
    shD                    :i   S SK r S SKr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JrJrJr  S SKJrJrJrJrJrJ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#  S SKJ$r$J%r%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8  S SK9J:r:J;r;J<r<J=r=J>r>J?r?  / S	Qr@\R                  rA\R                  R                  rC\R                  R                  R                  rFS
 rGS rHS rISS.S jrJS SKKJLrL  \M" 5       rN\NSSS.S\4S jjrOS rPS rQ\O" \*R                  SS9S 5       rS\O" \*R                  5      S 5       rU\O" \*R                  5      S 5       rV\O" \*R                  5      S 5       rW\O" \*R                  5      S 5       rX\O" \*R                  5      S 5       rY\O" \*R                  5      S 5       rZ\O" \*R                  5      S 5       r\\O" \*R                  SS9S  5       r]\L" \FR                  5      S!\64S" j5       r^\L" \FR                  5      \?" 5       S!\64S# j5       5       r_\O" \*R                  5      S$ 5       r`\O" \*R                  5      S% 5       ra\O" \*R                  5      S& 5       rb\O" \*R                  5      S' 5       rc\O" \*R                  5      S( 5       rd\O" \*R                  5      S) 5       re\O" \*R                  5      S* 5       rf\O" \*R                  5      S+ 5       rg\O" \*R                  5      S, 5       rh\?" 5       \=" S-\*R                  S.9S/\6S0\0S\64S1 j5       5       rjS/\6S0\0S\64S2 jrk\L" \FR                  5      \?" 5       S!\6S\64S3 j5       5       rl\O" \*R                  SS9S4 5       rm\O" \*R                  SS9S5\6S\64S6 j5       rnS/\6S\64S7 jro\O" \*R                  SS89S/\6S\64S9 j5       rq\O" \*R                  5      S/\6S\64S: j5       rr\O" \*R                  SS9S/\6S\64S; j5       rs\O" \*R                  SS9S/\6S\64S< j5       rt\O" \*R                  5      S/\6S\64S= j5       ru\P" \R                  R                  S>5      rx\O" \*R                  SS89S/\6S\64S? j5       ry\O" \*R                  \FR                  S89S@ 5       rz\O" \*R                  5      SA 5       r{\O" \*R                  5      SB 5       r|\O" \*R                  5      SC 5       r}\O" \*R                  5      SD 5       r~\O" \*R                  5      SE 5       r\?" 5        GSS/\6SF\SG\\GR                     S\64SH jj5       r\L" \FGR                  5      \?" 5       \=" SI\*R                  S.9 GSSJ\6SF\(SK\S\64SL jj5       5       5       r\L" \FGR
                  5      \?" 5          GSS/\6SM\\0   SN\\0   SO\\0   S\64
SP jj5       5       rS/\64SQ jr\O" \*R                  \SR9SS 5       rS/\6S\64ST jrS/\6S\64SU jr\O" \*R                  5      SV 5       r\L" \FGR                  5      \?" 5       \=" SW\*R                  S.9S SX.S/\6SY\S\64SZ jj5       5       5       r\O" \*R                  5      S[ 5       r\O" \*R                  5      S/\6S\64S\ j5       r\O" \*R                  SS9S] 5       r\O" \*R                  SS9S^ 5       r\O" \*R                  SS9S_ 5       r\O" \*R                  5      S` 5       r\O" \*R                  5      Sa 5       r\O" \*R                  5      Sb 5       r\O" \*R                  5      Sc 5       r\O" \*GR*                  SS89S/\6S\64Sd j5       r\O" \*R                  5      Se 5       r\O" \*R                  5      Sf 5       r\O" \*R                  SS9Sg 5       rSJ\6S\64Sh jr\NSSSSSS4S\4Si jjr\L" \FGR8                  5      \?" 5       \=" Sj\*R                  S.9SSk.S/\\6\04   Sl\\6\04   Sm\\0   4Sn jj5       5       5       r\" \*R                  SSSo9Sp 5       r\" \*R                  Sq9S/\6Sl\6S\64Sr j5       r\" \*R                  Sq9S/\6Sl\6S\64Ss j5       r\" \*R                  Sq9S/\6Sl\6S\64St j5       r\" \*R                  Sq9S/\6Sl\6S\64Su j5       r\" \*R                  Sq9S/\6Sl\6S\64Sv j5       r\" \*R                  SSw9S/\\6\04   Sl\\6\04   4Sx j5       r\L" \FGRH                  5      \?" 5       SSy.S/\\6\04   Sl\\6\04   Sz\\   4S{ jj5       5       r\" \*R                  SSw9S/\6Sl\6S\64S| j5       r\" \*GR*                  Sq9S/\\6\04   Sl\\6\04   S\64S} j5       r\?" 5       S/\\6\04   Sl\\6\04   S\A4S~ j5       r\" \RT                  R                  SSS9S/\\6\04   Sl\\6\04   4S j5       rS/\ASl\AS\A4S jrS/\ASl\AS\A4S jr\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\L" \FGR^                  5      \?" SS5      SJ\6S\\6\64   4S j5       5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSw9S/\6Sl\6S\64S j5       r\" \*R                  SSw9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S!\6S\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       rS\S/\6Sl\6S\S\SS4S jr   GSS/\6Sl\6S\S\S\S\64S jjr\" \*R                  SSSo9S/\6Sl\64S j5       r\" \*R                  SSw9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  Sq9S/\6Sl\64S j5       r\O" \*R                  5      S/\64S j5       r\" \*R                  Sq9S/\6Sl\64S j5       r\" \*R                  Sq9S/\6Sl\64S j5       r\" \*R                  SSw9S/\6Sl\6S\64S j5       r\" \*R                  Sq9S/\6Sl\6S\64S j5       r\" \*R                  Sq9S/\6Sl\6S\64S j5       r\" \*R                  SS9S/\6Sl\6S\64S j5       r\" \*R                  SSw9S/\6Sl\6S\64S j5       r\" \*R                  SSSo9S/\6Sl\6S\64S j5       r\" \*R                  Sq9S/\6Sl\6S\64S j5       r\L" \FGR                  5      \?" 5        GSS/\\6\04   Sl\\6\04   Sm\04S jj5       5       r\L" \FGR                  5      \?" 5       \=" Sj\*R                  S.9SSk.S/\\6\04   Sl\\6\04   Sm\04S jj5       5       5       r\" \*R                  SSSS9S/\6Sl\6S\64S j5       r\L" \FGR                  5      \?" 5       \=" Sj\*R                  S.9S/\\6\04   Sl\\6\04   4S j5       5       5       r\" \RT                  R                  SSS9S/\\6\04   Sl\\6\04   4S j5       r\L" \FGR                  5      \?" 5       \=" S\*R                  S.9SS.SJ\6S\6S\6S0\0S\64
S jj5       5       5       r\L" \FGR                  5      \?" 5       \=" S\*R                  S.9SS.SJ\6S\6S\6S0\0S\64
S jj5       5       5       r\L" \FGR                  5      \?" 5       \=" S\*R                  S.9  GSS/\6S\\7   S\\7   S\64S jj5       5       5       r\L" \FGR                  5      \?" 5        GSSJ\6S\\7   S\64S jj5       5       r\L" \FGR                  5      \?" 5        GSSJ\6S\\7   S\64S jj5       5       r\L" \FGR                  5      \?" 5       \=" Sj\*R                  S.9  GSS\AS/\\7   Sl\\7   4S jj5       5       5       r\L" \FGR                  5      \?" 5       \GR                  S.S/\6S\GR                  S\64S jj5       5       rSS.S/\ASl\A4S jjr\L" \FGR                  5      S/\6S\04S j5       r       GSS/\6S\\%   SG\\GR                     S\\   S\\GR                     S\\GR                     S\\   S\S\4S jjr\S 5       r\GR                     GSS\GR                  SG\GR                  S\S\S\\GR                     S\\\4   4S jj5       r\GR                     GSS\SG\GR                  S\S\S\\GR                     S\\\4   4S jj5       r\GR                     GSSG\GR                  S\S\S\\GR                     S\\\4   4
S jj5       r\GR                     GSS\AS\S\S\\GR                     S\\\4   4
S jj5       rS/\AS\4S jrS/\6S\64S jrSSSSSSS.S/\6S\S\S\S\\(   S\SG\\GR                     S\\A   S\2S\64S jjrS r\L" \FGR                  5      \?" 5         GSS/\6SF\\(   SK\S\64S jj5       5       r\L" \FGR                  5      \?" 5         GSS/\6SF\\(   SK\S\64S jj5       5       r\L" \FGR                  GR                  \FGR                  GR                  /5        GSSSS.S/\6SF\\\   \\\      4   SK\SG\\GR                     S\\A   S\64S jjj5       rS/\AS\A4S jr\L" \FGR                  5        GSSSS.S/\6SF\\\   \\\      4   SK\S\\A   S\64
S jjj5       r\L" \FGR                  5        GSSS.S/\6SF\\(   SK\S\\A   S\64
S jjj5       r\L" \FGR                  5        GSSS.S/\6SF\\(   SK\S\\A   S\64
S jjj5       rGSS jr\L" \FGR                  5      \?" 5          GSSS.S/\6SF\\(   S\\   SK\S\\0   S\64S jjj5       5       r\L" \FGR                  5      \?" 5          GSSS.S/\6SF\\\   \\\      4   S\\   SK\S\\0   S\64S jjj5       5       r\L" \FGR                  5        GSSSS.S/\6SF\\(   SK\S\64S jjj5       r\L" \FGR                  5      \?" SS5       GSSSSS.S/\6SF\\(   S\\   SK\S\\0   4
S jjj5       5       r\L" \FGR                  5      \?" SS5         GSSS.S/\6SF\\(   S\\   SK\S\\0   4
S jjj5       5       r\L" \FGR                  5      \?" 5       \=" S\*R                  S.9SSS.SJ\6S\6S\6S\0Sm\0S\64S jj5       5       5       rS\\6\	\6   4   S\6S\\6\\6S4   4   4S jrS\SF\S\6S\64S jrS\\6\	\6   4   S\6S\\6\\6S4   4   4S jrS\\6\	\6   4   S\6S\\6\\6S4   4   4S jr GSS/\6GS \3GS\4GS\\   S\64
GS jjr\L" \FGR                  5      \?" 5        GSS!\6GS\6GS \3GS\4GS\\   S\64GS jj5       5       rS\34GS jr\FGR                   GR                  GR                  \CGR                  5      \FGR                   GR                  GR                  \CGR                  5      S\\6   4GS j5       5       Gr S/\6GS \3S\64GS jGr\L" \FGR                  5      \?" 5       \=" GS	\*R                  S.9GSGS
\8SF\S\64GS jj5       5       5       Gr\?" 5       GS
\8S\64GS j5       GrS!\6S\64GS jGr\L" \FGR                  5      \?" 5        GSS!\6GS\\   S0\0S\64GS jj5       5       Gr	\GR                  S.S/\AS\GR                  S\A4GS jjGr\?" 5       GS
\8S\64GS j5       Gr\L" \FGR                  5      S/\AS\A4GS j5       GrS/\ASl\AS\A4GS jGrGSS/\6GS\SF\S\\6S4   4GS jjGrGSS/\6GS\GS\S\64GS jjGr\L" \FGR"                  5      \?" 5       S/\6S\'S\64GS j5       5       GrS/\6S\64GS jGrS/\6S\64GS jGrS/\6SF\GS\\\64   GS\S\64
GS jGrS/\AGS\(GS \S\\A\A\A4   4GS! jGrS5\6GS"\\   S\64GS# jGr\L" \FGR.                  GR                  5      S!\AGS$\\A   GS%\\A   GS&\GS'\GS(\GS)\GS \S\\A\A\A4   4GS* j5       Gr\L" \FGR0                  5      \?" SSGS+5      S!\AGS,\3GS$\\A   GS%\\A   GS \S\\A\A\A4   4GS- j5       5       Gr\GR2                  GR4                  GR7                  \FGR0                  GR                  5      GS. 5       Gr\L" \FGR:                  5      S/\6S\64GS/ j5       Gr\L" \FGR<                  5      \?" 5       S!\6GS0\1SF\GS1\1S\64
GS2 j5       5       Gr\FGR>                  GR@                  GR                  \CGR                  5               GSS!\AGS3\GS4\\   GS5\\   GS6\\A   GS7\GS8\GS9\GS:\\   GS;\\   GS<\\   S\A4GS= jj5       Gr\FGRB                  GR                  GR                  \CGR                  5              GSS!\AGS3\GS4\\   GS5\\   GS6\\A   GS7\GS9\GS:\\   GS\\   S\A4GS> jj5       Gr!GS?\3GS@\4GSA\GS \GSB\4
GSC jGr"\L" \FGRF                  5      \?" 5       S/\AS\A4GSD j5       5       Gr#S/\6GSE\S\64GSF jGr$S/\6GSG\3S\64GSH jGr%SJ\6S\6S\64GSI jGr&\L" \FGRN                  5      \?" 5       GSS/\6GSJ\(S\(S\64GSK jj5       5       Gr'\L" \FGRP                  5      \?" 5        GSS/\6GSM\S\'S\64GSN jj5       5       Gr(GS
\8SS4GSO jGr)\L" \FGRT                  5      \?" 5       GSGS
\8SF\S\64GSP jj5       5       Gr*\?" 5        GSS/\6SF\SG\\GR                     S\64GSQ jj5       Gr+\?" 5       GS
\8S\64GSR j5       Gr,\?" 5       GS
\8S\64GSS j5       Gr-S/\6SF\GST\3S\64GSU jGr.\L" \FGR^                  5      GSGSV\6SF\S\84GSW jj5       Gr/\?" 5       S5\5SF\GSX\5GSY\54GSZ j5       Gr0S5\5SF\GSX\5GSY\54GS[ jGr1\L" \FGRd                  5      \?" 5       S5\5SF\GSX\5S0\\0\54   4GS\ j5       5       Gr2\L" \FGRf                  5      S5\5SF\GSX\5S0\\0\54   4GS] j5       Gr3S5\5SF\GSX\5S0\\0\54   GS^\4
GS_ jGr4\?" 5       SSk.S5\5SF\GSX\5GSY\5Sm\04
GS` jj5       Gr5\L" \FGRl                  5      \?" 5       S5\5SF\GSX\54GSa j5       5       Gr6\L" \FGRn                  GRp                  5      GSS/\6SF\\(   S\64GSb jj5       Gr7\L" \FGRr                  5       GSSJ\AGSc\\   SF\S\\A   4GSd jj5       Gr9 GSS/\6GSe\\A\(4   SF\S\\6S4   4GSf jjGr:S/\6GSe\(S\\6S4   4GSg jGr;S/\6GSe\(S\\6S4   4GSh jGr<\L" \FGRz                  GR|                  5      \?" 5        GSSJ\6GSi\S\64GSj jj5       5       Gr=\L" \FGR~                  5      \?" 5          GSS!\6GS\6GSi\GSk\GSl\S\64GSm jj5       5       Gr?\L" \FGR                  5         GSSJ\6GSi\GSk\GSl\S\64
GSn jj5       Gr@\L" \FGR                  5      \?" 5          GSGSV\6GSi\GSk\GSl\S\64
GSo jj5       5       GrA\L" \FGR                  5      \?" 5       GS
\\6   S\64GSp j5       5       GrCGS
\\6   S\64GSq jGrBS/\6GSr\(S\84GSs jGrD\L" \FGR                  GR                  5      S/\64GSt j5       GrES/\6S\64GSu jGrF\L" \FGR                  5      S/\6S\64GSv j5       GrG\L" \FGR                  5      S/\6GSw\GSk\S\64GSx j5       GrHG\HGrI\L" \FGR                  5      SJ\6GSA\GS \GSB\S\64
GSy j5       GrJ\L" \FGR                  5      \?" 5       SJ\6GSA\GS \GSB\4GSz j5       5       GrKSSS.S/\6SF\SG\\GR                     S\\A   S\64
GS{ jjGrL\L" \FGR                  5      SSS.S/\6SF\SG\\GR                     S\\A   S\64
GS| jj5       GrM\L" \FGR                  5      SSS.S/\6SF\SG\\GR                     S\\A   S\64
GS} jj5       GrN\L" \FGR                  5      S/\6SF\S\64GS~ j5       GrO\L" \FGR                  GR                  5      S/\6GSG\3S\64GS j5       GrPSJ\6S\6S\64GS jGrQS/\6S\64GS jGrR\?" 5        GSS/\R                  GS\R                  SF\\   S\R                  4GS jj5       GrS\?" 5       S\GR                  SSS\GR                  GS.SG\\GR                     S\GR                  S\\%   GS\S\S\GR                  S\64GS jj5       GrU\?" 5       S\GR                  SSS4SG\\GR                     S\GR                  S\\%   GS\S\S\64GS jj5       GrV\L" \FGR                  5      \?" 5       SSSSGS.S/\6GS \3SG\\GR                     S\\GR                     S\\%   S\S\64GS jj5       5       GrW\L" \FGR                  5      \?" 5       SSSSGS.S/\6GS \3GS\4SG\\GR                     S\\GR                     S\\%   S\S\64GS jj5       5       GrX\L" \FGR                  GR                  5      \?" 5       S\GR                  SSSGS.SG\\GR                     S\GR                  S\\%   S\GS\S\64GS jj5       5       GrY\L" \FGR                  5      \?" 5       SSSSSGS.S/\6GS \3SG\\GR                     S\\GR                     S\\%   S\GS\S\64GS jj5       5       GrZ\L" \FGR                  GR                  5      \?" 5       S\GR                  SSSGS.SG\\GR                     S\GR                  S\\%   S\GS\S\64GS jj5       5       Gr[\L" \FGR                  5      \?" 5       SSSSSGS.S/\6GS \3SG\\GR                     S\\GR                     S\\%   S\GS\S\64GS jj5       5       Gr\\L" \FGR                  5      \?" 5       SSSSGS.S/\6GS \3GS\0SG\\GR                     S\\GR                     S\\%   S\S\64GS jj5       5       Gr]\L" \FGR                  5      \?" 5       SSSSS\GR                  GS.S/\6SG\\GR                     S\\%   S\\GR                     S\GS\S\GR                  S\64GS jj5       5       Gr^\L" \FGR                  GR                  \FGR                  GR                  /5      \?" 5          GSS\GR                  SSSGS.GS\0GS\\0   GSB\0SG\\GR                     S\GR                  S\\%   S\GS\S\64GS jjj5       5       Gr_\L" \FGR                  5      \?" 5       \=" GS\*R                  S.9GS\AGS\AGS$\\A\04   4GS j5       5       5       Grb\L" \FGR                  5      \?" 5       SS\GR                  SSGS.GS\\0\64   GS\\0\64   GS\0SG\\GR                     S\\%   S\GR                  S\GS\S\64GS jj5       5       Grc\L" \FGR                  5      \?" 5        GSSS\GR                  SSGS.GS\\0\64   GS\\0\64   GS\0GS\0SG\\GR                     S\\%   S\GR                  S\GS\S\64GS jjj5       5       Grd\GS
\	\6   GS\4GS j5       Gre\GS
\6GS\4GS j5       Gre\L" \FGR                  5      GS
\\6\\6   \\6   4   GS\S\\6   4GS j5       GreS!\6GS\\\'4   GS\\\'4   S\64GS jGrf\L" \FGR                  5      \?" 5       SS\GR                  SSGS.GSG\\3\\3   4   GS\4SG\\GR                     S\\%   S\GR                  GS\S\S\64GS jj5       5       Grg\L" \FGR                  5      \?" 5        GSS\GR                  SSSGS.GS\GS\\   SG\\GR                     S\GR                  S\\%   S\GS\S\64GS jjj5       5       Grh\L" \FGR                  GR                  \FGR                  GR|                  /5      \?" 5       S\GR                  SSSGS.GSG\3GS\0SG\\GR                     S\GR                  S\\%   S\GS\S\64GS jj5       5       GriSSSSS\GR                  GS.S/\6GS\0SG\\GR                     S\\GR                     S\\%   S\GS\S\GR                  S\64GS jjGrj\L" \FGR                  5      \?" 5       SSSSS\GR                  GS.S/\6SG\\GR                     S\\GR                     S\\%   S\GS\S\GR                  S\64GS jj5       5       Grk\L" \FGR                  5      \?" 5       SSSSS\GR                  GS.S/\6SG\\GR                     S\\GR                     S\\%   S\GS\S\GR                  S\64GS jj5       5       Grl\L" \FGR                  GR                  5      \?" 5       SSSSSGS.SG\\GR                     S\\%   S\\GR                     GS\S\S\64GS jj5       5       GrmS\GR                  SSGS.S/\0SG\\GR                     S\GR                  S\\%   S\S\64GS jjGrn  GSGSG\3GS\\\\4   GS\\\\4   SG\GR                  S\%S\64GS jjGro\L" \FGR                  5      \?" 5       S/\6GS\6S0\74GS j5       5       Grp\L" \FGR                  5      S/\6GS\6S0\7S\64GS j5       Grq   GSS/\6Sl\6S\S\S\S\4GS jjGrrS/\6Sl\6S\4GS jGrs\L" \FGR                  5      \?" SS9   GSSGS.S!\6GS0\\\\4      SF\\(   SK\SG\\GR                     S\64GS jjj5       5       Grt\L" \FGR                  5      \?" 5       SJ\6S\64GS j5       5       GruGS GrvG\v" \5      GrwG\v" \5      GrxG\v" \5      Gry\L" \FGR                  5      \?" 5       GSS/\6GS\S\64GS jj5       5       Grz\L" \FGR                  5      \?" 5       GSS/\6GS\S\64GS jj5       5       Gr{GS\GS\GSi\S\\\\4   4GS jGr|S\GS\GS\SG\GR                  S\GR                  S\4GS jGr}\L" \FGR                  5      \?" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSi\SG\GR                  S\GR                  S\%S\S\64GS jjj5       5       Gr~GS\GS\GSi\S\\\\4   4GS jGr\L" \FGR                  5      \?" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSi\SG\GR                  S\GR                  S\%S\S\64GS jjj5       5       Gr\L" \FGR                  5      \?" SS9SSGS.S/\7GS\6GS\GS\4GS jj5       5       Gr\L" \FGR                  5      \?" 5       \=" SI\*R                  S.9GSGS j5       5       5       Gr\L" \FGR                  5      \?" 5       \=" SI\*R                  S.9GSGS j5       5       5       Gr\L" \FGR
                  5      \?" 5       \=" SI\*R                  S.9GSGS j5       5       5       Gr\L" \FGR                  5      \?" 5       \=" SI\*R                  S.9GS GS j5       5       5       Gr\L" \FGR                  5      \?" 5       \=" GS\*R                  S.9   GSSSSSSGS.GS jj5       5       5       Gr\L" \FGR                  5      GSLSGS.GS jj5       Gr\O" \*R                  5      SJ\64GS j5       Gr\O" \*R                  5      SJ\64GS j5       Gr\L" \FGR                  5      \?" 5       GSSF\\(   4GS jj5       5       GrGS GrGS Gr\L" \FGR                  5      \?" 5       G\\=" GS\*R                  S.9GS 5       5       5       5       Gr\L" \FGR                  5      \?" 5       G\\=" GS\*R                  S.9GS 5       5       5       5       Gr\L" \FGR                   5      \?" 5       S5\6GS\6SF\GSX\4GS j5       5       Gr\Q" \S5      Gr\Q" \U5      Gr\Q" \V5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \W5      Gr\Q" \X5      Gr\Q" \Y5      Gr\Q" \Z5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \\5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \]5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \_5      Gr\Q" \5      Gr\Q" \`5      Gr\Q" \a5      Gr\Q" G\M5      Gr\Q" G\N5      Gr\Q" G\5      Gr\Q" \b5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \c5      Gr\Q" \e5      Gr\Q" \d5      Gr\Q" \f5      Gr\Q" \h5      Gr\Q" \g5      Gr\Q" \5      Gr\Q" \m5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \n5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \z5      Gr\Q" \5      Gr\Q" \5      Gr\Q" G\b5      Gr\Q" \{5      Gr\Q" \5      Gr\Q" \}5      Gr\Q" \~5      Gr\Q" \|5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \x5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" G\5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" G\{5      Gr\Q" G\z5      Gr\Q" \5      Gr\Q" \5      Gr\Q" \5      Gr\Q" G\5      Gr\Q" G\5      Gr\Q" G\5      Gr\Q" G\5      Gr\Q" \l5      Gr\" \FGR                  5      Gr\" \FGR                  5      Gr\" \FGR                  5      Gr\" \FGR                  5      Gr\" \FGR(                  5      Gr\" \FGRn                  5      Gr\" \FGR:                  5      Gr\" \FGR                  5      Gr\" \FGR                  5      Gr\" \FGR^                  5      Gr\" \FGR                  5      Gr\" \FGR                  5      GrGS GrGS GrGS GrGS\GR                  GS\\7\84   4GS jGr GSGS jGr SSSSGS.GS jGrS SGKrS SGKrS SGKrS SGKrS SGKrg(      N)IterableSequence)Enum)partialreducesingledispatchwraps)AnyCallablecastOptionaloverloadUnion)	sym_floatsym_int)BoolLikeDeviceLikeTypeDimDimsSequenceTypeDimsTypedtype_to_typeELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeFloatWithoutSymFloatIntLikeis_weakly_lesser_typeNumber
NumberTypeRealNumberTypeREDUCTION_OUTPUT_TYPE_KIND	ShapeType
StrideType
TensorLikeTensorLikeTypeTensorOrNumberLikeTypeTensorSequenceType)_maybe_convert_to_dtype_maybe_resize_out_safe_copy_out"elementwise_type_promotion_wrapper elementwise_unary_scalar_wrapperout_wrapper(  absacosacoshasinhasinatanatanhbitwise_notceilconj_physicalcoscoshcount_nonzerodeg2raddigammaerferfinverfcexpexpm1exponentialexp2fillfill_floorfrac	geometric	index_add
index_copyindex_copy_index_select
index_fillindex_fill_isfiniteisinfisposinfisneginfisnanisreali0lerplgammaloglog1plog2log10
log_normallog_softmaxmvlgammanormnormal
nan_to_numnegpositiverad2deg
reciprocalroundsigmoidsgnsignsignbitsinsincsinhsoftmaxsqrtsquaretantanhtracetruncaddatan2bitwise_andbitwise_left_shift
bitwise_orbitwise_right_shiftbitwise_xor	clamp_min	clamp_maxcopysigndiveqfloat_powerfloor_dividefmaxfminfmodgcdgegt	heavisidehypotigammaigammacimagiscloselcmle	logaddexp
logaddexp2logical_andlogical_not
logical_orlogical_xor	logsumexpltmaximumminimummulne	nextafterpowrealrpow	remainderrsubrtruediv	rfloordivsubtrue_dividetrunc_dividexlogyaddcdivaddcmulclampmasked_fillmasked_fill_whereclonecopy_toitemtoallamaxaminanycumsumcumprodmeandotvdotstdstd_meansumsum_to_sizeprodvarvar_meanaddralias
alias_copy
atleast_1d
atleast_2d
atleast_3d
as_stridedas_strided_copyas_strided_scatter
block_diagbroadcast_shapesbroadcast_tensorsbroadcast_tocatchunkcolumn_stackconjconstant_pad_nd
contiguous
diag_embeddiagdiagonaldiagonal_copydiagonal_scatterdsplitdstackexpand	expand_asexpand_copyflattenflipfliplrflipudhsplithstackmeshgridmovedimnarrownarrow_copynative_group_normnative_layer_normpermutepermute_copyravelrepeatreshape
reshape_asrollrot90rsqrtsplit_with_sizesstack	swap_axessqueezesqueeze_copytt_copyTtake_along_dimtensor_split	transposetranspose_copyunbind_copyunfoldunfold_copy	unsqueezeunsqueeze_copyviewview_as	view_copyvsplitvstackview_as_complex	unflattenunbindtriutriltriu_indicestril_indicesarangecauchyempty
empty_likeempty_permutedempty_stridedeyefull	full_likelinspacelogspace	new_emptynew_empty_stridednew_fullnew_ones	new_zerosones	ones_likerandnscalar_tensorzerozeros
zeros_likeallcloseequal	bucketize
is_complexrenormstftistftc                 6    U S L =(       d    U R                   S:g  $ )Nhputypedevices    h/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/torch/_refs/__init__.pyis_noncontiguous_supportedr6  n  s    T>1V[[E11    c                     S nSSK Jn  U  H!  n[        XC5      (       d  M  UR                  n  O   [	        U5      (       d  UR                  5       nU$ )Nr   )
FakeTensor)torch._subclasses.fake_tensorr9  
isinstancefake_devicer6  r   )input_tlistoutputr4  r9  r   s        r5  handle_noncontiguous_outputsr?  r  sK    F8a$$]]F 
 &f--""$Mr7  c            	      .  ^^^^ SSK Jn  [        S [        S U 5       5       5      n[	        U5      S:X  a  g U H  m[        T[        5      (       a  M   e   S/[        [        S U 5       5      -  m[        U5       H  u  mm[        SS[	        T5      -
  S5       Hp  mU" TT   S:H  5      (       a  TT   S:  a  [        S5      eTT   TT'   M4  U" TT   S:g  5      (       d  MI  [        R                  " TT   TT   :H  UUUU4S	 j5        Mr     M     T$ )
Nr   guard_size_obliviousc              3   V   #    U  H  n[        U[        5      (       a  U4OUv   M!     g 7fNr;  r   .0xs     r5  	<genexpr>$_broadcast_shapes.<locals>.<genexpr>  s*      9A 1g&&A-9s   ')c                 
    U S L$ rD   rH  s    r5  <lambda>#_broadcast_shapes.<locals>.<lambda>  s    !4-r7     c              3   8   #    U  H  n[        U5      v   M     g 7frD  len)rG  shapes     r5  rI  rJ    s     4VESZZV   z9Attempting to broadcast a dimension with negative length!c            
      ,   > STT    ST ST  ST ST 3
$ )Nz.Attempting to broadcast a dimension of length z at z ! Mismatching argument at index z had z0; but expected shape should be broadcastable to rL  )arg_idxcommon_shapeidxrT  s   r5  rN  rO    s:    LUSVZLX\]`\a b55<IU5' J22>Ar7  )%torch.fx.experimental.symbolic_shapesrB  tuplefilterrS  r;  r   r   max	enumeraterange
ValueErrortorch_check)_shapesrB  shapesrX  rY  rZ  rT  s      @@@@r5  _broadcast_shapesrf    s$   J /9 F 6{a %**** 
 	
