backwardrA  F  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)rE   maximumlog1pnew_fulllogr   )r   r   r   r   r   s        r0   binary_cross_entropyrG  i  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$   r   )rE   r   r"   r,   r   r   )rs   r   r   r   r   EPSILONr  s          r0   binary_cross_entropy_backwardrJ    sa     G6M*U[[T9JPW-XXFINN(((**,&Mr/   c                 t    [         R                  " [         R                  " U * U-  5      5      n[        X25      $ r9   )rE   rD  ro   r   )r   r   r   r   s       r0   soft_margin_lossrL    s,     ;;uyy%&12D00r/   c                     X -  [         R                  " X!-  5      S-
  -  nU[        R                  R                  :X  a  XAR                  5       -  nU$ rc   )rE   r   r"   r,   r   r   )rs   r   r   r   r_   s        r0   soft_margin_loss_backwardrN    sG     %v})E)IJJINN(((**,.
r/   otherpc                 .    [         R                  X-
  US9$ )N)rP  )r   r   )r   rO  rP  s      r0   distrR    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       $ )Nr%   rZ   Tmemory_formatr   )powr   rE   	ones_likecontiguous_formatr-  r   matmulmT	clamp_minsqrt)	rS  rT  x1_normx1_padx2_normx2_padx1_x2_r  s	            r0   _euclidean_distrf    s     ffQimmB%G__WE4K4KLFffQimmB%G__WE4K4KLF
))RVVBZ12
6C
))R)2
.CZZFA##%%r/   input_sizesstartendstepc                 T    U R                  U5      n[        R                  " X`X#XE5      $ r9   )	new_zerosrE   slice_scatter)rs   rg  rV   rh  ri  rj  r_   s          r0   slice_backwardrn    s)     &&{3JzCNNr/   r$   c                    SSK Jn  U R                  5       nUS:X  a  [        S5      e[        R
                  " U R                  5       U5      n[        U R                  5       5      n[        U R                  5       5      nUS::  a  [        S5      eUb  UOSn	Ub  UO[        R                  n
U	S:  a  XU   -  n	U
S:  a  XU   -  n
U	S:  a  Sn	OXU   :  a  Xq   n	U" U
[        R                  :H  5      (       a  Xq   n
OX:  a  U	n
OXU   :  a  Xq   n
U R                  5       XU   -  -   nX-
  nX-   S-
  U-  Xq'   X==   U-  ss'   U R                  (       a  [        S5      eU R                  XxU5      $ )Nr   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_shapesrq  rV   RuntimeErrorrJ   r*  listr+  stridesysmaxsizestorage_offsetis_quantizedNotImplementedError
as_strided)r   rV   rh  ri  rj  rq  ndimsizesstrides	start_valend_valrx  lens                r0   slice_forwardr    sr    L88:DqyIJJ

 
 S
1CE4;;=!Gqy899*I_c#++G1}3Z	{:1}		3Z	J	W344*			:	*((*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$ )zb
Normalize start and end such that both are in the range
[0, x.get_size()[dim]] and start <= end.
rW   c                 N   > U c  U$ U S:  a  U T-   n [        [        X5      U5      $ rz   r   r   )valr   r   defaultdim_sizes       r0   
clamp_wrap(_normalize_start_end.<locals>.clamp_wrap  s.    ;N7.C3s?E**r/   r   )r  int)r=   rV   rh  ri  r  r  s        @r0   _normalize_start_endr    sF     wws|H+# + ua1-E
S8
4C:r/   srcc           	      h   [         R                  " U R                  U5      nU R                  U   n[	        XX45      u  p4[        U R                  5      nXC-
  US-
  -   U-  Xr'   UR                  U5      nUS:X  a  XF:X  a  US:X  a  UR                  5       $ 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   rZ   )rJ   r*  r|  r  r  rt  expandclonerV   rE   aranger  onesboollogical_andviewr   rp   _unsafe_masked_index)r   r  rV   rh  ri  rj  r  src_sizeindicesidxmask
mask_shapes               r0   rm  rm    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      $ r9   )rl  rE   select_scatter)rs   rg  rV   r  r_   s        r0   select_backwardr  E  s'     &&{3J
DDr/   offsetdim1dim2c                 T    U R                  U5      n[        R                  " XPX#U5      $ r9   )rl  rE   diagonal_scatter)rs   rg  r  r  r  r_   s         r0   diagonal_backwardr  L  s)    
 &&{3J!!*6NNr/   input_dtypec                 H    U R                   U:w  a  UR                  U5      nU$ r9   )r   r<   )rs   r_   r  s      r0   _cast_grad_to_input_dtyper  U  s&     K']];/
r/   outputc                 r    X-  nXA[         R                  " XBSS9-  -
  n[        XU5      R                  5       $ NTr  )rE   r   r  
contiguous)rs   r  rV   r  new_grad_outputr_   s         r0   _softmax_backward_datar  ]  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      $ r  )rE   ro   r   r  )rs   r  rV   r  r_   s        r0   _log_softmax_backward_datar  o  s=     uyy0599d4   J %[kJJr/   c                     XS-  -   X!S-
  -  -
  n[        [        R                  [        R                  US9nU" SXd5      R	                  S5      nU" SX-  U5      R	                  S5      n	X-   $ )z/Utility function to implement im2col and col2imr%   r$   r   r  r   rZ   )r   rE   r  int64r\   )
input_dkernel_d
dilation_d	padding_dstride_dr  blocks_d	arange_kwblocks_d_indiceskernel_grids
             r0    _im2col_col2im_indices_along_dimr  {  su     Q&!|)DDHEKKGI !H7AA!D Ax4jAKKBOK ))r/   kernel_sizedilationpaddingru  c           
      
  ^^^^^^ [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        [         R                  " [        T5      S:H  S 5        SS jnU" TS5        U" TS5        U" TS	S
S9  U" TS5        U R                  m[        T5      n[         R                  " US;   =(       a    [	        S TSS   5       5      U4S j5        [        S [        TSS  TTTT5       5       5      m[         R                  " [	        S T 5       5      UUUUUU4S j5        US:H  nU(       d  U R                  S5      n U R                  u  ppTu  pTu  pTu  nnTu  nn[        U
UUXU R                  5      n[        UUUXU R                  5      n[        R                  " XXU45      nUR                  S5      R                  S5      nUS S 2S S 2UU4   nUR                  SSSSSS5      nUR                  S5      nUR                  S5      nUR                  XU-  U-  UU-  5      nU(       d  UR                  S5      nU$ )Nr%   c                      g)Nz"im2col(): only 2D kernel supportedr&   r&   r/   r0   r   im2col.<locals>.<lambda>  s    0Tr/   c                      g)Nz$im2col(): only 2D dilation supportedr&   r&   r/   r0   r   r    s    -Sr/   c                      g)Nz#im2col(): only 2D padding supportedr&   r&   r/   r0   r   r    s    ,Qr/   c                      g)Nz"im2col(): only 2D stride supportedr&   r&   r/   r0   r   r    s    +Or/   c                    ^ ^ U(       a  [        S T  5       5      O[        S T  5       5      n[        R                  " UU U4S j5        g )Nc              3   *   #    U  H	  oS :  v   M     g7fr   Nr&   .0rP  s     r0   	<genexpr>1im2col.<locals>.check_positive.<locals>.<genexpr>       (%Qq5%   c              3   *   #    U  H	  oS :  v   M     g7fr  r&   r  s     r0   r  r         ;REqFEr  c                     > T ST  3$ Nz& should be greater than zero, but got r&   param
param_names   r0   r   0im2col.<locals>.check_positive.<locals>.<lambda>      ZL(NugVr/   r  rE   r   r  r  strictconds   ``  r0   check_positiveim2col.<locals>.check_positive  4    ,2s(%((;RE;R8RV	
r/   r  r  r  Fr  ru  r   r@  c              3   *   #    U  H	  oS :g  v   M     g7fr  r&   r  ds     r0   r  im2col.<locals>.<genexpr>       :z!Avzr  r   c                      > S[        T 5       3$ )NzmExpected 3D or 4D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: tupler  s   r0   r   r         --25\N<r/   c              3   \   #    U  H"  u  pp4nS USU-  -   X4S -
  -  -
  S -
  U-  -   v   M$     g7f)r$   r%   Nr&   )r  r   paddilkersts         r0   r  r    sD      '
"Cc 	
S1s7]S!G_,q0R77'
s   *,rX  c              3   *   #    U  H	  oS :  v   M     g7fr  r&   )r  cs     r0   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$ )	Nz!Given an input with spatial size rX  , kernel_size=, dilation=
, padding=	, stride=z9, the calculated shape of the array of sliding blocks is z*, but its components must be at least one.r  )r  r  output_sizer  r  ru  s   r0   r   r    sJ    3E%*4E3F G"m;xj 9)9VH -]D	Fr/   r@  r   rZ   r$   r      T)rE   r   r  r  r  r  zipr\   r  r  r   r  permuter+  r$  squeeze)r   r  r  r  ru  r  r|  batched_input	batch_dimr%  input_hinput_wstride_hstride_w	padding_h	padding_w
dilation_h
dilation_wkernel_hkernel_wblocks_row_indicesblocks_col_indicespadded_inputr  num_blocks_rownum_blocks_colr  r  s    ````                     @@r0   im2colr    sl    
LL[!Q&(TU	LLX!#%ST	LLW"$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$ s  snnnn
n	f s  snnf )Nr%   c                      g)Nzonly 2D output_size supportedr&   r&   r/   r0   r   col2im.<locals>.<lambda>  s    0Or/   c                      g)Nzonly 2D kernel supportedr&   r&   r/   r0   r   r    s    0Jr/   c                      g)Nzonly 2D dilation supportedr&   r&   r/   r0   r   r    s    -Ir/   c                      g)Nzonly 2D padding supportedr&   r&   r/   r0   r   r    s    ,Gr/   c                      g)Nzonly 2D stride supportedr&   r&   r/   r0   r   r    s    +Er/   Tc                    ^ ^ U(       a  [        S T  5       5      O[        S T  5       5      n[        R                  " UU U4S j5        g )Nc              3   *   #    U  H	  oS :  v   M     g7fr  r&   r  s     r0   r  1col2im.<locals>.check_positive.<locals>.<genexpr>  r  r  c              3   *   #    U  H	  oS :  v   M     g7fr  r&   r  s     r0   r  r    r  r  c                     > T ST  3$ r  r&   r  s   r0   r   0col2im.<locals>.check_positive.<locals>.<lambda>  r  r/   r  r  s   ``  r0   r  col2im.<locals>.check_positive  r  r/   r  r  r  Fr  ru  r  )r%   r   c              3   *   #    U  H	  oS :g  v   M     g7fr  r&   r  s     r0   r  col2im.<locals>.<genexpr>   r  r  rX  c                      > S[        T 5       3$ )NzmExpected 2D or 3D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: r  r  s   r0   r   r    r  r/   r   r$   c                     > STS    ST  3$ )Nz|Expected size of input's first non-batch dimension to be divisible by the product of kernel_size, but got input.shape[-2] = rX  z and kernel_size=r&   )r  r  s   r0   r   r    s!     ==B2YK H"m%r/   rZ   c                  :   > ST ST ST ST ST ST  STS    S	3$ 
NzGiven output_size=r  r  r  r  z , expected input.size(-1) to be 	 but got rZ   .r&   Lr  r  r  r  r  ru  s   r0   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   r0   r   r    r+  r/   r   r@  r  
accumulater  )rE   r   r  r  r  r  r\   r$  r  r  r  r^   rl  prodr   _unsafe_index_putr   r  r   )#r   r  r  r  r  ru  r  r|  prod_kernel_sizer   r  r  r  r  colr  out_hout_wr  r  r  r  r	  r
  r  r  indices_rowindices_colorP  output_padded_sizer  r  r*  r  s#    `````                           @@r0   col2imr9    s    
LL[!Q&(OP	LL[!Q&(JK	LLX!#%IJ	LLW"$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$ NrV  )type_asr  rJ   r   )rs   r  ru   rP   s       r0   native_dropout_backwardr=  C  s@     
[1E9	:AA11+> 	B 	A Hr/   
input_size	dimensionr+  c                    [        U5      S:X  a  [        R                  " U S5      $ [        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       $ )Nr   r  rZ   r$   r9   Tr-  )r  rE   squeeze_copyrJ   r*  r  r  int32unfoldflattenmovedimrl  r   r0  r  )	r   r>  r?  r+  rj  rV   r  r_   r  s	            r0   unfold_backwardrF  R  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      $ [         R                  " [         R                  " US:  US:*  5      XSU-
  -  -  UR                  S[	        S5      5      5      $ )Nrn   r   r&   nan)rE   rp   r  rE  r  )rs   r   rG  lohis        r0   logit_backwardrL  e  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       $ rz   )r   native_dropoutr  )r   rP  rM  s      r0   dropoutrP  z  s1     a""5U3A66{{}r/   out0out1c                    U(       a  US:w  a  US:X  a9  [         R                  " U 5      [         R                  " U [         R                  S94$ 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$   r   z?result type Float can't be cast to the desired output type Longrn   )	rE   r  r  r   is_floating_pointrs  	rand_liker  rZ  )r   rP  rM  	bool_maskress        r0   rO  rO    s     a6$$U+U-=-=e5::-VWW{{,,Q  OOE*Q.	%sQw"88uuEJJ?@@r/   half_to_floatc                 $   SSK Jn  U R                  5       n U(       a   U R                  [        R
                  :X  d   e[        R                  " U [        R                  R                  S9u  pEU R                  U5      n U" U R                  5       S:H  5      (       a  [        R                  " U 5      nO-[        R                  " XSS9n[        R                  " X-
  5      nU[        R                  " XaSS9-  nU(       d  UR                  U5      nU$ Nr   guard_or_falser7   T)r  )rr  r\  r  r   rE   halfrJ   rK   ELEMENTWISE_TYPE_PROMOTION_KINDDEFAULTr<   r   ro   amaxr   )	r=   rV   rX  r\  r>   rB   unnormalizedx_maxr  s	            r0   _softmaxrd    s     E 	
Aww%**$$$&+&>&>	uDDLL'# 	
Aaggi1n%%yy|

