
    8h]M                    j   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/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:  S SK;J<r<J=r=J>r>J?r?J@r@JArA  / S	QrB\R                  rC\R                  R                  rE\R                  R                  R                  rHS
 rIS rJS rKSS.S jrLS SKMJNrN  \O" 5       rP\PSSS.S\4S jjrQS rRS rS\Q" \,R                  SS9S 5       rU\Q" \,R                  5      S 5       rW\Q" \,R                  5      S 5       rX\Q" \,R                  5      S 5       rY\Q" \,R                  5      S 5       rZ\Q" \,R                  5      S 5       r[\Q" \,R                  5      S 5       r\\Q" \,R                  5      S 5       r^\Q" \,R                  SS9S  5       r_\N" \HR                  5      S!\84S" j5       r`\N" \HR                  5      \A" 5       S!\84S# j5       5       ra\Q" \,R                  5      S$ 5       rb\Q" \,R                  5      S% 5       rc\Q" \,R                  5      S& 5       rd\Q" \,R                  5      S' 5       re\Q" \,R                  5      S( 5       rf\Q" \,R                  5      S) 5       rg\Q" \,R                  5      S* 5       rh\Q" \,R                  5      S+ 5       ri\Q" \,R                  5      S, 5       rj\A" 5       \?" S-\,R                  S.9S/\8S0\2S\84S1 j5       5       rlS/\8S0\2S\84S2 jrm\N" \HR                  5      \A" 5       S!\8S\84S3 j5       5       rn\Q" \,R                  SS9S4 5       ro\Q" \,R                  SS9S5\8S\84S6 j5       rpS/\8S\84S7 jrq\Q" \,R                  SS89S/\8S\84S9 j5       rs\Q" \,R                  5      S/\8S\84S: j5       rt\Q" \,R                  SS9S/\8S\84S; j5       ru\Q" \,R                  SS9S/\8S\84S< j5       rv\Q" \,R                  5      S/\8S\84S= j5       rw\R" \R                  R                  S>5      rz\Q" \,R                  SS89S/\8S\84S? j5       r{\Q" \,R                  \HR                  S89S@ 5       r|\Q" \,R                  5      SA 5       r}\Q" \,R                  5      SB 5       r~\Q" \,R                  5      SC 5       r\Q" \,R                  5      SD 5       r\Q" \,R                  5      SE 5       r\A" 5        GSS/\8SF\SG\\GR                     S\84SH jj5       r\N" \HGR
                  5      \A" 5       \?" SI\,R                  S.9 GSSJ\8SF\*SK\S\84SL jj5       5       5       r\N" \HGR                  5      \A" 5          GSS/\8SM\\2   SN\\2   SO\\2   S\84
SP jj5       5       rS/\84SQ jr\Q" \,R                  \SR9SS 5       rS/\8S\84ST jrS/\8S\84SU jr\Q" \,R                  5      SV 5       r\N" \HGR                  5      \A" 5       \?" SW\,R                  S.9S SX.S/\8SY\S\84SZ jj5       5       5       r\Q" \,R                  5      S[ 5       r\Q" \,R                  5      S/\8S\84S\ j5       r\Q" \,R                  SS9S] 5       r\Q" \,R                  SS9S^ 5       r\Q" \,R                  SS9S_ 5       r\Q" \,R                  5      S` 5       r\Q" \,R                  5      Sa 5       r\Q" \,R                  5      Sb 5       r\Q" \,R                  5      Sc 5       r\Q" \,GR.                  SS89S/\8S\84Sd j5       r\Q" \,R                  5      Se 5       r\Q" \,R                  5      Sf 5       r\Q" \,R                  SS9Sg 5       rSJ\8S\84Sh jr\PSSSSSS4S\4Si jjr\N" \HGR<                  5      \A" 5       \?" Sj\,R                  S.9SSk.S/\\8\24   Sl\\8\24   Sm\\2   4Sn jj5       5       5       r\" \,R                  SSSo9Sp 5       r\" \,R                  Sq9S/\8Sl\8S\84Sr j5       r\" \,R                  Sq9S/\8Sl\8S\84Ss j5       r\" \,R                  Sq9S/\8Sl\8S\84St j5       r\" \,R                  Sq9S/\8Sl\8S\84Su j5       r\" \,R                  Sq9S/\8Sl\8S\84Sv j5       r\" \,R                  SSw9S/\\8\24   Sl\\8\24   4Sx j5       r\N" \HGRL                  5      \A" 5       SSy.S/\\8\24   Sl\\8\24   Sz\\   4S{ jj5       5       r\" \,R                  SSw9S/\8Sl\8S\84S| j5       r\" \,GR.                  Sq9S/\\8\24   Sl\\8\24   S\84S} j5       r\A" 5       S/\\8\24   Sl\\8\24   S\C4S~ j5       r\" \RX                  R                  SSS9S/\\8\24   Sl\\8\24   4S j5       rS/\CSl\CS\C4S jrS/\CSl\CS\C4S jr\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\N" \HGRb                  5      \A" SS5      SJ\8S\\8\84   4S j5       5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSw9S/\8Sl\8S\84S j5       r\" \,R                  SSw9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S!\8S\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       rS\S/\8Sl\8S\S\SS4S jr   GSS/\8Sl\8S\S\S\S\84S jjr\" \,R                  SSSo9S/\8Sl\84S j5       r\" \,R                  SSw9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  Sq9S/\8Sl\84S j5       r\Q" \,R                  5      S/\84S j5       r\" \,R                  Sq9S/\8Sl\84S j5       r\" \,R                  Sq9S/\8Sl\84S j5       r\" \,R                  SSw9S/\8Sl\8S\84S j5       r\" \,R                  Sq9S/\8Sl\8S\84S j5       r\" \,R                  Sq9S/\8Sl\8S\84S j5       r\" \,R                  SS9S/\8Sl\8S\84S j5       r\" \,R                  SSw9S/\8Sl\8S\84S j5       r\" \,R                  SSSo9S/\8Sl\8S\84S j5       r\" \,R                  Sq9S/\8Sl\8S\84S j5       r\N" \HGR                  5      \A" 5        GSS/\\8\24   Sl\\8\24   Sm\24S jj5       5       r\N" \HGR                  5      \A" 5       \?" Sj\,R                  S.9SSk.S/\\8\24   Sl\\8\24   Sm\24S jj5       5       5       r\" \,R                  SSSS9S/\8Sl\8S\84S j5       r\N" \HGR                  5      \A" 5       \?" Sj\,R                  S.9S/\\8\24   Sl\\8\24   4S j5       5       5       r\" \RX                  R                  SSS9S/\\8\24   Sl\\8\24   4S j5       r\N" \HGR                  5      \A" 5       \?" S\,R                  S.9SS.SJ\8S\8S\8S0\2S\84
S jj5       5       5       r\N" \HGR                  5      \A" 5       \?" S\,R                  S.9SS.SJ\8S\8S\8S0\2S\84
S jj5       5       5       r\N" \HGR                  5      \A" 5       \?" S\,R                  S.9  GSS/\8S\\9   S\\9   S\84S jj5       5       5       r\N" \HGR                  5      \A" 5        GSSJ\8S\\9   S\84S jj5       5       r\N" \HGR                  5      \A" 5        GSSJ\8S\\9   S\84S jj5       5       r\N" \HGR                  5      \A" 5       \?" Sj\,R                  S.9  GSS\CS/\\9   Sl\\9   4S jj5       5       5       r\N" \HGR                  5      \A" 5       \GR                  S.S/\8S\GR                  S\84S jj5       5       rSS.S/\CSl\C4S jjr\N" \HGR                  5      S/\8S\24S j5       r       GSS/\8S\\'   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\CS\S\S\\GR                     S\\\4   4
S jj5       rS/\CS\4S jrS/\8S\84S jrSSSSSSS.S/\8S\S\S\S\\*   S\SG\\GR                     S\\C   S\4S\84S jjrS r\N" \HGR                  5      \A" 5         GSS/\8SF\\*   SK\S\84S jj5       5       r\N" \HGR                  5      \A" 5         GSS/\8SF\\*   SK\S\84S jj5       5       r\N" \HGR                  GR                  \HGR                  GR                  /5        GSSSS.S/\8SF\\\   \\\      4   SK\SG\\GR                     S\\C   S\84S jjj5       rS/\CS\C4S jr\N" \HGR                  5        GSSSS.S/\8SF\\\   \\\      4   SK\S\\C   S\84
S jjj5       r\N" \HGR                  5        GSSS.S/\8SF\\*   SK\S\\C   S\84
S jjj5       r\N" \HGR                  5        GSSS.S/\8SF\\*   SK\S\\C   S\84
S jjj5       rGSS jr\N" \HGR                  5      \A" 5          GSSS.S/\8SF\\*   S\\   SK\S\\2   S\84S jjj5       5       r\N" \HGR                  5      \A" 5          GSSS.S/\8SF\\\   \\\      4   S\\   SK\S\\2   S\84S jjj5       5       r\N" \HGR                  5        GSSSS.S/\8SF\\*   SK\S\84S jjj5       r\N" \HGR                  5      \A" SS5       GSSSSS.S/\8SF\\*   S\\   SK\S\\2   4
S jjj5       5       r\N" \HGR                  5      \A" SS5         GSSS.S/\8SF\\*   S\\   SK\S\\2   4
S jjj5       5       r\N" \HGR                  5      \A" 5       \?" S\,R                  S.9SSS.SJ\8S\8S\8S\2Sm\2S\84S jj5       5       5       rS\\8\	\8   4   S\8S\\8\\8S4   4   4S jrS\SF\S\8S\84S jrS\\8\	\8   4   S\8S\\8\\8S4   4   4S jrS\\8\	\8   4   S\8S\\8\\8S4   4   4S jr GSS/\8GS \5GS\6GS\\   S\84
GS jjr\N" \HGR                   5      \A" 5        GSS!\8GS\8GS \5GS\6GS\\   S\84GS jj5       5       Gr S\54GS jGr\HGR                  GR                  GR	                  \EGR
                  5      \HGR                  GR                  GR	                  \EGR                  5      S\\8   4GS j5       5       GrS/\8GS \5S\84GS jGr\N" \HGR                  5      \A" 5       \?" GS	\,R                  S.9GSGS
\:SF\S\84GS jj5       5       5       Gr\A" 5       GS
\:S\84GS j5       Gr	S!\8S\84GS jGr
\N" \HGR                  5      \A" 5        GSS!\8GS\\   S0\2S\84GS jj5       5       Gr\GR                  S.S/\CS\GR                  S\C4GS jjGr\A" 5       GS
\:S\84GS j5       Gr\N" \HGR                  5      S/\CS\C4GS j5       GrS/\CSl\CS\C4GS jGrGSS/\8GS\SF\S\\8S4   4GS jjGrGSS/\8GS\GS\S\84GS jjGr\N" \HGR&                  5      \A" 5       S/\8S\)S\84GS j5       5       GrS/\8S\84GS jGrS/\8S\84GS jGrS/\8SF\GS\\\84   GS\S\84
GS jGrS/\CGS\*GS \S\\C\C\C4   4GS! jGrS5\8GS"\\   S\84GS# jGr\N" \HGR2                  GR                  5      S!\CGS$\\C   GS%\\C   GS&\GS'\GS(\GS)\GS \S\\C\C\C4   4GS* j5       Gr\N" \HGR4                  5      \A" SSGS+5      S!\CGS,\5GS$\\C   GS%\\C   GS \S\\C\C\C4   4GS- j5       5       Gr\GR6                  GR8                  GR;                  \HGR4                  GR                  5      GS. 5       Gr\N" \HGR>                  5      S/\8S\84GS/ j5       Gr\N" \HGR@                  5      \A" 5       S!\8GS0\3SF\GS1\3S\84
GS2 j5       5       Gr \HGRB                  GRD                  GR	                  \EGR
                  5               GSS!\CGS3\GS4\\   GS5\\   GS6\\C   GS7\GS8\GS9\GS:\\   GS;\\   GS<\\   S\C4GS= jj5       Gr!\HGRF                  GR                  GR	                  \EGR
                  5              GSS!\CGS3\GS4\\   GS5\\   GS6\\C   GS7\GS9\GS:\\   GS\\   S\C4GS> jj5       Gr#GS?\5GS@\6GSA\GS \GSB\4
GSC jGr$\N" \HGRJ                  5      \A" 5       S/\CS\C4GSD j5       5       Gr%S/\8GSE\S\84GSF jGr&S/\8GSE\S\84GSG jGr'S/\8GSH\5S\84GSI jGr(SJ\8S\8S\84GSJ jGr)\N" \HGRT                  5      \A" 5       GSS/\8GSK\*S\*S\84GSL jj5       5       Gr*\N" \HGRV                  5      \A" 5        GSS/\8GSN\S\)S\84GSO jj5       5       Gr+GS
\:SS4GSP jGr,\N" \HGRZ                  5      \A" 5       GSGS
\:SF\S\84GSQ jj5       5       Gr-\A" 5        GSS/\8SF\SG\\GR                     S\84GSR jj5       Gr.\A" 5       GS
\:S\84GSS j5       Gr/\A" 5       GS
\:S\84GST j5       Gr0S/\8SF\GSU\5S\84GSV jGr1\N" \HGRd                  5      GSGSW\8SF\S\:4GSX jj5       Gr2\A" 5       S5\7SF\GSY\7GSZ\74GS[ j5       Gr3S5\7SF\GSY\7GSZ\74GS\ jGr4\N" \HGRj                  5      \A" 5       S5\7SF\GSY\7S0\\2\74   4GS] j5       5       Gr5\N" \HGRl                  5      S5\7SF\GSY\7S0\\2\74   4GS^ j5       Gr6S5\7SF\GSY\7S0\\2\74   GS_\4
GS` jGr7\A" 5       SSk.S5\7SF\GSY\7GSZ\7Sm\24
GSa jj5       Gr8\N" \HGRr                  5      \A" 5       S5\7SF\GSY\74GSb j5       5       Gr9\N" \HGRt                  GRv                  5      GSS/\8SF\\*   S\84GSc jj5       Gr:\N" \HGRx                  5       GSSJ\CGSd\\   SF\S\\C   4GSe jj5       Gr< GSS/\8GSf\\C\*4   SF\S\\8S4   4GSg jjGr=S/\8GSf\*S\\8S4   4GSh jGr>S/\8GSf\*S\\8S4   4GSi jGr?\N" \HGR                  GR                  5      \A" 5        GSSJ\8GSj\S\84GSk jj5       5       Gr@\N" \HGR                  5      \A" 5          GSS!\8GS\8GSj\GSl\GSm\S\84GSn jj5       5       GrB\N" \HGR                  5         GSSJ\8GSj\GSl\GSm\S\84
GSo jj5       GrC\N" \HGR                  5      \A" 5          GSGSW\8GSj\GSl\GSm\S\84
GSp jj5       5       GrD\N" \HGR                  5      \A" 5       GS
\\8   S\84GSq j5       5       GrFGS
\\8   S\84GSr jGrES/\8GSs\*S\:4GSt jGrG\N" \HGR                  GR                  5      S/\84GSu j5       GrHS/\8S\84GSv jGrI\N" \HGR                  5      S/\8S\84GSw j5       GrJ\N" \HGR                  5      S/\8GSx\GSl\S\84GSy j5       GrKG\KGrL\N" \HGR                  5      SJ\8GSA\GS \GSB\S\84
GSz j5       GrM\N" \HGR                  5      \A" 5       SJ\8GSA\GS \GSB\4GS{ j5       5       GrNSSS.S/\8SF\SG\\GR                     S\\C   S\84
GS| jjGrO\N" \HGR                  5      SSS.S/\8SF\SG\\GR                     S\\C   S\84
GS} jj5       GrP\N" \HGR                  5      SSS.S/\8SF\SG\\GR                     S\\C   S\84
GS~ jj5       GrQ\N" \HGR                  5      S/\8SF\S\84GS j5       GrR\N" \HGR                  GR                  5      S/\8GSH\5S\84GS j5       GrSSJ\8S\8S\84GS jGrTS/\8S\84GS jGrU\A" 5        GSS/\R                  GS\R                  SF\\   S\R                  4GS jj5       GrV\A" 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\84GS jj5       GrX\A" 5       S\GR                  SSS4SG\\GR                     S\GR                  S\\'   GS\S\S\84GS jj5       GrY\N" \HGR                  5      \A" 5       SSSSGS.S/\8GS \5SG\\GR                     S\\GR                     S\\'   S\S\84GS jj5       5       GrZ\N" \HGR                  5      \A" 5       SSSSGS.S/\8GS \5GS\6SG\\GR                     S\\GR                     S\\'   S\S\84GS jj5       5       Gr[\N" \HGR                  GR                  5      \A" 5       S\GR                  SSSGS.SG\\GR                     S\GR                  S\\'   S\GS\S\84GS jj5       5       Gr\\N" \HGR                  5      \A" 5       SSSSSGS.S/\8GS \5SG\\GR                     S\\GR                     S\\'   S\GS\S\84GS jj5       5       Gr]\N" \HGR                  GR                  5      \A" 5       S\GR                  SSSGS.SG\\GR                     S\GR                  S\\'   S\GS\S\84GS jj5       5       Gr^\N" \HGR                  5      \A" 5       SSSSSGS.S/\8GS \5SG\\GR                     S\\GR                     S\\'   S\GS\S\84GS jj5       5       Gr_\N" \HGR                  5      \A" 5       SSSSGS.S/\8GS \5GS\2SG\\GR                     S\\GR                     S\\'   S\S\84GS jj5       5       Gr`\HGR                  GR                  GR	                  \EGR
                  5       GSGS \8S\8S\\GR                     S\84GS jj5       Gra\N" \HGR                  5      \A" 5       SSSSS\GR                  GS.S/\8SG\\GR                     S\\'   S\\GR                     S\GS\S\GR                  S\84GS jj5       5       Grb\N" \HGR                  GR                  \HGR                  GR                  /5      \A" 5          GSS\GR                  SSSGS.GS\2GS\\2   GSB\2SG\\GR                     S\GR                  S\\'   S\GS\S\84GS jjj5       5       Grc\N" \HGR                  5      \A" 5       \?" GS\,R                  S.9GS\CGS\CGS$\\C\24   4GS j5       5       5       Grf\N" \HGR                  5      \A" 5       SS\GR                  SSGS.GS\\2\84   GS\\2\84   GS\2SG\\GR                     S\\'   S\GR                  S\GS\S\84GS jj5       5       Grg\N" \HGR                  5      \A" 5        GSSS\GR                  SSGS.GS\\2\84   GS\\2\84   GS\2GS\2SG\\GR                     S\\'   S\GR                  S\GS\S\84GS jjj5       5       Grh\GS
\	\8   GS\4GS j5       Gri\GS
\8GS\4GS j5       Gri\N" \HGR                  5      GS
\\8\\8   \\8   4   GS\S\\8   4GS j5       GriS!\8GS\\\)4   GS\\\)4   S\84GS jGrj\N" \HGR                  5      \A" 5       SS\GR                  SSGS.GSH\\5\\5   4   GS\6SG\\GR                     S\\'   S\GR                  GS\S\S\84GS jj5       5       Grk\N" \HGR                  5      \A" 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\84GS jjj5       5       Grl\N" \HGR                  GR                  \HGR                  GR                  /5      \A" 5       S\GR                  SSSGS.GSH\5GS\2SG\\GR                     S\GR                  S\\'   S\GS\S\84GS jj5       5       GrmSSSSS\GR                  GS.S/\8GS\2SG\\GR                     S\\GR                     S\\'   S\GS\S\GR                  S\84GS jjGrn\N" \HGR                  5      \A" 5       SSSSS\GR                  GS.S/\8SG\\GR                     S\\GR                     S\\'   S\GS\S\GR                  S\84GS jj5       5       Gro\N" \HGR                  5      \A" 5       SSSSS\GR                  GS.S/\8SG\\GR                     S\\GR                     S\\'   S\GS\S\GR                  S\84GS jj5       5       Grp\N" \HGR                  GR                  5      \A" 5       SSSSSGS.SG\\GR                     S\\'   S\\GR                     GS\S\S\84GS jj5       5       GrqS\GR                  SSGS.S/\2SG\\GR                     S\GR                  S\\'   S\S\84GS jjGrr  GSGSH\5GS\\\\4   GS\\\\4   SG\GR                  S\'S\84GS jjGrs\N" \HGR                  5      \A" 5       S/\8GS\8S0\94GS j5       5       Grt\N" \HGR                  5      S/\8GS\8S0\9S\84GS j5       Gru   GSS/\8Sl\8S\S\S\S\4GS jjGrvS/\8Sl\8S\4GS jGrw\N" \HGR                  5      \A" SS9   GSSGS.S!\8GS0\\\\4      SF\\*   SK\SG\\GR                     S\84GS jjj5       5       Grx\N" \HGR                  5      \A" 5       SJ\8S\84GS j5       5       GryGS GrzG\z" \5      Gr{G\z" \5      Gr|G\z" \5      Gr}\N" \HGR                  5      \A" 5       GSS/\8GS\S\84GS jj5       5       Gr~\N" \HGR                  5      \A" 5       GSS/\8GS\S\84GS jj5       5       GrGS\GS\GSj\S\\\\4   4GS jGrS\GS\GS\SG\GR                  S\GR                  S\4GS jGr\N" \HGR                  5      \A" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSj\SG\GR                  S\GR                  S\'S\S\84GS jjj5       5       GrGS\GS\GSj\S\\\\4   4GS jGr\N" \HGR
                  5      \A" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSj\SG\GR                  S\GR                  S\'S\S\84GS jjj5       5       Gr\N" \HGR                  5      \A" SS9SSGS.S/\9GS\8GS\GS\4GS jj5       5       Gr\N" \HGR                  5      \A" 5       \?" SI\,R                  S.9GS GS j5       5       5       Gr\N" \HGR                  5      \A" 5       \?" SI\,R                  S.9GSGS j5       5       5       Gr\N" \HGR                  5      \A" 5       \?" SI\,R                  S.9GSGS j5       5       5       Gr\N" \HGR                  5      \A" 5       \?" SI\,R                  S.9GSGS j5       5       5       Gr\N" \HGR                  5      \A" 5       \?" GS\,R                  S.9   GS SSSSSGS.GS jj5       5       5       Gr\N" \HGR                  5      GSMSGS.GS jj5       Gr\Q" \,R                  5      SJ\84GS j5       Gr\Q" \,R                  5      SJ\84GS j5       Gr\N" \HGR                  5      \A" 5       GSSF\\*   4GS jj5       5       GrGS GrGS Gr\N" \HGR$                  5      \A" SS9G\\?" GS\,R                  S.9GS 5       5       5       5       Gr\N" \HGR&                  5      \A" SS9G\\?" GS\,R                  S.9GS 5       5       5       5       Gr\N" \HGR(                  5      \A" 5       S5\8GS\8SF\GSY\4GS j5       5       Gr\S" \U5      Gr\S" \W5      Gr\S" \X5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \Y5      Gr\S" \Z5      Gr\S" \[5      Gr\S" \\5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \^5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \_5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \a5      Gr\S" \5      Gr\S" \b5      Gr\S" \c5      Gr\S" G\P5      Gr\S" G\Q5      Gr\S" G\5      Gr\S" \d5      Gr\S" \5      Gr\S" \5      Gr\S" \e5      Gr\S" \g5      Gr\S" \f5      Gr\S" \h5      Gr\S" \j5      Gr\S" \i5      Gr\S" \5      Gr\S" \o5      Gr\S" \5      Gr\S" \5      Gr\S" \p5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \|5      Gr\S" \5      Gr\S" \5      Gr\S" G\f5      Gr\S" \}5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \~5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \z5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" G\5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" G\5      Gr\S" G\~5      Gr\S" \5      Gr\S" \5      Gr\S" \5      Gr\S" G\5      Gr\S" G\5      Gr\S" G\5      Gr\S" G\5      Gr\S" \n5      Gr\" \HGR                  5      Gr\" \HGR                  5      Gr\" \HGR                  5      Gr\" \HGR                  5      Gr\" \HGR,                  5      Gr\" \HGRt                  5      Gr\" \HGR>                  5      Gr\" \HGR                  5      Gr\" \HGR                  5      Gr\" \HGRd                  5      Gr\" \HGR                  5      Gr\" \HGR                  5      GrGS Gr GS GrGS GrGS\GR                  GS\\9\:4   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definitely_contiguous'definitely_contiguous_for_memory_format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    N/var/www/fran/franai/venv/lib/python3.13/site-packages/torch/_refs/__init__.pyis_noncontiguous_supportedr8  p  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_tensorr;  
isinstancefake_devicer8  r   )input_tlistoutputr6  r;  r   s        r7  handle_noncontiguous_outputsrA  t  sK    F8a$$]]F 
 &f--""$Mr9  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     r7  	<genexpr>$_broadcast_shapes.<locals>.<genexpr>  s*      9A 1g&&A-9s   ')c                 
    U S L$ rF   rJ  s    r7  <lambda>#_broadcast_shapes.<locals>.<lambda>  s    !4-r9     c              3   8   #    U  H  n[        U5      v   M     g 7frF  len)rI  shapes     r7  rK  rL    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 rN  )arg_idxcommon_shapeidxrV  s   r7  rP  rQ    s:    LUSVZLX\]`\a b55<IU5' J22>Ar9  )%torch.fx.experimental.symbolic_shapesrD  tuplefilterrU  r=  r   r   max	enumeraterange
ValueErrortorch_check)_shapesrD  shapesrZ  r[  r\  rV  s      @@@@r7  _broadcast_shapesrh    s$   J /9 F 6{a %**** 
 	