4s4V4546L $F+R#e*_b1C#L$5$:;;:>$S  %*#JS!%eCjAo66 %s3A 2 ,  r7  T)preserve_cpu_scalar_tensorsc                 `   ^ ^^ [        S U 5       6 mUU 4S jm[        UU4S jU 5       5      $ )Nc              3   h   #    U  H(  n[        U[        5      (       a  UR                  OS v   M*     g 7frD  )r;  r#   rT  rG  r   s     r5  rI  #_maybe_broadcast.<locals>.<genexpr>  s%     	G$QZ:..!''D
8$s   02c                 d  > U c  g [        U [        5      (       a  U $ [        U [        5      (       a]  T(       a  [        R                  " U 5      (       a  U $ [        R
                  " U R                  T5      (       d  U R                  T5      $ U $ [        S[        [        U 5      5      -   S-   5      e)Nz#Unexpected type when broadcasting: !)r;  r   r#   utilsis_cpu_scalar_tensor
same_shaperT  r   RuntimeErrorstrr2  )rH  rT  rY  rg  s     r5  __maybe_broadcast+_maybe_broadcast.<locals>.__maybe_broadcast  s    96""H:&&*u/I/I!/L/L##AGG\::xx--H5DGDsJ r7  c              3   6   >#    U  H  nT" UT5      v   M     g 7frD  rL  )rG  rH  rs  rY  s     r5  rI  rk    s     BT"1l33Ts   )rf  r\  )rg  argsrs  rY  s   ` @@r5  _maybe_broadcastrw    s-    $	G$	GL$ BTBBBr7  )register_decompositionF)aten_op
extra_metaexact_dtypereturnc                0   ^ ^^^ S[         4UUUU 4S jjnU$ )Nprimc                   >^  [        T 5      [        TS9[        [        STS9S[        S[        4UU 4S jj5       5       5       5       nT[
        L a!  [        R                  " T T R                  5      mTb  [        T5      " U5        U$ )Nr{  atype_promoting_argstype_promotion_kindr  r|  c                 D   > Tb  T" U 5        T" U 5      n[        U /U5      $ rD  )r?  )r  r>  rz  r~  s     r5  _ref>_make_elementwise_unary_reference.<locals>.inner.<locals>._ref  s*     %1!WF/V<<r7  )
r	   r,   r+   r*   r$   infer_aten_oprn  get_aten_op__name__rx  )r~  r  ry  r{  rz  r  s   ` r5  inner0_make_elementwise_unary_reference.<locals>.inner  s     
t		-	)	+ & 3

	=N 	=~ 	=	

 
* 
. 
	= m#''dmm<G"7+D1r7  r   )r  ry  rz  r{  r  s   ```` r5  !_make_elementwise_unary_referencer    s    H  0 Lr7  c                    ^  U 4S jnXl         [        R                  " 5       R                  R                  S   Ul        U$ )a  
This function defines an alias of another function and sets its __name__ argument.
It also sets its __module__ argument to the module of the caller.
Note that when naively doing `alias = fn`, we have that `alias.__name__ == "fn"`, and
`alias.__module__ == fn.__module__`.
c                     > T" U 0 UD6$ rD  rL  )rv  kwargsfns     r5  _fn_make_alias.<locals>._fn  s    4"6""r7  r  )r  inspectcurrentframef_back	f_globals
__module__)r  namer  s   `  r5  _make_aliasr    s5    # L))+22<<ZHCNJr7  c                    ^  [        T 5      U 4S j5       nT R                   S3nX!l        [        [        [        U5      5      " U5      nSSKJn  U" T 5      R                  nX$;  a  UR                  U5        U$ )z
Given a function with out variant (i.e. using `out_wrapper()), it returns its in-place variant
See https://github.com/pytorch/pytorch/wiki/Developer-FAQ#how-do-in-place-operations-work-in-pytorch
c                     > T" U /UQ7SU 0UD6$ )NoutrL  )r  rv  r  r  s      r5  r  _make_inplace.<locals>._fn	  s    !,d,,V,,r7  _r   )	getmodule)	r	   r  rx  getattratenr  r  __all__append)r  r  inplace_namer  _alls   `    r5  _make_inplacer    ss     2Y- - kk]!$LL
 |!<
=c
BC "R=  DL!Jr7  r  c                 .    [         R                  " U 5      $ rD  )primsr-   r  s    r5  r-   r-     s    
 99Q<r7  c                 .    [         R                  " U 5      $ rD  )r  r.   r  s    r5  r.   r.   #      ::a=r7  c                 .    [         R                  " U 5      $ rD  )r  r/   r  s    r5  r/   r/   (      ;;q>r7  c                 .    [         R                  " U 5      $ rD  )r  r1   r  s    r5  r1   r1   -  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r0   r  s    r5  r0   r0   2  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r2   r  s    r5  r2   r2   7  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r3   r  s    r5  r3   r3   <  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r4   r  s    r5  r4   r4   A  s    Qr7  c                 .    [         R                  " U 5      $ rD  )r  r5   r  s    r5  r5   r5   F      
 ::a=r7  inputc                 B    [         R                  " U R                  5      $ rD  )rn  is_complex_dtypedtyper  s    r5  r+  r+  N  s    !!%++..r7  c                 |    [         R                  " U R                  5      (       d  U $ [        R                  " U 5      $ rD  )rn  r  r  r  r6   r  s    r5  r6   r6   S  s/     !!%++..u%%r7  c                 .    [         R                  " U 5      $ rD  )r  r7   r  s    r5  r7   r7   [      99Q<r7  c                 .    [         R                  " U 5      $ rD  )r  r8   r  s    r5  r8   r8   `  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r;   r  s    r5  r;   r;   e      ==r7  c                 .    [         R                  " U 5      $ rD  )r  r<   r  s    r5  r<   r<   j  r  r7  c                 .    [         R                  " U 5      $ rD  )r  erf_invr  s    r5  r=   r=   o  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r>   r  s    r5  r>   r>   t  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r?   r  s    r5  r?   r?   y  r  r7  c                 .    [         R                  " U 5      $ rD  )r  r@   r  s    r5  r@   r@   ~  r  r7  c                 .    [         R                  " U 5      $ rD  )r  rB   r  s    r5  rB   rB     r  r7  za,r  r  valuec                 N   [        U [        5      (       d   e[        U[        5      (       d   e[        R                  " U R
                  5      n[        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        R                  " X5      $ Nzvalue argument of type  cannot be safely cast to type rm  )r;  r#   r   rn  r   r  r   r2  ra  r  rC   )r  r  python_typemsgs       r5  rC   rC     s     a$$$$eV$$$$%%agg.K&&tE{K@@'U}4ST_S``abo::ar7  c                 ^    [         R                  " X5      n[         R                  " X5        U $ rD  )r  rC   r   )r  r  rs      r5  rD   rD     s!    

1A	MM!Hr7  c                 .    [         R                  " U 5      $ rD  )rb  r'  r  s    r5  r%  r%    s     E""r7  c                 .    [         R                  " U 5      $ rD  )r  rE   r  s    r5  rE   rE         
 ;;q>r7  rH  c                     [         R                  " [         R                  " [         R                  " U 5      5      [         R                  " U 5      5      n[         R
                  " X5      $ rD  )rb  r   rE   r-   rh   r   )rH  trunc_xs     r5  rF   rF     s<    
 iiEIIaL15::a=AG99Q  r7  c                     [        U [        5      (       d   e[        R                  " [        R
                  " U R                  5      S 5        [        R                  " U 5      $ )Nc                      g)Nz#imag only supports complex tensors.rL  rL  r7  r5  rN  imag.<locals>.<lambda>  s    1Vr7  )	r;  r#   rb  rc  rn  r  r  r  r   r  s    r5  r   r     sF    a$$$$	LLqww')V ::a=r7  )ry  c                     [         R                  " U R                  5      (       d%  [         R                  " U R                  5      (       a  [        R
                  " U 5      $ [        U [        R                  S9$ )Nr  )	rn  is_float_dtyper  r  r  rN   r"  rb  boolr  s    r5  rN   rN     sM    
 AGG$$(>(>qww(G(G~~a  Qejj))r7  c                    [         R                  " U R                  5      (       aQ  [        R                  " [        [        R                  " U 5      5      [        [        R                  " U 5      5      5      $ [         R                  " U R                  5      (       a"  [        R                  " U 5      [        S5      :H  $ [        R                  " U [        R                  S9$ )Ninfr  )rn  r  r  rb  r   rO   r   r   r  r-   floatr'  r  r  s    r5  rO   rO     s    agg&&ejjm 4eEJJqM6JKKAGG$$yy|uU|++AUZZ00r7  c                 ,  ^  [         R                  " [        R                  " T R                  5      (       + U 4S j5        [        R
                  " T R                  5      (       a  T [        S5      :H  $ [         R                  " T [         R                  S9$ )Nc                  "   > ST R                    3$ )Nz7Complex dtype is not supported for isposinf, got dtype r  r  s   r5  rN  isposinf.<locals>.<lambda>      I!''Sr7  r  r  	rb  rc  rn  r  r  r  r  r'  r  r  s   `r5  rP   rP     sf    
 
LL""177++S AGG$$E%L  AUZZ00r7  c                 ,  ^  [         R                  " [        R                  " T R                  5      (       + U 4S j5        [        R
                  " T R                  5      (       a  T [        S5      :H  $ [         R                  " T [         R                  S9$ )Nc                  "   > ST R                    3$ )Nz7Complex dtype is not supported for isneginf, got dtype r  r  s   r5  rN  isneginf.<locals>.<lambda>  r  r7  z-infr  r  r  s   `r5  rQ   rQ     sf    
 
LL""177++S AGG$$E&M!!AUZZ00r7  c                 .    [         R                  " X 5      $ rD  r  r   r  s    r5  rR   rR     s    88A>r7  r]   c                     [         R                  " U R                  5      (       a  [        R                  " U 5      S:H  $ [        R
                  " U [        R                  S9$ )Nr   r  )rn  r  r  rb  r   r"  r  r  s    r5  rS   rS     sA    
 agg&&zz!}!!??1EJJ//r7  c                 .    [         R                  " U 5      $ rD  )r  	bessel_i0r  s    r5  rT   rT     s     ??1r7  c                 .    [         R                  " U 5      $ rD  )r  rV   r  s    r5  rV   rV     s    <<?r7  c                 .    [         R                  " U 5      $ rD  )r  rW   r  s    r5  rW   rW     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rX   r  s    r5  rX   rX     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rY   r  s    r5  rY   rY     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rZ   r  s    r5  rZ   rZ      r  r7  dimr  c           	          U=(       d    U R                   n[        R                  " U5      n[        X5      n[        U[	        XQSS9-
  U5      $ )NTkeepdim)r  rn  get_computation_dtyper'   r   )r  r  r  result_dtypecomputation_dtypea_s         r5  r\   r\   &  sF     #AGGL33LA	 	6B"2	"4(H#H,WWr7  selfr  r  c                 X   [        U[        5      (       d  U4nU R                  5       S:X  a9  [        R                  " [        R
                  " U 5      X5      R                  5       $ [        R                  " [        R                  " U 5      USS9n[        R                  " X3R                  5       [        S5      :H  S5      nU(       a  UO[        R                  " X15      n[        R                  " [        R
                  " X-
  5      X5      nUR                  5       R                  U5      $ )Nr   Tr  r  )r;  r   numelrb  r   r?   rW   r   r   r   r-   r  r   rt   )r  r  r  maxesmaxes_squeezedresults         r5  r   r   2  s     c8$$fzz|qyy4#7;;==JJuzz$'d;EeYY[E%L%@!DE%U5==+DNYYuyy.=F::<N++r7  nanposinfneginfc                    [        U [        5      (       d   e[        R                  " U R                  5      (       d%  [        R
                  " U R                  5      (       a  U R                  5       $ Uc  SnUc*  [        R                  " U R                  5      R                  nUc*  [        R                  " U R                  5      R                  n[        R                  " [        R                  " U 5      X5      n[        R                  " [        R                  " U 5      X45      n[        R                  " [        R                  " U 5      X$5      nU$ )N        )r;  r#   rn  is_boolean_dtyper  is_integer_dtyper   rb  finfor^  minr   rR   rQ   rP   )r  r  r  r  r   s        r5  r`   r`   F  s     a$$$$agg&&%*@*@*I*Iwwy
{~QWW%))~QWW%))[[Q0F[[*F;F[[*F;FMr7  c                 h    [         R                  " U R                  [         R                  LS 5        g )Nc                      g)NzNegation, the `-` operator, on a bool tensor is not supported. If you are trying to invert a mask, use the `~` or `logical_not()` operator instead.rL  rL  r7  r5  rN  _neg_meta.<locals>.<lambda>e  s     r7  )rb  rc  r  r  r  s    r5  	_neg_metar  b  s#    	LL	uzz!	
r7  )rz  c                 .    [         R                  " U 5      $ rD  )r  ra   r  s    r5  ra   ra   m  s     99Q<r7  c                     [        U [        5      (       d   eU R                  [        R                  L a  Sn[        U5      eU $ )Nz'positive does not support bool tensors.)r;  r#   r  rb  r  rq  )r  r  s     r5  rb   rb   v  s:    a$$$$ww%**73Hr7  c                     [        U [        5      (       d   e[        R                  " U R                  5      (       a  [
        R                  " U 5      $ U $ rD  )r;  r#   rn  r  r  r  r   r  s    r5  r   r     s=    a$$$$agg&&zz!}Hr7  c                 .    [         R                  " U 5      $ rD  )r  rd   r  s    r5  rd   rd     s    Ar7  r  )decimalsr  c                    US:X  a  [         R                  " U 5      $ SU-  nSU* -  n[         R                  " [         R                  " [         R                  " X5      5      U5      $ )Nr   
   )r  re   r   )r  r  ten_powten_neg_pows       r5  re   re     sQ     1}{{1~h,hY'yyUYYq%:;[IIr7  c                 .    [         R                  " U 5      $ rD  )r  r   r  s    r5  r   r     r  r7  c                 R    [        S[        S[        [        U 5      5      5      5      $ )NrP  )r   rt   r?   ra   r  s    r5  rf   rf     s    q#aSV-..r7  c                     [         R                  " U R                  5      (       a-  U R                  5       n[        R
                  " US:H  SX-  5      $ U R                  5       $ Nr   )rn  r  r  r-   rb  r   rh   )r  a_abss     r5  rg   rg     sH    
 agg&&{{5A:q!)44vvxr7  c                 .    [         R                  " U 5      $ rD  )r  rh   r  s    r5  rh   rh     r  r7  c                 .    [         R                  " U 5      $ rD  )r  ri   r  s    r5  ri   ri     s    
 ==r7  c                 .    [         R                  " U 5      $ rD  )r  rj   r  s    r5  rj   rj     r  r7  c                     [         R                  U -  n [        R                  " U S:H  S[        R                  " U 5      U -  5      $ Nr   rP  )mathpirb  r   rj   r  s    r5  rk   rk     s3    !A;;qAvq%))A,"233r7  c                 .    [         R                  " U 5      $ rD  )r  rl   r  s    r5  rl   rl     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rn   r  s    r5  rn   rn     r  r7  c                     [        X 5      $ rD  )r   r  s    r5  ro   ro     s    
 q9r7  c                 .    [         R                  " U 5      $ rD  )r  rp   r  s    r5  rp   rp     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rq   r  s    r5  rq   rq     r  r7  c                 .    [         R                  " U 5      $ rD  )r  rs   r  s    r5  rs   rs     r  r7  c                   ^ U R                   m[        R                  " [        R                  " T5      U4S j5        U R                  5       n[        R                  " [        U5      S:g  S 5        [        R                  " US   S:H  S 5        U R                  5       n[        R                  " US   S:H  S 5        US S n[        R                  " [        R                  " S	 U 5       5      S
 5        [        R                  " U R                  5       S-  S:H  S 5        [        R                  " U [        R                  " T5      5      R                  S5      $ )Nc                     > ST  3$ )Nz^view_as_complex is only supported for floating pointtensors, but got a tensor of scalar type: rL  )input_dtypes   r5  rN  !view_as_complex.<locals>.<lambda>  s     55@MCr7  r   c                      g)Nz-Input tensor must have one or more dimensionsrL  rL  r7  r5  rN  r,        ?r7  rV     c                      g)Nz+Tensor must have a last dimension of size 2rL  rL  r7  r5  rN  r,         =r7  rP  c                      g)Nz/Tensor must have a last dimension with stride 1rL  rL  r7  r5  rN  r,        Ar7  c              3   0   #    U  H  oS -  S:H  v   M     g7f)r/  r   NrL  )rG  strides     r5  rI  "view_as_complex.<locals>.<genexpr>
  s     84aZ1_4s   c                      g)NzCTensor must have a stride divisible by 2 for all but last dimensionrL  rL  r7  r5  rN  r,    s    Ur7  c                      g)Nz0Tensor must have a storage_offset divisible by 2rL  rL  r7  r5  rN  r,    s    Br7  )r  rb  rc  rn  r  sizerS  r5  builtinsr   storage_offsetr  view_element_typecorresponding_complex_dtyper   )r  sizesold_stridesdimsr+  s       @r5  r
  r
    s   **K	LL[)	C
 IIKE	LLE
a? 
LLb	Q=
 ++-K	LLB1A sD	LL8488U 
LL!Q&B ""e//<gbkr7  c           	      @   ^ ^^^^^^^ S[         4UUUUUUUU 4S jjnU$ )Nr~  c                   >^  Tc  T R                   m[        T 5      [        ST	S9S[        [        [
        4   S[        [        [
        4   S[        4UU UUU4S jj5       5       nT(       a  [        5       " U5      nTUl         T[        L a  [        R                  " T T5      mTb  T(       a  [        T5      " U5        U$ )Nr  br  r  rD  r|  c                   > [         R                  " T=(       d    [        U [        5      (       + U4S j5        [         R                  " T=(       d    [        U[        5      (       + U4S j5        [         R                  " T=(       d,    [        U [        5      =(       a    [        U[        5      (       + U4S j5        [	        X5      u  pT" X5      n[        X/U5      $ )Nc                     > T  S3$ )Nzc: Received a lhs Python scalar to an elementwise binary operation that does not accept lhs scalars!rL  r  s   r5  rN  Q_make_elementwise_binary_reference.<locals>.inner.<locals>._ref.<locals>.<lambda>0      4& !> >r7  c                     > T  S3$ )Nzc: Received a rhs Python scalar to an elementwise binary operation that does not accept rhs scalars!rL  rG  s   r5  rN  rH  5  rI  r7  c                     > T  S3$ )Nz?: Receive two Number inputs to an elementwise binary operation!rL  rG  s   r5  rN  rH  ;  s    4& _`r7  )rb  _check_valuer;  r   rw  r?  )r  rD  r>  r  r~  supports_lhs_python_scalarsupports_rhs_python_scalarsupports_two_python_scalarss      r5  r  ?_make_elementwise_binary_reference.<locals>.inner.<locals>._ref%  s     *G*Q2G.G>
 *G*Q2G.G>
 + I"1f-G*Q2GH`
 $A)DA!ZF/??r7  )r  r	   r*   r   Tensorr   r,   r  rn  r  rx  )
r~  r  ry  has_outr  should_register_decompositionrM  rN  rO  r  s
   ` r5  r  1_make_elementwise_binary_reference.<locals>.inner   s    <==D	t	+ * 3

	@VZ'(	@VZ'(	@ 	@ 	@	

 

	@. =&Dm#''d3G#@"7+D1r7  r  )	r  ry  r  rR  rM  rN  rO  rS  r  s	   ```````` r5  "_make_elementwise_binary_referencerU    s    *H * *X Lr7  rC  alpharD  rW  c                   [        X5      u  pUb  [        U [        5      (       a  U R                  OUR                  n[        R
                  " U5      nU[        :w  aB  [        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        U[        5      (       a  [        R                  " X5      nOX-  n[        R                  " X5      n[        X/U5      $ )z'
Reference implementation of torch.add
alpha argument of type r  rm  )rw  r;  r#   r  rn  r   r  r   r2  ra  r  r   rt   r?  r  rD  rW  r  r  r  r>  s          r5  rt   rt   P  s      A!DA%a44!''))%0$u'B'BK(
 (
 ,DK=8WXcWddefCS/!a$$		!#A	AYYq_F'77r7  )r  rM  rN  c                 .    [         R                  " X5      $ rD  )r  ru   rC  s     r5  ru   ru   s       ;;qr7  )r  c                 .    [         R                  " X5      $ rD  )r  rv   rC  s     r5  rv   rv   |       Q""r7  c                 .    [         R                  " X5      $ rD  )r  
shift_leftrC  s     r5  rw   rw          A!!r7  c                 .    [         R                  " X5      $ rD  )r  rx   rC  s     r5  rx   rx     ra  r7  c                 .    [         R                  " X5      $ rD  )r  shift_right_arithmeticrC  s     r5  ry   ry     s     ''--r7  c                 .    [         R                  " X5      $ rD  )r  rz   rC  s     r5  rz   rz     r^  r7  )r  rM  c                    [        U[        5      (       a4  [        U [        5      (       a  [        XR                  U R
                  S9nOl[        U [        5      (       aW  [        U[        5      (       aB  U R
                  UR
                  :w  a(  SU R
                   SUR
                   S3n[        U5      e[        [        U5      [        [        U 5      5      [        U 5      5      $ )Nr  r4  /Expected divisor (b) to be on the same device (&) as dividend (a), but it is found on rm  )r;  r   rQ  r$  r  r4  rq  r   ri   ra   r-   )r  rD  r  s      r5  r}   r}     s     !VAv!6!6!77188<	Av		:a#8#8QXX=Q?zIopqpxpxoyyz{3SQ[#a&11r7  )rounding_moderj  c                    Uc  [        X5      $ US:X  a  [        X5      $ US:X  a  [        X5      $ SU S3n[        U5      e)z'
Reference implementation of torch.div
rs   rE   zLdiv expected rounding_mode to be one of None, 'trunc', or 'floor' but found .)r   r   r   ra  )r  rD  rj  r  s       r5  r~   r~     sV     1  	'	!A!!	'	!A!!\]j\kklmor7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r         
 88A>r7  c                 Z   [        U [        5      (       d  [        U[        5      (       d   e[        U[        5      (       a=  US:X  a  U R                  5       $ US:X  a  X -  $ US:X  a  [        R
                  " U 5      $ O[        U [        5      (       a  U S:X  a  [        R                  " US5      $ U S:X  a`  [        R                  " UR                  5      (       d%  [        R                  " UR                  5      (       a  [        R                  " U5      $ [        R                  " X5      $ )N      ?g       @      ?T)r;  r$   r   r   rb  rn   rC   rn  r  r  r  rB   r  r   rC  s     r5  r   r     s     a((Jq.,I,III!V8779#X5L#X::a=  	Av		8::a&&8  ))U-C-CAGG-L-L::a= 99Q?r7  c                 v   [        U [        5      (       a   [        U[        5      (       a  [        S5      e[        R                  " X5      nUc   e[        R
                  " U5      (       a  [        R                  nO[        R                  n[        X5      n [        X5      n[        X5      u  p[        X5      $ )Nz=Receive two Number inputs to an elementwise binary operation!)r;  r   ra  rn  get_higher_dtyper  rb  
complex128float64r'   rw  r   r  rD  r  s      r5  r   r     s    
 !VAv!6!6K
 	

 ""1(Ee$$   	 )A)AA!DAq9r7  )r  rO  rS  c                 H  ^ [        U [        5      (       a-  [        U[        5      (       a  [        U 5      n [        U5      nGO@[        U[        5      (       a4  [        U [        5      (       a  [        XR                  U R
                  S9nO[        U [        5      (       a4  [        U[        5      (       a  [        XR                  UR
                  S9n O[        U [        5      (       a  [        U[        5      (       a  U R
                  UR
                  :w  aj  U R
                  [        R
                  " S5      :X  a(  SU R
                   SUR
                   S3n[        U5      e[        R                  " XR
                  S9n[        U [        5      (       a  [        U[        5      (       d   eU R                  m[        R                  " T5      (       a  [        X5      $ [        R                  " T5      (       a  [        X5      $ [        R                  " SU4S j5        g )	Nrg  cpurh  ri  rm  r3  Fc                     > T  S3$ )Nz not supported for floor_dividerL  r  s   r5  rN  floor_divide.<locals>.<lambda>A  s    ug-L$Mr7  )r;  r   r$  rQ  r  r4  rb  rq  r  
device_putrn  r  _floor_divide_floatr  _floor_divide_integerrc  )r  rD  r  r  s      @r5  r   r   #  sy    !VAv!6!6!!	Av		:a#8#8!77188<	Av		:a#8#8!77188<	Av		:a#8#8QXX=Q88u||E**CAHH:Mstut|t|s}}~Cs##  884Aa  Z6%:%:::GGEE"""1((				&	&$Q**UMNr7  c                 |   [        X5      u  pU R                  R                  (       d  [        R                  " X5      $ [
        R                  " U 5      [
        R                  " U5      :g  R                  [
        R                  " X5      S:g  5      n[        R                  " X5      [        X R                  5      -
  $ r  )
rw  r  	is_signedr  r~   rb  ri   r   r   r'   )r  rD  offsets      r5  r}  r}  D  s~    A!DA77yy mmA%--"22??