140yy+EIIlFFF<(Mr/   )r  c                 (   SSK Jn  U R                  5       n U(       a   U R                  [        R
                  :X  d   e[        R                  " U [        R                  R                  S9u  pEU R                  U5      n U" U R                  5       S:H  5      (       a  U nO[        R                  " XSS9nX-
  n[        R                  " [        R                  " [        R                  " U5      USS95      nXh-
  n	U(       d  U	R                  U5      n	U	$ rZ  )rr  r\  r  r   rE   r^  rJ   rK   r_  r`  r<   r   ra  rF  r   ro   )
r=   rV   rX  r\  r>   rB   shiftedrc  shifted_logsumexpr  s
             r0   _log_softmaxrh    s     E 	
Aww%**$$$&+&>&>	uDDLL'# 	
Aaggi1n%%

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$   r   )rV   r|  index_selectr   )r   r  ri  rj  rk  r   s         r0   	embeddingrn    sb     ::<1444||q!!!W-<<1++a.C
r/   num_weightsc                 d   [         R                  " U [         R                  R                  S9u  pVU R	                  U5      n [        U[        R                  5      nU(       aU  UR                  U45      n[        R                  " U5      n[        R                  Xq/USS9nXq   n	X	R                  S5      -  n [        X:H  U R                  5      n
U R                  U
S5      nU R                  U4U R                   UR                  S  -   5      n[        R                  X/USS9R	                  U5      $ )Nr]  Tr-  rZ   r   )rJ   rK   r_  r`  r<   r   rE   longrl  rZ  r   r0  r\   r^   r|  masked_fillr  )rs   r  ro  ri  rj  r>   rB   countsr  grad_weights_scaler  r   grad_weights                r0   embedding_dense_backwardrv    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$ rc   r&   )r=   rP   is      r0   r/  r/    s    	A	 Hr/   tensors
num_chunksc                 Z   / nU  H  nUR                  5       nXQ   U-   S-
  U-  U-  nXeU   :w  a9  S/S-  UR                  U-
  S-
  -  SXeU   -
  /-   n[        R                  XGS5      nUS U [        R
                  " US/5      -   nUR                  UR                  U5      5        M     U$ )Nr$   r   r%   rZ   )r+  r|  r   constant_pad_ndrE   Sizeappendr$  )	ry  rV   rz  padded_tensorstensortensor_sizepad_along_dimr  	view_sizes	            r0   
_pad_chunkr    s    
 Nkkm$)J6:zIJV,,#'V[[3.23C 007 C ))&q9F%

J3C(DD	fnnY78  r/   c                 X    U S   R                   nU  H  nUR                   U:w  d  M    g   g)Nr   FTr|  )ry  r|  r  s      r0   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/   r0   r   +leading_dimension_matches.<locals>.<lambda>%  s    ]r/   )r+  rE   r   )ry  rV   leading_dim_sizesr  s       r0   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$   c                      g)Nz&_chunk_cat expects positive num_chunksr&   r&   r/   r0   r   ._preprocess_chunk_cat_inputs.<locals>.<lambda>.  s    *Rr/   r   c                      g)Nz0_chunk_cat expects a non-empty input tensor listr&   r&   r/   r0   r   r  0  s    "Tr/   c                      g)Nz#_chunk_cat expects non-empty tensorr&   r&   r/   r0   r   r  5  s    1Vr/   c                      g)Nz8_chunk_cat expects all input tensors with the same dtyper&   r&   r/   r0   r   r  8      Nr/   c                      g)Nz8_chunk_cat expects all inputs tensors on the same devicer&   r&   r/   r0   r   r  <  r  r/   c                      g)NzK_chunk_cat expects non-negative dim when input tensors have different ndimsr&   r&   r/   r0   r   r  C  s    ar/   c                      g)Nz3_chunk_cat expects dim < ndim for all input tensorsr&   r&   r/   r0   r   r  H      Mr/   )rE   r   r  r   r  r   r  rJ   r*  rV   r|  r  )ry  rV   rz  expected_dtypeexpected_devicer  s         r0   _preprocess_chunk_cat_inputsr  )  s"   
 
LLq"RS	LLGqT QZ%%Naj''OV\\^a')VWLLN*N	
 	MM_,N	
  w$$WQZ^^%5s;1Ha	
 FLLkk!M 
 g+Jr/   r   c                     [        XU5      n[        XU5      nUc  [        R                  " XAS-   5      $ [        R                  " XAS-   US9  U$ )Nr$   )r   )r  r  rE   r-  )ry  rV   rz  r   r  s        r0   
_chunk_catr  N  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   rV  Tr  )	r   split_with_sizesr  rE   r[  r  r   r  r   )r   r  rV   r   splitssr  splits           r0   split_with_sizes_copyr  _  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      $ r9   )r   r  r   )r   r  rV   s      r0   unsafe_splitr  r  s    ::U44r/   c                 B    [         R                  R                  XU5      $ r9   )r   r  r  )r   r  rV   s      r0   unsafe_split_with_sizesr  w  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_intrZ   )r  detachrr  r  r[   rE   r  )	r   r  rV   rg  r  chunksr  rx  r  s	            r0   r  r  ~  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      $ [        n[        R                  R                  5       =n(       a  UR                  =n(       a  UR                  nU" 5          U Vs/ s H  owR                  5       PM     nnS S S 5        U R                  WU5      $ s  snf ! , (       d  f       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   r0   r   Atensor_split_tensor_indices_or_sections_py_impl.<locals>.<lambda>  s     <<E;eMr/   )r  typer   rE   r  rV   r   itemr;   r   tensor_splitr   _guardsdetect_fake_mode	shape_envignore_fresh_unbacked_symbols)
r   r  rV   sectionsctx	fake_moder  rx  r  r  s
            @r0   /tensor_split_tensor_indices_or_sections_py_implr    s$    &,,11U:::%++u{{:::*..0I	LLQ()q.	M
 A~-224(G,,,,  //7799I9",,,I,99C
 U)CD)CAvvx)CGD    #.. E Us   EE%EE
Emat1mat2c                     U R                  5       (       d+  U R                  5       (       d  [        U5      n[        U5      nU[        R                  " X5      -  nUS:X  a  U$ XSU -  -   $ rz   )rT  
is_complexr  rE   mm)r   r  r  rj   rt   r   s         r0   addmmr    s_     !!##DOO,=,=4yE

%((4&
&Cqy
 r/   use_geluc                     [        XX#U5      nU(       a:  U R                  (       a  [        R                  USS9$ [        R                  U5      $ [        R	                  U5      $ )Nr   )r   )r  is_cudar   gelurelu)r   r  r  rj   rt   r  r   s          r0   _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 -  -   $ rz   )rT  r  r  rE   mvr   )r   r  r  rj   rt   r   s         r0   addmvr    ss     !!##DOO,=,=4yE