4s4V4546L $F+R#e*_b1C#L$5$:;;:>$S  %*#JS!%eCjAo66 %s3A 2 ,  r9  T)preserve_cpu_scalar_tensorsc                 `   ^ ^^ [        S U 5       6 mUU 4S jm[        UU4S jU 5       5      $ )Nc              3   h   #    U  H(  n[        U[        5      (       a  UR                  OS v   M*     g 7frF  )r=  r%   rV  rI  r   s     r7  rK  #_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_shaperV  r   RuntimeErrorstrr4  )rJ  rV  r[  ri  s     r7  __maybe_broadcast+_maybe_broadcast.<locals>.__maybe_broadcast  s    96""H:&&*u/I/I!/L/L##AGG\::xx--H5DGDsJ r9  c              3   6   >#    U  H  nT" UT5      v   M     g 7frF  rN  )rI  rJ  ru  r[  s     r7  rK  rm    s     BT"1l33Ts   )rh  r^  )ri  argsru  r[  s   ` @@r7  _maybe_broadcastry    s-    $	G$	GL$ BTBBBr9  )register_decompositionF)aten_op
extra_metaexact_dtypereturnc                0   ^ ^^^ S[         4UUUU 4S jjnU$ )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$ )Nr}  atype_promoting_argstype_promotion_kindr  r~  c                 D   > Tb  T" U 5        T" U 5      n[        U /U5      $ rF  )rA  )r  r@  r|  r  s     r7  _ref>_make_elementwise_unary_reference.<locals>.inner.<locals>._ref  s*     %1!WF/V<<r9  )
r	   r.   r-   r,   r&   infer_aten_oprp  get_aten_op__name__rz  )r  r  r{  r}  r|  r  s   ` r7  inner0_make_elementwise_unary_reference.<locals>.inner  s     
t		-	)	+ & 3