1@PTU@UVF99Q?4VWWEEEr7  c                    [        X5      n[        [        X5      U5      n[        [	        U S5      [	        US5      5      n[        US5      n[        XT5      n[        U[        US5      U5      n[        U5      n[        [        X75      S5      n[        U[        US5      U5      n[        X5      n[        SUR                  UR                  S9n	[        [        US5      U[        X5      5      n[        [        US5      Xx5      $ )Nr   rP  rq  rg  )r   r   r   rz   r   r   rv   r   rE   r   rt   r$  r  r4  r}   )
r  rD  modr~   different_signed_inputsnon_zero_remaindermask	floor_div	basic_divzero_tensors
             r5  r|  r|  O  s    
q*C
c!k1
%C *"Q(Bq!H=C)CD
c#qk3
'C c
Ic#!3'DdC	1-y9IA!IAQAQRK baj)Xk-MNI Aq900r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r   h       ::ar7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r   q  r  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r   z  r  r7  mantissaexponentc                 h    [         R                  R                  [        R                  " U 5      5      $ rD  )rb  return_typesfrexpr  r  s    r5  r  r    s$     ##EKK$566r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s     99Q?r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     rn  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     rn  r7  valuesc                    [         R                  " U S5      n[         R                  " [         R                  " U S5      [         R                  " U 5      5      n[         R
                  " USS5      n[         R
                  " X!U5      nU$ r   )rb  r   r   r   rR   r   )r  r  input_eq_zeroinput_lt_zerozeros_and_onesr>  s         r5  r   r     sa     HHUA&M$$UXXeQ%7U9KLM[[15N[[?FMr7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     r\  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s     <<r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s     ==r7  r  rtolatolc                    ^ ^^^^ [         R                  " TR                  TR                  :H  UUU 4S j5        [         R                  " TS:  U U4S j5        [         R                  " TS:  UU 4S j5        g )Nc                  B   > T ST R                    STR                    S3$ )Nz4: Attempting to compare tensors of different dtypes  and rm  r  )r  rD  r  s   r5  rN  #_check_close_args.<locals>.<lambda>  s'    4&LQWWIUZ[\[b[bZccder7  r   c                     > T  ST S3$ )Nz6: rtol must be greater than or equal to zero, but got rm  rL  )r  r  s   r5  rN  r        4&NtfTUVr7  c                     > T ST  S3$ )Nz6: atol must be greater than or equal to zero, but got rm  rL  )r  r  s   r5  rN  r    r  r7  )rb  rL  r  rc  r  r  rD  r  r  s   `````r5  _check_close_argsr    sV     
	177e 
LL	V 
LL	Vr7  	equal_nanc           
      0   [        SXX#S9  [        X5      nU(       ar  [        R                  " U R                  5      (       d%  [        R
                  " U R                  5      (       a(  [        U[        [        U 5      [        U5      5      5      nUS:X  a  US:X  a  U$ [        R                  " U R                  5      (       dy  [        R
                  " U R                  5      (       dT  [        R                  " U [        R                  " 5       5      n [        R                  " U[        R                  " 5       5      n[        U[        [        X5      5      5      n[        [!        X5      5      n[        U[        [#        U5      [%        Xv5      5      5      nU$ )Nztorch.iscloser  r   )r  r   rn  r  r  r  r   r   rR   r  convert_element_typerb  get_default_dtypert   r-   r   r   rN   r   )	r  rD  r  r  r  closeallowed_erroractual_errorr   s	            r5  r   r     s    ?a4KqHEe**17733u7M7Magg7V7V5+eAha"AB qyTQY ((1G1G1P1P&&q%*A*A*CD&&q%*A*A*CDc#a,/0Ms1y>L {8L12l3RSF Mr7  c                    U R                   nU[        R                  [        R                  4;   nU(       aJ  [        R
                  " U [        R                  5      n [        R
                  " U[        R                  5      n[        R                  " X5      n[        R                  " US:H  SU5      n[        R                  " [        R                  " X5      U-  5      nU(       d  U$ [        R
                  " XR5      $ r   )r  rb  int8int16r  r  int32r   r   r-   r~   )r  rD  r  promote_to_intgress         r5  r   r     s     GGE uzz5;;77N&&q%++6&&q%++6		!AAFAq!A
))EIIaOa'
(C$3P%*D*DS*PPr7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r      rn  r7  c                    [         R                  " U 5      [         R                  " U5      :  n[         R                  " X U5      n[         R                  " X!U 5      n[         R                  " [         R                  " [         R
                  " [         R                  " U 5      5      5      [         R                  " U 5      [         R                  " U5      :H  5      n[        R                  " U R                  5      (       d%  [        R                  " UR                  5      (       a  [         R                  " U5      S:  n[         R                  " Xd[         R                  " [         R                  " U5      [         R                  " U5      -   5      5      n[         R                  " XWU[         R                  " [         R                  " XC-
  5      5      -   5      n[         R                  " U5      n	[         R                  " U	[        [        S5      [        S5      5      U5      $ [         R                  " XPU[         R                  " [         R                  " XC-
  5      5      -   5      $ )Nr   r  )rb  r   r   r   r   rN   rn  r  r  rW   r?   rX   rR   complexr  )
r  rD  r  max_min_inf_maskneg_min_maskinf_valsnon_nan_valsnan_masks
             r5  r   r   (  s~    ::a=EJJqM)D;;t"D;;t"D  %..A78%**Q-5::VW=:XH agg&&%*@*@*I*Izz$'!+;;		%))D/EIIdO*K L
 {{u{{599T[3I'J J
 ;;t${{8WU5\5<%H,WW{{8u{{599T[;Q/R(RSSr7  c                 H   [         R                  " [        R                  " U R                  5      =(       d     [        R                  " UR                  5      (       + S 5        X:  n[         R
                  " X U5      n[         R
                  " X!U 5      n[         R                  " [         R                  " U 5      X:H  5      nS[        R                  " S5      -  nU[         R                  " [         R                  " XC-
  5      5      U-  -   n[         R
                  " XPU5      $ )Nc                      g)Nz)logaddexp2 doesn't support complex dtypesrL  rL  r7  r5  rN  logaddexp2.<locals>.<lambda>M      ;r7  rp  r/  )rb  rc  rn  r  r  r   r   rO   r!  rW   rX   rB   )r  rD  r  r  r  r  	inv_log_2r   s           r5  r   r   E  s     
LL##AGG,O0F0Fqww0OP;
 6D;;t"D;;t"D  Q8Hdhhqk!IEKK

4; 789DDF;;xF++r7  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r  rn  r  r  rC  s     r5  r   r   Y  G     !!!''**F!!!''**F5Lr7  c                 \    [         R                  " U R                  5      (       d  U S:H  $ U ) $ r  r  r  s    r5  r   r   d  s'    !!!''**Av2Ir7  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  n[        X5      $ r  )rn  r  r  rx   rC  s     r5  r   r   k  sK     !!!''**F!!!''**Far7  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r  r  rC  s     r5  r   r   w  r  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     rn  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r          ==r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     r  r7  )r  rO  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s    
 99Q?r7  c                 .    [         R                  " X5      $ rD  r  rC  s     r5  r   r     rn  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s     ??1  r7  c                 .    [         R                  " X5      $ rD  )r  r   rC  s     r5  r   r     s     ??1  r7  rP  c                 p    [        U [        5      (       a  Sn[        U5      e[        R                  " XUS9$ )Nz?Received a Number for the first argument, but expected a TensorrV  )r;  r   ra  rb  r   )r  rD  rW  r  s       r5  r   r     s1     !VOo99Q''r7  c                   [        X5      u  p[        U [        5      (       a|  [        U[        5      (       ag  [        R                  " [
        R                  " U R                  5      (       + =(       a%    [
        R                  " UR                  5      (       + S 5        US:w  a  [        U [        5      (       a  U R                  OUR                  n[
        R                  " U5      n[
        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        U[        R                  5      (       a  [        R                  " X5      nOX-  n[        R                  " X5      n[!        X/U5      $ )z'
Reference implementation of torch.sub
c                      g)NzwSubtraction, the `-` operator, with two bool tensors is not supported. Use the `^` or `logical_xor()` operator instead.rL  rL  r7  r5  rN  sub.<locals>.<lambda>  s    Cr7  rP  rY  r  rm  )rw  r;  r#   rb  rc  rn  r  r  r   r   r2  ra  rQ  r  r   r   r?  rZ  s          r5  r   r     s     A!DA!Z  Z:%>%>&&qww//W8N8Nqww8W4W	
 z%a44!''))%0**4;DD+DK=8WXcWddefCS/!a&&		!#A
 	AYYq_F'77r7  r   )r  r  ry  rO  c                 .    [         R                  " X5      $ rD  )r  r~   rC  s     r5  r   r     s     99Q?r7  c           
         [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U[        5      (       a4  [        U [        5      (       a  [        XR                  UR                  S9n OH[        U [        5      (       a3  [        U[        5      (       a  [        XR                  U R                  S9n[        U [        5      (       d   e[        U[        5      (       d   e[         R                  " [         R                  " U S5      S[         R                  " U [         R                  " U5      5      5      n[         R                  " [         R                  " U5      [        S5      U5      $ )Nc                      g)Nz/Expected either argument a or b to be a Tensor"rL  rL  r7  r5  rN  xlogy.<locals>.<lambda>	  r3  r7  rg  r   r  )rb  rc  r;  r#   r   r$  r  r4  r   r   r   rW   rR   r  )r  rD  rhss      r5  r   r      s     
LL1j!>Z:%>A !Z  Z6%:%:!77188<	Az	"	"z!V'<'<!77188< a$$$$a$$$$
++ehhq!na1eiil)C
DC;;u{{1~uU|S99r7  )r  ry  rO  c                     [         R                  " U 5      n[         R                  " U5      (       a  [        R                  " X5      $ [        [        R                  " X5      5      $ rD  )rn  	get_dtyper  r  r~   rs   rv  s      r5  r   r     sD     OOAEe$$yy1!!r7  )r  tensor1tensor2r  r  r  c                   ^^ Tb\  U R                   n[        R                  " U5      m[        R                  " [        R
                  " [        T5      T5      UU4S j5        U TU-  U-  -   $ )z+
Reference implementation of torch.addcdiv
c                  (   > S[        T5       ST  S3$ r  r1  r  r  s   r5  rN  addcdiv.<locals>.<lambda>B      -d5k]:YZeYffghr7  r  rn  r   rb  rL  r   r2  r  r  r  r  r  r  s      ` @r5  r   r   -  _      

))%0''U[Ah	

 %'/G+++r7  c                   ^^ Tb\  U R                   n[        R                  " U5      m[        R                  " [        R
                  " [        T5      T5      UU4S j5        U TU-  U-  -   $ )z+
Reference implementation of torch.addcmul
c                  (   > S[        T5       ST  S3$ r  r1  r  s   r5  rN  addcmul.<locals>.<lambda>]  r  r7  r  r  s      ` @r5  r   r   H  r  r7  )r  r	  r^  r	  r^  c                    Uc  Uc  Sn[        U5      eUbX  [        R                  " U 5      n[        R                  " [        R                  " X5      U5      n[        R
                  " XPU5      n UbX  [        R                  " U 5      n[        R                  " [        R                  " X5      U5      n[        R
                  " XPU5      n U $ )Nz+clamp called but both min and max are none!)ra  rb  rR   rx   r   r   r   )r  r	  r^  r  a_isnan	conditions         r5  r   r   c  s     {s{;o
++a.$$UXXa%5w?	
 KK	c*
++a.$$UXXa%5w?	KK	c*Hr7  c                 *    [         R                  " XS9$ )N)r	  rb  r   )r  r	  s     r5  r{   r{          ;;t%%r7  c                 *    [         R                  " XS9$ )N)r^  r  )r  r^  s     r5  r|   r|     r  r7  predc                    ^  Ub  Uc  [         e[        R                  " T XSS9  [        R                  " T R
                  [        R                  L U 4S j5        [        T X5      u  m p[        R                  " T X5      $ ) Tallow_cpu_scalar_tensorsc                  "   > ST R                    3$ )Nz#expected predicate to be bool, got r  )r  s   r5  rN  where.<locals>.<lambda>  s    5djj\Br7  )
NotImplementedErrorrn  check_same_devicerb  rc  r  r  rw  r  r   )r  r  rD  s   `  r5  r   r     sh     	yAI!!	D!F	LL

ejj B
 "$-JD!;;tQ""r7  memory_formatr  c                .    [         R                  " XS9nU$ Nr  )r  r   )r  r  r   s      r5  r   r     s    
 [[8FMr7  )allow_cross_devicec                    U(       dB  U R                   UR                   :w  a(  SUR                    SU R                    S3n[        U5      e[        R                  " X5      $ )NzAttempting to copy from device z to device z*, but cross-device copies are not allowed!)r4  rq  r  r   )r  rD  r   r  s       r5  r   r     sK    !((ahh"6/zQXXJNxy3==r7  c                     U R                  5       S:w  a  SU R                  5        S3n[        U5      e[        R                  " U R                  5      nU" [
        R                  " U 5      5      $ )NrP  zCan't convert a tensor with z elements to a number!)r  ra  rn  r   r  r  r   )r  r  number_types      r5  r   r     sW    wwyA~,QWWYK7MNo %%agg.Kuzz!}%%r7  r4  copylayout
pin_memorynon_blockingc                 V   U(       + =(       a    US L =(       d    U R                   U:H  =(       a{    US L =(       d    U R                  U:H  =(       aZ    US L =(       d    U R                  U:H  =(       a9    US L =(       d.    U[        R                  :H  =(       d    [
        R                  " XS9$ r  )r4  r  r  rb  preserve_formatrn  is_contiguous_for_memory_format)r  r4  r  r  r  r  r  r  s           r5  _to_will_aliasr    s      
	
t^1qxx61
	
d].agg.
	
 t^1qxx61
	
 T! U 5 55U44QTr7  c                      [         erD  )r  )rv  r  s     r5  _to_dispatchr    s    
r7  c                     U UUUUS.nU$ N)r4  r  r  r  r  rL  r4  r  r  r  r  r  s         r5  
_to_devicer    s!     $&F Mr7  c                 >    [         R                  " U 5      UUUUS.nU$ r  )rb  r4  r  s         r5  _to_device_strr    s*     ,,v&$&F Mr7  c                     U UUUS.nU$ )N)r  r  r  r  rL  )r  r  r  r  r  s        r5  	_to_dtyper    s     $&	F Mr7  otherc                 `    U R                   nU R                  nU R                  nUUUUUUS.nU$ )N)r4  r  r  r  r  r  )r4  r  r  )r  r  r  r  r4  r  r  r  s           r5  	_to_otherr  )  sA     \\FKKE\\F $&F Mr7  	to_kwargsc                    / SQnSU;   a4  [        US   [        5      (       a  [        R                  " US   5      US'   U H  nX1;   d  M
  US:X  a  X   [        R                  L dy  US:X  a_  X   R
                  U R                  R
                  :X  a9  X   R                  (       a:  X   R                  U R                  R                  :X  d  [        XS 5      X   :X  d  M  UR                  U5        M     g )N)r  r4  r  r  r4  r  )	r;  rr  rb  r4  r	  r2  indexr  pop)r  r  options_to_checkkws       r5  _canonicalize_to_argumentsr  A  s    E9Ih,?!E!E#ll9X+>?	(?&9=E<Q<Q+Q(N!**ahhmm;%M//9=3F3F!((..3X A4(IM9 b! r7  c                 "   [        U5      S:w  a  [        U0 UD6nSU;  d   e[        X5        [        U 40 UD6(       a  U $ SU;   a  UR	                  S5      OSnSU;   a  UR	                  S5      OSnU(       d*  UR                  SU R                  5      U R                  :w  aI  U(       dB  SU;  a<  SU;  a6  S	U;  a0  [        R                  " XR                  SU R                  5      5      $ [        R                  " U 40 UD6n[        XP5        U$ )
Nr   r  r  Fr  r  r  r4  r  )rS  r  r  r  r  getr  r  r  rb  r  r   )r  rv  r  r  r  r   s         r5  r   r   Y  s    
4yA~t.v. v%%%q)a"6"!'6!16::fuD1?61I6::n-uL 
&**Wagg.!''9F*V#V# ))!ZZ-IJJa*6*FFMr7  )has_identityaccepts_dim_tupler@  keepdimsr  r  r~  r"  r#  r@  r$  r  output_dtype_kindc                  ^  [        T [        5      (       d   eT R                  S:  a  [        ST R                   S35      eUb4  [        U[        5      (       d   eUb  XgR                  :w  a  [        S5      eU(       d  Ub  [        U[
        5      (       d   e[        U[
        5      (       a  U4n[        R                  " T R                  U5      nU(       dH  T R                  S:H  =(       d     [        R                  " U 4S jU 5       5      n	U	(       d  [        S5      e[        R                  " T X5      u  p[        T U
5      m U" T U5      nU(       a|  [        T R                  5       Vs/ s H  oU;  a  T R                  U   OSPM     nn[        T R                  5       Vs/ s H  oU;  d  M
  UPM     nn[        R                  " XU5      nUb@  Uc   eUb  XR                  :w  a  [        S	5      e[!        X|R                  5      n[#        XS
9$ UR                  U:w  a  Ub  [        R$                  " X5      nU$ s  snf s  snf )N@   zReceived a tensor with z? dimensions, but only tensors with up to 64 dims are supported!z4dtype argument and out dtype must match in reductionr   c              3   B   >#    U  H  nTR                   U   v   M     g 7frD  rT  rG  ir  s     r5  rI  _reduction.<locals>.<genexpr>  s     1Kd!''!*d   zJreducing over zero-size dimension for reduction operation without identityrP  z7Expected the dtype of reduction result and out to match	copy_fromr   )r;  r#   ndimrq  r  r   rn  reduction_dimsrT  r:  r   reduction_dtypesr'   r`  r  broadcast_in_dimr(   r)   r  )r  r~  r"  r#  r@  r$  r  r  r%  valid_shaper  r  r   r+  output_shapebroadcast_dimss   `               r5  
_reductionr7    s
    a$$$$vv{%affX-lm
 	
 #z****		!"J  |z$4444$w.DffkKX\\1Kd1K%K\  ',&<&<	'# 	 #45A!T]FDI!&&MRMqtm
:MR%*166]D]tm!]D''nM
'''!:I   \\2<<|||#(@++FAM! SDs   . I'	I4Ic                 D  ^  [        [        T R                  5      n[        T S0 5      n[        5       " U5      m [	        T 5      SS.U 4S jj5       nT R                   S3nXCl        UR
                  R                  U5        [        [        [        U5      5      " U5        U$ )zc
Given a view function (e.g. torch.diagonal) generates its copy variant (e.g. torch.diagonal_copy)
__annotations__Nr  c                 R   > T" USU 0UD6nU b  U$ [         R                  " S U5      $ )Nr  c                 <    U R                  [        R                  S9$ r  )r   rb  contiguous_formatrM  s    r5  rN  3_make_copy_from_view.<locals>._fn.<locals>.<lambda>  s    aggE,C,CgDr7  )pytreetree_map)r  rv  r  r   r  s       r5  r  !_make_copy_from_view.<locals>._fn  s8    T-s-f-?MD
 	
r7  _copy)r  r  r  r,   r	   r9  updaterx  )r  aten_fnannotationsr  	copy_names   `    r5  _make_copy_from_viewrG    s     dBKK(G"/4K	w	B
2Y 
 
 ;;-u%IL{+7434S9Jr7  c                     [         R                  " [         R                  " [         R                  " U 5      XS95      nU R                  [         R                  :X  a  UR                  [         R                  S9nU$ )Nr  r  )rb  r   r   r  uint8r   )r  r  r  r   s       r5  r   r     sS     uyy):):1)=sTUFww%++-Mr7  c                 p   [        U [        R                  5      n[        U[        [
        45      (       a   [        U5      S:X  a  UR                  5       nOUR                  XS9R                  S5      nU R                  [        R                  L a%  [        R                  " U[        R                  5      $ U$ )Nr   )r  r  F)r'   rb  r  r;  listr\  rS  r   r   r   r  rI  r  r  )r  r  r  r  r   s        r5  r   r     s     
!EJJ	/B#e}%%#c(a-C144U; 	ww%++))&%++>>Mr7  )r  r  c          
      h   Ucw  Ub  UR                   nOg[        R                  " U R                   5      (       d%  [        R                  " U R                   5      (       a  [        R
                  nOU R                   nUS:X  d  U/ :X  a  S n[        U [        R                  UUUU[        R                  S9$ NrL  r@  r$  r  r  r%  )r  rn  r  r  rb  int64r7  r  r   r    SAMEr  r  r  r  r  s        r5  r   r     s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I			499 r7  c           
        ^ ^^ [         R                  " TSS9m[        R                  " [         R                  " TT R
                  5      U U4S j5        [         R                  " TT R
                  5      (       a%  [        T5      S:  a  [        R                  " T 5      $ T R                  [        T5      -
  m[        [        T5      5      [        U UU4S j[        T[        T5      5       5       5      -   n[        R                  " T USS S9$ )NFvalidatec                  *   > ST ST R                    S3$ )Nzsum_to_size: size "z" is not expandable to size ""r)  r  rT  s   r5  rN  sum_to_size.<locals>.<lambda>!	  s    %eW,I!''RSTr7  r   c              3   n   >#    U  H*  nTUT-
     S :X  d  M  TR                   U   S :w  d  M&  Uv   M,     g7frP  Nr)  )rG  r+  r  leading_dimsrT  s     r5  rI  sum_to_size.<locals>.<genexpr>(	  s@      50A\!"a' 	
,-GGAJ!O 	
0s   55	5T)r  r  r  )rn  extract_shape_from_varargsrb  rc  is_expandable_torT  is_same_shaperS  r  view_ofr0  r\  r`  r   )r  rT  reduce_dimsr[  s   `` @r5  r   r   	  s     ,,UUCE	LLuagg.T 5!''**s5zA~}}Q66CJ&Ll+,u 5|SZ05 0 K
 99QKTBBr7  c          
      h   Ucw  Ub  UR                   nOg[        R                  " U R                   5      (       d%  [        R                  " U R                   5      (       a  [        R
                  nOU R                   nUS:X  d  U/ :X  a  S n[        U [        R                  UUUU[        R                  S9$ rM  )r  rn  r  r  rb  rO  r7  r  r   r    rP  rQ  s        r5  r   r   0	  s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I	

499 r7  r:  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ NrL  Fr@  r$  r  r  r"  r%  )r7  r  r   r    rP  r  r  r  r  s       r5  r   r   N	  E     byC2I	