%((4%
%Cqy

yy{a{r/   r   rstdgammaNCHxWgroupoutput_maskc
           	      \  ^^^^^^ [         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-  n
[        R                  " TU
T-  :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$ )NzExpect input to have z	 elementsr&   )r  r  r  s   r0   r   ,native_group_norm_backward.<locals>.<lambda>	  s    'A}I>r/   c                  .   > ST  ST STR                    3$ )NzExpect mean to have shape (, z
, but got r  )r  r  r   s   r0   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 rZ   )r   )r  r  s   r0   r   r    s)    's*<eN_U[[]<hieg<hir/   c                     > ST  ST 3$ )NzExpect number of channels z, to be evenly-divisible by number of groups r&   )r  r  s   r0   r   r    s    ,QC/[\a[bcr/   r%   r   r   rn   rZ   r$   r  r@  )rJ   check_same_devicecheck_same_shaperE   r   r   r  r   r  r   r\   r$  r  r  r^   r<   r   )rs   r   r   r  r  r  r  r  r  r  cpgdsdbd_inputd_gammad_biasr  ds_valdb_valc1c2c3s     ` `````             r0   native_group_norm_backwardr    s    
D$ 
5N	4F	LLQ$> 
LL

q%j P 
LL+!+i
 u*C	LL	S5[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$ r  )r  	enumerater   r  r   )rs   r   r   r  r  r  r  r  r  r  rQ  rR  r  r  r_   rx  rP   s                    r0   native_group_norm_backward_outr  M  sc    " (D!%F d#J&!1=jmQWW5Q
4P "
 r/   c                 .    U b  U R                  U5      $ U $ r9   r<   )r=   r   s     r0   _maybe_castr  j  s    }ttE{Hr/   grad_outnormalized_shapebiasc                   ^" UR                   nUR                  5       n	[        R                  " UR                  5      m"U"4S jXXV4 5       u  ppU
c   eU	[        U5      -
  nXS  nUS U n/ n/ n[        U	5       H-  nUU:  a  UR                  U5        M  UR                  U5        M/     [        U5      n[        U5      nSSK	J
n  U" US:H  5      (       d  U" US:H  5      (       a[  US   (       a  UR                  U5      OS US   (       a  UR                  XS  5      OS US   (       a  UR                  XS  5      4$ S 4$ [        X;R                  5       5      n[        XKR                  5       5      nUc   eX-
  U-  nUb  X-  nOU
nUU-  n[        R                  " UUS5      n[        R                  " UU5      n[        R                  " UUS5      n[        R                  " UU5      nUU-
  U-
  nS nS n S n!US   (       a  UU-  U-  nUS   (       a3  Ub0  [        U5      S:  a  [        R                  " U
U-  US5      n OU
U-  n US   (       a;  Ub8  [        U5      S:  a  [        R                  " U
US5      n!OU
R!                  5       n![#        UUR                  5      [#        U Ub  UR                  OS 5      [#        U!Ub  UR                  5      4$ S 5      4$ )Nc              3   j   >#    U  H(  nUb  UR                  T[        R                  S9OUv   M*     g 7fr;  )r<   rE   r[  r  r=   r>   s     r0   r  -native_layer_norm_backward.<locals>.<genexpr>  s?      9 1A = 	
e.E.EF	 1s   03r   rp  r$   r%   TF)r  rV   rJ   get_computation_dtyper   r  r[   r~  r/  rr  rq  rl  r^   rE   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_indicesrx  r  Mrq  x_hat
grad_x_hatabr  r  r  rQ   r  d_weightr  r>   s#                                     @r0   native_layer_norm_backwardr  q  s    ++KJ33EKK@9 60	95M{ $$$,--DU#JUd#J#%#%:9$$Q'$$Q'	  	ZAZAKQ!V$$(=a1f(E(E,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$u,H1~)/ !A%YY}.?GF"((*F 	GU[[)Hf.@flldKF$*:DJJE  AEE 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$ r  )r  r  r   r  r   )r  r   r  r   r  r   r  r  rQ  rR  r  r  r_   rx  rP   s                  r0   native_layer_norm_backward_outr    s`     ()tF d#J&!=jmQWW5Q14P "
 r/   c           	      `   / n[        [        U5      5       H(  nUR                  U R                  5       U-
  S-
  5        M*     [        R
                  " U R                  5      nU R                  U5      nUc  U[        R                  [        R                  4;   a/  [        R                  " [        R                  5      R                  nO1[        R                  " [        R                  5      R                  nOUn[        R                  " [        R                  R                   R"                  R%                  [        R&                  " US5      R)                  USS9U5      5      n	UR+                  U	5      n
Ub  U
R+                  U5      n
U R,                  =(       d    US L=(       a    UR,                  n[        R.                  " U 5      nU[        R0                  [        R2                  4;   nU(       d'  U(       d   U
R5                  5       n
U	R5                  5       n	U
R7                  U 5      nX4$ )Nr$   r%   Tr  )r[   r  r~  rV   rJ   r  r   r<   rE   r   r   finforG  r   rsqrtopsr   addScalarrY  r   r   	is_nestedr   channels_lastchannels_last_3dr  r<  )r   r  r   rG  dims_to_reducerx  r>   upcasted_inputeps_valrqrst_inputupcasted_resultr  rW  is_channels_lastr  s                  r0   _fused_rms_normr    s    !#N3'()eiikAo12 * 33EKK@XX/0N { @@kk%--044Gkk%--044G++ 			!!IIna(--.$-OQX	
K %((5O)--f5 LF$$6$K6;K;KI//6M$) 
 -)446!,,. $$U+Fr/   c                 f   UR                   nUR                  5       n[        R                  " UR                  5      nU R                  U[        R                  S9n	UR                  U[        R                  S9n
Ub  UR                  U[        R                  S9OS nU	c   eU[        U5      -
  nXlS  nUS U n/ n/ n[        U5       H-  nUU:  a  UR                  U5        M  UR                  U5        M/     [        U5      n[        U5      nSSKJn  U" US:H  5      (       d  U" US:H  5      (       a=  US   (       a  UR                  U5      OS US   (       a  UR                  XlS  5      4$ S 4$ [        X:R                  5       5      nUb  X-  nOU	nS nS nX-  nUS   (       a'  [        R                   " UU-  USS9nUUU-  U-  -
  U-  nUS   (       a0  Ub-  U	U-  n[        U5      S:  a  [        R                   " UUSS9nOUn[#        UUR                  5      [#        UUR                  5      4$ )NrV  r   r[  r$   Tr  F)r  rV   rJ   r  r   r<   rE   r[  r  r[   r~  r/  rr  r\  rl  r^   r   r  )r  r   r  r  r   r  r  r  r>   r  r  r  r   r  r  r  r  rx  r  r  r\  r  r  r
  r  sum_vald_weight_full_shapes                              r0   _fused_rms_norm_backwardr!    sR    ++KJ33EKK@KK)@)@   M +5;R;RSJ  			#53J3J	K 
 $$$,--DU#JUd#J#%#%:9$$Q'$$Q'	  	ZAZADa1fQ!7!7,7NEOOK(3>q>EOOK./
 	
GK
 	

 T>>#34D"0
"
 $G!%HE1~))EJ.4EtTg 55=1~+1+e3 !A%yy#):EH +H 	GU[[)Hekk* r/   running_meanrunning_varmomentum
functionalc	                 .   S/[        [        SU R                  5       5      5      -   n	[        R                  " U R
                  5      n
UnUnU(       Ga'  [        R                  " U R
                  5      n
U R                  U
S9n[        R                  " XSSS9u  p[        R                  " X-   5      nX-
  U-  n[        R                  " X5      n[        R                  " UU	5      nUb&  UU-  SU-
  U-  -   nU(       d  UR                  U5        Ubg  U R                  5       U R                  S   -  n[        R                  " X5      nUUUS-
  -  -  nUU-  SU-
  U-  -   nU(       d  UR                  U5        OUb  Uc   eUR                  U
SS9nUnUR                  U
SS9nUnUnS[        R                  " XG-   5      -  nU R                  R                   S:w  a  UnUnO"U R#                  S	5      nU R#                  S	5      n[%        XR                  5       S-
  5      n[%        UU R                  5       S-
  5      nX-
  U-  nUb1  UR'                  5       n[%        XR                  5       S-
  5      nUU-  nUb1  UR'                  5       n[%        X R                  5       S-
  5      nUU-   nU R                  R                   S:X  a2  UR                  U R
                  S9nUR                  U R
                  S9nUR                  U R
                  S9UUUU4$ )
Nr   r%   r   T)rV   
correctionr  r$   )r   r   r  r   )rt  r[   rV   rJ   r  r   r<   rE   var_meanr  r   copy_r   r  r_  r  r  rl  r^   rD  )r   r   r  r"  r#  r   r$  rG  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                           r0   native_batch_norm_helperr6  b  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				$ r/   r0  save_invstdc                 2    [        XX#XEXgS5	      u  pn
  nXU
4$ NFr6  r   r   r  r"  r#  r   r$  rG  r  r0  r1  r]   s               r0   native_batch_normr<    s1     *Bt;(QV*&Fy!Q i''r/   c           
          Uc  Uc  [         R                  XX%Xg5      $ 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_legitrs  $_native_batch_norm_legit_no_training)r   r   r  r"  r#  r   r$  rG  s           r0   native_batch_norm_decompositionr@    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$   r   )r+  rE   r  r   r  r  r  r   )r  r  rV   r  r  r]   r  s          r0   unsafe_chunk_py_implrC    s    {{3H#a'F2JQ8q=+126az62",V0Ch0N"OQJyy~~55==fSVWW99>>&&--f#FF 3s   B0c           
      N    [         R                  R                  U UUUUSUU5      $ r9  )r   r>  r  )r   r   r  r"  r#  r$  rG  s          r0   r?  r?    s5     ((00	 	r/   c                 2    [        XX#XEXgS5	      u  pn
  nXU
4$ r9  r:  r;  s               r0   r>  r>    s1     *Bt;(QV*&Fy!Q i''r/   c                 6    [        XUS S X4US5	      u  pgn  n	XgU4$ r9  r:  )
r   r   r  r   r$  rG  r  r0  r1  r]   s
             r0   !_native_batch_norm_legit_no_statsrG  (  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$ )NT#new_running_mean should not be None"new_running_var should not be Noner:  )r   r   r  r"  r#  r   r$  rG  r  r0  r1  r,  r-  s                r0   #_native_batch_norm_legit_functionalrK  7  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$ )a  
Return a reserve tensor for batch norm, used only by cudnn to pass forward state to the
backward pass. This is needed for `_batch_norm_with_update` and `_batch_norm_no_update`,
which support a variety of backends including cudnn. We create this tensor here to get
the correct shape in the traced graph if we detect that will call the cudnn kernel,
and rely on DCE to avoid materializing this tensor.
Tr   )r   layoutr  )
rE   _C_select_batch_norm_backend_BatchNormBackendCudnn(_get_cudnn_batch_norm_reserve_space_sizeemptyuint8rM  r  )	r   r   r  r"  r#  rG  r   backendreserve_sizes	            r0   _get_batch_norm_reserve_tensorrW  P  s      hh11t;cG L%((,,222xxHH
 ;;EKKU\\ r/   c                 R    [        U UUUUSUUS5	      u  pxn	  n
[        XX#XFSS9nXxX4$ )NTFr   r6  rW  r   r   r  r"  r#  r$  rG  r  r0  r1  r]   reserves               r0   _batch_norm_with_updater]  m  sU     *B
*&Fy!Q -t;dG i00r/   c                 x    [        XX#USXVS5	      u  nnn	n
n[        XX#XFSS9nU
c   S5       eUc   S5       eXxXX4$ )NTrY  rI  rJ  rZ  )r   r   r  r"  r#  r$  rG  r  r0  r1  new_rmnew_rvr\  s                r0   "_batch_norm_with_update_functionalra    su      	!t;hT	 -t;dG DDDCCCy6BBr/   c                 R    [        U UUUUSUUS5	      u  pxn	  n
[        XX#XFSS9nXxX4$ )NFrY  rZ  r[  s               r0   _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$ )Nr   rn   )rE   rU  r<   rT  r<  )r   rP  	generatorr  rW  s        r0   _fused_dropout_decompositionrf    sY     OOE"Q&***=D
,,u