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

 
* 
. 
	= m#''dmm<G"7+D1r9  r   )r  r{  r|  r}  r  s   ```` r7  !_make_elementwise_unary_referencer    s    H  0 Lr9  c                    ^  U 4S jnXl         [        R                  " 5       R                  R                  S   Ul        U$ )a  
This function defines an alias of another function and sets its __name__ argument.
It also sets its __module__ argument to the module of the caller.
Note that when naively doing `alias = fn`, we have that `alias.__name__ == "fn"`, and
`alias.__module__ == fn.__module__`.
c                     > T" U 0 UD6$ rF  rN  )rx  kwargsfns     r7  _fn_make_alias.<locals>._fn  s    4"6""r9  r  )r  inspectcurrentframef_back	f_globals
__module__)r  namer  s   `  r7  _make_aliasr    s5    # L))+22<<ZHCNJr9  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$ )NoutrN  )r  rx  r  r  s      r7  r  _make_inplace.<locals>._fn  s    !,d,,V,,r9  _r   )	getmodule)	r	   r  rz  getattratenr  r  __all__append)r  r  inplace_namer  _alls   `    r7  _make_inplacer    ss     2Y- - kk]!$LL
 |!<
=c
BC "R=  DL!Jr9  r  c                 .    [         R                  " U 5      $ rF  )primsr/   r  s    r7  r/   r/     s    
 99Q<r9  c                 .    [         R                  " U 5      $ rF  )r  r0   r  s    r7  r0   r0   %      ::a=r9  c                 .    [         R                  " U 5      $ rF  )r  r1   r  s    r7  r1   r1   *      ;;q>r9  c                 .    [         R                  " U 5      $ rF  )r  r3   r  s    r7  r3   r3   /  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r2   r  s    r7  r2   r2   4  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r4   r  s    r7  r4   r4   9  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r5   r  s    r7  r5   r5   >  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r6   r  s    r7  r6   r6   C  s    Qr9  c                 .    [         R                  " U 5      $ rF  )r  r7   r  s    r7  r7   r7   H      
 ::a=r9  inputc                 B    [         R                  " U R                  5      $ rF  )rp  is_complex_dtypedtyper  s    r7  r-  r-  P  s    !!%++..r9  c                 |    [         R                  " U R                  5      (       d  U $ [        R                  " U 5      $ rF  )rp  r  r  r  r8   r  s    r7  r8   r8   U  s/     !!%++..u%%r9  c                 .    [         R                  " U 5      $ rF  )r  r9   r  s    r7  r9   r9   ]      99Q<r9  c                 .    [         R                  " U 5      $ rF  )r  r:   r  s    r7  r:   r:   b  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r=   r  s    r7  r=   r=   g      ==r9  c                 .    [         R                  " U 5      $ rF  )r  r>   r  s    r7  r>   r>   l  r  r9  c                 .    [         R                  " U 5      $ rF  )r  erf_invr  s    r7  r?   r?   q  r  r9  c                 .    [         R                  " U 5      $ rF  )r  r@   r  s    r7  r@   r@   v  r  r9  c                 .    [         R                  " U 5      $ rF  )r  rA   r  s    r7  rA   rA   {  r  r9  c                 .    [         R                  " U 5      $ rF  )r  rB   r  s    r7  rB   rB     r  r9  c                 .    [         R                  " U 5      $ rF  )r  rD   r  s    r7  rD   rD     r  r9  za,r  r  valuec                 N   [        U [        5      (       d   e[        U[        5      (       d   e[        R                  " U R
                  5      n[        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        R                  " X5      $ Nzvalue argument of type  cannot be safely cast to type ro  )r=  r%   r   rp  r   r  r   r4  rc  r  rE   )r  r  python_typemsgs       r7  rE   rE     s     a$$$$eV$$$$%%agg.K&&tE{K@@'U}4ST_S``abo::ar9  c                 ^    [         R                  " X5      n[         R                  " X5        U $ rF  )r  rE   r   )r  r  rs      r7  rF   rF     s!    

1A	MM!Hr9  c                 .    [         R                  " U 5      $ rF  )rd  r)  r  s    r7  r'  r'    s     E""r9  c                 .    [         R                  " U 5      $ rF  )r  rG   r  s    r7  rG   rG         
 ;;q>r9  rJ  c                     [         R                  " [         R                  " [         R                  " U 5      5      [         R                  " U 5      5      n[         R
                  " X5      $ rF  )rd  r   rG   r/   rj   r   )rJ  trunc_xs     r7  rH   rH     s<    
 iiEIIaL15::a=AG99Q  r9  c                     [        U [        5      (       d   e[        R                  " [        R
                  " U R                  5      S 5        [        R                  " U 5      $ )Nc                      g)Nz#imag only supports complex tensors.rN  rN  r9  r7  rP  imag.<locals>.<lambda>  s    1Vr9  )	r=  r%   rd  re  rp  r  r  r  r   r  s    r7  r   r     sF    a$$$$	LLqww')V ::a=r9  )r{  c                     [         R                  " U R                  5      (       d%  [         R                  " U R                  5      (       a  [        R
                  " U 5      $ [        U [        R                  S9$ )Nr  )	rp  is_float_dtyper  r  r  rP   r$  rd  boolr  s    r7  rP   rP     sM    
 AGG$$(>(>qww(G(G~~a  Qejj))r9  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$ )Ninfr  )rp  r  r  rd  r   rQ   r   r   r  r/   floatr)  r  r  s    r7  rQ   rQ     s    agg&&ejjm 4eEJJqM6JKKAGG$$yy|uU|++AUZZ00r9  c                 ,  ^  [         R                  " [        R                  " T R                  5      (       + U 4S j5        [        R
                  " T R                  5      (       a  T [        S5      :H  $ [         R                  " T [         R                  S9$ )Nc                  "   > ST R                    3$ )Nz7Complex dtype is not supported for isposinf, got dtype r  r  s   r7  rP  isposinf.<locals>.<lambda>      I!''Sr9  r  r  	rd  re  rp  r  r  r  r  r)  r  r  s   `r7  rR   rR     sf    
 
LL""177++S AGG$$E%L  AUZZ00r9  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$ )Nz7Complex dtype is not supported for isneginf, got dtype r  r  s   r7  rP  isneginf.<locals>.<lambda>  r  r9  z-infr  r  r  s   `r7  rS   rS     sf    
 