499	 	r7  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ rd  )r7  r  r   r    rP  rf  s       r5  r   r   f	  rg  r7  c                 @    Uc  [        U [        5      (       a  U nS n X4$ rD  )r;  r  )r  unbiaseds     r5  _dim_var_dispatchrk  ~	  s(     JsD11=r7  
correctionrj  rm  c                    [        X5      u  p[        R                  " X$5      nUS:X  d  U/ :X  a  S n[        U [	        [
        R                  US9UUS S S[        R                  S9nU$ )NrL  rl  Tre  )	rk  rn  set_correctionr7  r   r  r   r    COMPLEX_TO_FLOAT)r  r  rj  r  rm  r   s         r5  r   r   	  sl     &c4MC%%h;J
byC2I			j14EE	F Mr7  c                "   [        X5      u  p[        R                  " X$5      n[        R                  " U [        R
                  5      u  pV[        X5      n [        R                  " XXCS9n[        R                  " U5      nUc   e[        X5      $ N)rm  r  )
rk  rn  ro  r2  r    rp  r'   rb  r   rn   )	r  r  rj  r  rm  opmath_dtyper  a_vara_stds	            r5  r   r   	  s     &c4MC%%h;J00	%66L 	 0AIIaEEJJuE"500r7  c          
        ^ ^^	 US:X  d  U/ :X  a  S nTm	Tc  T R                   m[        T [        R                  UUTS [        R
                  S9n[        R                  " [        R                  " T5      =(       d    [        R                  " T5      UU	4S j5        [        U[        5      (       a  U4n[        R                  " T R                  U5      nT R                  S:X  a  SO$[!        ["        R$                  U 4S jU 5       S5      n['        XW5      nTc  T R                   OTn[)        XX5      nUb5  [        U[*        5      (       d   e[-        XER                  5      n[/        XTS9$ U$ )NrL  rN  c                     > STc  SOS ST  3$ )Nz&mean(): could not infer output dtype. Inputr   z> dtype must be either a floating point or complex dtype. Got: rL  )r  
orig_dtypes   r5  rN  mean.<locals>.<lambda>	  s"    4$,w*= >77<g?r7  r   rP  c              3   B   >#    U  H  nTR                   U   v   M     g 7frD  r)  r*  s     r5  rI  mean.<locals>.<genexpr>	  s     7QDq
Dr-  r.  )r  r7  r  r   r    KEEP_PROMOTED_TYPErb  rc  rn  r  r  r;  r   r1  rT  r0  r   operatorr   r   r'   r#   r(   r)   )
r  r  r  r  r  r   r@  nelemr  ry  s
   `  `     @r5  r   r   	  s.    byC2IJ}			4GGF 
LLU#Du'='=e'D	
 #sf-D1A&7QD7QST"UE'F#m177L$V:F
#z****\\2<<Mr7  out0out1)rj  r  rm  c                T   [        X5      u  p[        R                  " X$5      n[        R                  " U [        R
                  5      u  pVU R                  n[        X5      n [        R                  " XXCS9u  p[        R                  " U5      n
Uc   e[        X5      [        X5      4$ rr  )rk  rn  ro  r2  r    rp  r  r'   rb  r   rn   )r  r  rj  r  rm  rs  r  original_dtypert  a_meanru  s              r5  r   r   	  s     &c4MC%%h;J00	%66L WWN0ANN1jRMEJJuE-7 r7  c                P    [        X5      u  p[        XX#US9n[        XU5      nXV4$ )Nrl  )rk  r   r   )r  r  rj  r  rm  vms          r5  r   r   
  s1     &c4MCAH*=AQWA4Kr7  )r  vec1vec2)betarW  r  r  r  c                  ^ ^^^^^ [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  S:H  U4S j5        TS4TS44 H  u  nm[        U[        5      (       d  M  [         R                  " [
        R                  " T R                  5      =(       aG    [
        R                  " TR                  5      =(       a     [
        R                  " TR                  5      U4S j5        M     T R                  TR                  S   TR                  S   5      m [
        R                  " T R                  5      (       a  [         R                  " [        [        T5      [        5      U4S j5        [         R                  " [        [        T5      [        5      U4S	 j5        T(       d5  T(       a  [         R                  " TT5      $ [         R                  " T S
5      $ [         R                  " T T(       a  [         R                  " TT5      5      $ [         R                  " T S
5      5      $ [         R                  " [        [        T5      [!        T R                  5      5      UU 4S j5        [         R                  " [        [        T5      [!        T R                  5      5      UU 4S j5        TS:X  a  T[         R                  " TT5      -  $ TT -  T[         R                  " TT5      -  -   $ )NrP  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec1, but got -Dr0  )r  s   r5  rN  addr.<locals>.<lambda>$
      <TYYKrJr7  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec2, but got r  r  )r  s   r5  rN  r  (
  r  r7  rW  r  c                     > ST  S3$ )NzBoolean z$ only supported for Boolean results.rL  )arg_names   r5  rN  r  0
  s    (8*,PQr7  r   c                      > S[        T 5       3$ )Nzexpected bool/int beta but got r1  r  s   r5  rN  r  7
  s    5d4j\Br7  c                      > S[        T 5       3$ )Nz expected bool/int alpha but got r1  r  s   r5  rN  r  ;
  s    6tDzlCr7  Fc                  :   > S[        T 5       STR                   3$ Nzcannot safely convert z to r2  r  )r  r  s   r5  rN  r  G
  s    ,T$ZLTZZLIr7  c                  :   > S[        T 5       STR                   3$ r  r  )rW  r  s   r5  rN  r  K
  s    ,T%[Mdjj\Jr7  )rb  rc  r0  r;  r  rn  r  r  r   rT  r   r2  intouterr  r   r   )r  r  r  r  rW  argr  s   ````` @r5  r   r   
  s    
LL		QJ 
LL		QJ !'*T6N;Xc4  LL&&tzz2 7**4::67**4::6Q	 < ;;tzz!}djjm4Ddjj))!$t*c2B	
 	!$u+s3C	
 .35;;tT*Uu9UU##+0D$' 6;oodE6R 
 	!$t*mDJJ.GHI	
 	!$u+}TZZ/HIJ	
 195;;tT222$;T4)@!@@@r7  r  rv  .c                    U(       d,  [        U [        R                  R                  5      (       a  U nO1[        U [        R                  R                  5      (       a   eU 4U-   n[	        S U 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_1d`.c              3   \   #    U  H"  oR                   S :  a  UO[        US5      v   M$     g7f)rP  r   N)r0  r  rG  r  s     r5  rI  atleast_1d.<locals>.<genexpr>^
  s#     Eu!VVq[i1o5us   *,rP  r   )r;  collectionsabcr   r\  rS  )r  rv  args_r  s       r5  r   r   U
  ss     JsKOO$<$<==c;??#;#;<<<<
EuE
ECc(Q,3*CF*r7  at_least_fnc                 V    U " U5      n[        U[        5      (       d   e[        X15      $ rD  )r;  r#   r  )r  r  r  arg_s       r5  _unsqueeze_atleastr  d
  s,     sDdJ''''Tr7  c                 L  ^ U(       d,  [        U [        R                  R                  5      (       a  U nO1[        U [        R                  R                  5      (       a   eU 4U-   n[	        [
        [        S5      m[        U4S jU 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_2d`.r   c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)r/  Nr  )rG  r  unsqueeze_atleast_1ds     r5  rI  atleast_2d.<locals>.<genexpr>w
  $     Mu!VVq[&:1&==u   &)rP  )	r;  r  r  r   r   r  r   r\  rS  )r  rv  r  r  r  s       @r5  r   r   m
  s     JsKOO$<$<==c;??#;#;<<<<"#5z1E
MuM
MCc(Q,3*CF*r7  c                 L  ^ U(       d,  [        U [        R                  R                  5      (       a  U nO1[        U [        R                  R                  5      (       a   eU 4U-   n[	        [
        [        S5      m[        U4S jU 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_3d`.rV  c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)   Nr  )rG  r  unsqueeze_atleast_2ds     r5  rI  atleast_3d.<locals>.<genexpr>
  r  r  rP  r   )	r;  r  r  r   r   r  r   r\  rS  )r  rv  r  r  r  s       @r5  r   r   |
  s     JsKOO$<$<==c;??#;#;<<<<"#5z2F
MuM
MCc(Q,3*CF*r7  r9  r5  r;  c                 Z    Ub  UOU R                  5       n[        R                  " XX$5      $ rD  )r;  r  r   )r  r9  r5  r;  storage_offset_ints        r5  r   r   
  s1     )4!:J:J:L  AV@@r7  srcc                 @    Uc  SOUn[         R                  " XX#U5      $ r  )r  r   )r  r  r9  r5  r;  r  s         r5  r   r   
  s'     -4.##E>PQQr7  c                  :    [         R                  " [        U 6 5      $ rD  )rb  Sizerf  )re  s    r5  r   r   
  s    ::'011r7  c                      [        U 5      S:X  a  [        U S   [        5      (       d  U S   n [        [	        U SS065      $ )NrP  r   rg  F)rS  r;  rQ  rK  rw  tensorss    r5  r   r   
  s?     7|qGAJ!?!?!* 'MuMNNr7  c                     [        U5      [        U R                  5      -
  n[        [        U[        U R                  5      U-   5      5      n[        R
                  " XU5      $ rD  )rS  rT  r\  r`  r  r3  )r  r9  startr@  s       r5  r   r   
  sI    IAGG$Euc!''lU234D!!!400r7  r  r  c                   ^
^^^ S n[        U 5      S:X  a  Sn[        U5      eU  H  n[        U[        5      (       a  M   e   [        R
                  " U SS06  SSKJn  S m
[        U 5       He  u  mmT
c  TR                  S:w  a  Tm
M  M  TR                  S:w  d  M1  [        R                  " TR                  T
R                  :H  U
UU4S j5        Mg     T
c  U S   m
T
R                  n/ n[        U 5       H  u  mn[        U5      [        UR                  5      :w  aF  UR                  S:X  d   e[        R                  " U" UR                  S   S:H  5      U
U4S	 j5        Mn  UR                  S:X  a  U" UR                  S   S:H  5      (       a  M  UR                  U5        M     U" U 5      n[        U5      S:X  aB  U S   m [        [        S
 U  5       5      5      n	[#        STR$                  TR&                  U	US9$ [        R(                  " US   R                  U5      n[        R*                  " US   R                  U5        [,        R.                  " Xq5      R1                  US9$ ! [          a    Sn	 Nf = f)Nc                     S nU  HM  n[         R                  " U5      nU[        R                  :X  a  Us  $ Ub  X:w  a  [        R                  s  $ UnMO     Uc   eU$ rD  )rn  suggest_memory_formatrb  r=  )inputsformatr   fs       r5   cat_compute_output_memory_format-cat.<locals>.cat_compute_output_memory_format
  sb    A++A.AE+++!fk...F  !!!r7  r   z3cat expects at least one tensor, but received zero!r  FrA  rP  c                  D   > ST R                    STR                    ST S3$ )N6Number of dimensions of tensors must match.  Expected z-D tensors, but got z-D for tensor number  in the listr  )exampler+  r   s   r5  rN  cat.<locals>.<lambda>
  s.       '~-A!&& J%%&C|5r7  c                  *   > ST R                    ST S3$ )Nr  z*-D tensors, but got 1-D for tensor number r  r  )r  
tensor_idxs   r5  rN  r  	  s"     #LL> *!!+L:r7  c              3   8   #    U  H  oR                   v   M     g 7frD  )requires_gradrF  s     r5  rI  cat.<locals>.<genexpr>   s     $Fg__grU  r   r  r4  r  r  r  )rS  ra  r;  r#   rn  r  r[  rB  r_  r0  rb  rc  rT  r  r  r   	Exceptionr  r  r4  canonicalize_dimvalidate_idxr  r   r   )r  r  r  r  tensorrB  rT  filteredr  r  r  r+  r   r  s             @@@@r5  r   r   
  sB   
 7|qCo&*----  
WEuEJ$ G'"1?vv{  vv{FFgll*5 #  !*MMEH'0
Fu:V\\**;;!###LL %V\\!_%9::$ {{a$8aA9M$N$NOOF#3 16 5W=M
8}AJ	" !$Fg$F!FGM ''88''
 	
 
 
 !!1!13
7C	x{''-99X#)))FF  	"!M	"s   I- -I<;I<c                 >    [        S U  5       5      n[        US5      $ )Nc              3      #    U  H7  oR                   S :  a  UO UR                  UR                  5       S 45      v   M9     g7frZ  )r0  r   r  rF  s     r5  rI  column_stack.<locals>.<genexpr>5  s3      @G1VVaZQYY	1~66s   ?ArP  )r\  r   r  aligned_tensorss     r5  r   r   3  s(     @G O ""r7  c                     [         R                  " U R                  5      (       d  U $ U R                  (       a  [        R
                  " U 5      $ [        R                  " U 5      $ rD  )rn  r  r  	is_sparserb  r6   r  r   r  s    r5  r   r   ;  sC    !!%++..""5))::er7  padc           	        ^^
^^^^ [         R                  " [        T5      S-  S:H  U4S j5        U R                  m[        T5      m[        T5      S-  nTU-
  m[         R                  " TU:  UU4S j5        U n[	        TT5       Hx  m
STT
-
  S-
  -  mTT   S:  a*  UR                  T
TT   * UR                  T
   TT   -   5      nTTS-      S:  d  MO  UR                  T
SUR                  T
   TTS-      -   5      nMz     [        R                  " S T 5       5      (       a  UR                  5       $ [        TS T 5      n[	        U5       Ha  m
[        T5      T
S-   S-  -
  mTTT
-      TT   -   TTS-      -   n[         R                  " US:  U
UUUU4S j5        UR                  U5        Mc     [        R                  " U 5      n[         R                  " UU R                  U R                  U R                   US9nUS:X  a   U R                  [         R"                  :X  a  S	n[         R$                  " X5      nUn	[	        TT5       Hw  m
STT
-
  S-
  -  mTT   S:  a)  U	R                  T
TT   U	R                  T
   TT   -
  5      n	TTS-      S:  d  MN  U	R                  T
SU	R                  T
   TTS-      -
  5      n	My     [&        R(                  " X5        U$ )
Nr/  r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals rR  )r  s   r5  rN  !constant_pad_nd.<locals>.<lambda>K  s    CCH:Nr7  c                  (   > S[        T5       ST  S3$ )Nz`Length of pad should be no more than twice the number of dimensions of the input. Pad length is z while the input has  dimensions.rR  )l_inpr  s   r5  rN  r  V  s      225c(;P'r7  rP  c              3   *   #    U  H	  oS :  v   M     g7f)r   NrL  )rG  ps     r5  rI  "constant_pad_nd.<locals>.<genexpr>m  s     '3aE3s   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r  rP  zG resulted in a negative output size, which is invalid. Check dimension z of your input.rL  )r+  input_sizesl_diffr  pad_idxs   r5  rN  r  w  sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr7  r  F)rb  rc  rS  rT  r`  r   r:  r   r   rK  r  rn  r  r  r  r4  r  r  rC   r  r   )r  r  r  l_padc_input	new_shapenew_dimr  r>  c_outputr+  r  r  r  r  s    `        @@@@@r5  r   r   D  s   
 
LLC1N
 ++KEHMEU]F	LL	 G65!uqy1}%w<!nnQWw}}Q7G#g,7VWGw{annQ7==+;c'A+>N+NOG "" ||'3'''}}[&)*I5\c(q1uk*fqj)CL83w{;KKaKM M	
 	!  //6M[[kk||))#F zekkUZZ/ZZ&FH65!uqy1}%w<13w<!2S\!AH w{q q!X^^A->Wq[AQ-QRH " 
MM($Mr7  c                    [         R                  " U[         R                  :g  S 5        [        R                  " XS9(       a  U $ [         R
                  " XS9$ )Nc                      g)Nz@preserve memory format is unsupported by the contiguous operatorrL  rL  r7  r5  rN  contiguous.<locals>.<lambda>  s    Rr7  r  )rb  rc  r	  rn  r
  r   )r  r  s     r5  r   r     sE     
LL...R
 ,,QL;;q66r7  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%dstack expects a non-empty TensorListrL  rL  r7  r5  rN  dstack.<locals>.<lambda>      +Rr7  r/  )rb  rc  rS  r   r   r  s     r5  r   r     1    	LLW!#RS '*O""r7  c                   ^ SSK Jn  [        U5      S:X  a&  [        US   [        5      (       a  [        US   5      n[        R                  " [        U5      [        U R                  5      :  S 5        [        U5      [        U R                  5      -
  n[        U5      n[        U R                  5       H\  u  nmXS-   nX   n[        R                  " U" UT:H  5      =(       d    U" TS:H  5      =(       d    US:H  U4S j5        US:w  a  UOTXF'   M^     [        R                  " U5        [        R                  " X[        [        U[        U R                  5      U-   5      5      5      $ )Nr   rA  rP  c                      g)Nz3expand: the requested shape has too few dimensions!rL  rL  r7  r5  rN  expand.<locals>.<lambda>  s    Er7  rV  c                     > ST  S3$ )Nz3expand: attempting to expand a dimension of length rm  rL  rM  s   r5  rN  r    s    I!ANr7  )r[  rB  rS  r;  r   r\  rb  rc  rT  rK  r_  rn  validate_shaper  r3  r`  )	r  rT  rB  r  shape_rZ  
offset_idxrequested_lengthrH  s	           @r5  r   r     s,   J
 5zQ:eAh99eAh	LLE
c!''l"E
 Z#agg,&F%[FAGG$Q\
 , !1Q!67 &#AF+&2%N		
 2BR1G-Q % 
 !!	5vs177|f'<=> r7  c                 8    U R                  UR                  5      $ rD  )r   rT  rC  s     r5  r   r     s    88AGGr7  chunksc           	         US::  a  SU S3n[        U5      e[        R                  " U R                  U5      nU R                  U   n[
        R                  " XA-  5      n[
        R                  " XE-  5      nXE-  n[        U5       Vs/ s H  n[        XX-  U5      PM     n	nUS:w  a  U	R                  [        XXe-  U5      5        [        U	5      $ s  snf )Nr   z%Expected at least one chunk, but got rm  )ra  rn  r  r0  rT  r!  r5   rE   r`  r   r  r\  )
r  r  r  r  length
chunk_sizefull_chunkstail_chunk_sizer+  r   s
             r5  r   r     s    {5fXQ?o

 
 
-CWWS\F6?+J**V01K)OBGBTUBTQfQQ^Z8BTFU!fQ[%=OP= Vs   	C	start_dimend_dimc                 H   [         R                  " U R                  U5      n[         R                  " U R                  U5      nX:X  a  U R                  S:w  a  U $ [        R                  " XU5      u  p4Ub  [        R
                  " XU5      $ [        R                  " XU5      $ r  )rn  r  r0  r  _collapse_view_helpercollapse_viewcollapse)r  r	  r
  r  _new_stridess        r5  r   r     s    &&qvvy9I$$QVVW5G ! $99!PI""199 >>!00r7  c                    [        U[        5      (       d   [        U[        5      (       d  [        S5      e[        R
                  " U R                  U5      n[        R                  " U5        [        R                  " X5      $ )Nz!dims has to be a sequence of ints)
r;  r\  rK  ra  rn  canonicalize_dimsr0  validate_no_repeating_dimsr  rev)r  r@  s     r5  r   r      s\     dE"":dD+A+A<==""16640D	$$T*99Qr7  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )Nr/  zInput must be >= 2-d.rP  r0  rq  r   r  s    r5  r   r     %    vvz2334=r7  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )NrP  zInput must be >= 1-d.r  r  r  s    r5  r   r     r  r7  r  r  c                 t  ^^^ [        T[        5      (       a`  [        R                  " TR	                  5       S:H  =(       a     [
        R                  " TR                  5      S 5        TR                  5       m[        [        T5      m[        R                  " U R	                  5       S:  S 5        [        R                  " TS:  S 5        [
        R                  " U R                  U5      nU R                  U5      m[        R                  " [        T* T:*  =(       a    TT:*  UU4S j5        TS:  a  TT-   m[        R                  " TTT-
  :*  UUU4S j5        [!        U R"                  5      nTXA'   U R%                  X@R'                  5       U R)                  5       U R'                  U5      T-  -   5      $ )Nr   c                      g)Nz'start must be an 0-dim integral Tensor.rL  rL  r7  r5  rN  narrow.<locals>.<lambda>#  s    =r7  c                      g)Nz-narrow() cannot be applied to a 0-dim tensor.rL  rL  r7  r5  rN  r  '  s    &Ur7  c                      g)Nz&narrow(): length must be non-negative.rL  rL  r7  r5  rN  r  (  s    &Nr7  c                     > ST *  ST  ST S3$ )Nz0start out of range (expected to be in range of [, z], but got )rL  )
dim_lengthr  s   r5  rN  r  .  s#    BJ;-rR\Q]]hinhoopqr7  c                     > ST ST ST  S3$ )Nzstart (z) + length (z) exceeds dimension size (z).rL  )r!  r  r  s   r5  rN  r  4  s    '%VH4NzlZ\]r7  )r;  r#   rb  rc  r  rn  r  r  r   r   r  r  r0  r9  _check_with
IndexErrorrK  rT  r   r5  r;  )r  r  r  r  r  r!  s     `` @r5  r   r     sO   
 %$$IIK1D!7!7!D=	
 

eE	LL1UV	LL1NO

 
 
-CJ		u4*!4q
 qy
"	LLf$$] QWWIIN<<88:q//1AHHSME4II r7  	norm_dimsepsc                 >   [         R                  " U R                  U5      n[         R                  " U R                  5      n[        X5      n[        U[        5      (       d   e[        R                  " XASSS9u  pV[        R                  " XR-   5      nXF-
  U-  nXU4$ )a  Computes mean and 1/std of a tensor along norm_dims.

Used as a helper function for normalization layers.

Args:
    a (Tensor): input tensor
    norm_dims (DimsType): dimensions to normalize over
    eps (float): epsilon for numerical stability

Returns:
    out (Tensor): normalized tensor.
    mean (Tensor): mean of the tensor along norm_dims.
    rstd (Tensor): 1/std of the tensor along norm_dims.
FT)r  rj  r  )rn  r  r0  r  r  r'   r;  r#   rb  r   r   )	r  r%  r&  r  a_acc
biased_varr   rstdr  s	            r5  
_normalizer+  =  s    " ''	:I33AGG<#A9EeZ((((~~udJ ;;z'(D<4
Cd?r7  
dimensionsc                 V    [        U5       H  n[        R                  " X5      n M     U $ rD  )sortedrb  r  )rH  r,  r  s      r5  _unsqueeze_multipler/  [  s$    j!OOA# "Hr7  weightbias
batch_sizenum_channelsflattened_inner_size
num_groupsc                   ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " UT-  S:H  U U4S j5        SS/n[         R                  " T UTUT-  U/5      n	[	        XU5      u  pnU
R                  T R                  5      n
S/[        [        ST R                  5      5      -   nS nUb  [        X-5      nS nUb  [        X5      nUb  X-  n
Ub  X-   n
[        U
T R                  5      n
[        UT R                  5      n[        UT R                  5      n[         R                  " X5      n[         R                  " X5      nXU4$ )Nr/  c                  "   > ST R                    3$ )Nz=Expected at least 2 dimensions for input tensor but received r  r  s   r5  rN  #native_group_norm.<locals>.<lambda>n  s    OPUPZPZ|\r7  r   c                  .   > SST R                    ST 3-   $ )NzDExpected number of channels in input to be divisible by num_groups, zbut got input of shape z and num_groups = r)  )r  r5  s   r5  rN  r8  r  s!    V#EKK=0B:,
OPr7  r  )rb  rc  r0  r   r+  r  rT  rK  r`  r/  r'   r  r   )r  r0  r1  r2  r3  r4  r5  r&  r1  input_reshapedr  r   r*  r6  unsqueeze_biasunsqueeze_weights   `     `         r5  r   r   a  sO    
LL

a\ 
LLz!Q&	P VN]]	Z!;=QRN !EOCt
((5;;
CS4a 455NN,TB.vF#$!"
!#u{{
3C"45D"45D ==.D==.Dtr7  out2normalized_shapec                   ^ ^^^ [        T5      n[        R                  " US:  U4S j5        [        R                  " TS L =(       d    TR                  [	        T5      :H  UU4S j5        [        R                  " TS L =(       d    TR                  [	        T5      :H  UU4S j5        [        R                  " T R
                  U:  =(       a(    T R                  T R
                  U-
  S  [	        T5      :H  U U4S j5        T R                  5       m Tb  TR                  5       mTb  TR                  5       mT R
                  U-
  n[        [        UT R
                  5      5      n[        T Xt5      u  pn
Tc	  Tb  UT-   nOTb	  Tc  UT-  nOTb  Tb  UT-  T-   n[        UT R                  5      nT R                  R                  S;   a,  [        U	T R                  5      n	[        U
T R                  5      n
XU
4$ )NrP  c                      > S[        T 5      -   $ )NzzExpected normalized_shape to be at least 1-dimensional, i.e., containing at least one element, but got normalized_shape = )rr  )r>  s   r5  rN  #native_layer_norm.<locals>.<lambda>  s     I

 r7  c                  R   > S[        TR                  5      -   S-   [        T 5      -   $ )NzQExpected weight to be of same shape as normalized_shape, but got weight of shape  and normalized_shape = rr  rT  )r>  r0  s   r5  rN  rA    s3     
fll
 %% 
	 r7  c                  R   > S[        T R                  5      -   S-   [        T5      -   $ )NzMExpected bias to be of same shape as normalized_shape, but got bias of shape rC  rD  )r1  r>  s   r5  rN  rA    s2     
djj/ %% 
	 r7  c                  p   > S[        T5      -   S-   [        T5      -   S-   [        T R                  5      -   $ )NzGiven normalized_shape=z, expected input with shape z, but got input of size rD  )r  r>  s   r5  rN  rA    sI    )