%q
1C;r/   )r   rM  r  
pin_memorynon_blockingrW  r  rg  rh  rW  c                
   U(       a  U[         R                  :X  d   S5       eU(       a   S5       e[        U [         R                  [        [
        [        [        45      (       d   eUc7  Uc4  Uc1  [        U [         R                  5      (       a  U R                  5       $ 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$ )NTODOFr  TrV  )rE   stridedr;   r   r  r  r  complexr  scalar_tensorr  r  _primsconvert_element_type
device_put)	r=   r   rM  r  rg  rh  rW  dtype_convertedx_tensors	            r0   _to_copyrs    s1    5==08&80!6!>a%,,UD'BCCCC~%-M,Aa&&779HO!U\\""&&q)f7!5||88IH"O<<**8\J<<44XE {{8AAOr/   c                 ,    [         R                  U 5      $ r9   )r   alias)r=   s    r0   nop_decompositionrv    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<  rl  rE   rT  )r   r   r  r"  r#  r   rx  ry  r  r	  r  s              r0   cudnn_batch_normr{    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 $ rc   )r  r|  r  r\   )r=   broadcast_maskr   r  s       r0   _broadcast_batch_norm_backwardr~   	  sF    /
19dVVm0ED!A 0 Hr/   r\  c                 *    [        U UUUUUUUUU	5
      $ r9   )native_batch_norm_backward)r  r   r   r"  r#  r0  r7  rM  rG  r  r\  s              r0   batch_norm_backwardr  '	  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r9   r  r  s     r0   r  -native_batch_norm_backward.<locals>.<genexpr>^	  s/      	
A $%=a7
s   #&r%   z$rank of the input must be at least 2r$   rn   )r   rJ   r  r  rV   r/  rt  rE   r  r[   r~  r~  r   r   r<   r  )'r  r   r   r"  r#  r0  r7  rM  rG  r  r  weight_dtyper  r  r  running_mean_castrunning_var_castsave_mean_castsave_invstd_castr  
input_rankr   num_featuresr   r5  r}  reduction_axesrx  r   grad_output_sumdot_p	grad_mean
proj_scale
grad_scaleprojr_   ru  	grad_biasr>   s'                                         @r0   r  r  C	  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#  r0  r7  rM  rG  r  rQ  rR  r  r  r_   rx  rP   s                    r0   native_batch_norm_backward_outr  	  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
      $ NT)TTTr   r  )r   rs   r   r"  r#  r0  r  ry  s           r0   miopen_batch_norm_backwardr  	  s5     ** r/   reserveSpacec	                 B    [         R                  UU UUUUUSU/ SQ5
      $ r  r  )	r   rs   r   r"  r#  r0  r  ry  r  s	            r0   cudnn_batch_norm_backwardr  	  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$ )Nz9adaptive_avg_pool2d(): Expected 3D or 4D tensor, but got r&   r  s   r0   r   %adaptive_avg_pool2d.<locals>.<lambda>
  s    KD6Rr/   rX  r   c                  "   > S[        T 5       S3$ )Nzjadaptive_avg_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has shape r(  r  r  s   r0   r   r  
  s     99>uaIr/   rZ   c              3   .   #    U  H  u  pX-  v   M     g 7fr9   r&   )r  rx  r7  s      r0   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  rx  r7  r  s       r0   r  r  
  s"      
+OaQ!O+Os   c                 2    [         R                  " X-  USS9$ )Ntruncrounding_moderE   divr  r	  r  s      r0   start_index(adaptive_avg_pool2d.<locals>.start_index"
  s    yy99r/   c                 F    [         R                  " U S-   U-  U-   S-
  USS9$ )Nr$   r  r  r  r  s      r0   	end_index&adaptive_avg_pool2d.<locals>.end_index%
  s&    yy!a%1q1,awGGr/   c                    > [         R                  " UT[         R                  S9nT" X!U 5      nX-  S-   nX-  nUS:H  =(       d    X-  S:H  (       + nU(       a  US-  nOUS:X  a  US-  n[         R                  " UT[         R                  S9nUR                  S5      U-   nU(       aQ  [         R                  " U S-
  UR
                  UR                  S9n	[         R                  " X5      nT" X!U 5      n
X-
  nOUnXXv4$ )Nr  r$   r   rZ   r  )rE   r  r  r\   rm  r   r  minimum)in_sizeout_sizeorangei0	maxlengthin_size_modadaptive	range_maxr  maxvali1lengthr  r  r  s               r0   compute_idx(adaptive_avg_pool2d.<locals>.compute_idx(
  s    hvU[[I73 '!+	(#q(GH,Ba,GHNIANILL6M	ll2* ((!399SZZF --,C 6W5BWFFI//r/   .r@  )r   rZ   r   c                     [        U[        5      (       a  X4$ 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$ )Nr   rZ   rX  r@  r   )r;   r   r\   r^   rE   rr  )valsr  r  r  rV   r  s         r0   
maybe_mask'adaptive_avg_pool2d.<locals>.maybe_maskP
  sp    fg&&< 7N7 0 0 44Dby(q1$$T5D&vt4F<r/   )r  rV   r   )r  r  r  rE   r   r  r  nnr%  
avg_pool2dr^   r   r
   r[   )r   r  r  ru  kernelr  idxhlength_hrange_max_h
adaptive_hidxwlength_wrange_max_w
adaptive_wr  r  retrx  jr  r  r|  r  r  s                      @@@@@r0   adaptive_avg_pool2dr  
  s   
 \\FKKEu:D	LLR [[FI	
  Ry;r?"a'E"IB,G1,LG#eBCj+*FGG 
+.uRSz;+O
 
 xx""--eVDD:H0@ /:%)[QS_.U+DK.9%)[QS_.U+DK'a0$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  rZ   Fr-  )rJ   alert_not_deterministicr   operatorr   r  r|  r   r  r  r  r$  rl  rt  r0  )	r   r  r  rV   nchwindices_nc_shapeindices_flatr  s	            r0   _max_unpoolndr  p
  s    
!!M#m"DE	djj3$/	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$ )Nz2elements in indices should be type int64 but got: r   )r  s   r0   r   max_unpool2d.<locals>.<lambda>
  s    DW]]OTr/   r%   c                  "   > S[        T 5       S3$ )NzMThere should be exactly two elements (height, width) in output_size, but got 
 elements.r  r  s   r0   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   r0   r   r  
  s    %%)YYK|=r/   c                  <   > STR                    ST R                    3$ NzBExpected shape of indices to be same as that of the input tensor (z%) but got indices tensor with shape: r  )r  r   s   r0   r   r  
  s'    PQUQ[Q[P\ ]229--Br/   r$   r   c                  *   > STR                    ST  S3$ )NzZmax_unpooling2d(): Expected input to have non-zero size for non-batch dimensions, but got  with dimension  being empty.r  )rx  r   s   r0   r   r  
  s     ::,&6qcHr/   )
rE   r   r   r  r  r|  r  r[   r+  r  )r   r  r  rx  s   ```@r0   max_unpool2dr  
  s     
LL$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      $ )Nc                      g)Nz(elements in indices should be type int64r&   r&   r/   r0   r   max_unpool3d.<locals>.<lambda>
  s    .Xr/   r@  r  c                  $   > ST R                    S3$ )NzLInput to max_unpooling3d should be a 4d or 5d Tensor, but got a tensor with r  r  r   s   r0   r   r  
  s    ^_d_i_i^jjvwr/   r   c                  "   > S[        T 5       S3$ )NzVThere should be exactly three elements (depth, height, width) in output_size, but got r  r  r  s   r0   r   r  
  r  r/   c                  "   > S[        T 5       S3$ )NzRThere should be exactly three elements (depth, height, width) in stride, but got: r  r  ru  s   r0   r   r  
  s    dehioepdqq{|r/   c                  "   > S[        T 5       S3$ )NzSThere should be exactly three elements (depth, height, width) in padding, but got: r  r  )r  s   r0   r   r  
  s    efijqfress}~r/   c                  <   > STR                    ST R                    3$ r  r  )r  r   s   r0   r   r  
  s'    PQVQ\Q\P] ^229--Br/   r$   r   c                  *   > STR                    ST  S3$ )NzZmax_unpooling3d(): Expected input to have non-zero size for non-batch dimensions, but got r  r  r  )rx  r   s   r0   r   r  
  s      ;;-'7s-Ir/   r%   c                     > ST  3$ )Nz5strides should be greater than zero, but got stride: r&   r  s   r0   r   r  
  s    GxPr/   )
rE   r   r   r  r|  r  r  r[   r+  r  )r   r  r  ru  r  rx  s   `````@r0   max_unpool3dr  
  s?    
LL$&X 
LL