LL""177++S AGG$$E&M!!AUZZ00r9  c                 .    [         R                  " X 5      $ rF  r  r   r  s    r7  rT   rT     s    88A>r9  r_   c                     [         R                  " U R                  5      (       a  [        R                  " U 5      S:H  $ [        R
                  " U [        R                  S9$ )Nr   r  )rp  r  r  rd  r   r$  r  r  s    r7  rU   rU     sA    
 agg&&zz!}!!??1EJJ//r9  c                 .    [         R                  " U 5      $ rF  )r  	bessel_i0r  s    r7  rV   rV     s     ??1r9  c                 .    [         R                  " U 5      $ rF  )r  rX   r  s    r7  rX   rX     s    <<?r9  c                 .    [         R                  " U 5      $ rF  )r  rY   r  s    r7  rY   rY     r  r9  c                 .    [         R                  " U 5      $ rF  )r  rZ   r  s    r7  rZ   rZ     r  r9  c                 .    [         R                  " U 5      $ rF  )r  r[   r  s    r7  r[   r[     r  r9  c                 .    [         R                  " U 5      $ rF  )r  r\   r  s    r7  r\   r\   "  r  r9  dimr  c           	          U=(       d    U R                   n[        R                  " U5      n[        X5      n[        U[	        XQSS9-
  U5      $ )NTkeepdim)r  rp  get_computation_dtyper)   r   )r  r  r  result_dtypecomputation_dtypea_s         r7  r^   r^   (  sF     #AGGL33LA	 	6B"2	"4(H#H,WWr9  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   numelrd  r   rA   rY   r   r   r   r/   r  r   rv   )r  r  r  maxesmaxes_squeezedresults         r7  r   r   4  s     c8$$fzz|qyy4#7;;==JJuzz$'d;EeYY[E%L%@!DE%U5==+DNYYuyy.=F::<N++r9  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%   rp  is_boolean_dtyper  is_integer_dtyper   rd  finfor`  minr   rT   rS   rR   )r  r  r  r  r  s        r7  rb   rb   H  s     a$$$$agg&&%*@*@*I*Iwwy
{~QWW%))~QWW%))[[Q0F[[*F;F[[*F;FMr9  c                 h    [         R                  " U R                  [         R                  LS 5        g )Nc                      g)NzNegation, the `-` operator, on a bool tensor is not supported. If you are trying to invert a mask, use the `~` or `logical_not()` operator instead.rN  rN  r9  r7  rP  _neg_meta.<locals>.<lambda>g  s     r9  )rd  re  r  r  r  s    r7  	_neg_metar  d  s#    	LL	uzz!	
r9  )r|  c                 .    [         R                  " U 5      $ rF  )r  rc   r  s    r7  rc   rc   o  s     99Q<r9  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  rd  r  rs  )r  r  s     r7  rd   rd   x  s:    a$$$$ww%**73Hr9  c                     [        U [        5      (       d   e[        R                  " U R                  5      (       a  [
        R                  " U 5      $ U $ rF  )r=  r%   rp  r  r  r  r   r  s    r7  r   r     s=    a$$$$agg&&zz!}Hr9  c                 .    [         R                  " U 5      $ rF  )r  rf   r  s    r7  rf   rf     s    Ar9  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  rg   r   )r  r  ten_powten_neg_pows       r7  rg   rg     sQ     1}{{1~h,hY'yyUYYq%:;[IIr9  c                 .    [         R                  " U 5      $ rF  )r  r   r  s    r7  r   r     r  r9  c                 R    [        S[        S[        [        U 5      5      5      5      $ )NrR  )r   rv   rA   rc   r  s    r7  rh   rh     s    q#aSV-..r9  c                     [         R                  " U R                  5      (       a-  U R                  5       n[        R
                  " US:H  SX-  5      $ U R                  5       $ Nr   )rp  r  r  r/   rd  r   rj   )r  a_abss     r7  ri   ri     sH    
 agg&&{{5A:q!)44vvxr9  c                 .    [         R                  " U 5      $ rF  )r  rj   r  s    r7  rj   rj     r  r9  c                 .    [         R                  " U 5      $ rF  )r  rk   r  s    r7  rk   rk     s    
 ==r9  c                 .    [         R                  " U 5      $ rF  )r  rl   r  s    r7  rl   rl     r  r9  c                     [         R                  U -  n [        R                  " U S:H  S[        R                  " U 5      U -  5      $ Nr   rR  )mathpird  r   rl   r  s    r7  rm   rm     s3    !A;;qAvq%))A,"233r9  c                 .    [         R                  " U 5      $ rF  )r  rn   r  s    r7  rn   rn     r  r9  c                 .    [         R                  " U 5      $ rF  )r  rp   r  s    r7  rp   rp     r  r9  c                     [        X 5      $ rF  )r   r  s    r7  rq   rq     s    
 q9r9  c                 .    [         R                  " U 5      $ rF  )r  rr   r  s    r7  rr   rr     r  r9  c                 .    [         R                  " U 5      $ rF  )r  rs   r  s    r7  rs   rs     r  r9  c                 .    [         R                  " U 5      $ rF  )r  ru   r  s    r7  ru   ru     r  r9  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: rN  )input_dtypes   r7  rP  !view_as_complex.<locals>.<lambda>  s     55@MCr9  r   c                      g)Nz-Input tensor must have one or more dimensionsrN  rN  r9  r7  rP  r.        ?r9  rX     c                      g)Nz+Tensor must have a last dimension of size 2rN  rN  r9  r7  rP  r.        =r9  rR  c                      g)Nz/Tensor must have a last dimension with stride 1rN  rN  r9  r7  rP  r.        Ar9  c              3   0   #    U  H  oS -  S:H  v   M     g7f)r1  r   NrN  )rI  strides     r7  rK  "view_as_complex.<locals>.<genexpr>  s     84aZ1_4s   c                      g)NzCTensor must have a stride divisible by 2 for all but last dimensionrN  rN  r9  r7  rP  r.    s    Ur9  c                      g)Nz0Tensor must have a storage_offset divisible by 2rN  rN  r9  r7  rP  r.    s    Br9  )r  rd  re  rp  r  sizerU  r7  builtinsr   storage_offsetr  view_element_typecorresponding_complex_dtyper   )r  sizesold_stridesdimsr-  s       @r7  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r9  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  rF  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!rN  r  s   r7  rP  Q_make_elementwise_binary_reference.<locals>.inner.<locals>._ref.<locals>.<lambda>2      4& !> >r9  c                     > T  S3$ )Nzc: Received a rhs Python scalar to an elementwise binary operation that does not accept rhs scalars!rN  rI  s   r7  rP  rJ  7  rK  r9  c                     > T  S3$ )Nz?: Receive two Number inputs to an elementwise binary operation!rN  rI  s   r7  rP  rJ  =  s    4& _`r9  )rd  _check_valuer=  r   ry  rA  )r  rF  r@  r  r  supports_lhs_python_scalarsupports_rhs_python_scalarsupports_two_python_scalarss      r7  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/??r9  )r  r	   r,   r   Tensorr    r.   r  rp  r  rz  )
r  r  r{  has_outr  should_register_decompositionrO  rP  rQ  r  s
   ` r7  r  1_make_elementwise_binary_reference.<locals>.inner"  s    <==D	t	+ * 3

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

 

	@. =&Dm#''d3G#@"7+D1r9  r  )	r  r{  r  rT  rO  rP  rQ  rU  r  s	   ```````` r7  "_make_elementwise_binary_referencerW    s    *H * *X Lr9  rE  alpharF  rY  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      $ )z'
Reference implementation of torch.add
alpha argument of type r  ro  )ry  r=  r%   r  rp  r   r  r   r4  rc  r  r   rv   rA  r  rF  rY  r  r  r  r@  s          r7  rv   rv   R  s      A!DA%a44!''))%0$u'B'BK(
 (
 ,DK=8WXcWddefCS/!a$$		!#A	AYYq_F'77r9  )r  rO  rP  c                 .    [         R                  " X5      $ rF  )r  rw   rE  s     r7  rw   rw   u       ;;qr9  )r  c                 .    [         R                  " X5      $ rF  )r  rx   rE  s     r7  rx   rx   ~       Q""r9  c                 .    [         R                  " X5      $ rF  )r  
shift_leftrE  s     r7  ry   ry          A!!r9  c                 .    [         R                  " X5      $ rF  )r  rz   rE  s     r7  rz   rz     rc  r9  c                 .    [         R                  " X5      $ rF  )r  shift_right_arithmeticrE  s     r7  r{   r{     s     ''--r9  c                 .    [         R                  " X5      $ rF  )r  r|   rE  s     r7  r|   r|     r`  r9  )r  rO  c                    [        U[        5      (       a4  [        U [        5      (       a  [        XR                  U R
                  S9nOl[        U [        5      (       aW  [        U[        5      (       aB  U R
                  UR
                  :w  a(  SU R
                   SUR
                   S3n[        U5      e[        [        U5      [        [        U 5      5      [        U 5      5      $ )Nr  r6  /Expected divisor (b) to be on the same device (&) as dividend (a), but it is found on ro  )r=  r   rS  r&  r  r6  rs  r   rk   rc   r/   )r  rF  r  s      r7  r   r     s     !VAv!6!6!77188<	Av		:a#8#8QXX=Q?zIopqpxpxoyyz{3SQ[#a&11r9  )rounding_moderl  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
ru   rG   zLdiv expected rounding_mode to be one of None, 'trunc', or 'floor' but found .)r   r   r   rc  )r  rF  rl  r  s       r7  r   r     sV     1  	'	!A!!	'	!A!!\]j\kklmor9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r         
 88A>r9  c                 Z   [        U [        5      (       d  [        U[        5      (       d   e[        U[        5      (       a=  US:X  a  U R                  5       $ 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      $ )N      ?g       @      ?T)r=  r&   r   r   rd  rp   rE   rp  r  r  r  rD   r  r   rE  s     r7  r   r     s     a((Jq.,I,III!V8779#X5L#X::a=  	Av		8::a&&8  ))U-C-CAGG-L-L::a= 99Q?r9  c                 v   [        U [        5      (       a   [        U[        5      (       a  [        S5      e[        R                  " X5      nUc   e[        R
                  " U5      (       a  [        R                  nO[        R                  n[        X5      n [        X5      n[        X5      u  p[        X5      $ )Nz=Receive two Number inputs to an elementwise binary operation!)r=  r   rc  rp  get_higher_dtyper  rd  
complex128float64r)   ry  r   r  rF  r  s      r7  r   r     s    
 !VAv!6!6K
 	

 ""1(Ee$$   	 )A)AA!DAq9r9  )r  rQ  rU  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 )	Nri  cpurj  rk  ro  r5  Fc                     > T  S3$ )Nz not supported for floor_dividerN  r  s   r7  rP  floor_divide.<locals>.<lambda>C  s    ug-L$Mr9  )r=  r   r&  rS  r  r6  rd  rs  r  
device_putrp  r  _floor_divide_floatr	  _floor_divide_integerre  )r  rF  r  r  s      @r7  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((				&	&$Q**UMNr9  c                 |   [        X5      u  pU R                  R                  (       d  [        R                  " X5      $ [
        R                  " U 5      [
        R                  " U5      :g  R                  [
        R                  " X5      S:g  5      n[        R                  " X5      [        X R                  5      -
  $ r  )
ry  r  	is_signedr  r   rd  rk   r   r   r)   )r  rF  offsets      r7  r  r  F  s~    A!DA77yy mmA%--"22??