 
() 
  %	%
 ekk
r7  )rx  mtia)rS  rb  rc  rT  r\  r0  r   rK  r`  r+  r'   r  r4  r2  )r  r>  r0  r1  r&  normalized_ndimaxisr1  r  r   r*  s   ````       r5  r   r     s    *+O	LL1	  
LL$A&,,%0@*AA	  
LL=

e,<&==	  
LL

o% 	UKKo589UCS=TT		 E""$ ::'D%ejj12N <OCt~$*Dj		Fl		 0FlT!
!#u{{
3C||O+&tU[[9&tU[[9tr7  c                     [        U6 $ rD  )r   )	fake_modefuncrv  r  s       r5  native_layer_norm_fakerM    s    d##r7  c                     [         R                  " U R                  [         R                  " U5      5      n[        R
                  " X5      $ rD  )rn  r  r0  extract_dims_from_varargsr  r   )r  r@  _permutations      r5  r   r     s7    **	//5L ??1++r7  r  maxnormc                 v  ^^	 [         R                  " [        U[        5      (       + S 5        [         R                  " US:  S 5        [         R                  " [        T[        5      (       + S 5        [         R                  " TS:  U4S j5        U R                  m	[         R                  " T	S:  U	4S j5        [
        R                  " T	U5      n[        [        T	5      5      nXB	 [
        R                  " U R                  5      nXPR                  :w  a!  [         R                  R                  XUSUS	9nO[         R                  R                  XUSS
9nSn[         R                  " UT:  TXg-   -  S5      nXPR                  :w  a   [        R                  " XR                  5      nX-  R!                  5       $ )Nc                      g)Nzrenorm: p must be real-valuedrL  rL  r7  r5  rN  renorm.<locals>.<lambda>  s    5Tr7  r   c                      g)Nz'renorm: non-positive norm not supportedrL  rL  r7  r5  rN  rT    s     Ir7  c                      g)Nz#renorm: maxnorm must be real-valuedrL  rL  r7  r5  rN  rT    s    2Wr7  c                     > ST  3$ )Nz,renorm: expected maxnorm to be >= 0 but got rL  )rQ  s   r5  rN  rT    s     LWIVr7  rP  c                     > ST  S3$ )Nz/renorm: input needs at least 2 dimensions, got  dimensionsrL  r  s   r5  rN  rT    s    A${Sr7  T)r  r  r  gHz>rp  )rb  rc  r;  r  r0  rn  r  rK  r`  r  r  linalgvector_normr   r  r  r   )
r  r  r  rQ  ra  acc_typer^   r&  norm_factorr0  s
      `     @r5  r,  r,    s_   
 
LLZ7++-TU	LLQIJ	LLw((*W 
LL1V ::D	LLqS
 
 
 s
+CuT{#K **5;;7H;;||''k4x ( 
 ||''+t'L
C++dWng.DcJK;;00kkJ++--r7  n_fft
hop_length
win_lengthwindowcenterpad_mode
normalizedonesidedreturn_complexalign_to_windowc                   ^ ^^^^^ [         R                  " TS L =(       d    TR                  T R                  :H  U U4S j5        [         R                  " U(       + =(       d    U
S L S5        Ub  UOTS-  mUb  UOTmU	cZ  T R                  5       =(       d+    TS L=(       a     [        R
                  " TR                  5      n[         R                  " US5        OU	n[         R                  " [        R                  " T R                  5      =(       d     [        R
                  " T R                  5      S 5        [         R                  " ST R                  s=:*  =(       a    S:*  Os  S 5        T R                  nUS:X  a  T R                  S	5      m U(       a  S
T R                  -
  nTS-  n/ [        R                  " SU5      QT R                  Qn[        R                  T R                  U5      X/U5      m T R                  T R!                  5       US  5      m T R!                  S5      m[         R                  " S	Ts=:  =(       a    T:*  Os  UU4S j5        [         R                  " TS	:  U4S j5        [         R                  " S	Ts=:  =(       a    T:*  Os  U4S j5        [         R                  " TS L =(       d    TR                  T4:H  UU4S j5        TT:  aS  Tc*  [         R"                  " TT R                  T R                  S9mTT-
  S-  n[        R%                  TUTT-
  U-
  /5      mT R'                  STTS9m U(       d(  U
(       a!  TT-
  S-  n[        R                  T UU/U5      m Tb  T T-  m [        R
                  " T R                  5      nUb  UOU(       + nU(       a  SOS nU(       a=  [         R                  " U(       + S 5        [         R(                  R+                  T SUS9nO[         R(                  R)                  T SUS9nUR-                  SS5        US:X  a  UR/                  S	5      nU(       a  U$ [         R0                  " U5      $ )Nc                  B   > ST R                    3STR                    3-   $ )NzAstft input and window must be on the same device but got self on  and window on r3  r  ra  s   r5  rN  stft.<locals>.<lambda>$  s'    OPUP\P\~^/0r7  z6stft only supports align_to_window for center = False.   zstft requires the return_complex parameter be given for real inputs, and will further require that return_complex=True in a future PyTorch release.c                      g)Nz:stft expected a tensor of floating point or complex valuesrL  rL  r7  r5  rN  rl  A  s    Lr7  rP  r/  c                      g)Nzstft expected a 1D or 2D tensorrL  rL  r7  r5  rN  rl  C  s    /Pr7  r   r  c                     > ST  ST 3$ )Nzstft expected 0 < n_fft <= z, but got n_fft=rL  )r  r^  s   r5  rN  rl  S  s    -fX5EeWMr7  c                     > ST  3$ )Nz0stft expected hop_length > 0 but got hop_length=rL  )hop_length_s   r5  rN  rl  W  s    B;-Pr7  c                     > ST  3$ )Nz9stft expected 0 < win_length <= n_fft but got win_length=rL  )win_length_s   r5  rN  rl  [  s    KK=Yr7  c                  0   > ST  S3STR                    3-   $ )Nz8expected a 1D window tensor of size equal to win_length=r  zbut got window with size r)  )rt  ra  s   r5  rN  rl  _  s#    F{mSUV)&,,89r7  rg  rV  )	dimensionr9  steporthoc                      g)Nz9Cannot have onesided output if window or input is complexrL  rL  r7  r5  rN  rl  x      Or7  r  r^   )rb  rc  r4  r+  rn  r  r  r  r0  r  	itertoolsr   rT  r  r  r  r9  r!  r   r  fftrfft
transpose_squeeze_view_as_real)r  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  return_complex_original_ndim
extra_dims
pad_amountextended_shapeleftinput_pad_amountcomplex_fftr^   r  rr  r  rt  s   ``  `                @@@r5  r-  r-    s    
LL$7&--5<<7	
 
LL
-o-@
 !+ 6*EQJK * 6*EK**, 
$G5#9#9&,,#G 	 	c	
 )	LLU[[)PU-C-CEKK-PL 
LLejj%%A%'PQJJM"^
aZ
I9++Az:IU[[IN3j5MxX

5::<
45ZZ]F	LL	EVM 
LLaP 
LL	K  5 Y 
LL$8&,,;.8	
 U>ZZ5;;u||TF#)%%ftU[5H45O.PQLL2ELDEo!K/A5!13C DhO((5K#/x_H 7dDOO	
 iinnUn6iimmErm5NN1all1o!3>u'9'9#'>>r7  c
                 	  ^ ^ [         R                  " TS L =(       d    TR                  T R                  :H  U U4S j5        Ub  UOUS-  n
Ub  UOUn[         R                  " [        R                  " T R
                  5      U U4S j5        T R                  S5      nT R                  S5      nXUS-
  -  -   n[         R                  " T R                  5       S:  S 5        [         R                  " S	T R                  s=:*  =(       a    S
:*  Os  U 4S j5        Ub  UOX:g  nU(       a"  [         R                  " US	-  S-   U:H  S 5        O[         R                  " X:H  S 5        [         R                  " SU
s=:  =(       a    U:*  Os  S 5        [         R                  " SUs=:  =(       a    U:*  Os  S 5        [         R                  " TS L =(       d    TR                  U4:H  S 5        TcA  [        R                  " T R
                  5      n[         R                  " UUT R                  S9nOTnX:w  a%  X-
  S	-  n[        R                  UUX-
  U-
  4S5      nT R                  nT R                  S	:X  a  T R                  S5      m T R                  SS	5      m U(       a  SOS nU	(       a=  [         R                  " U(       + S 5        [         R                   R#                  T SUS9m O[         R                  " TS L =(       d%    [        R                  " TR
                  5      (       + S 5        U(       d  T R%                  SSUS	-  S-   S9m [         R                   R'                  T SUS9m T R                  S	5      U:X  d   eT UR)                  SSU/5      -  n[        R+                  UUR                  S5      U4SUU
S9n[        R+                  UR-                  S	5      R/                  SX45      UR                  S5      U4SUU
S9nUUR                  S5      :X  d   eUUR                  S5      :X  d   eU(       a  US	-  OSnUb  UU-   nOU(       a  XS	-  -
  nOUn[1        SUU-
  5      nUR%                  SUUS9nUR%                  SUUS9nUU-  nUS	:X  a  UR3                  S5      nUU:  a2  [4        R6                  " S5        [        R                  USUU-
  4S5      nU$ )Nc                  B   > ST R                    3STR                    3-   $ NzBistft input and window must be on the same device but got self on rj  r3  rk  s   r5  rN  istft.<locals>.<lambda>  s(    PQVQ]Q]P^_/0r7  rm  c                  @   > ST R                    STR                    3-   $ r  r3  rk  s   r5  rN  r    s!    Pofmm_=>r7  rV  rP  r   c                      g)Nz"istft input tensor cannot be emptyrL  rL  r7  r5  rN  r    s    ,Pr7  r/  r  c                  "   > ST R                    3$ )Nz8istft expected a tensor with 2 or 3 dimensions, but got r  r  s   r5  rN  r    s    J5::,Wr7  c                      g)Nzistft expected the frequency dimension (3rd to the last) of the input tensor to match n_fft / 2 + 1 when onesided=True, but got {fft_size}rL  rL  r7  r5  rN  r    s    Rr7  c                      g)N)zistft expected the frequency dimension (3rd to the last) of the input tensor to match n_fft when onesided=False, but got {fft_size}rL  rL  r7  r5  rN  r    s     r7  c                      g)Nz+istft expected 0 < hop_length <= win_lengthrL  rL  r7  r5  rN  r    r1  r7  c                      g)Nz&istft expected 0 < win_length <= n_fftrL  rL  r7  r5  rN  r    s    *Rr7  c                      g)NzDInvalid window shape. window has to be 1D and length of `win_length`rL  rL  r7  r5  rN  r    s    Vr7  rg  rx  c                      g)Nz9cannot have onesided output if window or input is complexrL  rL  r7  r5  rN  r    rz  r7  r{  c                      g)Nz:Complex windows are incompatible with return_complex=FalserL  rL  r7  r5  rN  r        Pr7  )r  r  r  )r  r  r9  rw  zThe length of signal is shorter than the length parameter. Result is being padded with zeros in the tail. Please check your center and hop_length settings)rb  rc  r4  rn  r  r  r9  r  r0  rT  corresponding_real_dtyper!  r  r   r  r   r}  ifftr   irfftr  unfold_backwardr   r   r^  r   warningswarn)r  r^  r_  r`  ra  rb  rd  re  r  rf  rr  rt  n_framesfft_sizeexpected_output_signal_len	onesided_
real_dtypewindow_r  r  r^   y_tmpywindow_envelopr  ends   `   `                     r5  r.  r.    sy    
LL$7&--5<<7	
 !+ 6*EQJK * 6*EK	LLu{{+	
 zz"~Hzz"~H!&1)E!E	LL"$PQ	LL	UZZ1W %0h6GIQJNh&	
 		
 
LL	K&&;&= 
LL	K  5 "R 
LL$8&,,;.8V
 ~33EKK@
**[
5<<P#)&&wu7JT7Q0RTUVJJMzzQ"OOAq!E 7dDMO	
 		u"48dNF%"8"8"FFP	
 LLRq!aLHE		2D9::a=E!!!GLL!Q//EZZ]$>? 	 	A ))Aq(23ZZ]$>? * N &222%)<)<Q)???? EQJaEfn	(A:5(C%K F	QeF3A#**qf*MN	NAIIaL
''`	
   Q.H(H$I1MHr7  a_shapea_striderv  rw  c                   ^^^	^
 [        U 5      n[        R                  " XRSS9m	US:X  a  SOU T	   m
US:X  a  SOUT	   n[        R                  " TT
:*  U	U
U4S j5        [        R                  " TS:  U4S j5        [        U 5      n[        U5      nUR                  T5        UR                  U5        T	U:  a  UT	   T-
  T-  S-   UT	'   UT	==   T-  ss'   Xx4$ )NT)wrap_scalarr   rP  c                     > ST  ST ST 3$ )Nz%Maximum size for tensor at dimension z is z but size is rL  )r  max_sizer9  s   r5  rN  *_get_unfold_shape_stride.<locals>.<lambda>&  s    7uD
-X\W]^r7  c                     > ST  S3$ )NzStep is z but must be > 0rL  rw  s   r5  rN  r  +  s    (4& 01r7  )rS  rn  r  rb  rc  rK  r  )r  r  rv  r9  rw  a_ndimlast_striderT  stridesr  r  s      ``    @@r5  _get_unfold_shape_strider    s     \F

 
 
ECaKqWS\H{!K	LL^
 
LLq1
 ME8nG	LLNN;
V|Cj4'D014c
>r7  c                    [         R                  " USS9n[        R                  " [	        U5      [	        U R
                  5      :  S 5        [	        U5      S:X  a  [        R                  " U 5      $ [	        U5      U R                  -
  nS/U-  nU R
                   H  nUR                  U5        M     [        S [        X15       5       5      nSU;   aJ  [        R                  " UU R                  U R                  U R                  [         R                  " U 5      S9$ Un[         R                   " U5      n[#        U5       H  u  p[%        XgX['        US5      5      u  pgM      [)        [#        U5      5      n	U	R+                  [,        R.                  " S5      SS	9  [        U	6 u  pU R1                  U5      n[        R                  " U5      nUR3                  U
5      nUR5                  U5      $ )
NFrS  c                      g)Nzbrepeat: Number of dimensions of repeat dims can not be smaller than number of dimensions of tensorrL  rL  r7  r5  rN  repeat.<locals>.<lambda>>  s    tr7  r   rP  c              3   .   #    U  H  u  pX-  v   M     g 7frD  rL  )rG  padded_sizerepeat_sizes      r5  rI  repeat.<locals>.<genexpr>I  s      (G$K 	!(Gs   r  T)keyreverse)rn  r]  rb  rc  rS  rT  r   r0  r  r\  zipr  r  r4  r  r  make_contiguous_strides_forr_  r  r^  rK  sortr~  
itemgetterr   r   r   )r  repeat_shapenum_new_dimensionspadded_shapedim_sizetarget_shapeurtensor_shapeurtensor_strider  enumerated_stridepermute_order_sorted_striderepeat_xtensorcloned_resultpermuted_results                  r5  r   r   8  s    33L5QL	LLLS\)t
 <A{{1~\*QVV33++LGGH%   (+L(G L 	L{{''88//55a8
 	
 "N77EO"<0*BSC!<L+
' 1 Y78x2215tD$'):$;!M XXn-N KK/M $++M:O ""<00r7  
allow_copyc                j  ^^ SSK JnJn  [        R                  " USS9n[        R
                  " X R                  5       5      nU" U R                  5       S:H  5      (       a   [        X[        R                  " U5      5      $ U R                  S:X  a;  U nU H  nUS:X  d   e[        US5      nM     XPL a  [        R                  " U 5      $ U$ [        U5      S:X  aE  U nU R                   H  nUS:X  d   e[        US5      nM     XPL a  [        R                  " U 5      $ U$ U R!                  5       (       a  [        U5      S:X  a7  U R                  S:  a'  ["        R                  " X R                  5       /S/5      $ [        U5      S:X  a5  U R                  S:X  a%  US   nUS   n["        R                  " XU/US/5      $ SmU mU GHs  nTTR                  :  aC  US:X  d   eTR                  S-
  n	[        R$                  " TU	TR                  U	   5      mTS-   mMW  U" UTR                  T   :H  5      (       a  TS-   mM{  TR                  T   n
TnU" X-  S:g  5      (       a+  US-   nU
TR                  U   -  n
U" X-  S:g  5      (       a  M+  UT:w  ax  [        R&                  " TTU5      u  pUcN  U(       a  [        R(                  " X5      s  $ SU R                   S	U R+                  5        S
U S3n[-        U5      e[/        TTU5      mU" X:g  5      (       a  [        R$                  " TTU5      mTS-   mGMv     TTR                  :  aJ  ["        R0                  " TR                  T   S:H  UU4S j5        [        TT5      mTTR                  :  a  MJ  TU L a  [        R                  " U 5      $ T$ )Nr   )rB  sym_eqFrS  rP  rV  r/  z Cannot view a tensor with shape z and strides z as a tensor with shape rm  c                  .   > ST ST R                   T    3$ )Nza.size(z) expected to be 1 but got r)  )r  rZ  s   r5  rN  &_reshape_view_helper.<locals>.<lambda>  s    gcU"=bhhsm_Mr7  )r[  rB  r  rn  r]  
infer_sizer  r   r  r0  r  r  r`  rS  rT  r   is_contiguousrb  	split_dimr  r   r5  ra  r   rc  )r  r  rT  rB  r  _ar  dim0dim1last_dimaccumr  r  r  r  r  rZ  s                  @@r5  _reshape_view_helperr  r  sk   R ,,UUCE UGGI.E AGGIN++!E$E$Ee$LMM 	vv{FQ;;2r"B  7==##I 5zQggFQ;;RB  7==##Iu:?qvvz##A	{QC88u:?qvv{8D8D##Ad|dAY??* C	
B"''>Q;;ww{H Xrxx/ABB'C  "((3- 788'C
 "5>Q#677'CBHHSM)E #5>Q#677 #: ',&A&A"c3&O#I  ==228	qxxzlZrsxryyz{ o%S#&B  00S&1BAgY ^ -HHSMQM	
 R - 
Qw}}Q	r7  rT  c                      [        U /UQ7SS06$ )Nr  Tr  rW  s     r5  r   r     s    ;E;d;;r7  c                 @    U R                  UR                  5       5      $ rD  )r   r9  r  r  s     r5  r   r     s    <<

%%r7  shiftsc                    [         R                  " U R                  U5      n[        U[        5      (       d  U4n[        U[        5      (       d  U4nU R                  5       S:X  a  U R                  5       $ U R                  5       S:X  a!  [        U5      S:  a  [        SUS    S35      e[        U5      n[        U5      nUS:w  d  US:w  a  US:X  a  [        S5      eUS:X  aK  US:X  aE  [        R                  " [        R                  " U 5      US5      R                  U R                  5      $ X4:w  a  [        SU SU 35      eUS:  d   eUSS nUSS n[        R                  " XS   4US   5      n[        R                  " XuU5      $ US   nU R                  U   n	XS   -
  U	-  n
[        R                   " XR"                  S	9nU R%                  U[        R&                  " X-   U	5      5      $ )
z/Reference implementation of :func:`torch.roll`.r   zDimension specified as z but tensor has no dimensionsrP  z`shifts` requiredz*shifts and dimensions must align. shifts: z, dims: Nr3  )rn  r  r0  r;  r   r  r   r  rS  r$  rq  rb  r   r   r  rT  r  r4  rK   r   )r  r  r@  
len_shiftslen_dimstail_shifts	tail_dimsfirst_dim_rolledr  r9  r  rZ  s               r5  r   r     s    ""16640Dfh''dH%%w 	wwyA~wwyuuw!|D	A%d1gY.KL
 	
 VJ4yHQ(a-?233 q=Z1_::emmA.:??HH!<ZLQYPZ[  !||QRjH	 ::a)tAw?zz*CC q'C773<D1I%E
,,tHH
-C>>#uzz%+t<==r7  r   rP  kc                    [        U5      S:w  a  [        S[        U5       35      eU R                  S:  a  [        SU R                   35      e[        R                  " U R                  U5      nUS   US   :X  a  [        SUS    SUS    35      eUS-  nUS:X  a6  [
        R                  " [
        R                  " XS   45      US   US   5      $ US:X  a  [
        R                  " X5      $ US	:X  a6  [
        R                  " [
        R                  " XS   45      US   US   5      $ U R                  [
        R                  S
9$ )z0Reference implementation of :func:`torch.rot90`.r/  z2expected total rotation dims == 2, but got dims = z/expected total dims >= 2, but got total dims = r   rP  z7expected rotation dims to be different, but got dim0 = z and dim1 = rm  r  r  )
rS  rq  r0  rn  r  rb  r   r   r   r=  )r  r  r@  s      r5  r   r   .  s9    4yA~@TL
 	
 	vvzLQVVHUVV ""16640DAw$q'Ed1gYl[_`a[bZcd
 	
 	
AAAvuzz!1gZ8$q'47KK	
azz!""	
auzz!1gZ8$q'47KKwwU%<%<w==r7  c                     U S   R                   n[        S[        U 5      5       H1  nX   R                   U:X  a  M   SU SX   R                    SU 35       e   g )Nr   rP  z4stack expects each tensor to be equal size, but got z at entry 0 and z
 at entry )rT  r`  rS  )r  entry_shaper+  s      r5  _check_stack_inputsr  N  si    !*""K1c'l#z;. 	
B;- P:##$Jqc3	
. $r7  c                    [        U 5      S:  d   S5       e[        R                  " U S   R                  S-   U5      nX S   R                  :  ae  [	        U 5        [        U S   R                  5      nUR                  U[        U 5      5        [        R                  " X5      nUR                  U5      $ [        R                  " U  Vs/ s H  oUR                  U5      PM     snU5      $ s  snf )Nr   z$stack expects a non-empty TensorListrP  )rS  rn  r  r0  r  rK  rT  insertrb  r   r  r  )r  r  wrapped_dimresult_sizesr  r   s         r5  r   r   W  s     w<!CCC((1)<cBKQZ__$G$GAJ,,-KW6ii-xx%% 99@1kk+.@#FF@s   	C+c                    U=(       d    U R                   n[        R                  " U5      n[        X5      nU R	                  5       S:X  a  [        U5      nO[        XQSS9n[        XW-
  5      n[        [        U[        XaSS95      U5      $ )Nr   Tr  )	r  rn  r  r'   r  r?   r   r   r   )r  r  r  r  r  r  a_expa_maxs           r5  rm   rm   i  sz     #AGGL33LA	 	6BwwyA~BRd+BJ"E3u489< r7  c                     [         R                  " [        U 5      S:  S 5        [        U 6 nUS   R                  S:X  a  [        US5      $ [        US5      $ )Nr   c                      g)Nz%hstack expects a non-empty TensorListrL  rL  r7  r5  rN  hstack.<locals>.<lambda>  r  r7  rP  )rb  rc  rS  r   r0  r   r  s     r5  r   r   }  sQ    	LLW!#RS '*Oq!#?A&&""r7  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%vstack expects a non-empty TensorListrL  rL  r7  r5  rN  vstack.<locals>.<lambda>  r  r7  )rb  rc  rS  r   r   r  s     r5  r	  r	    r  r7  r>  c                 *   [         R                  " U R                  U5      n[        R                  " [        U5      S:g  S 5        U R                  [        U R                  S U 5      [        U5      -   [        U R                  US-   S  5      -   5      $ )Nr   c                      g)Nz"unflatten: sizes must be non-emptyrL  rL  r7  r5  rN  unflatten.<locals>.<lambda>  s    *Nr7  rP  )	rn  r  r0  rb  rc  rS  r  r\  rT  )r  r  r>  s      r5  r  r    so    

 
 
-C	LLUq"NO66%&u5aggcAgi>P8QQRRr7  r   c                 X  ^ SSK Jn  [        R                  " U R                  T5      m[
        R                  " [        U R                  5      S:  S 5        U" U R                  T   S:H  5      (       a  g[        U4S j[
        R                  " X R                  T   T5       5       5      $ )Nr   rA  c                      g)Nz5Dimension specified as 0 but tensor has no dimensionsrL  rL  r7  r5  rN  unbind.<locals>.<lambda>  s    Gr7  rL  c              3   R   >#    U  H  n[         R                  " UT5      v   M     g 7frD  )rb  r   )rG  sr  s     r5  rI  unbind.<locals>.<genexpr>  s#      
+SaEMM!S!!+Ss   $')r[  rB  rn  r  r0  rb  _check_indexrS  rT  r\  r   )r   r  rB  s    ` r5  r  r    s    J

 
 
-C	AGGqG AGGCLA-.. 
+0+=+=as+S
 
 	
r7  r  r  c                 \    U R                  [        R                  S9R                  XU5      $ r  )r   rb  r=  rJ   )rH  r  r  r  s       r5  rI   rI     s+    77!8!879EEF r7  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        U R                  S:X  a  U R                  S5      OU n[        S 5      4U-  T4-   nX4U'   U $ )NrP  c                  $   > ST R                    S3$ Nz(Index should have dimension 1 or 0 (got r   r  r  s   r5  rN  index_copy_.<locals>.<lambda>      :5::,aHr7  r   )rn  r  r0  rb  rc  r  slice)rH  r  r  r  r  rZ  s     `   r5  rJ   rJ     sq    