fw 
LLKA	
 
LLFq| 
LLG~ 
LLw}}$	
 1ejj!JJqMA	
 " 
LLq	A9&)a-9F1IMP
 a88r/   )rt   r  c          	          [        XX#SUS9$ )NTinplacert   
_index_addr=   rV   r  r  rt   s        r0   
index_add_r  
  s     aeTGGr/   c          	          [        XX#SUS9$ )NFr  r  r  s        r0   	index_addr  
  s     aeU%HHr/   r  c                x  ^^^^^^ [         R                  " U R                  T5      m[        R                  " TR                  S:*  U4S j5        TR                  S:X  a  TR                  S5      OSmUR                  S:  a  UR                  T5      OSm[        R                  " TT:H  UUU4S j5        TS:w  an  [         R                  " U R                  5      m[        R                  " T[        L =(       d     [         R                  " [        T5      T5      UU4S j5        UT-  nU R                  S:H  nU(       a  U R                  S5      OU nST-  T4-   nU(       a  [        R                  O[        R                  n	U	" XxUSS9n
U(       a  U $ U(       a  U
R                  S5      $ U
R!                  5       $ )	Nr$   c                  $   > ST R                    S3$ Nz(Index should have dimension 1 or 0 (got r;  r  r  s   r0   r   _index_add.<locals>.<lambda>      :5::,aHr/   r   c                     > ST ST ST < 3$ )NzNumber of indices (z') should be equal to tensor.size(dim) (z), for dim=r&   )rV   
index_sizer  s   r0   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  )rt   python_types   r0   r   r	  "  s    -d5k]:YZeYffghr/   r9   Tr-  )rJ   canonicalize_dimsr|  rE   r   r+  dtype_to_typer   r  is_weakly_lesser_typer  r\   r   
index_put_	index_putr   r  )r=   rV   r  r  r  rt   zero_dimrS  r  r  r   r  r  r  s    ``  `     @@@r0   r   r   	  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$ )Nr   c                      g)Nz#received an empty list of sequencesr&   r&   r/   r0   r   pad_sequence.<locals>.<lambda>4  s    -Rr/   r$   c              3   B   #    U  H  oR                  S 5      v   M     g7fr  r+  )r  r=   s     r0   r  pad_sequence.<locals>.<genexpr>8  s     /Y&&))Ys   )r   r   rV   r  )
rE   r   r  r+  r   rE  r[   r   r|  r  )	sequencesbatch_firstpadding_valuesequences_sizemax_sizetrailing_dimsmax_lenout_dimsr   dim_paddingsrx  currseqrows                r0   pad_sequencer(  1  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=   rV   r  r  s       r0   index_copy_r.  L  s    qud;;r/   c                     [        XX#SS9$ )NFr*  r+  r-  s       r0   
index_copyr0  Q  s     que<<r/   c                  ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        U R                  S:H  nU(       a  U R                  S5      OU nTR                  S:X  a  TR                  S5      OTmSU-  T4-   nU(       a  [        R                  O[        R                  nU" XgU5      n	U(       a  U $ U(       a  U	R                  S5      $ U	R                  5       $ )Nr$   c                  $   > ST R                    S3$ r  r  r  s   r0   r   _index_copy.<locals>.<lambda>]  r
  r/   r   r9   )rJ   r  r|  rE   r   r\   r   r  r  r   r  )
r=   rV   r  r  r  r  rS  r  r  r   s
     `       r0   r,  r,  W  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(  )rE   r  rl  ro   r   r  is_xpurD  )r   r   rq   r   s       r0   log_sigmoid_forwardr6  m  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$ )N)r7  r8  r   r  re  )prims_uniform_helperr  r   r   r  )r=   r7  r8  re  s       r0   uniformr<  z  s=       	cNt_ggxx r/   c                 8    U R                  [        XX#5      5      $ r9   )r*  r<  )r   r7  r8  re  s       r0   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$ [        R                  " SS 5        g )Nr%   c                      gNz9Must specify exactly one of output_size and scale_factorsr&   r&   r/   r0   r   .upsample_compute_output_size.<locals>.<lambda>      Or/   c                      gN r&   r&   r/   r0   r   rB    s    Rr/   c                      grA  r&   r&   r/   r0   r   rB    rC  r/   c                      grE  r&   r&   r/   r0   r   rB    s    rr/   Fc                      grA  r&   r&   r/   r0   r   rB    s    Rr/   )r  rE   r   r  r  r~  r   )r>  r  scale_factorsspatial_dimensionsrx  r  s         r0   upsample_compute_output_sizerL    s    Z1,T!O	
 	S%);;ZH 4O	
 	S'+==zJm,DA1v{"":!e#4s1v#=>""7:!e+<q+@#AB	 -
 	LLRr/   c                     U c  g X   $ r9   r&   )scalesr  s     r0   get_scale_valuerO    s    ~;r/   rJ  c                 ~    [        U R                  5       X5      nU(       a  UOS /[        U5      -  n[        XU5      $ r9   rL  r+  r  _upsample_nearestr   r  rJ  osizerN  s        r0   _upsample_nearest_vecrU    s<     ){RE&TFSZ,?  U622r/   c                 |    [        U R                  5       X5      nU(       a  UOS /[        U5      -  n[        XUSS9$ NTexactrQ  rS  s        r0   _upsample_nearest_exact_vecrZ    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$ )Nr   r   r  r$   rZ   )r  r[   r  rE   r  r   r  r<   r  r\   r~  )r   r  rN  rY  r  num_spatial_dimsr  r  rT  isizeru   output_indicesinput_indicesr]   s                 r0   !_compute_upsample_nearest_indicesr`    s     G;'SsF#$ --12/5y/D*+%-e5==V(1U:>>u{{K'!+a/0A)33B7M 1}%+ %, Nr/   )preserve_memory_formatr  rN  c                     [        XU/5      $ r9   rR  r   r  rN  s      r0   upsample_nearest1dre    s     U&::r/   c                     [        XU/SS9$ rW  rc  rd  s      r0   upsample_nearest_exact1drg  
  s     U&FFr/   scales_hscales_wc                     [        XX#/5      $ r9   rc  r   r  rh  ri  s       r0   upsample_nearest2drl    s     U(1EFFr/   c                     [        XX#/SS9$ rW  rc  rk  s       r0   _upsample_nearest_exact2drn  %  s     U(1ETRRr/   scales_dc                     [        XX#U/5      $ r9   rc  r   r  ro  rh  ri  s        r0   upsample_nearest3drr  4  s     U(h1OPPr/   c                     [        XX#U/SS9$ rW  rc  rq  s        r0   _upsample_nearest_exact3drt  B  s     X:$ r/   rY  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$ )NrX  r@  r$   cudarV  )r`  r   _unsafe_indexr|  rJ   r   r  r  r  rE   r[  r  )	r   r  rN  rY  spatial_indicesr  r  rW  
n_channelss	            r0   rR  rR  T  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$ s  snf )Nr  r@  r   r%   r   )r  r[   r  )params
has_biaseshas_projections
group_sizerx  s        r0   gather_paramsr  o  s|    o
	
	

v;#q(5#f+5(38CK3T3Taf()3T  s   "A>c                 x    U(       a%  U SU-     USU-     pTU SU-  S-      USU-  S-      pvOX   X   pTSu  pgXEXg4$ )Nr%   r$   NNr&   )r{  hiddensrx  bidirectional
cur_params
cur_hiddenbidir_paramsbidir_hiddens           r0   params_hiddensr    s[    !'AAJ%+AEAI%6A	8Jl!'GJJ%/"<==r/   c                 ~    X:  d   eUR                  U R                  SX!U-
  5      5        U R                  SSU5      $ rz   )r~  r,  )r  last_batch_size
batch_sizer  s       r0   update_hidden_for_packedr    sA    '''NN:$$Q
j4PQRQ:..r/   c           	      t    X:X  a  U $ X:  d   e[         R                  " U UR                  SXU-
  5      45      $ rz   )rE   concatr,  )r  r  r  
inp_hiddens       r0    update_hidden_for_packed_reverser    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$   r%   r   rZ   )
r,  rE   r  rt  r  r  r  r~  reverser-  )inphiddenr{  r|  	hidden_fnbatch_sizesr  	ih_weight	hh_weightih_biashh_biasstep_outputr  r  r  	split_inprx  r   
hidden_outs                      r0   one_layer_rnn_datar    sC    q	Iq	I%fQi4G%fQi4GK"$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$ )Nc                 D   > T" [         R                  " XU5      U -   5      $ r9   r   linearrx  r  r  r  r  r  nonlinearitys         r0   rQ   rnn_cell.<locals>.inner  s    AHHZGDqHIIr/   r&   r  rQ   s   ` r0   rnn_cellr    s    J Lr/   c                    ^  U 4S jnU$ )Nc                 r   > [         R                  " XU5      n T" [         R                  " XU5      U -   5      $ r9   r  r  s         r0   rQ   rnn_cell_data.<locals>.inner  s.    HHQ7+AHHZGDqHIIr/   r&   r  s   ` r0   rnn_cell_datar    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  flipr\   r~  r  rE   r-  r   )r  r  r{  r|  r  r  r  r  r  r  precomputed_inputr  r  rx  r   s                  r0   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$   r%   r   F)
rE   r
  r+  r\   r  r  r   mkldnn_rnn_layerr  r   )r  r  r{  r|  r  w0w1w2w3hxcxr  modehidden_size
num_layersr  r  rM  outputsra   hycys                         r0   mkldnn_one_layer_lstmr    sS   	B	BAYAY[[#[[#			Q	B			Q	BKD''!*KJ MKE ..
C	B	Biinn--55