1@PTU@UVF99Q?4VWWEEEr9  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      $ )Nr   rR  rs  ri  )r   r   r   r|   r   r   rx   r   rG   r   rv   r&  r  r6  r   )
r  rF  modr   different_signed_inputsnon_zero_remaindermask	floor_div	basic_divzero_tensors
             r7  r~  r~  Q  s    
q*C
c!k1
%C *"Q(Bq!H=C)CD
c#qk3
'C c
Ic#!3'DdC	1-y9IA!IAQAQRK baj)Xk-MNI Aq900r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r   j       ::ar9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r   s  r  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r   |  r  r9  mantissaexponentc                 h    [         R                  R                  [        R                  " U 5      5      $ rF  )rd  return_typesfrexpr  r  s    r7  r  r    s$     ##EKK$566r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     99Q?r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     rp  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     rp  r9  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$ r"  )rd  r   r   r   rT   r   )r  r  input_eq_zeroinput_lt_zerozeros_and_onesr@  s         r7  r   r     sa     HHUA&M$$UXXeQ%7U9KLM[[15N[[?FMr9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     r^  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     <<r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     ==r9  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 ro  r  )r  rF  r  s   r7  rP  #_check_close_args.<locals>.<lambda>  s'    4&LQWWIUZ[\[b[bZccder9  r   c                     > T  ST S3$ )Nz6: rtol must be greater than or equal to zero, but got ro  rN  )r  r  s   r7  rP  r        4&NtfTUVr9  c                     > T ST  S3$ )Nz6: atol must be greater than or equal to zero, but got ro  rN  )r  r  s   r7  rP  r    r  r9  )rd  rN  r  re  r  r  rF  r  r  s   `````r7  _check_close_argsr    sV     
	177e 
LL	V 
LL	Vr9  	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   rp  r  r  r  r   r   rT   r  convert_element_typerd  get_default_dtyperv   r/   r   r   rP   r   )	r  rF  r  r  r  closeallowed_erroractual_errorr  s	            r7  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 Mr9  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  rd  int8int16r  r  int32r   r   r/   r   )r  rF  r  promote_to_intgress         r7  r   r     s     GGE uzz5;;77N&&q%++6&&q%++6		!AAFAq!A
))EIIaOa'
(C$3P%*D*DS*PPr9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r   "  rp  r9  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  )rd  r   r   r   r   rP   rp  r  r  rY   rA   rZ   rT   complexr  )
r  rF  r  max_min_inf_maskneg_min_maskinf_valsnon_nan_valsnan_masks
             r7  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Sr9  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 dtypesrN  rN  r9  r7  rP  logaddexp2.<locals>.<lambda>O      ;r9  rr  r1  )rd  re  rp  r  r  r   r   rQ   r#  rY   rZ   rD   )r  rF  r  r  r  r  	inv_log_2r  s           r7  r   r   G  s     
LL##AGG,O0F0Fqww0OP;
 6D;;t"D;;t"D  Q8Hdhhqk!IEKK

4; 789DDF;;xF++r9  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r  rp  r  r  rE  s     r7  r   r   [  G     !!!''**F!!!''**F5Lr9  c                 \    [         R                  " U R                  5      (       d  U S:H  $ U ) $ r  r  r  s    r7  r   r   f  s'    !!!''**Av2Ir9  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  n[        X5      $ r  )rp  r  r  rz   rE  s     r7  r   r   m  sK     !!!''**F!!!''**Far9  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r  r  rE  s     r7  r   r   y  r  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     rp  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r          ==r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     r  r9  )r  rQ  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s    
 99Q?r9  c                 .    [         R                  " X5      $ rF  r  rE  s     r7  r   r     rp  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     ??1  r9  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     ??1  r9  rR  c                 p    [        U [        5      (       a  Sn[        U5      e[        R                  " XUS9$ )Nz?Received a Number for the first argument, but expected a TensorrX  )r=  r   rc  rd  r   )r  rF  rY  r  s       r7  r   r     s1     !VOo99Q''r9  c                   [        X5      u  p[        U [        5      (       a|  [        U[        5      (       ag  [        R                  " [
        R                  " U R                  5      (       + =(       a%    [
        R                  " UR                  5      (       + S 5        US:w  a  [        U [        5      (       a  U R                  OUR                  n[
        R                  " U5      n[
        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        U[        R                  5      (       a  [        R                  " X5      nOX-  n[        R                  " X5      n[!        X/U5      $ )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.rN  rN  r9  r7  rP  sub.<locals>.<lambda>  s    Cr9  rR  r[  r  ro  )ry  r=  r%   rd  re  rp  r  r  r   r   r4  rc  rS  r  r   r   rA  r\  s          r7  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7r9  r   )r  r  r{  rQ  c                 .    [         R                  " X5      $ rF  )r  r   rE  s     r7  r   r     s     99Q?r9  c           
         [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U[        5      (       a4  [        U [        5      (       a  [        XR                  UR                  S9n OH[        U [        5      (       a3  [        U[        5      (       a  [        XR                  U R                  S9n[        U [        5      (       d   e[        U[        5      (       d   e[         R                  " [         R                  " U S5      S[         R                  " U [         R                  " U5      5      5      n[         R                  " [         R                  " U5      [        S5      U5      $ )Nc                      g)Nz/Expected either argument a or b to be a Tensor"rN  rN  r9  r7  rP  xlogy.<locals>.<lambda>  r5  r9  ri  r   r  )rd  re  r=  r%   r   r&  r  r6  r   r   r   rY   rT   r  )r  rF  rhss      r7  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9r9  )r  r{  rQ  c                     [         R                  " U 5      n[         R                  " U5      (       a  [        R                  " X5      $ [        [        R                  " X5      5      $ rF  )rp  	get_dtyper	  r  r   ru   rx  s      r7  r   r     sD     OOAEe$$yy1!!r9  )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  r3  r  r  s   r7  rP  addcdiv.<locals>.<lambda>D      -d5k]:YZeYffghr9  r  rp  r   rd  rN  r   r4  r  r  r  r  r  r  s      ` @r7  r   r   /  _      

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

 %'/G+++r9  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  r3  r  s   r7  rP  addcmul.<locals>.<lambda>_  r  r9  r  r  s      ` @r7  r   r   J  r  r9  )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 $ )Nz+clamp called but both min and max are none!)rc  rd  rT   rz   r   r   r   )r  r  r`  r  a_isnan	conditions         r7  r   r   e  s     {s{;o
++a.$$UXXa%5w?	
 KK	c*
++a.$$UXXa%5w?	KK	c*Hr9  c                 *    [         R                  " XS9$ )N)r  rd  r   )r  r  s     r7  r}   r}          ;;t%%r9  c                 *    [         R                  " XS9$ )N)r`  r  )r  r`  s     r7  r~   r~     r  r9  predc                    ^  Ub  Uc  [         e[        R                  " T XSS9  [        R                  " T R
                  [        R                  L U 4S j5        [        T X5      u  m p[        R                  " T X5      $ ) Tallow_cpu_scalar_tensorsc                  "   > ST R                    3$ )Nz#expected predicate to be bool, got r  )r  s   r7  rP  where.<locals>.<lambda>  s    5djj\Br9  )
NotImplementedErrorrp  check_same_devicerd  re  r  r  ry  r  r   )r  r  rF  s   `  r7  r   r     sh     	yAI!!	D!F	LL

ejj B
 "$-JD!;;tQ""r9  memory_formatr  c                .    [         R                  " XS9nU$ Nr  )r  r   )r  r  r  s      r7  r   r     s    
 [[8FMr9  )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      $ )NzAttempting to copy from device z to device z*, but cross-device copies are not allowed!)r6  rs  r  r   )r  rF  r  r  s       r7  r   r     sK    !((ahh"6/zQXXJNxy3==r9  c                     U R                  5       S:w  a  SU R                  5        S3n[        U5      e[        R                  " U R                  5      nU" [
        R                  " U 5      5      $ )NrR  zCan't convert a tensor with z elements to a number!)r  rc  rp  r   r  r  r   )r  r  number_types      r7  r   r     sW    wwyA~,QWWYK7MNo %%agg.Kuzz!}%%r9  r6  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  )r6  r  r  rd  preserve_formatrp  is_contiguous_for_memory_format)r  r6  r  r  r  r  r  r	  s           r7  _to_will_aliasr    s      
	
t^1qxx61
	
d].agg.
	
 t^1qxx61
	
 T! U 5 55U44QTr9  c                      [         erF  )r  )rx  r  s     r7  _to_dispatchr    s    
r9  c                     U UUUUS.nU$ N)r6  r  r	  r  r  rN  r6  r  r	  r  r  r  s         r7  
_to_devicer    s!     $&F Mr9  c                 >    [         R                  " U 5      UUUUS.nU$ r  )rd  r6  r  s         r7  _to_device_strr  	  s*     ,,v&$&F Mr9  c                     U UUUS.nU$ )N)r  r	  r  r  rN  )r  r	  r  r  r  s        r7  	_to_dtyper    s     $&	F Mr9  otherc                 `    U R                   nU R                  nU R                  nUUUUUUS.nU$ )N)r6  r  r  r	  r  r  )r6  r  r  )r  r	  r  r  r6  r  r  r  s           r7  	_to_otherr  +  sA     \\FKKE\\F $&F Mr9  	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  r6  r  r  r6  r  )	r=  rt  rd  r6  r  r4  indexr  pop)r  r  options_to_checkkws       r7  _canonicalize_to_argumentsr!  C  s    E9Ih,?!E!E#ll9X+>?	(?&9=E<Q<Q+Q(N!**ahhmm;%M//9=3F3F!((..3X A4(IM9 b! r9  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$ )
Nr   r  r  Fr	  r  r  r6  r  )rU  r  r!  r  r  getr  r  r  rd  r  r   )r  rx  r  r  r	  r  s         r7  r   r   [  s    
4yA~t.v. v%%%q)a"6"!'6!16::fuD1?61I6::n-uL 
&**Wagg.!''9F*V#V# ))!ZZ-IJJa*6*FFMr9  )has_identityaccepts_dim_tuplerB  keepdimsr  r  r  r$  r%  rB  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$ s  snf s  snf )N@   zReceived a tensor with z? dimensions, but only tensors with up to 64 dims are supported!z4dtype argument and out dtype must match in reductionr   c              3   B   >#    U  H  nTR                   U   v   M     g 7frF  rV  rI  ir  s     r7  rK  _reduction.<locals>.<genexpr>  s     1Kd!''!*d   zJreducing over zero-size dimension for reduction operation without identityrR  z7Expected the dtype of reduction result and out to match	copy_fromr   )r=  r%   ndimrs  r  r   rp  reduction_dimsrV  r<  r   reduction_dtypesr)   rb  r  broadcast_in_dimr*   r+   r  )r  r  r$  r%  rB  r&  r  r  r'  valid_shaper  r  r  r-  output_shapebroadcast_dimss   `               r7  
_reductionr9    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$ r  )r   rd  contiguous_formatrO  s    r7  rP  3_make_copy_from_view.<locals>._fn.<locals>.<lambda>  s    aggE,C,CgDr9  )pytreetree_map)r  rx  r  r  r  s       r7  r  !_make_copy_from_view.<locals>._fn  s8    T-s-f-?MD
 	
r9  _copy)r  r  r  r.   r	   r;  updaterz  )r  aten_fnannotationsr  	copy_names   `    r7  _make_copy_from_viewrI    s     dBKK(G"/4K	w	B
2Y 
 
 ;;-u%IL{+7434S9Jr9  c                     [         R                  " [         R                  " [         R                  " U 5      XS95      nU R                  [         R                  :X  a  UR                  [         R                  S9nU$ )Nr  r  )rd  r   r   r  uint8r   )r  r  r  r  s       r7  r   r     sS     uyy):):1)=sTUFww%++-Mr9  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)   rd  r  r=  listr^  rU  r   r   r   r  rK  r  r  )r  r  r  r  r  s        r7  r   r     s     
!EJJ	/B#e}%%#c(a-C144U; 	ww%++))&%++>>Mr9  )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$ NrN  rB  r&  r  r  r'  )r  rp  r  r	  rd  int64r9  r  r   r"   SAMEr  r  r  r  r  s        r7  r   r     s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I			499 r9  c           
        ^ ^^ [         R                  " TSS9m[        R                  " [         R                  " TT R
                  5      U U4S j5        [         R                  " TT R
                  5      (       a%  [        T5      S:  a  [        R                  " T 5      $ 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  rV  s   r7  rP  sum_to_size.<locals>.<lambda>#	  s    %eW,I!''RSTr9  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rR  Nr+  )rI  r-  r  leading_dimsrV  s     r7  rK  sum_to_size.<locals>.<genexpr>*	  s@      50A\!"a' 	
,-GGAJ!O 	
0s   55	5T)r  r  r  )rp  extract_shape_from_varargsrd  re  is_expandable_torV  is_same_shaperU  r  view_ofr2  r^  rb  r   )r  rV  reduce_dimsr]  s   `` @r7  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Br9  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$ rO  )r  rp  r  r	  rd  rQ  r9  r  r   r"   rR  rS  s        r7  r   r   2	  s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I	