!
!!&&#
.C	LL

aH
 &&A+A1A;.3
%
)CcFHr7  c                     [        XX#SS9$ )NFinplace_index_fillrH  r  r  r  s       r5  rL   rL     s    
 quU;;r7  c                     [        XX#SS9$ )NTr  r  r  s       r5  rM   rM     s     quT::r7  r  c                X  ^^ [         R                  " TR                  S:*  U4S j5        [        T[        5      (       a)  [         R                  " TR                  S:H  U4S j5        O5[         R
                  " TU R                  U R                  U R                  S9mU R                  S:H  nU(       a  U R                  S5      OU n[        UR                  5      nTR                  5       Xq'   TR                  U5      mU(       a  [        R                  O[         R                   nU" XaTT5      n	U(       a  U $ U(       a  U	R#                  S5      R%                  5       n	U	R'                  5       U R'                  5       :w  a)  [         R(                  " U 5      n
U
R+                  U	5        U
n	U	$ )NrP  c                  $   > ST R                    S3$ r
  r  r  s   r5  rN  _index_fill.<locals>.<lambda>  r  r7  r   c                  $   > ST R                    S3$ )Nz<Only supports 0-dimensional value tensor. Got a tensor with r  r  r  s   r5  rN  r    s     !!&L:r7  )r  r  r4  )rb  rc  r0  r;  r#   r$  r  r  r4  r  rK  rT  r  r   rQ  rJ   rI   r   r   r5  r  copy_)rH  r  r  r  r  zero_dimr  rT  rI   r  new_outs     ``       r5  r  r    s:    
LL

aH %$$JJ!O:	
 ##''8888	
 vv{H"AAMEEJLLE'.##E4D4DJ
QUE
*C++a.&&(C::<188:%&&q)GMM#C
r7  c                \    U R                  [        R                  S9R                  UUUUS9$ )Nr  rV  )r   rb  r=  
index_add_)rH  r  r  r  rW  s        r5  rH   rH     s:     77!8!879DD	 E  r7  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        TR                  S:X  a  TR                  S5      mU R                  S:X  a6  [        R                  " U 5      R                  STU R                  T5      5      $ [        S 5      4U-  T4-   nX   $ )NrP  c                  $   > ST R                    S3$ r
  r  r  s   r5  rN  index_select.<locals>.<lambda>  r  r7  r   )
rn  r  r0  rb  rc  r  r  rI   r   r  )rH  r  r  rZ  s     ` r5  rK   rK     s     
!
!!&&#
.C	LL

aH zzQ"vv{ "--aE8JKK;.3
%
)C6Mr7  c                   ^ ^ SSK Jm  UcY  [        S [        T R                  5       5       5      nU(       a  [
        R                  " T U5      $ [
        R                  " T 5      $ T R                  n[        R                  " X15      n[        U[        5      (       a  U4OUnUS:X  a-  [        U5      S:X  d  US:X  d   e[
        R                  " T 5      $ [        U U4S jU 5       5      n[        U5      S:X  a  [
        R                  " T 5      $ [        U5      S:X  a  [
        R                  " T U5      $ [        U5      n[        USS9nU H  n[        T U5      m M     T $ )	Nr   rA  c              3   :   #    U  H  u  pUS :X  d  M  Uv   M     g7frZ  rL  )rG  rZ  r9  s      r5  rI  squeeze.<locals>.<genexpr>$  s     J*<YS	SS*<s   	r  c              3   f   >#    U  H&  nT" TR                   U   S :H  5      (       d  M"  Uv   M(     g7frZ  r)  )rG  dr  rB  s     r5  rI  r$  0  s'     JDq$8q$IDs   !1	1rP  T)r  )r[  rB  r\  r_  rT  r  r   r`  r0  rn  r  r;  r   rS  rK  r.  )r  r  r@  r0  	dims_listr+  rB  s   `     @r5  r   r     s   J
{J)AGG*<JJ)-u}}Q%C5==3CC66D

!
!$
,CS))C6sDqy4yA~--}}Q JDJJD
4yA~}}Q
4yA~}}Q%%T
Iy$/IAqM Hr7  split_sizesc                   ^ ^^ [        [        T5      5       H  n[        R                  " TU   S 5        M      [        R                  " [
        [        R                  " T5      T R                  T   :H  UU U4S j5        / nT R                  5       nT He  n[        T R                  5      nXgT'   UR                  T R                  UT R                  5       U5      5        UT R                  5       T   U-  -   nMg     U$ )Nc                      g)NzCsplit_with_sizes expects split_sizes have only non-negative entriesrL  rL  r7  r5  rN  "split_with_sizes.<locals>.<lambda>E  s    Yr7  c                  V   > S[         R                  " T5       STR                  T     3$ )NzSplit sizes add up to z but got the tensor's size of )r:  r   rT  )r  r  r(  s   r5  rN  r+  J  s,    (k)B(CCabfblblmpbqarsr7  )r`  rS  rb  _check_is_sizer#  ra  r:  r   rT  r;  rK  r  r   r5  )r  r(  r  r+  splitsr  
split_sizer  s   ```     r5  r   r   <  s     3{#$NY	
 %
 
[!TZZ_4s F  "F!
$	## 	dooiGH$++-,z99 " Mr7  indices_or_sectionsc                    [         R                  " U R                  U5      nU R                  S:X  a  Sn[        U5      e[	        U[
        5      (       al  UR                  R                  S:X  d  SUR                   3n[        U5      eUR                  [        R                  :w  a  SUR                   3n[        U5      e[	        U[        5      (       d%  [	        U[
        5      (       a  UR                  S:X  a  [	        U[        5      (       a  UOUR                  5       nUS::  a  SU 3n[        U5      eU R                  U   n[        R                   " Xe-  5      nXe-  n/ n	[#        U5       H   n
X:  a  US-   OUnU	R%                  U5        M"     ['        [(        R+                  X	US95      $ Un[	        U[
        5      (       a;  UR                  S:w  a  S	UR                   S
3n[        U5      eUR-                  5       nS/[/        U5      -   U R                  U   /-   n[#        [1        U5      S-
  5       Vs/ s H  oUS-      X   -
  PM     n	n['        [(        R+                  X	US95      $ s  snf )Nr   zXtensor_split: received a rank zero tensor, but expected a tensor of rank one or greater!rx  z\tensor_split: if indices_or_sections is a tensor it must be on the CPU, but received one on zgtensor_split: if indices_or_sections is a tensor it must have long dtype,  but received one with dtype zAtensor_split: number of sections must be greater than 0, but was rP  r  zntensor_split: non-scalar indices_or_sections tensors must have only one dimension, but received a tensor with rY  )rn  r  r0  ra  r;  r#   r4  r2  r  rb  longr   r   r   rT  r!  rE   r`  r  r\  r  r   tolistrK  rS  )r  r0  r  _dimr  sectionsr  min_split_sizenum_splits_one_extrar(  	split_idxr/  indicesr+  s                 r5  r   r   \  s|   
 !!!&&#.Dvv{ho %z22"))..%7'':'A'A&BD  S/!$$

200C0I0I/JL  S/! %w//&
338K8P8PTU8U -v66  $))+ 	 q=UV^U_`CS/!774=H$78'2xI 4 "# 
 z* ) T**1t*DEE &):66"''1,22E2J2J1K;X  !o%)002G#W%7<A#g,QRBR<ST<Sqq1u~
2<STT**1t*DEE Us   ;I0c                   ^ ^^^ [         R                  " T R                  S:  U 4S j5        T R                  S:X  a  SOSm[        T[        5      (       aK  Tm[         R                  " TS:g  =(       a    T R
                  T   T-  S:H  U UU4S j5        [        T TT5      $ [         R                  " [        T[        [        45      U4S j5        Tn[        T UT5      $ )NrP  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.hsplit requires a tensor with at least 1 dimension, but got a tensor with  dimensions!rr  r0  r  s   r5  rN  hsplit.<locals>.<lambda>      ^!&&kr7  r   c                  |   > S[        T5      -   S-   [        T R                  T   5      -   S-   [        T5      -   S-   $ )Nz0torch.hsplit attempted to split along dimension z , but the size of the dimension $ is not divisible by the split_size rm  rD  )r  r  r/  s   r5  rN  r?    sS    Bc(45 aggcl#$ 9	9
 j/" r7  c                      > S[        T 5       3$ )Nzhsplit(): received an invalid combination of arguments. Expected indices_or_sections to be of type int, list of ints or tuple of ints but got type r1  r0  s   r5  rN  r?         !4568r7  
rb  rc  r0  r;  r   rT  r   _check_typerK  r\  )r  r0  r(  r  r/  s   `` @@r5  r   r     s     
LL	!	
 vv{!C%w//(
1_?
!:a!?	
 Az3//	&u6	
 &K;,,r7  c                   ^ ^^ [         R                  " T R                  S:  U 4S j5        [        T[        5      (       aJ  Tm[         R                  " TS:g  =(       a    T R
                  S   T-  S:H  U U4S j5        [        T TS5      $ [         R                  " [        T[        [        45      U4S j5        Tn[        T US5      $ )Nr/  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.vsplit requires a tensor with at least 2 dimension, but got a tensor with r=  r>  r  s   r5  rN  vsplit.<locals>.<lambda>  r@  r7  r   c                  0   > ST R                   S    ST S3$ )NzQtorch.vsplit attempted to split along dimension 0, but the size of the dimension r   rB  rm  r)  )r  r/  s   r5  rN  rJ    s%    3771:,6,r7  c                      > S[        T 5       3$ )Nzvsplit(): received an invalid combination of arguments. Expected indices_or_sections to be of type int, list of ints or tuple of ints but got type r1  rD  s   r5  rN  rJ    rE  r7  rF  )r  r0  r(  r/  s   `` @r5  r  r    s     
LL	!	
 %w//(
1_=j!8A!=
	
 Az1--	&u6	
 &K;**r7  r  c                    ^ U R                  5       m[        R                  " TS;   U4S j5        TS:X  a  [        R                  " X5      $ [        R                  " X5      $ )N)rP  r/  c                     > ST  S3$ )Nz'diag(): Supports 1D or 2D tensors. Got DrL  r  s   r5  rN  diag.<locals>.<lambda>  s    "I$q Qr7  rP  )r  rb  rc  r   r   )r  r  r0  s     @r5  r   r     sQ     88:D	LLQ qy--""400r7  r  dim2c                    ^^ [         R                  " U 5      nUR                  X#U5      m[        R                  " TR
                  TR
                  :H  UU4S j5        [        TT5        U$ )Nc                  <   > STR                    ST R                    3$ )NzCexpected src to have a size equal to the diagonal of the input.Got z for a diagonal of shape r)  )r   r  s   r5  rN  "diagonal_scatter.<locals>.<lambda>  s"     yyk24::,@r7  )rn  clone_preserve_stridesr   rb  rc  rT  r   )r  r  r  r  rQ  r  r   s    `    @r5  r   r     sX     
&
&u
-C<<d+D	LL

cii	@
 D#Jr7  c                   ^^ U R                  5       n[        R                  " TUS9m[        R                  " TUS9m[        R                  " TT:g  UU4S j5        U R                  5       nUS:  a<  [        [        U R                  5       T   U R                  5       T   U-
  5      S5      nO;[        [        U R                  5       T   U-   U R                  5       T   5      S5      nUS:  a7  US:  a  XQU R                  5       T   -  -  nOXQU R                  5       T   -  -  n[        U R                  5       5       VVs/ s H  u  pxUTT4;  d  M  UPM     n	nnU	R                  U5        [        U R                  5       5       VVs/ s H  u  pxUTT4;  d  M  UPM     n
nnU
R                  U R                  5       T   U R                  5       T   -   5        U R                  XUS9nU$ s  snnf s  snnf )z,
Reference implementation of torch.diagonal
)rZ  rankc                     > ST  ST 3$ Nz(diagonal dimensions cannot be identical r  rL  r  rQ  s   r5  rN  diagonal.<locals>.<lambda>(       HbQUPVWr7  r   )r9  r5  r;  )r  rn  r  rb  rc  r;  r^  r	  r9  r5  r_  r  r   )r  r  r  rQ  num_dimsr;  	diag_sizer+  r  r>  r  r   s     ``        r5  r   r     s    xxzH!!d:D!!d:D	LLW ((*N{DIIK-tyy{4/@6/IJAN	DIIK-6		D8IJAN	1}Q;t{{}T':::Nt{{}T':::N$TYY[1K141QtTl5JQ1EK	LL&t{{}5O5TQ4,9Nq5GONN4;;=&t)<<=__%_WFM L Ps   G-G-
G3G3c                 *  ^^ U R                   S-   n[        R                  " UTS9m[        R                  " UTS9mTT:  a  TTsmmU* n[        R                  " TT:g  UU4S j5        U R                  S5      nUS:w  a  [        U R                  5      n[        R                  " U5      US'   [        R                  " X`R                  U R                  SS9nUS:  a  Xp4OX4n[        R                  " USS9n U[        R                  " U5      -  nU R                  T5      R                  ST5      n [        R                   " XPR                  [        R"                  S	9n	[        R                   " XU-   U R                  [        R"                  S	9n
XR                  S5      :H  n[%        ['        U R                  5      5       Vs/ s H  oTT4;   a  UOSPM     nnUR)                  U5      n[        R*                  " X5      R-                  5       $ s  snf )
z.
Reference implementation of torch.diag_embed
rP  )rW  rZ  c                     > ST  ST 3$ rY  rL  rZ  s   r5  rN  diag_embed.<locals>.<lambda>Z  r\  r7  rV  r   Fr  r4  r  r2  r4  r  )r0  rn  r  rb  rc  r9  rK  rT  r:  r-   r&  r  r4  r   r  r   r  rO  r`  rS  r   mask_tensorr   )r   r  r  rQ  rW  r  t_shapezpaira_rangeb_rangecondr+  
cond_shapes     ``          r5  r   r   C  s    66A:D!!t6D!!t6D d{4
d	LLW
 vvbzH{qww-ll6*KKwwqxxuU!v!IId#HLL(( 	
D!!"d+A ll8HHEKKHGll6!!((%++G
 ''++D@Ec!''l@ST@S1D$</(Q6@SJT<<
#D T%0022 Us   Hc                   ^^
^ U  Vs/ s H*  oR                  5       S::  a  UR                  SS5      OUPM,     nn[        R                  " S U 5       5      nUS   R                  m
/ nSn[        U5       H  u  mm[        R                  " TR                  5       S:H  UU4S j5        [        R                  " TR                  T
:H  U
UU4S j5        TR                  u  pg[        R                  " Xe4T
TR                  S9n[        R                  " XcU-
  U-
  4T
TR                  S9n	U[        R                  " UTU	4SS	9/-  nXW-  nM     [        R                  " USS	9$ s  snf )
z.
Reference implementation of torch.block_diag
rP  rV  c              3   >   #    U  H  oR                   S    v   M     g7frZ  r)  )rG  r  s     r5  rI  '_block_diag_iterable.<locals>.<genexpr>  s     BzVazs   r   r/  c                  2   > ST  STR                  5        S3$ )Nz5Input tensors must have 2 or fewer dimensions. Input z has rY  r2  )r+  r  s   r5  rN  &_block_diag_iterable.<locals>.<lambda>  s      CuVZZ\N+7r7  c                  0   > ST  ST STR                    S3$ )NzCInput tensors must all be on the same device. Input 0 is on device z and input z is on device rl  r3  )r4  r+  r  s   r5  rN  rp    s&     $$*8;qcVWYr7  rc  r2  )r  r  r:  r   r4  r_  rb  rc  rT  r&  r  r   )r  r  
tensors_2dncolsr   	col_startrowcolr  rightr4  r+  s    `        @@r5  _block_diag_iterablerx  }  sL    KRJQjjla/ArV;'   LLBzBBE]!!FFIz*	6JJLA7	

 	MMV#Y	

 <<{{C+F&,,O)#c)*6
 	599dFE2:;;	# +& 99V##;s   1E"c                      [        U 5      $ )z
This is used as an input to PythonRefInfo. `torch.block_diag`
expects arguments splatted, but `aten.block_diag` expects only
one argument that is a list of Tensors.
)rx  r  s    r5  r   r     s      ((r7  r6  c                    U R                   S:  a  [        SU R                    S35      e[        U[        5      (       a>  US:X  d  U R                  S   U-  S:w  a"  [        SSU R                  S    SU S	3-   5      e[        XS5      $ )
Nr  zPtorch.dsplit requires a tensor with at least 3 dimension, but got a tensor with r=  r   r/  z3torch.dsplit attempted to split along dimension 2, zbut the size of the dimension rB  rm  )r0  rq  r;  r   rT  r   )r  r6  s     r5  r   r     s    vvz^_`_e_e^ffrs
 	
 (G$$(a-1771:;PTU;UA.qwwqzl:^_g^hhijk
 	
 Q''r7  c                     U R                   S:  a  [        SU R                    S35      e[        R                  " U SU R                   S:  a  S5      $ S5      $ )Nr/  z7t() expects a tensor with <= 2 dimensions, but self is rO  r   rP  )r0  rq  rb  r   r  s    r5  r   r     sS     	vvzEaffXQO
 	
 ??1aaffqj88a88r7  c                 l    [         R                  " U R                  S;   S 5        U R                  5       $ )N)r   r/  c                      g)NzcThe use of `x.T` on tensors of dimension other than 0 or 2 to reverse their shape is not supported.rL  rL  r7  r5  rN  T.<locals>.<lambda>  s    7r7  )rb  rc  r0  r   r  s    r5  r   r     s,    	LL	&	
 335Lr7  c                 .    [         R                  " U 5      $ rD  )r  r`  r  s    r5  r   r     r  r7  r  c                 ,   [         R                  " U R                  X45      u  p4U R                  S::  d  X:X  a  [        R                  R                  U 5      $ [        [        SU R                  5      5      nXEU'   X5U'   [        R                  " X5      $ )NrP  r   )
rn  r  r0  r  r   defaultrK  r`  rb  r   )r  r  r  _dim0_dim1rP  s         r5  r   r     st    **166D<@LEvv{dlzz!!!$$a()L==))r7  c                 t    [        U R                  U R                  5       XU5      u  pEU R                  XE5      $ rD  )r  rT  r5  r   )r  rv  r9  rw  rT  r  s         r5  r  r    s4     .

DKKM9DNE ??5**r7  c                 \    U R                  XU5      R                  [        R                  S9$ r  )r  r   rb  r=  )r  rv  r9  rw  s       r5  r  r    s0     ;;y-33-- 4  r7  c                   UR                   n[        R                  " Xc5      nUS:X  a  U " UR                  S5      SXES9$ UR                  US-   5      n[        R
                  " UR                  U   UR                  S9nUR                  S5      U:*  n[        Xc-
  S-
  5       H  n	UR                  S5      nM     [        R                  " XU5      n
U " XXES9$ )Nr   )r  r  r  rP  r3  rV  )
r0  rn  r  r  rb  r  rT  r4  r`  r   )rL  initr  r  r  r  r0  rgr  r  masked_as              r5  _cumsumprod_commonr    s     66D

 
 
+CqyAKKN@@	C!GA	aggcl188	4B<<?b D4:>"~~b! #{{4D)H88r7  c          	      "    [        [        SXX#S9$ )Nr   rL  r  r  r  r  r  )r  r   r  r  r  r  s       r5  r   r     s     3Q!ESSr7  c          	      "    [        [        SXX#S9$ )NrP  r  )r  r   r  s       r5  r   r   $  s     4a1UTTr7  c                 x    U R                   S-   n[        R                  " X!5      n[        R                  " X4US9$ )NrP  r  )r0  rn  r  r  expand_dims)r  r  r0  s      r5  r  r  0  s6     66A:D

 
 
+CQT22r7  c                      [        U /UQ7SS06$ )Nr  Fr  rW  s     r5  r  r  =  s    <E<e<<r7  c                 @    U R                  UR                  5       5      $ rD  )r  r9  r  s     r5  r  r  C  s    99UZZ\""r7  c                     [        U S5      $ )N)rV  )r   r  s    r5  r   r   H  s    1er7  r:  c                   ^ ^ [         R                  " T R                  TR                  :H  U U4S j5        [         R                  " [        R                  " TR
                  5      U4S j5        Uc6  [         R                  " T R                  S5      STR                  S5      5      $ [        T R                  5      nTR                  U5      X2'   [        R                  " UTR                  5       5      n[        TU5      n[        TR                  5      nT R                  U5      Xb'   [        R                  " UT R                  5       5      n[        T U5      n[         R                  " XrU5      $ )Nc                  >   > ST R                    STR                    S3$ )Nz]torch.take_along_dim(): input and indices should have the same number of dimensions, but got z dimensions for input, and z dimensions for indicesr  )r  r:  s   r5  rN   take_along_dim.<locals>.<lambda>T  s%    --.VVH4O||n35r7  c                  $   > ST R                    S3$ )Nz?torch.take_along_dim(): dtype of indices should be int but got z insteadr  )r:  s   r5  rN  r  ]  s    M}}oX'r7  rV  r   )rb  rc  r0  rn  r  r  gatherr  rK  rT  r9  infer_size_shapesr   )r  r:  r  
self_sizesbroadcast_shapeindices_broadcastindices_sizesself_broadcasts   ``      r5  r   r   N  s    
LL	',,	
 
LLw}}-	
 {||AFF2J7<<+;<<!'']
!,,s+
11*gllnM(/BW]]+VVC[11-J%a9||N1BCCr7  r  r  r4  r  r  r  r  c           
        ^ [         R                  " T[         R                  :g  S 5        [        R                  " U5      nT[         R
                  :X  a  [        R                  " U5      nOmT[         R                  :X  a  [        R                  " U5      nOB[         R                  " T[         R                  :H  U4S j5        [        R                  " U5      n[         R                  " UUU UUUUS9$ )Nc                      g)Nz8torch.empty: the Preserve memory format is not supportedrL  rL  r7  r5  rN  empty.<locals>.<lambda>  s    Jr7  c                     > ST  S3$ )Nz/torch.empty: received an unknown memory format rm  rL  r  s   r5  rN  r    s    Em_TUVr7  r  r  r4  r  r  )rb  rc  r	  rn  r]  r=  r  channels_last_3d!make_channels_last_3d_strides_forchannels_last!make_channels_last_2d_strides_forr  )r  r  r4  r  r  r  rT  r  s        `  r5  r  r  s  s     
LL...J
 ,,U3E///33E:	%00	099%@U000V	
 99%@# r7  c                 2    [         R                  " U UUUUS9$ )Nrb  )r  r  )rT  physical_layoutr  r  r4  r  r  s          r5  r  r    s&     # r7  r  r  r4  r  c                    Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UUUUUS9$ )Nr  r4  r  r  )r  r  r4  rb  r  )r  r9  r  r  r4  r  s         r5  r  r    sQ     }AGG%EQXXVFQXXVF;; r7  c          	          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UUUUUUS9$ )z<
Reference implementation of torch.Tensor.new_empty_strided
r  )r  r  r4  rb  r  )r  r9  r5  r  r  r4  r  s          r5  r  r    sV      }AGG%EQXXVFQXXVF r7  r  c           
          [         R                  " U5      nU c  [        R                  " 5       n [        R                  " UU [        R
                  :X  a  SOSU UUUUS9$ NFr   r  rn  r]  rb  r  r  r  r  r  r4  r  r  r9  s         r5  r&  r&    sZ     ++D1D}'')::%**$!# r7  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  r4  rb  r  r  r  r9  r  r  r4  r  r  s          r5  r   r     sm     }AGG%EQXXVFQXXVF::"177uzz1q# r7  c           
          [         R                  " U5      nU c  [        R                  " 5       n [        R                  " UU [        R
                  :X  a  SOSU UUUUS9$ NTrP  r  r  r  s         r5  r!  r!    sZ     ++D1D}'')::## r7  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  s          r5  r  r  2  sm     }AGG%EQXXVFQXXVF::!!''ejj0a# r7  
fill_valuec          	          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UUUUUUS9$ )Nr  )r  r  r4  rb  r  )r  r9  r  r  r  r4  r  s          r5  r  r  M  sT     }AGG%EQXXVFQXXVF:: r7  )r  r4  r  r  r  r  c          
      L   Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUnU[        R                  :w  a$  [        R
                  " U R                  UUUUUUS9$ [        R                  " U 5      n[        R                  " U R                  UUUUUUS9$ )Nr  r  )
r  r  r4  rb  r	  r  rT  rn  3compute_elementwise_output_logical_to_physical_permr  )r  r  r4  r  r  r  r  logical_to_physical_perms           r5  r  r  g  s     }AGG%EQXXVFQXXVF---{{GG'!'
 	