!G$ 
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)r  )rM  )	transposer[   r  r~  rE   r-  rV   rP  )r   r  r{  r|  r  rP  rM  r  r  layer_fnfinal_hiddensrx  r  r  r  r  fwd_inp
fwd_hiddenbwd_inp
bwd_hiddens                       r0   _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$ Nr   Fr  )	unbindr  r  r   r  r  rE   r   stackr   r  r{  r|  r  rP  rM  r  r  r  r   r  s               r0   rnn_tanh_inputr  L  p     YYq\F6u5F$%**)=>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$ r  )	r  r  r  r   r  r  rE   r  r  r  s               r0   rnn_relu_inputr  k  r  r/   c	                     UR                  S5      n	[        X4S5      n[        U U	UUUUUUS[        [        U[        [        R                  5      S95
      u  pU
[        R                  " US5      4$ Nr   Fr  r  )	r  r  r  r   r  r  rE   r  r  datar  r  r{  r|  r  rP  rM  r  r  r   r  s               r0   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  rE   r   r  r  s               r0   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   )r  r  r  r  r  	hr_weight	chunk_dimgateschunked_gatesin_gateforget_gate	cell_gateout_gater  r  s                  r0   	lstm_cellr    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  r\   r   r  r  r  r~  r  rE   r-  r   )r  r  r{  r|  r  r  r  r  r  r  r  r  r  r  r   s                  r0   one_layer_lstmr    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@  rZ   r  )r  rE   r  rt  r,  r  r   r  r~  r  r  r  r  r-  )r  r  r{  r|  r  r  r  r  r  r  r  r  r  r  r  orig_hxorig_cxr  r  rx  r  hidden0hidden1r   s                           r0   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$   r  r   r%   T)rE   rN  _get_mkldnn_enabledrt  r	   from_iterabler  r  popr   r  bfloat16requires_gradr+  )
r   r  r{  ry  tdevicesr  dtypesr   r}  s
             r0   
use_mkldnn2select_one_layer_lstm_function.<locals>.use_mkldnnH  s    xx++--'DH$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       r0   select_one_layer_lstm_functionr  9  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+  rt  r  r  r  rE   r  )r   r  r{  r|  r  rP  rM  r  r  r  r  r   r  s                r0   	lstm_implr  k  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)r  )
r  r  r+  rt  r  r  r   r  rE   r  r  s               r0   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$   r%   r   )r  r   r  r   r   r  r  r  r  r  r  chunked_igateschunked_hgates
reset_gate
input_gatenew_gates              r0   gru_cellr	    s    YYq!_NXXjW=CCAqIN #nQ&77@@BJ #nQ&77@@BJq!^A%6%CDJJLH!Z/(::r/   c                 N   [         R                  " XU5      R                  SS5      n[         R                  " XU5      R                  SS5      nUS   US   -   R                  5       nUS   US   -   R                  5       n	US   US   U-  -   R	                  5       n
X-
  U	-  U
-   $ )Nr   r$   r   r%   r  r  s              r0   gru_cell_datar    s    XXcg6<<QBNXXjW=CCAqIN #nQ&77@@BJ #nQ&77@@BJq!^A%6%CDJJLH!Z/(::r/   c	                     [        X4S5      n[        U UR                  S5      UUUUUUS[        [        U[
        S95
      u  pU	[        R                  " U
S5      4$ )NFr   r  )r  r  r  r   r  r  rE   r  )r  r  r  r{  r|  r  rP  rM  r  r   r  s              r0   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	  rE   r  )r   r  r{  r|  r  rP  rM  r  r  r   r  s              r0   gru_implr    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$   )rL  r+  rO  rE   r  r   _upsample_bilinear2d_aar   r  align_cornersrJ  rT  scale_hscale_ws          r0   upsample_bilinear2d_aa_vecr    sP     ){REmQ/GmQ/G99>>11mg r/   c                     [        U R                  5       X5      n[        US5      n[        US5      n[        R                  R
                  R                  XX%U5      $ r  )rL  r+  rO  rE   r  r   _upsample_bicubic2d_aar  s          r0   upsample_bicubic2d_aa_vecr    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      $ r9   )rL  r+  r  _upsample_linear)r   r  r  rJ  rT  rN  s         r0   _upsample_linear_vecr    s7     ){RE+]$#e*1DFE-@@r/   r  c                     [        XX#/5      $ r9   r  )r   r  r  ri  s       r0   upsample_linear1dr   "  s     EzJJr/   c                     [        XX#U/5      $ r9   r  )r   r  r  rh  ri  s        r0   upsample_bilinear2dr"  -  s     E(?STTr/   c                     [        XX#XE/5      $ r9   r  )r   r  r  ro  rh  ri  s         r0   upsample_trilinear3dr$  <  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$   rn   r   r&   )r  r  r  ru   s       r0   _compute_scaler&  M  s@    5=\#(S.1HqH#/EAIsU{U7CUUr/   c                 ,    U(       a  X-  $ XS-   -  S-
  $ Nr   r&   )ru   	dst_indexr  s      r0   _compute_source_indexr*  T  s       C(3..r/   weightsweights_precisionc                     [        S [        X5       5       5      SUS-
  -  -   nX2-	  n[        R                  " USS5      R	                  [        R
                  5      $ )Nc              3      #    U  HF  u  pUR                  [        R                  5      UR                  [        R                  5      -  v   MH     g 7fr9   )r<   rE   rB  )r  r  r  s      r0   r  %_sum_tensors_uint8.<locals>.<genexpr>^  s5      :K$!U[[ADD--:Ks   AAr$   r      )_sum_tensorsr  rE   r   r<   rT  )r  r+  r,  r  s       r0   _sum_tensors_uint8r2  [  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   )rE   r  r   r  r  r   )r+  
max_weightmax_weight_precision
precisionsvaluesr  s         r0   _compute_weight_precisionr9  e  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$   r%   r]  c                 `  > [        XT	U5      n[        R                  " UTR                  S9R	                  T
S9n[        XET	5      R                  SS9nUR                  " UR                  S   /S/U-  Q76 nUR	                  [        R                  5      nUS-   R                  U S-
  S9nXgU4$ )Nr  r   r   r   r   r$   r   )
r&  rE   r  r  r<   r*  r   r$  r  r  )inp_sizer  rN  nsqueezescale_factorrx  x_f32r=   xp1r  r   r   s            r0   
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   rn   rv     rV  )r  r  rJ   rK   r_  INT_TO_FLOATr  r  rt  r
   r[   r   rw  r   r~  reversedr   r<   rE   r   r   r  r  r[  r;   r   r  rT  round)r   r  r  rN  ry  	inp_sizesn_dimsr]   rA  rx  r<  r  r8  xs_f32xsxp1svsr  kr  vxscalev1v2r  rW  r   s   ` `                       @r0   r  r  n  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""$$MQ V
s   ?I1
I9*I>r  r	  c                 4    U R                   UR                   :H  $ r9   r  )r  r	  s     r0   is_same_sizerS    s    77aggr/   c                 ,    [         R                  X5      $ r9   )r   r  )r=   r  rL   s      r0   _reshape_aliasrU    s     99Qr/   c                 ,    [         R                  X5      $ r9   )r   r  )r=   r  s     r0   rw  rw    s    ::a!!r/   c                 .    [         R                  XX#5      $ r9   )r   r  )r=   r  r   r.  s       r0   r0  r0    s    >>!e88r/   c                    U HK  nUc  M  [         R                  " UR                  [         R                  [         R                  4;   S 5        MM     [         R                  " UR                  [         R
                  :H  S 5        SSKJn  U" U R                  5       S:H  5      (       a;  [         R                  R                  X5      nU R                  UR                  U5      $ [        [        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      $ )Nc                      gNz3tensors used as indices must be long or int tensorsr&   r&   r/   r0   r   &_unsafe_masked_index.<locals>.<lambda>  r  r/   c                      gNz*tensors used as masks must be bool tensorsr&   r&   r/   r0   r   r[        <r/   r   r[  r$   r  )rE   r   r   rq  r  r  rr  r\  r   _meta_registrationsmeta_index_TensorrE  r  r[   r  r   r+  r   rw  rr  )r=   r  r  fillr  r\  meta_resultrx  s           r0   r  r    s   LL

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

ejj <
 Eaggi1n%%//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rZ  r&   r&   r/   r0   r   5_unsafe_masked_index_put_accumulate.<locals>.<lambda>  r  r/   c                      gr]  r&   r&   r/   r0   r   re    r^  r/   r   r$   r  Tr-  )rE   r   r   rq  r  r  r   r  r[   r  r   r+  rr  r   r0  )r=   r  r  r8  r  rx  masked_values          r0   #_unsafe_masked_index_put_accumulaterh    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   )rV   r  r  rE   rp   r\   gatherr   r"   r+   r   rE  r  r   r<   r-   r,   )r   r   r   r   r   rH  r%  r  wr&  safe_target_r  r!  wsums                 r0   _nll_loss_forwardrn    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      $ )Nr   r%   r7  r$   r8  r9  r:  r;  rZ   z/weight tensor should be defined either for all z7 classes or no classes but got weight tensor of shape: )rV   r  r   rn  )r   r   r   r   r   r=  	n_classess          r0   nll_loss_forwardrq  9  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      $ r9   )rn  )r   r   r   r   r   s        r0   nll_loss2d_forwardrs  V  s     T6lKKr/   Ac                 0    US-   U -  US-   -
  U -  U -  S-   $ )Nr%   r   r$   r&   r=   rt  s     r0   _upsample_cubic_convolution1rw  d  s(    UaK1q5!Q&*Q..r/   c                 :    X-  SU-  -
  U -  SU-  -   U -  SU-  -
  $ )Nr     r@  r&   rv  s     r0   _upsample_cubic_convolution2rz  h  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  rn   r   r   r   )r  rE   r  rz  rw  r  )
r  rt  tt1tt2w03w12r  r  r  r  s
             r0    _upsample_get_cubic_coefficientsr  l  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      $ )Nc              3   .   #    U  H  u  pX-  v   M     g 7fr9   r&   r  r  r  s      r0   r  +_upsample_cubic_interp1d.<locals>.<genexpr>  s     E0DHR0Dr  )r  r1  r  )r  r  coeffs2s      r0   _upsample_cubic_interp1dr    s"    .r2GEF0DEEEr/   c                 6    [        [        R                  U 5      $ r9   )r   rE   r  )r  s    r0   r1  r1    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   )rE   r  linspace)r  r  r   r  r  s        r0   _linspace_from_neg_oner    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  r  r  rE   r  r  r%  r  )	r  r  rk  r  r   r  grid_xgrid_ygrid_ones	            r0   _make_base_grid_4dr    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$   r  )r   r   r  r   r  )r$   r%   )r%   r$   )r   r   r  )r  r  r  rk  r  r   r  r  r  grid_zr  s              r0   _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      $ )Nr  rZ   r   r$   rX  r%   )r  r  r]  r\   r   )	r  r+  r  r2  r]   r  rk  	base_gridgrids	            r0   _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  rZ   r@  r$   rX  r   )r  r  r]  r\   r   )
r  r+  r  r2  r]   r  r  rk  r  r  s
             r0   _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$ )Nr  c                      g)NzCaffine_grid_generator needs 4d (spatial) or 5d (volumetric) inputs.r&   r&   r/   r0   r   'affine_grid_generator.<locals>.<lambda>  s    Ur/   r@  r  )rE   r   r  r  r  )r  r+  r  s      r0   affine_grid_generatorr    sF     
LLD	VU 4yA~(MRR(MRRr/   r  interpolation_modepadding_mode_expand_gridc           	        ^ ^^^^^^^^^^ ^!^"^#^$^%^&^'^(^)^*^+^,^- [         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$ )NzInvalid interpolation mode r&   )r  s   r0   r   "_grid_sampler_2d.<locals>.<lambda>  s    -.@-ABr/   c                     > ST  3$ )NzInvalid padding mode r&   )r  s   r0   r   r    s    -B<.+Qr/   coordsr+  rW   c                 J   > T(       a  US-  S-
  OUS-  nUS-  S-
  nX-  U-   $ r(  r&   )r  r+  r   ofsr  s       r0   unnormalize%_grid_sampler_2d.<locals>.unnormalize  s6     %2tczCs
Sj3|c!!r/   	twice_low
twice_highc                 D   X:X  a  [         R                  " U 5      $ 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   )rE   r  r   fmodfloorr<   int8rp   )r  r  r  
coords_mincoords_spancoords2extraflipss           r0   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%   rZ   r   )r  r+  coords_reflectedr  r  r  s      r0   compute_coordinates-_grid_sampler_2d.<locals>.compute_coordinates  sx    1MQ;;vq$(33#6vq!tax.#Q #6vr1t8a<#P ;;/D1H==r/   c                 $   > T" X5      nT" X!5      $ r9   r&   )r  r+  	coords_unr  r  s      r0   compute_source_index._grid_sampler_2d.<locals>.compute_source_index  s    -	"933r/   r%   r$   rJ  ysc                    > [         R                  " SU :*  [         R                  " U T:  [         R                  " SU:*  UT:  5      5      5      $ rz   rE   r  )rJ  r  iHiWs     r0   in_bounds_cond(_grid_sampler_2d.<locals>.in_bounds_cond"  sF      GU&&rBw0A0A!r'2PR70ST
 	
r/   r  wsc                    >^^ T" X5      mT(       a  TOSm[        UUUU	U
4S jU R                  [        R                  S9UR                  [        R                  S9U4 5       5      $ )Nr$   c              3   x   >#    U  H/  n[         R                  " TUS 5      R                  TTTT5      v   M1     g7fr  )rE   rp   r  )r  r  r  r  r  oHoWs     r0   r  1_grid_sampler_2d.<locals>.clip.<locals>.<genexpr>1  s9      
M KKa#((Ar266Ms   7:r   )r  r<   rE   r  )rJ  r  r  r  r  r  r  r  r  r  r  s      @@r0   clip_grid_sampler_2d.<locals>.clip*  s\    b%
 A1 
 