499 r9  r<  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ NrN  FrB  r&  r  r  r$  r'  )r9  r  r   r"   rR  r  r  r  r  s       r7  r   r   P	  E     byC2I	

499	 	r9  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ rf  )r9  r  r   r"   rR  rh  s       r7  r   r   h	  ri  r9  c                 @    Uc  [        U [        5      (       a  U nS n X4$ rF  )r=  r  )r  unbiaseds     r7  _dim_var_dispatchrm  	  s(     JsD11=r9  
correctionrl  ro  c                    [        X5      u  p[        R                  " X$5      nUS:X  d  U/ :X  a  S n[        U [	        [
        R                  US9UUS S S[        R                  S9nU$ )NrN  rn  Trg  )	rm  rp  set_correctionr9  r   r  r   r"   COMPLEX_TO_FLOAT)r  r  rl  r  ro  r  s         r7  r   r   	  sl     &c4MC%%h;J
byC2I			j14EE	F Mr9  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)ro  r  )
rm  rp  rq  r4  r"   rr  r)   rd  r   rp   )	r  r  rl  r  ro  opmath_dtyper  a_vara_stds	            r7  r   r   	  s     &c4MC%%h;J00	%66L 	 0AIIaEEJJuE"500r9  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$ U$ )NrN  rP  c                     > STc  SOS ST  3$ )Nz&mean(): could not infer output dtype. Inputr   z> dtype must be either a floating point or complex dtype. Got: rN  )r  
orig_dtypes   r7  rP  mean.<locals>.<lambda>	  s"    4$,w*= >77<g?r9  r   rR  c              3   B   >#    U  H  nTR                   U   v   M     g 7frF  r+  r,  s     r7  rK  mean.<locals>.<genexpr>	  s     7QDq
Dr/  r0  )r  r9  r  r   r"   KEEP_PROMOTED_TYPErd  re  rp  r  r  r=  r   r3  rV  r2  r   operatorr   r   r)   r%   r*   r+   )
r  r  r  r  r  r  rB  nelemr  r{  s
   `  `     @r7  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<<Mr9  out0out1)rl  r  ro  c                T   [        X5      u  p[        R                  " X$5      n[        R                  " U [        R
                  5      u  pVU R                  n[        X5      n [        R                  " XXCS9u  p[        R                  " U5      n
Uc   e[        X5      [        X5      4$ rt  )rm  rp  rq  r4  r"   rr  r  r)   rd  r   rp   )r  r  rl  r  ro  ru  r  original_dtyperv  a_meanrw  s              r7  r   r   	  s     &c4MC%%h;J00	%66L WWN0ANN1jRMEJJuE-7 r9  c                P    [        X5      u  p[        XX#US9n[        XU5      nXV4$ )Nrn  )rm  r   r   )r  r  rl  r  ro  vms          r7  r   r   
  s1     &c4MCAH*=AQWA4Kr9  )r  vec1vec2)betarY  r  r  r  c                  ^ ^^^^^ [         R                  " TR                  S:H  U4S j5        [         R                  " TR                  S:H  U4S j5        TS4TS44 H  u  nm[        U[        5      (       d  M  [         R                  " [
        R                  " T R                  5      =(       aG    [
        R                  " TR                  5      =(       a     [
        R                  " TR                  5      U4S j5        M     T R                  TR                  S   TR                  S   5      m [
        R                  " T R                  5      (       a  [         R                  " [        [        T5      [        5      U4S j5        [         R                  " [        [        T5      [        5      U4S	 j5        T(       d5  T(       a  [         R                  " TT5      $ [         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      -  -   $ )NrR  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec1, but got -Dr2  )r  s   r7  rP  addr.<locals>.<lambda>&
      <TYYKrJr9  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec2, but got r  r  )r  s   r7  rP  r  *
  r  r9  rY  r  c                     > ST  S3$ )NzBoolean z$ only supported for Boolean results.rN  )arg_names   r7  rP  r  2
  s    (8*,PQr9  r   c                      > S[        T 5       3$ )Nzexpected bool/int beta but got r3  r  s   r7  rP  r  9
  s    5d4j\Br9  c                      > S[        T 5       3$ )Nz expected bool/int alpha but got r3  r  s   r7  rP  r  =
  s    6tDzlCr9  Fc                  :   > S[        T 5       STR                   3$ Nzcannot safely convert z to r4  r  )r  r  s   r7  rP  r  I
  s    ,T$ZLTZZLIr9  c                  :   > S[        T 5       STR                   3$ r  r  )rY  r  s   r7  rP  r  M
  s    ,T%[Mdjj\Jr9  )rd  re  r2  r=  r  rp  r  r  r   rV  r   r4  intouterr  r   r   )r  r  r  r  rY  argr  s   ````` @r7  r   r   
  s    
LL		QJ 
LL		QJ !'*T6N;Xc4  LL&&tzz2 7**4::67**4::6Q	 < ;;tzz!}djjm4Ddjj))!$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$;T4)@!@@@r9  r  rx  .c                    U(       d,  [        U [        R                  R                  5      (       a  U nO1[        U [        R                  R                  5      (       a   eU 4U-   n[	        S U 5       5      n[        U5      S:  a  U$ 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)rR  r   N)r2  r  rI  r  s     r7  rK  atleast_1d.<locals>.<genexpr>`
  s#     Eu!VVq[i1o5us   *,rR  r   )r=  collectionsabcr   r^  rU  )r  rx  args_r  s       r7  r   r   W
  ss     JsKOO$<$<==c;??#;#;<<<<
EuE
ECc(Q,3*CF*r9  at_least_fnc                 V    U " U5      n[        U[        5      (       d   e[        X15      $ rF  )r=  r%   r  )r  r  r  arg_s       r7  _unsqueeze_atleastr  f
  s,     sDdJ''''Tr9  c                 L  ^ U(       d,  [        U [        R                  R                  5      (       a  U nO1[        U [        R                  R                  5      (       a   eU 4U-   n[	        [
        [        S5      m[        U4S jU 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_2d`.r   c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)r1  Nr  )rI  r  unsqueeze_atleast_1ds     r7  rK  atleast_2d.<locals>.<genexpr>y
  $     Mu!VVq[&:1&==u   &)rR  )	r=  r  r  r   r   r  r   r^  rU  )r  rx  r  r  r  s       @r7  r   r   o
  s     JsKOO$<$<==c;??#;#;<<<<"#5z1E
MuM
MCc(Q,3*CF*r9  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`.rX  c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)   Nr  )rI  r  unsqueeze_atleast_2ds     r7  rK  atleast_3d.<locals>.<genexpr>
  r  r  rR  r   )	r=  r  r  r   r   r  r   r^  rU  )r  rx  r  r  r  s       @r7  r   r   ~
  s     JsKOO$<$<==c;??#;#;<<<<"#5z2F
MuM
MCc(Q,3*CF*r9  r;  r7  r=  c                 Z    Ub  UOU R                  5       n[        R                  " XX$5      $ rF  )r=  r  r   )r  r;  r7  r=  storage_offset_ints        r7  r   r   
  s1     )4!:J:J:L  AV@@r9  srcc                 @    Uc  SOUn[         R                  " XX#U5      $ r  )r  r   )r  r  r;  r7  r=  r  s         r7  r   r   
  s'     -4.##E>PQQr9  c                  :    [         R                  " [        U 6 5      $ rF  )rd  Sizerh  )rg  s    r7  r   r   
  s    ::'011r9  c                      [        U 5      S:X  a  [        U S   [        5      (       d  U S   n [        [	        U SS065      $ )NrR  r   ri  F)rU  r=  rS  rM  ry  tensorss    r7  r   r   
  s?     7|qGAJ!?!?!* 'MuMNNr9  c                     [        U5      [        U R                  5      -
  n[        [        U[        U R                  5      U-   5      5      n[        R
                  " XU5      $ rF  )rU  rV  r^  rb  r  r5  )r  r;  startrB  s       r7  r   r   
  sI    IAGG$Euc!''lU234D!!!400r9  r  r  c                   ^^^^ S n[        U 5      S:X  a  Sn[        U5      eU  H  n[        U[        5      (       a  M   e   [        R
                  " U SS06  SSKJnJn  S m[        U 5       He  u  mmTc  TR                  S:w  a  TmM  M  TR                  S:w  d  M1  [        R                  " TR                  TR                  :H  UUU4S j5        Mg     Tc  U S   mTR                  n/ n[        U 5       H  u  mn[        U5      [        UR                  5      :w  aF  UR                  S:X  d   e[        R                  " U" UR                  S   S:H  5      UU4S	 j5        Mn  UR                  S:X  a  U" UR                  S   S:H  5      (       a  M  UR                  U5        M     U" U 5      n	[        U5      S:X  aB  U S   m [        [!        S
 U  5       5      5      n
[%        STR&                  TR(                  U
U	S9$ [        R*                  " US   R                  U5      n[        R,                  " US   R                  U5        [.        R0                  " X5      R3                  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  $ UnMO     Uc   eU$ rF  )rp  suggest_memory_formatrd  r?  )inputsformatr   fs       r7   cat_compute_output_memory_format-cat.<locals>.cat_compute_output_memory_format
  sb    A++A.AE+++!fk...F  !!!r9  r   z3cat expects at least one tensor, but received zero!r  F)guard_or_falserD  rR  c                  D   > ST R                    STR                    ST S3$ )N6Number of dimensions of tensors must match.  Expected z-D tensors, but got z-D for tensor number  in the listr  )exampler-  r   s   r7  rP  cat.<locals>.<lambda>
  s.       '~-A!&& J%%&C|5r9  c                  *   > ST R                    ST S3$ )Nr  z*-D tensors, but got 1-D for tensor number r  r  )r  
tensor_idxs   r7  rP  r    s"     #LL> *!!+L:r9  c              3   8   #    U  H  oR                   v   M     g 7frF  )requires_gradrH  s     r7  rK  cat.<locals>.<genexpr>%  s     $Fg__grW  r   r  r6  r  r  r  )rU  rc  r=  r%   rp  r  r]  r  rD  ra  r2  rd  re  rV  r  r  r   	Exceptionr  r  r6  canonicalize_dimvalidate_idxr  r   r   )r  r  r  r  tensorr  rD  rV  filteredr  r  r  r-  r   r  s              @@@@r7  r   r   
  sC   
 7|qCo&*----  
WEuE* G'"1?vv{  vv{FFgll*5 #  !*MMEH'0
Fu:V\\**;;!###LL %V\\!_%9::$ {{aN6<<?a3G$H$H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      $ )Nc              3      #    U  H7  oR                   S :  a  UO UR                  UR                  5       S 45      v   M9     g7fr\  )r2  r   r  rH  s     r7  rK  column_stack.<locals>.<genexpr>:  s3      @G1VVaZQYY	1~66s   ?ArR  )r^  r   r  aligned_tensorss     r7  r   r   8  s(     @G O ""r9  c                     [         R                  " U R                  5      (       d  U $ U R                  (       a  [        R
                  " U 5      $ [        R                  " U 5      $ rF  )rp  r  r  	is_sparserd  r8   r  r   r  s    r7  r   r   @  sC    !!%++..""5))::er9  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$ )
Nr1  r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals rT  )r  s   r7  rP  !constant_pad_nd.<locals>.<lambda>P  s    CCH:Nr9  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.rT  )l_inpr  s   r7  rP  r  [  s      225c(;P'r9  rR  c              3   *   #    U  H	  oS :  v   M     g7f)r   NrN  )rI  ps     r7  rK  "constant_pad_nd.<locals>.<genexpr>r  s     '3aE3s   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r  rR  zG resulted in a negative output size, which is invalid. Check dimension z of your input.rN  )r-  input_sizesl_diffr  pad_idxs   r7  rP  r  |  sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr9  r  F)rd  re  rU  rV  rb  r   r<  r   r   rM  r  rp  r  r  r  r6  r  r  rE   r  r   )r  r  r  l_padc_input	new_shapenew_dimr  r@  c_outputr-  r  r  r  r  s    `        @@@@@r7  r   r   I  s   
 