 	AA!D  	 # r7  r  c          	         ^ ^^ [         R                  " U5        [         R                  " U5        [        R                  " [         R
                  " U5      5      n[        T [        5      (       a   e[        T[        5      (       a   e[        T[        5      (       a   eTc  T mSm [        R                  " TS:g  S 5        TS:  a  [        R                  " TT :  S 5        O!TS:  a  [        R                  " TT :*  S 5        S n[        R                  " U" T 5      =(       a    U" T5      UU 4S j5        [        R                  " U" T5      U4S j5        T TT4n	[        R                  " S U	 5       5      n
Uc,  U
(       a  [        R                  O[        R                  " 5       n[         R                  " U5      nU(       d  U
(       a!  [        T 5      n[        T5      n[        T5      nU[        R                  :X  d  U
(       a,  [        WS:  5      [        US:  5      -
  nWW-
  U-   U-
  U-  nO[         R"                  " TT -
  T-  5      nU(       a  [$        R&                  " UWWUUUS	9$ [$        R&                  " USS
[        R                  USS	9nU
(       a  [        R(                  O[         R*                  " X55      n[-        UU5      nT TU-  -   n[-        UU5      nU(       a  UR/                  S5        U$ )Nr   c                      g)Nzstep must be nonzerorL  rL  r7  r5  rN  arange.<locals>.<lambda>  s    $:r7  c                      gNz7upper bound and lower bound inconsistent with step signrL  rL  r7  r5  rN  r        Mr7  c                      gr  rL  rL  r7  r5  rN  r    r  r7  c                 f    [        U [        5      (       + =(       d    [        R                  " U 5      $ rD  )r;  r   r!  rN   rM  s    r5  	is_finitearange.<locals>.is_finite  s!    a!566J$--:JJr7  c                     > ST ST  3$ )Nzunsupported range: z -> rL  )r  r  s   r5  rN  r    s    %eWD6r7  c                     > ST  3$ )Nzstep must be finite but got rL  r  s   r5  rN  r    s    .tf5r7  c              3   B   #    U  H  n[        U[        5      v   M     g 7frD  rE  rG  r  s     r5  rI  arange.<locals>.<genexpr>  s     IDS
3 8 8D   )r  rw  r  r4  r  rP  FT)rn  check_layoutcheck_pin_memoryrb  r4  device_or_defaultr;  r  rc  r:  r   rO  r  r  r   r  r!  r5   r  iotar3  get_acc_typer'   requires_grad_)r  r  rw  r  r  r4  r  r  r  rv  integer_args
is_integerxstartxendxsteprg   r  r  r  r   s   ```                 r5  r  r    s    
v	:&\\%11&9:F%))))#w''''$(((( {	LL:;ax5LM	
 
5LM	

K 
LL%+Ys^6 
LL$5
 3D<<IDIIL}+1H1H1J''.J\s| |519oUQY/-%'#-%7C%K4/0zz'
 	
 JJkkE #

(:(:5(I  $E+<=ETE\!F$VU3Fd#Mr7  )r  r  r0  c                    X/n[        U[        5      (       a  U R                  SU5      nOUR                  U5        [        U[        5      (       d   eUR                  5       S:  n[        R                  " XBS-
  U5      n[        R                  " XAU 5      nXQU -
  -  U-   n[        R                  " [        U6 6 nUR                  5       U:w  a  [        R                  " Xx5      n[        X75      $ )NrL  rq  rP  )r;  r   r  r  rQ  r-   rb  r   rn  "compute_elementwise_output_stridesrw  r5  r  copy_stridedr?  )	r  r  r0  r  r  coeffbaser>  r5  s	            r5  rU   rU     s     \F&&!!F+fff%%%% ::<3DKKqj&1E;;t%(DEk"T)F557G7PQF}}& ##F3'77r7  )r  r4  r  r  r  stepsc          
        ^ ^^^^ [        T [        5      (       aC  [        R                  " T R	                  5       S:H  S 5        [        T [        R                  5      m [        T[        5      (       aC  [        R                  " TR	                  5       S:H  S 5        [        T[        R                  5      m[        R                  " S T TT4 5       5      (       a`  [        R                  " [        R                  " 5       5      mTc  TmOO[        R                  " [        R                  " T5      UU4S j5        OT=(       d    [        R                  " 5       m[        T[        R                  5      (       d   e[        R                  " [        T[        5      UU U4S j5        [        T[        5      (       d   e[        R                  " TS:  S 5        UUUUS.nTS:X  a  [        R                   " SS	T0UD6$ TS
:X  a~  [        T [        5      (       aN  [        R"                  " T44S	T0UD6n	[        R$                  R&                  R(                  R+                  U	T 5      $ [        R                   " T4T 4S	T0UD6$ [        R,                  " ST40 UD6n
[        R.                  " T5      (       d  [        R0                  " T5      (       a  [        R2                  OTn[        R4                  " U
[6        R8                  U5      u  p[;        [
        US9nTT -
  TS
-
  -  n[        R<                  " U
TS-  :  T X" U
5      -  -   TX" TS
-
  U
-
  5      -  -
  5      n[        UT5      $ )Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsrL  rL  r7  r5  rN  linspace.<locals>.<lambda>&  r  r7  c                      gr  rL  rL  r7  r5  rN  r  ,  r  r7  c              3   B   #    U  H  n[        U[        5      v   M     g 7frD  r;  r  r  s     r5  rI  linspace.<locals>.<genexpr>0       L8KJsG,,8Kr  c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype rL  )default_complex_dtyper  s   r5  rN  r  9  s    56K5LLrsxryzr7  c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (r  r   )r2  r  )r  r  r  s   r5  rN  r  B  sB     u+r$s),,-RU0D0D/EQHr7  c                      g)Nz$number of steps must be non-negativerL  rL  r7  r5  rN  r  F  s    %Kr7  )r  r4  r  r  r  rP  r  r/  )r  r   )r;  r$   rb  rc  r  r'   ru  r:  r   rn  r=  r  r  r  rG  r   r  r  opsr  r  r  r  r  r  rO  r2  r    rP  r   r   )r  r  r  r  r4  r  r  r  factory_kwargsempty_tensorr  	dtype_redr  r  cast_rgrw  r  r  s   ````             @r5  r  r    s    %((IIK1P	
 (u}}=#~&&GGINP	
 &c5==9||LU8KLLL % A A##%!
 =)ELL&&u-z
 2002eU[[)))) 
5'"	H
 eW%%%%	LL!KL  &	N zzzAA.AAze^,, ;;xOuOOL99>>&&..|UCC::uhMUMnMM 
a	1.	1B
 ""5))U-C-CE-J-J 	 
 !11
&++Y -5FGG %KEAI&D
++
UQYwr{""dWeai2-...C
 #3..r7  r  c                   Uc  [         R                  " 5       n[        R                  R	                  U5      (       a  [        U [        5      (       a  [        U 5      n OI[        U [        5      (       a4  [         R                  " U R                  5       S:H  S 5        [        X5      n [        U[        5      (       a  [        U5      nOI[        U[        5      (       a4  [         R                  " UR                  5       S:H  S 5        [        X5      n[        R                  " S XU4 5       5      (       a.  [        R                  " [         R                  " 5       5      n	U	nS n
O[         R                  n
[        U[         5      (       a   eUS:  a  ["        e[         R$                  " U UUU
UUUUS9n[        [         R&                  " X;5      U5      $ )Nr   c                      gNz:logspace only supports 0-dimensional start and end tensorsrL  rL  r7  r5  rN  logspace.<locals>.<lambda>      Tr7  c                      gr  rL  rL  r7  r5  rN  r    r  r7  c              3   B   #    U  H  n[        U[        5      v   M     g 7frD  r  r  s     r5  rI  logspace.<locals>.<genexpr>  r  r  r  )rb  r  r  rn  r  r;  r   r   r$   rc  r  r'   r:  r   r=  ru  r  r  r  r   )r  r  r  r  r  r4  r  r  r  r  _dtyperets               r5  r  r  p  so    }'') {{##E**eY''ENE~..LL		q T ,E9Ec9%%#,C^,,LL	QT *#5C||LU8KLLL % A A##%!
 &$((((ax!!
..#	C #599T#7??r7  indexingc                     g rD  rL  )r  r  s     r5  r   r         r7  c                     g rD  rL  )r  r  s     r5  r   r     r  r7  c                   ^ ^ [        US   [        [        45      (       a  [        U5      S:X  d   e[        US   5      n[        R
                  " [        R                  " S U 5       5      S 5        [        R
                  " [        U5      S:  S 5        [        [        U5      S-
  5       Ho  n[        R
                  " X   R                  XS-      R                  :H  S 5        [        R
                  " X   R                  XS-      R                  :H  S 5        Mq     SnT S	:X  a&  [        U5      S
:  nU(       a  US   US   /US
S  Q7nO[        R
                  " T S:H  U 4S j5        / nU Hw  m[        T[        5      (       d   e[        R
                  " TR                  S:H  =(       d    TR                  S:H  U4S j5        UR                  TR                  5       5        My     / n[        U5       He  u  nm[        T[        5      (       d   eTR                  S:X  a  TR!                  S5      mUR                  ["        R$                  " TXB45      5        Mg     U(       a  US   US   sUS'   US'   U$ )Nr   rP  c              3   B   #    U  H  n[        U[        5      v   M     g 7frD  r;  r#   r  s     r5  rI  meshgrid.<locals>.<genexpr>  s     @1Z:..r  c                      g)Nz)meshgrid expects its inputs to be tensorsrL  rL  r7  r5  rN  meshgrid.<locals>.<lambda>  r  r7  c                      g)Nz'meshgrid expects a non-empty TensorListrL  rL  r7  r5  rN  r    s    +Tr7  c                      g)Nz3meshgrid expects all tensors to have the same dtyperL  rL  r7  r5  rN  r    s    Ir7  c                      g)Nz4meshgrid expects all tensors to have the same devicerL  rL  r7  r5  rN  r    s    Jr7  Fxyr/  ijc                     > ST  3$ )NzDtorch.meshgrid: indexing must be one of "xy" or "ij", but received: rL  )r  s   r5  rN  r    s    !!)
,r7  c                     > ST  3$ )NzEtorch.meshgrid: Expected 0D or 1D tensor in the tensor list but got: rL  )r   s   r5  rN  r    s    [\][^_r7  r  )r;  rK  r\  rS  rb  rc  r:  r   r`  r  r4  r#   r0  r  r  r_  r  r  r3  )r  r  r+  swap_first_and_second_tensorsresult_shapegridsr   s   `     @r5  r   r     s%    '!*tUm,,7|q   
#	LL@@@;
 
LLW!#TU3w<!#$JA 4 44I	
 	JQ!6!66J	
 % %*!4(+G(9%(qz71:<<G	
 !L!Z((((FFaK&166Q;_	
 	AGGI&  #%E'"1!Z((((66Q;tAU++A|TBC	 # %"1XuQxa%(Lr7  sourcedestinationc                 l  ^^ [        T5      [        L a  T4m[        T5      [        L a  T4m[        R                  " [	        T5      [	        T5      :H  UU4S j5        U R
                  n[        [        R                  " UTS95      n[        [        R                  " UTS95      n[        U5      n[        U5      n[        R                  " [	        U5      [	        U5      :H  U4S j5        [        R                  " [	        U5      [	        U5      :H  U4S j5        [        [        XT5      5      n/ n	Sn
[        U5       HQ  nUR                  U5      nUb  U	R                  U5        M*  X;   a  U
S-  n
X;   a  M  U	R                  U
5        U
S-  n
MS     [        R                  " U [        U	5      5      nU$ )z+
Reference implementation of torch.movedim
c                  :   > S[        T5       S[        T 5       S3$ )Nz5movedim: Invalid source or destination dims: source (z> dims) should contain the same number of dims as destination (z dims)rK  )r  r  s   r5  rN  movedim.<locals>.<lambda>  s)    V~ ''+K'8&9Ar7  )rW  r:  c                  "   > S[        T 5       S3$ )Nz#movedim: repeated dim in `source` (r   r  )r  s   r5  rN  r    s    5d6l^1Er7  c                  "   > S[        T 5       S3$ )Nz(movedim: repeated dim in `destination` (r   r  )r  s   r5  rN  r     s    :4;L:MQOr7  r   rP  )r2  r  rb  rc  rS  r0  r\  rn  r  setdictr  r`  r!  r  r   )r  r  r  rW  ssdssssdssr  r@  sidir  r   s    ``           r5  r   r     sh    F|sKC"n 
LLFs;''	
 ::D	u&&D&A	BB	u&&D+F	GB
b'C
b'C 
LLB3s8E 
LLB3s8O
 	S[AD	
BDkEE"I=KKN )a )KKO!GB  ]]5%+.FMr7  )r  r4  r  r  r  r  c                    [         R                  " U5        [         R                  " U5        [         R                  " U 5      n Uc  [        R
                  " 5       OUnUc  [        R                  " S5      OUn[        R                  " U UUUUS9$ )Nrx  rb  )	rn  r  r  r]  rb  r  r4  r  r  )rT  r  r  r4  r  r  r  s          r5  r  r  9  sz     
v	:&,,U3E).E##%EE$*NU\\% F# r7  nr  c          	        ^ ^ Tc  T m[         R                  " T S:  U 4S j5        [         R                  " TS:  U4S j5        [         R                  " T [         R                  USS9n[         R                  " T[         R                  USS9nUR	                  S5      U:H  n	U[         R
                  L a  U	$ [         R                  " SUUUUSS9n
[         R                  " XS5      $ )	z'
Reference implementation of torch.eye
r   c                     > ST  3$ )Nz%n must be greater or equal to 0, got rL  )r   s   r5  rN  eye.<locals>.<lambda>h      #H!Lr7  c                     > ST  3$ )Nz%m must be greater or equal to 0, got rL  )r  s   r5  rN  r#  i  r$  r7  Frb  rV  r  r  )rb  rc  r  rO  r  r  r!  r   )r   r  r  r  r4  r  r  range_nrange_mrj  ones   ``         r5  r  r  V  s     	y	LLaLM	LLaLMll1EKKeTGll1EKKeTGR G+D

jj!
 {{4a((r7  c          	          [         R                  " U5        [         R                  " U5        Ub  UO[         R                  " [	        U5      5      nUb  UO[
        R                  " S5      n[        U UUUUUS9n[
        R                  " Xq5      $ )Nrx  r  )	rn  r  r  type_to_dtyper2  rb  r4  r  rC   )rT  r  r  r  r4  r  r  es           r5  r  r    s~     
v	:&&EE,?,?Z@P,QE)Vu||E/BF#	A ::a$$r7  r  r  r4  r  r  r  c          
      L    [         R                  " U UUUUUUS9n[        X5      $ )Nr,  )rb  r  rC   )	r  r  r  r  r4  r  r  r  r+  s	            r5  r  r    s6     		##	A r7  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NFr   r,  rb  r  r  r  r  r  r  r4  r  r  r  s          r5  r'  r'    sC     ??	"177uzz1q##	 	r7  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NTrP  r,  r/  r0  s          r5  r"  r"    sC     ??	!!''ejj0a##	 	r7  c           	          [         R                  " U5        [         R                  " U5      n[         R                  " U 5      n [         R                  " U5      n[
        R                  " USSU UUS9$ )Nr  rp  )r   r   r  r4  r  )rn  r  r]  dtype_or_defaultr  r  r_   )r  r4  r  r  r  rT  r  s          r5  r#  r#    se     
:&--e4F""5)E$$V,F<<# r7  c                   [         R                  " U5        [         R                  " U5        Ub  UO[         R                  " [	        U 5      5      nUb  UO[
        R                  " S5      n[        R                  " XUS9$ )Nrx  rg  )	rn  r  r  r*  r2  rb  r4  r  r$  )r  r  r  r4  r  s        r5  r$  r$    sc     
v	:&&EE,?,?Q,HE)Vu||E/BFqf==r7  lowhighc                P   [         R                  " U 5        [        U[        5      (       d   e[        U[        5      (       d   e[	        U5      n[	        U5      n[        U[
        R                  5      (       d   e[         R                  " U5      n[        R                  " XX#US9$ )N)r5  r6  r  r4  )
rn  r  r;  r   r   rb  r  canonicalize_devicer  _uniform_helper)rT  r5  r6  r  r4  s        r5  r9  r9    s     
c6""""dF####
C.CT?DeU[[))))&&v.F  dPVWWr7  r  c                 (  ^^ [         R                  " U R                  5      m[        U[        5      (       a  [        U5      nOUR                  m[        R                  " TS:H  U4S j5        U R                  R
                  SS[        R                  R                  5       S4;   =(       a    UR                  R
                  S:H  n[        R                  " U=(       d    UR                  U R                  :H  S 5        [         R                  " UR                  5      nU[        L a0  [        R                  " [         R                  " UT5      U4S j5        [        X R                  5      n[        R                  " XU 5      nUR!                  5       $ )	Nr   c                     > ST  S3$ )Nz@only supports a 0-dimensional value tensor, but got tensor with z
 dimensionrL  )
value_ndims   r5  rN  masked_fill.<locals>.<lambda>4  s    VWaVbblmr7  cudaxpur0  rx  c                      g)Nz,Expected `value` to be on same device as `a`rL  rL  r7  r5  rN  r=  >  s    Br7  c                     > ST  S3$ )Nzcould not convert to type z without overflowrL  )r  s   r5  rN  r=  I  s    0=NOr7  )rn  r   r  r;  r   r2  r0  rb  rc  r4  _C_get_privateuse1_backend_namer  r   r'   r   r   )r  r  r  
value_typeis_cpu_scalarr  r  r<  s         @@r5  r   r   (  s+    %%agg.K%  %[
 ZZ
!Om	
 HHMMuxxEEGOP +!!U* 	
 	5U\\QXX5B	
 ((5
W
 	''
K@O	
 $E773ED#A <<>r7  c                 V    [         R                  " XU5      nU R                  U5        U $ rD  )rb  r   r  )r  r  r  rD  s       r5  r   r   V  s&     	!5)AGGAJHr7  c                     [        SXX#S9  [        [        R                  " [        R                  " XX#US95      R                  5       5      $ )z,
Reference implementation of torch.allclose
ztorch.allcloser  )r  r  r  )r  r  rb  r   r   r   )r  rD  r  r  r  s        r5  r(  r(  `  s@     +qDL		%--4iPQVVX r7  c                 R   [         R                  " XSS9  [         R                  " X5        U R                  UR                  :w  a  g[	        U R
                  UR
                  5       H  u  p#X#:w  d  M    g   U R                  5       S:X  a  g[        [        [        X5      5      5      $ )NFr  r   T)
rn  r  check_same_dtyper0  r  rT  r  r   r   r   )r  rD  rH  r  s       r5  r)  r)  q  s}    	A5A	1  	vvAGGQWW%6 &
 	wwyA~BqHr7  r  c                ~   US:X  a'  Ub'  [        U[        5      (       d  [        U5      S::  d  Uc  Sn[        U[        5      (       a  U/n[        U[        5      (       a@  Uc  [	        [        U R                  5      5      n[        R                  R                  XX#US9$ [        R                  R                  XX#US9$ )Nfror/  r  )r;  r   rS  rr  r\  r`  r0  rb  rZ  matrix_normr[  )r  r  r  r  r  s        r5  r^   r^     s     	
U
z#s';';s3x1}	
#se!S ;ejj)*C||''#e'LL||''#e'LLr7  c                     [         R                  " U R                  S:H  S 5        [         R                  " [         R                  " U S5      5      $ )Nr/  c                      g)Nz6expected a matrix, but got tensor with dim {self.ndim}rL  rL  r7  r5  rN  trace.<locals>.<lambda>  s     Xr7  r   )rb  rc  r0  r   r   r  s    r5  rr   rr     s:     
LL		QX 99UZZa())r7  c                 p   ^  S[         [        [        4   S[         [        [        4   S[        4U 4S jjnU$ )Nr  rD  r|  c                    > T" X5      $ rD  rL  )r  rD  base_ops     r5  rop_make_r_binary_op.<locals>.rop  s     q}r7  )r   r$   r   )rR  rS  s   ` r5  _make_r_binary_oprU    s=    +,+, 
 Jr7  r   c                 r   [         R                  " U R                  S:  S 5        U R                  SS  u  p#[         R                  " X0R
                  S9R                  S5      [         R                  " X R
                  S9R                  S5      -
  U:  n[        R                  " X@5      R                  5       $ )Nr/  c                      g)Nz2triu: input tensor must have at least 2 dimensionsrL  rL  r7  r5  rN  triu.<locals>.<lambda>      Qr7  r  r3  rV  
rb  rc  r0  rT  r  r4  r  rn  rd  r   r  r   hwr  s        r5  r  r         
LL	!Q 7723<DAQxx(2226
,,q
*
4
4R
8	9	D T%0022r7  c                 r   [         R                  " U R                  S:  S 5        U R                  SS  u  p#[         R                  " X0R
                  S9R                  S5      [         R                  " X R
                  S9R                  S5      -
  U:*  n[        R                  " X@5      R                  5       $ )Nr/  c                      g)Nz2tril: input tensor must have at least 2 dimensionsrL  rL  r7  r5  rN  tril.<locals>.<lambda>  rY  r7  r  r3  rV  rZ  r[  s        r5  r  r    r^  r7  ru  rv  c                    U S:X  d  US:X  a  gUS:  a  [        USU-   5      O[        X-   S:  5      n[        S[        XU-   5      5      n[        S[        X U-   5      5      nXC-
  S-   nX4-   U-  S-  nXV-
  n[        SX-  5      n	XyU4$ )Nr   r   r   r   rP  r/  )r	  r  r^  )
ru  rv  r  m_first_row
m_last_row	n_row_alln_row_trapezoidtrapezoid_sizediff_rowrectangle_sizes
             r5  _get_tril_sizesrk    s    
ax3!8*01*#c1v:&#clQ>N:OKQCv./JAs3f-.I .2O "./AQFN*HHN+N;66r7  c                    ^ ^^^ [         R                  " TS:  U4S j5        [         R                  " TS:  U4S j5        [         R                  " T[         R                  [         R                  4;   UU 4S j5        g )Nr   c                     > ST  3$ )Nzrow must be non-negative, got rL  )ru  s   r5  rN  _trilu_checks.<locals>.<lambda>      %CC5#Ir7  c                     > ST  3$ )Nzcol must be non-negative, got rL  )rv  s   r5  rN  rn    ro  r7  c                     > ST ST  S3$ )NrV  z" not implemented for ''rL  )r  r  s   r5  rN  rn    s    "TF25';r7  )rb  rc  r  rO  )r  ru  rv  r  r  r  s   ````  r5  _trilu_checksrs    sO     
LLIJ	LLIJ	LL%++u{{++;r7  rx  c                l   [        SXX4U5        [        XU5      u  pxn	[        SU* 5      n
[        [        R
                  XEUS9nU" SU[        R                  S9nU	S-
  n[        R                  " U* [        R                  " X-  SU-  -   5      -   5      n[        R                  " USU	-  S-
  U-   U-  S-  -
  5      n[        X-   U5      n[        X5      nU" SXS9nUU-  X-
  S-   U
-   -   nUU-  n[        R                  " [        R                  " UU45      [        R                  " UU45      45      $ )Nr  r   r  r4  r  r  rq  r/  rP  )rs  rk  r^  r   rb  r  ru  rE   rn   r'   r   r   )ru  rv  r  r  r  r4  r  rh  rj  rd  
row_offset	arange_kwxs1rD  	row_inds1	col_inds1xs2	row_inds2	col_inds2s                      r5  r  r    s7    .#E:F2A#F2S/NKQJVzI
 A~U]]
;CcAQBAEAGO!<<=IC1{?Q#6#Bi"ORU"UUVI'	(>FI'	9I A~
3Cs
c/!3j@AIc	I;;	Iy)	*EIIy)6L,MN r7  c                     U S:X  d  US:X  a  gUS:  a  [        SX-
  5      OUn[        S[        X* 5      U-  5      n[        XUS-
  5      u  pVnX-  XV-   -
  nX-
  n	XU4$ )Nr   rc  rP  )r^  r	  rk  )
ru  rv  r  rd  rj  trapezoid_size_trilrectangle_size_trilr  	triu_sizerh  s
             r5  _get_triu_sizesr  ,  s    
ax3!8*01*#a&#K CW-34N 3B#FUVJ2W/a	0FGI/N;66r7  c                v   [        SXX4U5        [        XU5      u  pxn	[        SU5      n
[        [        R
                  XEUS9nU" SXS9nX-  nX-  nU" SU[        R                  S9nSU	-
  n[        R                  " U* [        R                  " UU-  SU-  -
  5      -
  5      n[        R                  " USU	-  S-
  U-
  U-  S-  -
  5      n[        UU5      n[        UU5      nU(       a  UX-  -   nUU
-   n[        R                  " [        R                  " UU45      [        R                  " UU45      45      $ )	Nr  r   ru  r  g      r/  rP  rq  )rs  r  r^  r   rb  r  ru  rE   rn   r'   r   r   )ru  rv  r  r  r  r4  r  rh  rj  rd  
col_offsetrw  r{  r|  r}  rx  rD  ry  rz  s                      r5  r  r  =  s:    .#E:F2A#F2S/NKQJVzI
 A~
3C
I	I A~U]]
;C{AQBAEAGO!<<=ICAOa$7)$Cy#PTW"WWXI'	59I'	59I
!67	J&I;;	Iy)	*EIIy)6L,MN r7  )	out_int32rw  
boundariesr  rw  c                
  ^ [         R                  " TR                  5       S:H  U4S j5        [        U [         R                  5      (       a  U O[         R
                  " U 5      n U(       a  [         R                  O[         R                  nTR                  S   nUS:X  a  [         R                  " U 5      $ [         R                  " U R                  U R                  [         R                  S9nXe-   nXgU-
  S-  -   nTU   n	U(       a  X:  n
OX:  n
[         R                  " XUS-   5      nUS:  a  [         R                  " U [         R                  S9n[        [         R"                  " U5      5      n[%        U5       Hs  n[         R                  " X-  X5      nXg:  n[         R                  " XXv-
  S-  -   S5      nTU   n	U(       a  X:  n
OX:  n
[         R                  " U
) U-  US-   U5      nMu     UR'                  US9$ )NrP  c                  ,   > ST R                  5        S3$ )Nz2boundaries tensor must be 1 dimension but got dim(r   r2  )r  s   r5  rN  bucketize.<locals>.<lambda>s  s    DZ^^EUDVVWXr7  rV  r   rc  r/  r  )rb  rc  r  r;  rQ  r  r  rO  rT  r'  r&  r4  r   r"  r  r  r!  rY   r`  r   )r  r  r  rw  	out_dtypen_boundariesr  r  midmid_valcond_midcond_updatenitersr  s    `            r5  r*  r*  h  s    
LLAX
 5<<((ell1oA(ekkI##B'Lq""
 KKDE

C ;1$
$CoG;<KKq1Eaooauzz:TYY|,-vA++h4c?C+K++kCKA3E+EqIC oG ";"<KK(k 937EJE  88)8$$r7  c                    ^ ^ Ub   e[         R                  " [        R                  " T R                  5      (       + =(       aQ    [        R
                  " T R                  5      (       + =(       a%    [        R                  " T R                  5      (       + U 4S j5        [         R                  " TS:  U4S j5        UT[         R                  " [        R                  [         R                  " T 5      S-
  -  5      -  -   $ )Nc                  "   > ST R                    3$ )NzwCauchy distribution is a continuous probability distribution.         dtype must be a floating point but you specified r  r  s   r5  rN  cauchy.<locals>.<lambda>       ::>**Gr7  r  c                     > ST  3$ )Nz-cauchy_ expects sigma > 0.0, but found sigma=rL  )sigmas   r5  rN  r    s    ?wGr7  rq  )rb  rc  rn  r  r  r  r  rp   r!  r"  	rand_like)r  medianr  	generators   ` ` r5  r  r    s     	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLG EEIIdgg1F1L&MNNNNr7  c                 v  ^ ^ Ub   e[         R                  " [        R                  " T R                  5      (       + =(       aQ    [        R
                  " T R                  5      (       + =(       a%    [        R                  " T R                  5      (       + U 4S j5        [         R                  " TS:  U4S j5        [         R                  " T 5      n[         R                  " UR                  5      R                  S-  nUSU-
  :  n[         R                  " XT* [         R                  " U5      5      nST-  U-  $ )Nc                  "   > ST R                    3$ )Nz|Exponential distribution is a continuous probability distribution.         dtype must be a floating point but you specified r  r  s   r5  rN  exponential.<locals>.<lambda>  r  r7  r  c                     > ST  3$ )Nz4exponential_ expects lambda > 0.0, but found lambda=rL  )rates   r5  rN  r    s    FtfMr7  r/  rp  rV  )rb  rc  rn  r  r  r  r  r  r  r&  r   rW   )r  r  r  uniform_valepsilonr  log_uniforms   ``     r5  rA   rA     s     	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLs
M
 //$'K kk+++,0014GsW},I++i599[3IJK9{""r7  c                   ^ ^ Ub   e[         R                  " [        R                  " T R                  5      (       + =(       a%    [        R
                  " T R                  5      (       + U 4S j5        [         R                  " ST:  =(       a    TS:  U4S j5        [         R                  " [         R                  " [         R                  " T 5      * 5      [        R                  " T* 5      -  5      S-   $ )Nc                  "   > ST R                    3$ )Nzgeometric not implemented for r  r  s   r5  rN  geometric.<locals>.<lambda>  s    0=r7  r   rP  c                     > ST  3$ )Nz0geometric_ expects p to be in (0, 1), but got p=rL  )r  s   r5  rN  r    s    B1#Fr7  )
rb  rc  rn  r  r  r  rE   rX   r  r!  )r  r  r  s   `` r5  rG   rG     s     	LL""4::.. 	3&&tzz22=
 