ee%++e.EKK0H"M
 
 	
r/   ixiyc                 2   > T	" XU5      u  p4nTTTXC4   U-  $ r9   r&   )
r  r  rk  idx_xidx_yw_C_idxN_idxr  r  s
         r0   get_summand%_grid_sampler_2d.<locals>.get_summand6  s*    ?bu+,r11r/   ).r   ).r$   r   c              3   <   >#    U  H  u  pnT" XU5      v   M     g 7fr9   r&   )r  r  r  rk  r  s       r0   r  #_grid_sampler_2d.<locals>.<genexpr>L  s*      
  "" s   c                 :   > T" U T5      nT" UT5      nT" X#S5      $ rc   r&   )r  r  r=   ra   r  r  r  r  s       r0   get_value_bounded+_grid_sampler_2d.<locals>.get_value_boundedk  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%   )r  )r  iy_ofscsr  ix_nwiy_nwtxs      r0   	get_coeff#_grid_sampler_2d.<locals>.get_coeffp  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r9   r&   )r  r  r  s     r0   r  r  z  s     :#y~~   r@  )rE   r   r   r  r  r  r  r  r  r   r  r1  rF  r\   r  r[   r  ).r  r  r  r  r  r  r  r]   twor=   ra   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tyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  s.   ` ````                     @@@@@@@@@@@@@@@@@@@r0   _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$ )N)r  r  r  r  )r  )r  r  r  r  r  s        r0   grid_sampler_2dr  ~  s      	-!# r/   c                 2  ^ ^ [         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  U U4S j5        [         R                  " T R                  S5      TR                  S5      :H  U U4S j5        T T-  R	                  SS9$ )Nr%   r$   c                  L   > ST R                  5        STR                  5        3$ )Nzmatrix @ vector expected, got r  r   r   r  s   r0   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 (r;  r  r  s   r0   r   r    s:    ,TYYq\N!DIIaL>RURZRZ[\R]Q^^_`r/   r   )rE   r   rV   r+  r   r  s   ``r0   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      $ rc   )r   
logsigmoidr   )r   r   r   
pos_weightr   
log_weightr   s          r0    binary_cross_entropy_with_logitsr    sr    
  1n.2
F
d"j1<<3E&EFF
d"Q\\$%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      $ )
Nr   r[  r   r%   FTr$   rZ   c              3   b   >#    U  H$  u  pnT" US :H  5      =(       d
    T" X:H  5      v   M&     g7fr  r&   )r  r   r   r+  r\  s       r0   r  should_fold.<locals>.<genexpr>  s9      "
D 	tqy!B^DM%BB"
s   ,/)r|  rr  r\  r  r   r  ru  rE  r~  r  r  rt  )
r  r  r  t1t2t1_shape	t1_strideexpected_strider+  r\  s
            @r0   should_foldr    s     $+<<7<<#?ggEWFBDGGqLRWW\	||qbhhjAo&&xxH		I cO!"&tb&99: ' !$tH_56"
  r/   )pass_is_out)r  c                
   SSK JnJn  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  Xe:  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      $ US:  Ga  US:  Ga  US:  a  U R1                  S5      OSnU R1                  S5      nU R                  S S nUS:  a  UR1                  S5      OUR1                  S5      nUS:  a  UR1                  S5      OSn/ n[3        US-
  5       H#  nUR%                  UR1                  U5      5        M%     US:X  a  US:X  a  U" US   US   :g  5      (       a}  U" US   S:H  5      (       a,  U R4                  (       a  [7        U R                  S5      U5      $ U" US   S:H  5      (       a+  UR4                  (       a  [7        XR                  S5      5      $ [        [        R8                  " UU5      5      nUUU/-   n[;        U5      nU R=                  U5      R'                  UUU5      nUS:H  nU(       a7  UU/-   nUR=                  U5      R'                  UU5      R                  S5      nO)UUU/-   nUR=                  U5      R'                  UUU5      nUnUS:  a  UR%                  U5        US:  a  UR%                  U5        U(       a/  UR?                  U5      R                  S5      RA                  U5      $ UR?                  U5      RA                  U5      $ [        RB                  " SS	 5        g )
Nr   )r\  guard_or_truer$   r%   rZ   rX  r   Fc                      g)Nz/both arguments to matmul need to be at least 1Dr&   r&   r/   r0   r   matmul.<locals>.<lambda>J  s    $Ur/   )"rr  r\  r  rV   rE   dotr  r   r  r\   r  r]  r  r  rt  r   r  r   r~  r$  r  r   _unsafe_viewr  r+  r[   r  r\  broadcast_shapesr/  r  bmmr  r   )r  r  r  r\  r  dim_tensor1dim_tensor2r  r  r  sizes_1output_shapefolded_dim1t2_is_matrix	t1_foldedr  r2  m1batch_tensor1m2rP  batch_tensor2rx  expand_batch_portiontensor1_expand_sizeexpand_batch_producttensor1_expanded
vector_rhstensor2_expand_sizetensor2_expandeds                                 r0   r\  r\    sg    T++-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 mA.-2BBCCmA.!3449N9Ngooa0'::mA.!3449N9Ngq'9::  $""=-@ 
 3aW<#$89 #>>*=>FF !R
 !A%
"6""=23-r21  #7"a"@&~~.ABJJ$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$   r]  r  r   rZ   r   rn   r%   r  r   c                    > [         R                  " U STS-
  5      n[         R                  " USTS-
  5      n[        R                  TS S X#/5      nU$ r  )rE   r   r   rw  )r  rJ  y_idxx_idxrN  in_hin_wr   s        r0   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r9   r&   )r  x_ofsr9  ra   s     r0   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r9   r&   r  s      r0   r  r>    s     J4IBG4Ir  )r  r   rE   rT  r2  r1  r  )ra   src_xr   ixs_ofsr9  weights_precision_x	weights_xs   ` r0   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r9   r&   )r  y_ofsrD  s     r0   r  -upsample_bicubic2d_default.<locals>.<genexpr>  s     ;7%,u%%7r  c              3   .   #    U  H  u  pX-  v   M     g 7fr9   r&   r  s      r0   r  rH    s     L6K(2bg6Kr  rV  )r  r&  rJ   rK   r_  rD  rE   r  r  r<   r*  r\   r  r   r  r  r   rT  r9  r   int16r  r2  r1  r  r   r  )r   r  r  r  r  r]   h_scale_factorw_scale_factorr   rx  r  x_floaty_floatr=   ra   yscalerO  iys_ofs	weights_yweights_precision_yrk  src_yr  rW  rD  r7  r8  rA  r9  rB  rC  s   `                       @@@@@@@r0   upsample_bicubic2d_defaultrT  M  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$   c                      g)Nz:Must specify exactly one of output_size and scale_factors.r&   r&   r/   r0   r   (upsample_bicubic2d_vec.<locals>.<lambda>  s    Lr/   c              3   T   #    U  H  u  p[        [        U5      U-  5      v   M      g 7fr9   )r   r   )r  rk  ru   s      r0   r  )upsample_bicubic2d_vec.<locals>.<genexpr>  s*       ?HA 	!u,-- ?s   &(r%   r  )	rE   r   r  r   r  r  r  r  rT  )r  r  r  rJ  r  r  s         r0   upsample_bicubic2d_vecrZ    s     
LL[D//14L (((#s(O  #AGGABK ? 
 )6}<G%amgVVr/   c                 *   ^  U 4S jn[        T UU5      $ )Nc                    > [         R                  " U * X-   TR                  S9nUS-
  US-
  UR                  5       -
  R                  5       -
  $ )Nr  r$   )rE   r  r  r   r   middler   dim_idxr  s       r0   r  _reflection_pad.<locals>.idx  sD    ,,ufnQXXFzVaZ'++-7<<>>>r/   _reflection_or_replication_padr  r  r  s   `  r0   _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$   )rE   r  r  r   r]  s       r0   r  _replication_pad.<locals>.idx  s4    ,,ufnQXXF{{7Avz22r/   ra  rc  s   `  r0   _replication_padrh    s     3 *	 r/   idx_fnc                 r  ^ [        U5      S-  m[        R                  " U R                  5       TS-   TS-   4;   U4S j5        U R                  T* S  nU R                  5       T-
  n[        T5       Vs/ s H  oQSTS-
  U-
  -     PM     nn[        T5       Vs/ s H  oQSTS-
  U-
  -  S-      PM     nnU n[        T5       HA  nS /UR                  5       -  n	U" Xe   X5   Xu   5      XU-   '   [        R                  X5      nMC     [        R                  " U5      n
UR                  U
S9nU$ 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   r0   r   0_reflection_or_replication_pad.<locals>.<lambda>  s"    .[q	sQwiwOr/   rV  )r  rE   r   rV   r  r[   r   rw  rJ   r   r  )r  r  ri  	inp_shapenc_dimrx  padding_leftpadding_rightr  r  rW  rV   s              @r0   rb  rb    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$   rZ   r  c                 B    U u  pn[         R                  " X:  X:*  5      $ r9   r  )index_rangerx  lbubs       r0   index_range_condition7_reflection_pad_backward.<locals>.index_range_condition  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   )r[   r;   r  rS   r   r   r  r  )r   r   index_rangesrx  upper_less_than_lowerrt  r  gr	  rV   rs   rw  s           r0   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 
)rZ   r   r$   )r  r  r[   r|  r~  rE   r  r  r  rS   r   r   r  r  	itertoolsr
   r  )rs   r=   r  r  dhwrx  rp  rq  r  
view_shapexyzcenterleft_reflectright_reflectrange_cr  r   r.  r]   areaoutsrz  r   rt  r	  rV   rw  s   `                       @@@r0   _reflection_pad_backwardr    s1   
 g,!
C''3$%.
).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$ )Nr  )rE   aminra  )r   rV   r  r  ra  s        r0   aminmaxr  Y  s,     ::dW5D::dW5D:r/   r   c                    [         R                  [        R                  " [        R                  " U 5      SU 5      XUS9$ )Nr   r   )r   r   rE   rp   isnan)r   rV   r  r   s       r0   nansumr  c  s0     88EKKD 11d;SQV8WWr/   r   rM  r  rg  rM  c          
      D    [         R                  R                  SU SXX4S9$ )Nr   r$   r  r   r  
start_step)ri  r   rM  r  rg  s        r0   arange_defaultr  i  s+     ;;!!	3f "  r/   c          
      B    [         R                  R                  XSX#XES9$ )Nr$   r  r  )rh  ri  r   rM  r  rg  s         r0   arange_startr  x  s)     ;;!!AU& "  r/   c                      SSK Jn  U" U 0 UD6$ )Nr   )out_dtype_dense)!torch._higher_order_ops.out_dtyper  )rL   rM   r  s      r0   out_dtype_decompr    s    AD+F++r/   marginc                   ^ ^^^	^
 [         R                  " T 5      m [         R                  " T5      mT R                  S   m
T R                  S   m	[         R                  " US:H  =(       d    US:H  S 5        [         R                  " T R
                  S:H  =(       a    T	S:g  U 4S j5        [         R                  " TR
                  S:H  =(       a    TR                  5       T
:H  U
U4S j5        TbY  [         R                  " T5      m[         R                  " TR
                  S:H  =(       a    TR                  5       T	:H  U	U4S j5        TR                  S5      m[         R                  " T STS9nX6-
  T -   nUR                  S5      nUS:X  a  UOXw-  nTb  UTT   -  n[         R                  " T	T R                  S	9n[         R                  " UT:g  US5      nU[        R                  R                  :X  a  UR!                  5       $ U[        R"                  R                  :X  a   UR%                  5       UR                  S   -  $ UR!                  SS
9$ )Nr   r$   r%   c                      g)Nz only p == 1 and p == 2 supportedr&   r&   r/   r0   r   #multi_margin_loss.<locals>.<lambda>  s    +Mr/   c                  "   > ST R                    3$ NzMExpected non-empty vector or matrix with optional 0-dim batch size, but got: r  r  s   r0   r   r    s    _`e`k`k_lmr/   c                  (   > ST  STR                    3$ )Nz#inconsistent target size, expected r'  r  )nframer   s   r0   r   r    s    5fXYv||nUr/   c                  (   > ST  STR                    3$ )Nz#inconsistent weight size, expected r'  r  )rV   r   s   r0   r   r    s    9#i~Vr/   r  r  r   )rE   
atleast_2d
atleast_1dr  r   r|  r   r\   rj  r^  r  r  rp   r"   r,   r   r   r-   r   )r   r   rP  r  r   r   urq   r  rV   r  s   ``  `    @@r0   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   r0   r   0multilabel_margin_loss_forward.<locals>.<lambda>  s    _`p_qrr/   c                     > ST ST  3$ )Nzinconsistent target size: z for input of size: r&   )r  orig_target_shapes   r0   r   r    s    ,->,??STdSefr/   r  rZ   Tr  r  r   rn   )r   rZ   )r  rE   r  r   r  r  r  r  rp   rj  anyr\   Tr^  r"   r,   r   r   r   r-   r<   r   r$  )r   r   r   rV   r  is_endend_idxtarget_masktidx0r  tidx1r  rq   r  r  s                @@r0   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!$AINN(((EEgE##%	imm))	)EEGEEgEU[[)112CDI<r/   )	attn_maskru   querykey	dropout_p	is_causalr  c                6  ^ ^^^ [         R                  " [         R                  " T 5      U 4S j5        [         R                  " T R                  5       S:H  =(       a-    TR                  5       S:H  =(       a    TR                  5       S:H  UU U4S j5        [         R                  " TS:H  U4S j5        [         R                  " T R                  S   TR                  S   :H  =(       a    TR                  S   TR                  S   :H  S 5        [
        R                  R                  T TTUTUS UT R                  S5      TR                  S5      :g  S	9	u  pxUR                  S
SSS5      R                  [         R                  S9R                  SS
SS5      nXx4$ )Nc                  "   > ST R                    3$ )Nz-query must be FP32, FP64, BF16, FP16 but got r   )r  s   r0   r   <scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>	  s    ?}Mr/   r@  c                  n   > STR                  5        ST R                  5        STR                  5        3$ )Nz,q, k, v must be a 4 dimensional tensor, got r  r   )r  r  r   s   r0   r   r    s1    >uyy{m2cggi[XZ[`[d[d[fZghr/   r   c                     > ST  3$ )Nz&dropout probability must be zero, got r&   )r  s   r0   r   r    s    $J9+"Vr/   r   c                      g)Nz&q, k, v should have the same head sizer&   r&   r/   r0   r   r    s    8r/   r$   )r  r  r  dropout_maskru   
enable_gqar%   r   rV  )rE   r   rT  rV   r  r   "_scaled_dot_product_attention_mathr  r+  r  r  r[  )	r  r  r   r  r  r  ru   r  attns	   ````     r0   *scaled_dot_product_flash_attention_for_cpur    sR    
LL&M 
LL		q@SWWY!^@		q0@h 
LLSV 
LLA%++a.(KSYYq\U[[^-K8
 ::BB::a=CHHQK/ C 
LFF 	q!Q"	%"9"9	:	Aq!	 
 <r/   c                 0   ^ [        U 5      U4S j5       nU$ )Nc                  <   > T" U 0 UD6nU S   R                  U5      $ rz   )r*  )rL   rM   r   outplace_ops      r0   
inplace_op$register_inplace.<locals>.inplace_opB  s%    4*6*Aw}}S!!r/   r   )aten_opr  r  s    ` r0   register_inplacer  A  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-   $ rB  )rT  r  r  rE   r   r;   numbersNumber)r   batch1batch2rj   rt   r  s         r0   baddbmmr  J  s     !!##DOO,=,=4yE
YYv&FeW^^,,
qydGNN++tqy{=r/   c                 ,    [         R                  " XSS9$ )Nr  r  r  )r   rO  s     r0   floor_divider  \  s     99T88r/   c                 b    [         R                  " [        R                  U R                  S5      $ rc   )rS   r   r  r   r  )r  s    r0   	sym_numelr  b  s    HLL!''155r/   r   r   c                    Uc  [         R                  R                  U / US9$ [         R                  R                  U / XS9$ )Nr   r  )r   r   dim_IntListIntList_out)r   r   r   s      r0   sum_defaultr  g  sA     {xx##D"E#::xx##D"E#CCr/   c           	      
   [        U [        R                  5      (       d  U $ Uc@  [        R                  R                  U [        [        U R                  5       5      5      5      $ [        R                  R                  X/5      $ r9   )	r;   rE   r   r   r   dimsrt  r[   rV   )r   rV   s     r0   squeeze_defaultr  t  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r9   r&   )r  rx  rV   s     r0   r  )_weight_norm_interface.<locals>.<genexpr>  s     @ 31CxQQ 3s   		r%   T)r  r   )
r  r[   r  r  r   rE   r  r  r   r<   )rN  r|  rV   keep_dim
norm_dtyper   s     `   r0   _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      $@g(\?r  r  )r;   rE   r   r  r  ner  r   rY  isin_defaultisin_sorting)elementstest_elementsr  r  s       r0   isinr    s     h--<<1E1EFmU\\2288H4488H44tc(..*:E&BBBHFCC=
 	