LLC1N
 ++KEHMEU]F	LL	 G65!uqy1}%w<!nnQWw}}Q7G#g,7VWGw{annQ7==+;c'A+>N+NOG "" ||'3'''}}[&)*I5\c(q1uk*fqj)CL83w{;KKaKM M	
 	!  //6M[[kk||))#F zekkUZZ/ZZ&FH65!uqy1}%w<13w<!2S\!AH w{q q!X^^A->Wq[AQ-QRH " 
MM($Mr9  c                    [         R                  " U[         R                  :g  S 5        [        XS9(       a  U $ [         R                  " XS9$ )Nc                      g)Nz@preserve memory format is unsupported by the contiguous operatorrN  rN  r9  r7  rP  contiguous.<locals>.<lambda>  s    Rr9  r  )rd  re  r  r   r   )r  r  s     r7  r   r     s?     
LL...R /qN;;q66r9  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%dstack expects a non-empty TensorListrN  rN  r9  r7  rP  dstack.<locals>.<lambda>      +Rr9  r1  )rd  re  rU  r   r   r  s     r7  r   r     1    	LLW!#RS '*O""r9  c                   ^^	 SSK JnJn  [        U5      S:X  a&  [	        US   [
        5      (       a  [        US   5      n[        R                  " [        U5      [        U R                  5      :  S 5        [        U5      [        U R                  5      -
  n[        U5      n[        U R                  5       Hj  u  nm	Xd-   nX   mU" TS:H  5      (       a  T	XW'   M$  [        R                  " U" T	S:H  TT	:H  5      UU	4S j5        [        R                  " TS:  5        TXW'   Ml     [        R                  " U5        [        R                  " X[        [!        U[        U R                  5      U-   5      5      5      $ )Nr   )r  sym_orrR  c                      g)Nz3expand: the requested shape has too few dimensions!rN  rN  r9  r7  rP  expand.<locals>.<lambda>  s    Er9  rX  c                     > ST ST  S3$ )Nz3expand: attempting to expand a dimension of length  -> ro  rN  )requested_lengthrJ  s   r7  rP  r     s    MaSPTUeTffghr9  )r]  r  r  rU  r=  r   r^  rd  re  rV  rM  ra  rp  validate_shaper  r5  rb  )
r  rV  r  r  r  shape_r\  
offset_idxr  rJ  s
           @@r7  r   r     s6   L
 5zQ:eAh99eAh	LLE
c!''l"E
 Z#agg,&F%[FAGG$Q\
 , *b011!"FLLqAv/145h LL)Q./!1F/ %4 
 !!	5vs177|f'<=> r9  c                 8    U R                  UR                  5      $ rF  )r   rV  rE  s     r7  r   r     s    88AGGr9  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 ro  )rc  rp  r  r2  rV  r#  r7   rG   rb  r   r  r^  )
r  r  r  r  length
chunk_sizefull_chunkstail_chunk_sizer-  r  s
             r7  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      $ r  )rp  r  r2  r  _collapse_view_helpercollapse_viewcollapse)r  r  r  r  _new_stridess        r7  r   r     s    &&qvvy9I$$QVVW5G ! $99!PI""199 >>!00r9  c                    [        U[        5      (       d   [        U[        5      (       d  [        S5      e[        R
                  " U R                  U5      n[        R                  " U5        [        R                  " X5      $ )Nz!dims has to be a sequence of ints)
r=  r^  rM  rc  rp  canonicalize_dimsr2  validate_no_repeating_dimsr  rev)r  rB  s     r7  r   r     s\     dE"":dD+A+A<==""16640D	$$T*99Qr9  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )Nr1  zInput must be >= 2-d.rR  r2  rs  r   r  s    r7  r   r     %    vvz2334=r9  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )NrR  zInput must be >= 1-d.r  r  r  s    r7  r   r   &  r  r9  r  r
  c                 t  ^^^ [        T[        5      (       a`  [        R                  " TR	                  5       S:H  =(       a     [
        R                  " TR                  5      S 5        TR                  5       m[        [        T5      m[        R                  " U R	                  5       S:  S 5        [        R                  " TS:  S 5        [
        R                  " U R                  U5      nU R                  U5      m[        R                  " [        T* T:*  =(       a    TT:*  UU4S j5        TS:  a  TT-   m[        R                  " TTT-
  :*  UUU4S j5        [!        U R"                  5      nTXA'   U R%                  X@R'                  5       U R)                  5       U R'                  U5      T-  -   5      $ )Nr   c                      g)Nz'start must be an 0-dim integral Tensor.rN  rN  r9  r7  rP  narrow.<locals>.<lambda>6  s    =r9  c                      g)Nz-narrow() cannot be applied to a 0-dim tensor.rN  rN  r9  r7  rP  r   :  s    &Ur9  c                      g)Nz&narrow(): length must be non-negative.rN  rN  r9  r7  rP  r   ;  s    &Nr9  c                     > ST *  ST  ST S3$ )Nz0start out of range (expected to be in range of [, z], but got )rN  )
dim_lengthr  s   r7  rP  r   A  s#    BJ;-rR\Q]]hinhoopqr9  c                     > ST ST ST  S3$ )Nzstart (z) + length (z) exceeds dimension size (z).rN  )r&  r
  r  s   r7  rP  r   G  s    '%VH4NzlZ\]r9  )r=  r%   rd  re  r  rp  r	  r  r   r   r  r  r2  r;  _check_with
IndexErrorrM  rV  r   r7  r=  )r  r  r  r
  r  r&  s     `` @r7  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 r9  	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  rl  r  )rp  r  r2  r  r  r)   r=  r%   rd  r   r   )	r  r*  r+  r  a_acc
biased_varr   rstdr  s	            r7  
_normalizer1  P  s    " ''	:I33AGG<#A9EeZ((((~~udJ ;;z'(D<4
Cd?r9  
dimensionsc                 V    [        U5       H  n[        R                  " X5      n M     U $ rF  )sortedrd  r  )rJ  r2  r  s      r7  _unsqueeze_multipler5  n  s$    j!OOA# "Hr9  weightbias
batch_sizenum_channelsflattened_inner_size
num_groupsc                 x  ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " UT-  S:H  U U4S j5        [        R                  " T R
                  5      n[        T U5      n	SS/n
[         R                  " U	UTUT-  U/5      n[        R                  " UR                  U
5      n
[         R                  " XSSS9u  p[         R                  " X-   5      nT R                  R                  S	:X  a  Ub  [         R                  " US
TUT-  S
/5      nX-  nU* U-  nUb#  [         R                  " US
TUT-  S
/5      nUU-   nUR                  5       R                  X4/US
/5      nUR                  5       R                  X4/US
/5      n[        [!        ST R                  5      5      n[#        UU5      n[#        UU5      nU	U-  U-   nOmX-
  U-  nUR%                  T R&                  5      nS/[        [!        ST R                  5      5      -   nUb  [#        UU5      nUU-  nUb  [#        UU5      nUU-   n[        UT R
                  5      n[        UT R
                  5      n[        UT R
                  5      n[         R(                  " X5      n[         R(                  " X5      nUX4$ )Nr1  c                  "   > ST R                    3$ )Nz=Expected at least 2 dimensions for input tensor but received r  r  s   r7  rP  #native_group_norm.<locals>.<lambda>  s    OPUPZPZ|\r9  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  r;  s   r7  rP  r>    s!    V#EKK=0B:,
OPr9  r  FTr-  rz  rR  )rd  re  r2  rp  r  r  r)   r   r  r   r   r6  r4  r   r   rM  rb  r5  r  rV  r   )r  r6  r7  r8  r9  r:  r;  r+  r  	input_accr3  input_reshapedr/  r   r0  weight_reshapedwrF  bias_reshapedr8  unsqueeze_wunsqueeze_br  unsqueeze_weightunsqueeze_biass   `     `                  r7  r   r   t  s    
LL

a\ 
LLz!Q&	P 33EKK@'/@AIVN]]	Z!;=QRN ,,^-@-@.QN~~UDJ ;;z'(D||E!f&8--Q
LJ$>B
 "EAI!MMq*lj&@!DM M!ALLN%%z&@<QRBSTLLN%%z&@<QRBSTeAuzz23)!^<)!^<+%3$,hhu{{#tE!UZZ$89926>J((C0~FN&C
!#u{{
3C"45D"45D ==.D==.Dr9  out2normalized_shapec                   ^ ^^^ [        T5      n[        R                  " US:  U4S j5        [        R                  " TS L =(       d    TR                  [	        T5      :H  UU4S j5        [        R                  " TS L =(       d    TR                  [	        T5      :H  UU4S j5        [        R                  " T R
                  U:  =(       a(    T R                  T R
                  U-
  S  [	        T5      :H  U U4S j5        [        T 5      m Tb  [        T5      mTb  [        T5      mT R
                  U-
  n[        [        UT R
                  5      5      n[        T Xt5      u  pn
Tc	  Tb  UT-   nOTb	  Tc  UT-  nOTb  Tb  UT-  T-   n[        UT R                  5      nT R                  R                  S;   a,  [        U	T R                  5      n	[        U
T R                  5      n
XU
4$ )NrR  c                      > S[        T 5      -   $ )NzzExpected normalized_shape to be at least 1-dimensional, i.e., containing at least one element, but got normalized_shape = )rt  )rJ  s   r7  rP  #native_layer_norm.<locals>.<lambda>  s     I

 r9  c                  R   > S[        TR                  5      -   S-   [        T 5      -   $ )NzQExpected weight to be of same shape as normalized_shape, but got weight of shape  and normalized_shape = rt  rV  )rJ  r6  s   r7  rP  rM    s3     
fll
 %% 
	 r9  c                  R   > S[        T R                  5      -   S-   [        T5      -   $ )NzMExpected bias to be of same shape as normalized_shape, but got bias of shape rO  rP  )r7  rJ  s   r7  rP  rM    s2     
djj/ %% 
	 r9  c                  p   > S[        T5      -   S-   [        T5      -   S-   [        T R                  5      -   $ )NzGiven normalized_shape=z, expected input with shape z, but got input of size rP  )r  rJ  s   r7  rP  rM    sI    )