LL	A!a%F ;;u{{EOOD$9#9:TZZ^KLqPPr7  c                   ^ ^ Ub   e[         R                  " [        R                  " T R                  5      (       + =(       aQ    [        R
                  " T R                  5      (       + =(       a%    [        R                  " T R                  5      (       + U 4S j5        [         R                  " ST:  U4S j5        [         R                  " T[         R                  " T 5      -  U-   5      $ )Nc                  "   > ST R                    3$ )Nzlog_normal not implemented for r  r  s   r5  rN  log_normal.<locals>.<lambda>  s    1$**>r7  r   c                     > ST  3$ )Nz-log_normal_ expects std > 0.0, but found std=rL  r   s   r5  rN  r     s    ?uEr7  )	rb  rc  rn  r  r  r  r  r?   
randn_liker  r   r   r  s   ` ` r5  r[   r[     s     	LL""4::.. 	3&&tzz22	3&&tzz22>	 
LL	CE 99S5++D11D899r7  )r   r   )r  r  r  r4  r  c          
        ^ Ub  U[         R                  :X  d   e[        T[        5      (       d  [         R                  " TS:  U4S j5        Uc  [        S U T4 5       5      n[         R                  " [        U5      S:  S 5        [         R                  " US L =(       a    US L S 5        [        S U 5       6 nUS   R                  nUS   R                  nO|[         R                  " [        U [        5      (       + =(       a    [        T[        5      (       + S 5        Uc  [         R                  " 5       OUnUc  [         R                  " S5      OUn[        R                  " US	S
UUSUS9n	TU	-  U -   $ )Nr   c                     > ST  3$ )Nz)normal expects std >= 0.0, but found std rL  r  s   r5  rN  normal.<locals>.<lambda>  s     I#Or7  c              3   T   #    U  H  n[        U[        5      (       d  M  Uv   M      g 7frD  r  rj  s     r5  rI  normal.<locals>.<genexpr>#  s     L;a*Q
2K;s   (	(c                      g)NzFnormal expects that either mean or std is a tensor, or size is definedrL  rL  r7  r5  rN  r  &  s    \r7  c                      g)Nz.Cannot pass layout, or pin_memory without sizerL  rL  r7  r5  rN  r  *  s    Dr7  c              3   8   #    U  H  oR                   v   M     g 7frD  r)  rj  s     r5  rI  r  -  s     "<Gq77GrU  c                      g)Nz>normal expects mean and std to be scalars when size is definedrL  rL  r7  r5  rN  r  3  s    Tr7  rx  r  rp  F)r   r   r  r4  r  r  )rb  stridedr;  r#   rc  r\  rS  rf  r  r4  r  r  r_   )
r   r   r9  r  r  r  r4  r  r  normal_sampless
    `        r5  r_   r_     sP   ( >Vu}}444c:&&1HO	
 |LD#;LLL1\	
 	dN1zT1D	

 !"<G"<=
  ""4,,PZZ5P1PT	
 .3]'')(.e$F\\N $&&r7  )r  c                ,    [        XU R                  XS9$ )N)r  r  )r_   rT  r  s       r5  normal_r  D  s    $TZZTGGr7  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-rad2deg is not supported for complex tensors.rL  rL  r7  r5  rN  rad2deg.<locals>.<lambda>M  r.  r7  gcܥL@rb  rc  rn  r  r  )r  M_180_PIs     r5  rc   rc   I  s6    	LL""4::..? CH?r7  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-deg2rad is not supported for complex tensors.rL  rL  r7  r5  rN  deg2rad.<locals>.<lambda>W  r.  r7  g9RFߑ?r  )r  M_PI_180s     r5  r:   r:   S  s6    	LL""4::..? EH?r7  c                 *    U S:g  R                  U5      $ r  )r   )r  r  s     r5  r9   r9   ]  s     AI??3r7  c                 v  ^ ^ [         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        UU 4S jn[         R                  " T R	                  5       TR	                  5       :H  U5        g )NrP  c                  N   > STR                  5        ST R                  5        S3$ )Nz1D tensors expected, but got zD and z	D tensorsr2  r  r  s   r5  rN  _dot_check.<locals>.<lambda>f  s!    /
|6%))+iXr7  c                  <   > STR                    ST R                    3$ )Nz:dot : expected both vectors to have same dtype, but found r  r  r  s   r5  rN  r  k  s    L::,eEKK=*r7  c            	         > STR                  5        ST R                  5        STR                  5        ST R                  5        S3	$ )Nz+inconsistent tensor size, expected tensor [z] and src [z.] to have thesame number of elements, but got r  z elements respectively)r  r  s   r5  numel_error_dot_check.<locals>.numel_erroro  sL    9$**,{SXS^S^S`Ra b004

~U5;;=/Qgi	
r7  )rb  rc  r  r  r  )r  r  r  s   `` r5  
_dot_checkr  c  sx    	LL
a,EIIK1,X
 
LL

ekk!	*
 
LL.<r7  c                 0   ^  [        T 5      U 4S j5       nU$ )Nc                 *   > [        X5        T" X5      $ rD  )r  )r  r  r  s     r5  wrapper#_dot_check_wrapper.<locals>.wrappery  s    4$r7  )r	   )r  r  s   ` r5  _dot_check_wrapperr  x  s     
2Y  Nr7  r  c                    U R                  5       (       a  U R                  5       (       a{  UR                  5       (       aA  [        R                  " U R	                  5       UR	                  5       5      R	                  5       $ [        R
                  " U R	                  5       U5      $ UR                  5       (       a%  [        R
                  " UR	                  5       U 5      $ X-  R                  5       $ rD  )r+  is_conjrb  r   r   r   r   r  s     r5  r   r     s     <<>>}}yyejjl;@@BBzz$))+u55]]__::ejjlD11Lr7  c                 ,   U R                  5       (       d  [        R                  " X5      $ U R                  5       (       am  UR                  5       (       a3  [        R                  " UR                  5       U R                  5       5      $ [        R                  " U R                  5       U5      $ UR                  5       (       a2  [        R                  " XR                  5       5      R                  5       $ U R                  5       U-  R                  5       $ rD  )r+  rb  r   r  r   r   r6   r   r  s     r5  r   r     s     ??yy%%||~~==??::ejjlDIIK8899TYY[%00	yyzz|,1133  5(--//r7  c                    [         R                  " U R                  U5      nS/U R                  -  nSXB'   US:  a  X0R                  U   -   n[        R
                  " U R                  U   U R                  S9R                  U5      U:H  n[        R                  " X5      R                  U R                  5      n[        R                  " XQU 5      $ )NrP  rV  r   r3  )rn  r  r0  rT  rb  r  r4  r  r  r   r   )rH  r  r  r  
mask_shaper  s         r5  select_scatterr    s     
 
 
-CqvvJJOqy$<<QXX6;;JG5PD
//#
#
*
*177
3C;;t!$$r7  c                 V    [        U [        R                  [        R                  45      $ rD  )r;  rb  TypedStorageUntypedStorage)objs    r5  
_isStorager  +  s     cE..0D0DEFFr7  c                    Sn[        U 5      n/ n[        U [        [        45      (       a  [	        U 5      nU(       a  XQR
                  -  nUR                  U5        [	        U5      U:  a"  [        S[        U 5      R                   S35      eUS:X  a   U$  U S   nUn [        U [        [        45      (       a  M  U$ ! [         a#    [        S[        U 5      R                   S35      ef = f)N   ztoo many dimensions 'rr  r   z.could not determine the shape of object type ')r  r;  rK  r\  rS  itemsizer  ra  r2  r  r  )seqscalar_typeMAX_DIMS
is_storager>  r  handles          r5  _compute_sizesr  0  s    HCJE
S4-
(
(S+++FVu: 4T#Y5G5G4HJKKQ; L	VF
  S4-
(
(" L  	@cASAS@TTUV 	s   B= =-C*c                    [        U [        5      (       a  [        R                  " 5       $ [        U [        5      (       a%  [        U [
        5      (       d  [        R                  $ [        U [        5      (       a  [        R
                  $ [        U [        5      (       a  [        R                  " 5       nU[        R                  L a  [        R                  $ U[        R                  L a  [        R                  $ U[        R                  L a  [        R                  $ [        S5      e[        U [        R                   5      (       a  U R"                  $ [        U [$        5      (       a"  ['        S[)        U 5      R*                   S35      e[        U [,        [.        45      (       a  S n[1        U 5      nUS:X  a  [        R                  " 5       $ [3        U5       HF  nX   n [5        U5      nUb  [        R6                  " X&5      nOUnU[        R                  L d  MD  Us  $    U$ [        S[)        U 5      R*                   35      e)Nz'invalid default scalar type for complexznew(): invalid data type 'rr  r   zCould not infer dtype of )r;  r   rb  r  r   r  rO  r   r  r  cfloatdoublecdoublehalfchalfrq  rQ  r  rr  	TypeErrorr2  r  rK  r\  rS  r`  _infer_scalar_typepromote_types)r  default_dtype
scalarTyper  r+  cur_itemitem_scalarTypes          r5  r  r  J  s   #y!!&&((#w
3(=(={{#x  zz#w//1EKK'<<ell*== ejj(;;HII#u||$$yy#s4T#Y5G5G4HJKK#e}%%
S Q;**,,vAvH 1:O%"00M
,
U]]* "!   
2493E3E2FG
HHr7  r  r  c           	         [        U[        5      (       aB  UR                  5       S:X  a.  UR                  5       R	                  U SSS9R                  S5      $ [        U[        5      (       a  UR                  5       R	                  U SSS9$ [        U[        5      (       a  [        R                  " XS9$ UnU(       d  [        R                  " S5      $ [        R                  " U Vs/ s H  n[        X5      PM     sn5      $ s  snf )NrP  rx  T)r  r4  r  rL  r  r   )r;  rQ  r  detachr   r  r   rb  r$  r  r   _recursive_build)r  r  r  r   s       r5  r  r  }  s     #v399;!#3zz|ZDINNrRR	C	 	  zz|ZDII	C	 	 ""399 C  	A [[M*:<MN Ns   (Dc                 B   [        U[        R                  5      (       an  [        R                  " U(       + S 5        UnU(       a  UR	                  5       nU(       a  UR
                  OUn	Ub  UOUR                  n
UR                  U
U	SUS9$ [        US5      (       a  [        $ Ub  UOU S   n
U(       a  [        U5      OUn	[        U5      (       a  [        $ [        R                  " U
5      R                  S:X  a  [        $ [        X5      nUR                  XSSS9nU$ )Nc                      g)Nz,Can't pin tensor constructed from a variablerL  rL  r7  r5  rN  )_internal_new_from_data.<locals>.<lambda>  s    $Rr7  F)r4  r  r  r  __cuda_array_interface__r4  meta)r  r  )r;  rb  rQ  rc  r  r  r4  r   hasattrNotImplementedr  r  r2  r  )optionsr  
device_optdatacopy_variables
copy_numpytype_inferencer  r   inferred_scalar_typer4  r  s               r5  _internal_new_from_datar    s    $%%NR	
 **,C,:syy)53::vv&	  
 	
 t/00 &1Zwx7HF7E-d3; $<<$$.!! ""6=6eRWX Mr7  )r  r4  r  r  c                $   [        U [        R                  5      (       a  [        R                  " S[
        SS9  US L n[        SS0Ub  UO[        R                  " 5       UU SSUUS9nUR                  5         U(       a  UR                  U5        U$ )NzTo copy construct from a tensor, it is recommended to use sourceTensor.detach().clone() or sourceTensor.detach().clone().requires_grad_(True), rather than torch.tensor(sourceTensor)r/  )
stacklevelr4  rx  T)r   r  r  r  )
r;  rb  rQ  r  r  UserWarningr  r  detach_r  )r  r  r4  r  r  r  
new_tensors          r5  r  r    s    $%%l		
 d]N( 
5"(?(?(A%J !!-0r7  rD  )F)r  NN)gh㈵>g:0yE>Fr  )NN)NNNNNFF)FFN)NF)NNFr  )r   rV  )	NNNTreflectFNNN)NNNTFNNF)rL  )rP  r  )r   r   rP  )r   r  rV  )r   NrP  )r  )r  rp  )rK  NF)r   rP  NrZ  )rP  r/  N(  r:  r  r  r|  r!  r~  r  collections.abcr   r   enumr   	functoolsr   r   r   r	   typingr
   r   r   r   r   r   rb  torch._prims_primsr  torch._prims_common_prims_commonrn  torch.utils._pytree_pytreer?  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   torch._prims_common.wrappersr'   r(   r)   r*   r+   r,   r  rQ  rB  DispatchKey_opsr  r  r6  r?  rf  rw  torch._decomprx  objectr  r  r  r  rp  r-   INT_TO_FLOATr.   r/   r1   r0   r2   r3   DEFAULTr4   r5   r+  r6   r7   r8   r;   r<   r=   r>   r?   r@   rB   	NO_OPMATHrC   rD   r%  rE   rF   r   ALWAYS_BOOLrN   rO   rP   rQ   rR   specialmultigammalnr]   rS   rT   rV   rW   rX   rY   rZ   r  r  r\   r   r  r`   r  ra   rb   r   rd   re   r   rf   rg   rh   ri   rj   rk   rl   rn   BOOL_TO_LONGro   rp   rq   rs   r
  rU  rt   ru   rv   rw   rx   ry   rz   r}   r~   rr  r   r   r   r   r}  r|  r   r   r   r  r\  r   r   r   r   r   r   r   r  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r{   r|   r   r   r	  r  r   r   r  r  r  registerr4  r  r  r  r  r  r  r   r7  rG  r   r   r   dim_IntListIntList_outrK  r   r   r   r   rk  r   r   r   r   r   r   r   r  r   r   r   r   r   r   r  py_implCompositeImplicitAutogradMetar   r   r   r   r   r=  r   r   r   r   r   r   r   r   r   r   r+  r/  r   r   _subclasses
fake_implsregister_op_implrM  r   r,  r-  rb  r.  r  r   r  r   r   r   r   r  r   rm   r   r	  r  r  rI   rJ   rL   rM   r  rH   rK   r   r@  r   r   r   r  r   r  r   r   r   r   rx  r   r   r   r   r   r   r  r  r  r   r   r  r  r  r   r   r  r  r  r  r  r&  r   r!  r  r  r  r  
start_step	start_outrU   r  r  r   r   r  r  r  r  r'  r"  r#  r$  r9  r   r   r(  r)  r^   rr   rU  r   r   r   r  r  rk  rs  r  r3  r  r  r*  r  rA   rG   r[   r_   r  rc   r:   r9   r  r  r   r   r  abs_acos_acosh_add_addcmul_addcdiv_asin_asinh_atan_atanh_atan2_bitwise_and_bitwise_left_shift_bitwise_not_bitwise_or_bitwise_right_shift_bitwise_xor_ceil_clamp_
clamp_min_
clamp_max_conj_physical_	copysign_cos_cosh_cumsum_cumprod_deg2rad_digamma_div_eq_erf_erfc_erfinv_exp_exp2_expm1_float_power_floor_floor_divide_fmod_frac_gcd_ge_gt_
heaviside_hypot_igamma_igammac_i0_lcm_le_lerp_lgamma_log10_log1p_log2_log_logical_and_logical_not_logical_or_logical_xor_lt_mul_	mvlgamma_nan_to_num_ne_neg_
nextafter_pow_rad2deg_reciprocal_
remainder_rsqrt_sgn_sigmoid_sign_sin_sinc_sinh_sqrt_square_sub_tan_tanh_tril_triu_true_divide_trunc_xlogy_cauchy_exponential_
geometric_log_normal_zero_r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  torch._refs._conversionstorch._refs.ffttorch._refs.linalgtorch._refs.nn.functionaltorch._refs.specialrL  r7  r5  <module>r     s7P          .  < < A A   # $ $ $     . l\	 
hh""zz~~2%P 9= C8 1   D 2 ##44	 ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#J#JK  L  ##++	 (/n / )/ **+& &  ,& ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q #7AA	 N 	 : 	 . 	 	 
	 ^ J >  		"# #> #  ## ##++	 ##++!N !~ !	!N ~  ##//* *> *	* ##B#N#NO1^ 1 1 P1 ##//1 1> 1	1 ##//1 1> 1	1 ##B#N#NO^   P
 u}}11:> ##//0n 0 0	0 ##00$'' ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q
  $(XX	X EKK X 	X X '#!7DD
 :?,
,',26,,	  (, ( !$#'#'		*	 Z  Z 	
   )4  ##++	 > N ~  ##B#O#OP Q 

##7?? 12 J^ J# Jn J	  $J ##B#O#OP Q ##B#O#OP/~ /. / Q/ ##++	 ##++	 ##//	 ##B#O#OP Q ##B#O#OP4 Q4
 ##B#O#OP Q ##B#O#OP Q ##00n  	 ##B#O#OP Q ##B#O#OP Q ##++	
!. !^ !L 	## %"&6 6t !#"7?? #'	8^Z'(8^Z'(8 J	8	  "8: $7DD$$

 $7??#> #n # ## $7??". "^ " "" $7??". "^ " "" $7??.> .n . .. $7??#> #n # ## $7DD$2^Z'(2-2>:3M-N2	2 !
 $(	^Z'(^Z'( C=	  "( $7CC$. ^  	 $7DD^Z'(^Z'( 4 ^Z'(^Z'(  l $==EE $"'
O^Z'(O-2>:3M-NO
O8FV F F6 F16 1f 1 12 $7??$$
N ~ . 
 $7??$$
N ~ . 
 $7??$#
N ~ . 
 

#Z$7 75)G#H 7 % $7 $7??$$
> n  
 $7CC$. ^  	 $7CC$. ^  	 $7??$$
^ ^  
 $7??$$
^  > 
 $7DD$$
n  N 
 $7DD$$
~ . ^ 

  	
  
2 ((( ( 	(
 ( (V $7??$$
Q> Qn Q
Q  $7CC$. ^  	 $7??$$
T TN T~ T
T0 $7??$$
,. ,^ , ,
, $7CC> n  ##B#N#NO>  P $7CC. ^  $7CC> n  $7CC$. ^  	 $7??~ . ^  $7??~ . ^  $7?? $> n  	 $7CC$. ^  	 $7AA$$
! !N !~ !
! $7??! !N !~ !!
 		" 	(^Z'(	(^Z'(	( 	(  #	( !#"7?? 	$8^Z'($8^Z'($8 	$8	  "$8N $7DD	 $	> n   

##"7DD:U>:-. :59S3T :	  $:& $==EE $
"^Z'("-2>:3M-N"
" %#67DD ,
,, ,
 , ,	  &,* %#67?? ,
,, ,
 , ,	  &,* 

##+7?? -1,0	(	) 
(	) 		  $4 ' -1&
&	(	)& &  (& ' -1&
&	(	)& &  (& 

##"7AA +/*.#
#&'# &'#	  $#. 

#?D?T?T).)<)<  $ 9= v &  		"&N &z & #& (,#'%)37!&^$ EKK  4.	
 U\\" E//0   
2    37LL;;  	
 E//0 
#s(^ "  37;;  	
 E//0 
#s(^ "  37	;;  E//0	
 
#s(^   37	  E//0	
 
#s(^ ."& "T "0. n V "##' <<
< 	<
 < 8
< < EKK < 
&	< 2< <~4 ! #

	(	
 
 	
  "
 ! #	(	  	  "$ --txx/C/CDE 6:
 $( 	x}htCy11	2 
 EKK  
&	  F:CC C, 		" 6:
  	x}htCy11	2  
&	  #: 		" #
 !	(	 
 
&	  #. 		" #
 !	(	 
 
&	  #. ! ##	 (,	(	 tn 	 $   "6 ! 6:#	1 (,11	x}htCy11	21 tn1 	1 $1 1  "1* 		" #*
 **	(	* * * #*Z &VV #  $'+	(	 tn	
  $  '0 &VV ##	 (,	(	 tn 	 $  ' 		"#07?? 7A
7A
7A 7A
 7A 7A 7A	  #7Av
+	~x77	8
+AO
+
>5!4556
+   # *8  +	~x77	8+AO+
>5!4556++	~x77	8+AO+
>5!4556+$ %)		A	A
	A 	A SM		A
 	A //0 %)RR	R R 	R
 SMR R  1R2 2 ''(M(MN''(8(89O4#7 O : OO1N 1) 1 1 !#$7AAsG# sG# sGn sG	  "sGn #, # # # >  ,,-?@PP $S	P2<PP  .Ph 8=7N7N77!&!4!477 #& #> # # $!f ! ! %!J F v ^ S s 5QTAT;U ,1~ 1# 1C 1 1$ 		"N "2 ~   #n  n  (-c>.A(BLOD").
666!"<> tCy ^  ..66711V1 6
1 	1
 1 1 1 
1 666!"1 81h ../VVV$AAA VA 6
	A
 
A 666!"A % 0AH ..t/E/E/M/MN$ O$ %,~ , , &, $#.#.,#.36#.AO#.#.  %#.N +??@ !% $##%)&*n?n?n? n? 	n?
 Vn? n? n? n? tnn? TNn? d^n? n? An?d KAAB !% $## PPP P 	P
 VP P P tnP SMP P CPh",9<DGOR8 $51f 51 51  %51p{N { { {D<~ <y <^ <
&^ &N &~ & 		",>N ,>H ,>H ,>n ,>  #,>^ 

#<B>>>)9>>  $><
!3 
 
 

#G% GC G G  $G   $(	 EKK  	 & #& #> # # #& #> # #S Sc S) S S $
n 
3 
/A 
 %
  * 3 z :  
: 
C 

 
J 
 (<<<$.<7<Z=S7T<  )< (();;;$.;7<Z=S7T; *;..	. . Z'(	. .b  	  	  " ))*J S    +" ))*~ HX$6 .  +8 --.56
#Cy/2	&\ /D DFDFvx/0DF 
DF >3	DFP&-&-,4&-
>3&-T$+$+,4$+
>3$+N 		& 1
11 1  '1 --. 	  	
    /$ & 	&
&& & 	&
 & '&R ( 	535353 53 	53
 53  )53p (!$$~"6 !$> !$  )!$H)n- ). )
(n 
( 
(5G 
( '9 9 (9$	 	N 	 

#^   $ '	* 	*s 	*# 	*. 	* (	* 	 $+
+%(+03+;>++ %+ (()n  C s   * $( 9 9 
	9 EKK 9 
&	9 90 $
 $( TT	T EKK 	T
 
&	T T %T %
 $( UU	U EKK 	U
 
&	U U &U '3 3c 3n 3 (3 		))*=N =I =. = +=
#. # #N #
^   AE!D||!D#ll!D19#!D
\\!D !DH  $( =='+).)@)@#EKK # LL# ^$	#
 # # &&# # #L  $( =='+ EKK  LL	
 ^$    $ '
 $(%)'+
 EKK 	
 U\\" ^$    (, ../ $(%)'+
 
 EKK  U\\" ^$    08 

**+ $( =='+EKK  LL ^$	
     ,0 '
 $(%)'+
 EKK 	
 U\\" ^$     (2 		))* $( =='+EKK  LL ^$	
     +0 &
 $(%)'+
 EKK 	
 U\\" ^$     '2 & $(%)'+
 
 EKK  U\\" ^$    '0 ( $('+%)).)>)>&& EKK & ^$	&
 U\\"& & & &&& &  )&R //1F1FGH $`
 $( =='+``	*	` `
 EKK ` LL` ^$` ` ` `  I`F 		"#27??8 8V 8U6:3E-F 8	  #82 & $('+ ==U/^+,U/	z>)	*U/ U/
 EKK U/ ^$U/ LLU/ U/ U/ U/  'U/p &
 	8@ $('+ ==8@^+,8@	z>)	*8@ 8@ 	8@ EKK 8@ ^$8@ LL8@ 8@ 8@ 8@  '8@v 
	h~. 	# 	 
	 
	~ 	 	 
	 &>ND$8%:OOP>> 
.> '>D;;#''(; s,,-; 	;~ **+
 $('+ ==E),,- EKK 	
 ^$ LL     ,6 ! ") $( =='+")
")}") EKK 	")
 LL") ^$") ") ") ")  "")P **DIIMM:;
 $( =='+%%% EKK 	%
 LL% ^$% % % %  <%> $(%)'+).)>)> EKK 	
 U\\" ^$   && . ( $(%)'+).)>)> EKK  U\\"	
 ^$   &&   ), ' $(%)'+).)>)> EKK  U\\"	
 ^$   &&   (, 

**+ $('+%)EKK  ^$ U\\"	
     ,8 $( =='+>> EKK > LL	>
 ^$> > >, $'$'XX	tS%	 X c5 
!X
 ;;X X X* (())> ) )@V )  *)X ))*+4J +   	
  
"^  4 & 		" &+"	M $(MMeSj!"M 
(	M 	M EKK M M  #M2 

#* *> *  $* [)l+	 		"3N 3c 3. 3  #3 		"3N 3c 3. 3  #3(7 73 7 7c3m8L 7$
	 
 ;;	
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  ==""	"	" "
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  =="&	&	& &
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 7%7%7% 	7%
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		1'
 
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 	   "
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9%
}-(#	Sd

!!!SBSd
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	u	
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
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S!J'9%
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
SSddd[)	u		u	

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J'd!$**-
&t7$T]]3"4;;/ #4;;/#DLL1#DLL1	dff	%%dnn5"4;;/%dnn5 +	G
4.If"'(>@R(R"SF 5r tU  L       r7  