r/   )re  c                :   Uc=  [         R                  " U R                  5       [         R                  U R                  S9nO=[         R                  " U R                  5       U[         R                  U R                  S9nX :  R                  U R                  5      nU$ )Nr  )re  r   r  )rE   randr+  r   r  r<   r   )r   re  raw_prP  s       r0   	bernoullir    so     

499;emmDKKP

IIK--;;	
 
$**%AHr/   r  c                L   U R                  5       S:X  a#  [        R                  " U [        R                  S9$ U R                  SUR
                  -  -   nU R                  U5      n[        [        SUR
                  * S-
  S5      5      nXA:H  R                  US9nU(       a  U) $ U$ )Nr   r   )r$   rZ   r$   r   )
r   rE   
empty_liker  r  r|  r  r  r[   r  )r  r  r  expanded_elem_shaper=   rV   rW  s          r0   r  r    s    ~~1

;;"..4-2D2D+DD)*A
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$   rZ   r   F)rD  rE   r-  sortr|  logical_notr  r0  r   searchsortedrp   r$  r  )r  r  r  r  elements_flattest_elements_flatall_elementssorted_elementssorted_orderduplicate_maskr  sorted_test_elementsr]   r  test_idxcmps                   r0   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!   $ rY   )r$  )r   r  	flatteneds      r0   taker    s     R Ir/   c                     Uc  [         R                  nU[         R                  :X  a  [        U5      n[        R                  XR                  US9$ r;  )rE   r[  preserve_formatr   r   resizer  )r   rO  rW  s      r0   	resize_asr    sB    //----e4;;t[[;FFr/   )FF)noner9   )r%   )r   NNr$   )rZ   FFr  r(  r  )r$   r$   F)Fr   )r   rn   N)r   r$   N)Fr  )NNN)r   r   FT)r   r   Fr9  )r   F(  rS   r~  r  r  rv  collections.abcr   r   
contextlibr   enumr   r   r   r	   r
   typingr   r   r   r   rE   torch._meta_registrationstorch._primsrn  r:  torch._prims_common_prims_commonrJ   torch.nn.functionalr  r%  r   r   r   r   torch._decompr   r  r   r   r   r   r   r   torch._prims_common.wrappersr   r   r   r   torch.utilsr   rH   torch.utils._pytreer   rN  DispatchKeyr    rt  str__annotations___opsr  r   r"   r_  r  rU   r`  compute_only_pw_cast_for_opmathpw_cast_for_opmath"pw_cast_for_opmath_non_tensor_argsrD  pw_cast_for_int_to_realr  r^   rg   ri   rr   r  r~   ra  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r   r   r   r   r   r,   r   r   _safe_softmaxr  r  r  r  r_   r  r  r   r  r(  r5  r>  rA  rG  rJ  rL  rN  rR  rf  rn  slicer  r  rm  r  r  r  r  r  r  r  r9  r=  rF  rL  rP  py_implCompositeImplicitAutogradAutogradrO  rd  rh  rn  rv  r/  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  r6  r<  r@  unsafe_chunkrC  r?  r>  no_statsrG  rK  rW  r]  ra  rc  _fused_dropoutrf  rs  r  rW  r  lift
lift_freshrv  r{  r~  r  r  r  r  r  _adaptive_avg_pool2dr  r  r  r  r  r  r   r(  r.  r0  r,  r6  r<  	Generatorr>  rL  rO  re  r  rl  rr  rU  _upsample_nearest_exact1drn  rt  rZ  r`  rg  rR  r  r  r  r  r  r  r  r  r  r  rnn_tanhr   r  rnn_relur  r  r  r  r  r  r  r  lstmr  r  r	  r  grur  r  r  r  r  r  r"  r$  r   r  r&  r*  r2  r9  r  rS  rU  r  rw  r0  r  rh  rn  rq  rs  rw  rz  r  r  r1  r  r  r  r  r  r  r  r  r  r  r  r\  upsample_bicubic2drT  rZ  reflection_pad1dreflection_pad2dreflection_pad3drd  replication_pad1dreplication_pad2dreplication_pad3drh  rb  reflection_pad1d_backwardreflection_pad2d_backwardreflection_pad3d_backwardr  r  r  r  rk  rM  r  rh  r  r  r  r  +_scaled_dot_product_flash_attention_for_cpur  r  r  r  r  r   r  r   rV   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_rF  scatter_r#  scatter_add_scatter_addscatter_reduce_scatter_reducesilu_r&   r/   r0   <module>rc     sFN       
 . "  % $ - -     #   , , 0 7   * ( hh"" c zz~~   %$)	''99' ' "	'T #*88@@# 
 uDDLL  &-88@@ & "
 "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 

))* 3?
3? 
3? C=	3?
 
#3? 3? +3?l (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   +0 ' $  	
    (& 556  	
   7:DI &\	  
&\	*T&\ 
tF| 
# 
"&\"	" "J 00$//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;	&/&/T 

# 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??@OOO 3iO 	O
 O VO 6
O dO 8FXf-x/??@O AOf 77;;< 3i 	
  V 6
 d ,, ,, ,, 8FXf-x/??@ =4 ,,445333i3 V3 
%	3
 66>3 63l 55==>GGG 3iG 	G
 VG dG 8FXf--.G ?GTO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 $  3 ,,d.?.?@A  B ++,-" ." //019 29 2234C 5C6 AABCM DM23 
3 3  V3  	3 
 3  66>3 l --.X~&L
LL VL 	L
 L 66>L ' /L6 //0X~&L
LL VL 	L
 L 66>L ' 1L/F /u / /5F 5u 5 5
 
3E 
(F%7 FV F F!Xf% !& !NN#'N05NEJ\\N&f & & &T &"/f / / / /T /"!V !49 !T !$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 ,,-  
  	
     .   	#   !	# ==>$)..:N:N1  ?1  d t @ [BBC>>?', vW  @ DvWr 0088$: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
 A #'!AA	A A 	A
 A A E?A 66>A RAH '   ( ))*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/   