 
() 
  %	%
 ekk
r9  )rz  mtia)rU  rd  re  rV  r^  r2  r   rM  rb  r1  r)   r  r6  r4  )r  rJ  r6  r7  r+  normalized_ndimaxisr3  r  r   r0  s   ````       r7  r   r     s    *+O	LL1	  
LL$A&,,%0@*AA	  
LL=

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

o% 	UKKo589UCS=TT		 uEF#$::'D%ejj12N <OCt~$*Dj		Fl		 0FlT!
!#u{{
3C||O+&tU[[9&tU[[9tr9  c                     [        U6 $ rF  )r   )	fake_modefuncrx  r  s       r7  native_layer_norm_fakerY    s    d##r9  c                     [         R                  " U R                  [         R                  " U5      5      n[        R
                  " X5      $ rF  )rp  r  r2  extract_dims_from_varargsr  r   )r  rB  _permutations      r7  r   r   	  s7    **	//5L ??1++r9  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       $ )Nc                      g)Nzrenorm: p must be real-valuedrN  rN  r9  r7  rP  renorm.<locals>.<lambda>  s    5Tr9  r   c                      g)Nz'renorm: non-positive norm not supportedrN  rN  r9  r7  rP  r`    s     Ir9  c                      g)Nz#renorm: maxnorm must be real-valuedrN  rN  r9  r7  rP  r`    s    2Wr9  c                     > ST  3$ )Nz,renorm: expected maxnorm to be >= 0 but got rN  )r]  s   r7  rP  r`    s     LWIVr9  rR  c                     > ST  S3$ )Nz/renorm: input needs at least 2 dimensions, got  dimensionsrN  r  s   r7  rP  r`  !  s    A${Sr9  T)r  r  r  gHz>rr  )rd  re  r=  r  r2  rp  r  rM  rb  r  r  linalgvector_normr   r  r  r   )
r  r  r  r]  rc  acc_typer`   r+  norm_factorr2  s
      `     @r7  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++--r9  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U(       d(  U
(       a!  TT-
  S-  n[        R                  T UU/U5      m T R'                  STTS9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-   $ )NzAstft input and window must be on the same device but got self on  and window on r5  r  rm  s   r7  rP  stft.<locals>.<lambda>J  s'    OPUP\P\~^/0r9  z6stft only supports align_to_window for center = False.   zstft requires the return_complex parameter be given for real inputs, and will further require that return_complex=True in a future PyTorch release.c                      g)Nz:stft expected a tensor of floating point or complex valuesrN  rN  r9  r7  rP  rx  g  s    Lr9  rR  r1  c                      g)Nzstft expected a 1D or 2D tensorrN  rN  r9  r7  rP  rx  i  s    /Pr9  r   r  c                     > ST  ST 3$ )Nzstft expected 0 < n_fft <= z, but got n_fft=rN  )r
  rj  s   r7  rP  rx  y  s    -fX5EeWMr9  c                     > ST  3$ )Nz0stft expected hop_length > 0 but got hop_length=rN  )hop_length_s   r7  rP  rx  }  s    B;-Pr9  c                     > ST  3$ )Nz9stft expected 0 < win_length <= n_fft but got win_length=rN  )win_length_s   r7  rP  rx    s    KK=Yr9  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+  )r  rm  s   r7  rP  rx    s#    F{mSUV)&,,89r9  ri  rX  )	dimensionr;  steporthoc                      g)Nz9Cannot have onesided output if window or input is complexrN  rN  r9  r7  rP  rx        Or9  r  r`   )rd  re  r6  r-  rp  r  r  r  r2  r  	itertoolsr   rV  r  r  r  r;  r#  r   r  fftrfft
transpose_squeeze_view_as_real)r  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  return_complex_original_ndim
extra_dims
pad_amountextended_shapeleftinput_pad_amountcomplex_fftr`   r  r~  r
  r  s   ``  `                @@@r7  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o!K/A5!13C DhOLL2ELDE((5K#/x_H 7dDOO	
 iinnUn6iimmErm5NN1all1o!3>u'9'9#'>>r9  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-   $ NzBistft input and window must be on the same device but got self on rv  r5  rw  s   r7  rP  istft.<locals>.<lambda>  s(    PQVQ]Q]P^_/0r9  ry  c                  @   > ST R                    STR                    3-   $ r  r5  rw  s   r7  rP  r    s!    Pofmm_=>r9  rX  rR  r   c                      g)Nz"istft input tensor cannot be emptyrN  rN  r9  r7  rP  r    s    ,Pr9  r1  r  c                  "   > ST R                    3$ )Nz8istft expected a tensor with 2 or 3 dimensions, but got r  r  s   r7  rP  r    s    J5::,Wr9  c                      g)Nzistft expected the frequency dimension (3rd to the last) of the input tensor to match n_fft / 2 + 1 when onesided=True, but got {fft_size}rN  rN  r9  r7  rP  r    s    Rr9  c                      g)N)zistft expected the frequency dimension (3rd to the last) of the input tensor to match n_fft when onesided=False, but got {fft_size}rN  rN  r9  r7  rP  r    s     r9  c                      g)Nz+istft expected 0 < hop_length <= win_lengthrN  rN  r9  r7  rP  r    r3  r9  c                      g)Nz&istft expected 0 < win_length <= n_fftrN  rN  r9  r7  rP  r    s    *Rr9  c                      g)NzDInvalid window shape. window has to be 1D and length of `win_length`rN  rN  r9  r7  rP  r    s    Vr9  ri  r  c                      g)Nz9cannot have onesided output if window or input is complexrN  rN  r9  r7  rP  r  	  r  r9  r  c                      g)Nz:Complex windows are incompatible with return_complex=FalserN  rN  r9  r7  rP  r        Pr9  )r  r  r
  )r  r  r;  r  zThe length of signal is shorter than the length parameter. Result is being padded with zeros in the tail. Please check your center and hop_length settings)rd  re  r6  rp  r  r  r;  r  r2  rV  corresponding_real_dtyper#  r  r   r  r   r  ifftr   irfftr  unfold_backwardr   r   r`  r   warningswarn)r  rj  rk  rl  rm  rn  rp  rq  r
  rr  r~  r  n_framesfft_sizeexpected_output_signal_len	onesided_
real_dtypewindow_r  r  r`   y_tmpywindow_envelopr  ends   `   `                     r7  r0  r0    sy    
LL$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$I1MHr9  a_shapea_strider  r  c                   ^^^	^
 [        U 5      n[        R                  " XRSS9m	US:X  a  SOU T	   m
US:X  a  SOUT	   n[        R                  " TT
:*  U	U
U4S j5        [        R                  " TS:  U4S j5        [        U 5      n[        U5      nUR                  T5        UR                  U5        T	U:  a  UT	   T-
  T-  S-   UT	'   UT	==   T-  ss'   Xx4$ )NT)wrap_scalarr   rR  c                     > ST  ST ST 3$ )Nz%Maximum size for tensor at dimension z is z but size is rN  )r  max_sizer;  s   r7  rP  *_get_unfold_shape_stride.<locals>.<lambda>N  s    7uD
-X\W]^r9  c                     > ST  S3$ )NzStep is z but must be > 0rN  r  s   r7  rP  r  S  s    (4& 01r9  )rU  rp  r  rd  re  rM  r  )r  r  r  r;  r  a_ndimlast_striderV  stridesr  r  s      ``    @@r7  _get_unfold_shape_strider  D  s     \F

 
 
ECaKqWS\H{!K	LL^
 
LLq1
 ME8nG	LLNN;
V|Cj4'D014c
>r9  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      $ )
NFrU  c                      g)Nzbrepeat: Number of dimensions of repeat dims can not be smaller than number of dimensions of tensorrN  rN  r9  r7  rP  repeat.<locals>.<lambda>f  s    tr9  r   rR  c              3   .   #    U  H  u  pX-  v   M     g 7frF  rN  )rI  padded_sizerepeat_sizes      r7  rK  repeat.<locals>.<genexpr>q  s      (G$K 	!(Gs   r  T)keyreverse)rp  r_  rd  re  rU  rV  r   r2  r  r^  zipr  r  r6  r  r  make_contiguous_strides_forra  r  r`  rM  sortr  
itemgetterr   r   r   )r  repeat_shapenum_new_dimensionspadded_shapedim_sizetarget_shapeurtensor_shapeurtensor_strider  enumerated_stridepermute_order_sorted_striderepeat_xtensorcloned_resultpermuted_results                  r7  r   r   `  s    33L5QL	LLLS\)t
 <A{{1~\*QVV33++LGGH%   (+L(G L 	L{{''88//55a8
 	
 "N77EO"<0*BSC!<L+
' 1 Y78x2215tD$'):$;!M XXn-N KK/M $++M:O ""<00r9  
allow_copyc                   ^
^ SmU m
U GHK  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T
R                  T   :X  a  TS-   mMq  T
R                  T   nTnXS-  S:w  a!  US-  nUT
R                  U   -  nXS-  S:w  a  M!  UT:w  ax  [        R                  " T
TU5      u  pxUcN  U(       a  [        R
                  " X5      s  $ SU R                   SU R                  5        SU S3n	[        U	5      e[        T
TU5      m
XS:w  a  [        R                  " T
TU5      m
TS-   mGMN     TT
R                   :  aJ  [        R                  " T
R                  T   S:H  U
U4S j5        [        T
T5      m
TT
R                   :  a  MJ  T
U L a  [        R                  " U 5      $ T
$ )Nr   rR  z Cannot view a tensor with shape z and strides  as a tensor with shape ro  c                  .   > ST ST R                   T    3$ )Nza.size(z) expected to be 1 but got r+  )r  r\  s   r7  rP  /_reshape_view_helper_core_alg.<locals>.<lambda>  s    gcU"=bhhsm_Mr9  )r2  r  	split_dimrV  r  r   r7  rc  r   rd  re  r   rb  )r  rV  r  r
  last_dimaccumr  r  r  r  r  r\  s             @@r7  _reshape_view_helper_core_algr    s   ( C	
B"''>Q;;ww{H Xrxx/ABB'C RXXc]"'Cn!1HCRXXc]"E n! #: ',&A&A"c3&O#I  ==228	qxxzlZrsxryyz{ o%S#&B ?S&1BAgU Z -HHSMQM	
 R - 
Qw}}Q	r9  c                   [         R                  " USS9n[         R                  " X R                  5       5      nU R                  5       S:X  a   [	        X[         R
                  " U5      5      $ U R                  S:X  a;  U nU H  nUS:X  d   e[        US5      nM     X0L a  [        R                  " U 5      $ U$ [        U5      S:X  aE  U nU R                   H  nUS:X  d   e[        US5      nM     X0L a  [        R                  " U 5      $ U$ [        U 5      (       a  [        U5      S:X  a7  U R                  S:  a'  [        R                  " X R                  5       /S/5      $ [        U5      S:X  a5  U R                  S:X  a%  US   nUS   n[        R                  " XU/US/5      $ [        [         R"                  US5      n[        R$                  " U R                  5       U:H  SU R                   SU S	35        ['        XU5      $ )
NFrU  r   rR  rX  r1  z&Could not reshape a tensor with shape r  ro  )rp  r_  
infer_sizer  r   r  r2  r  r  rb  rU  rV  r   r   rd  r   r  r   re  r  )r  r  rV  _ar
  dim0dim1shape_numels           r7  _reshape_view_helperr    s   ,,UUCE UGGI.E 	wwyA~!E$E$Ee$LMM 	vv{FQ;;2r"B  7==##I 5zQggFQ;;RB  7==##IQu:?qvvz##A	{QC88u:?qvv{8D8D##Ad|dAY??ua0K	LL		[ 
0	9QRWQXXYZ ):>>r9  rV  c                      [        U /UQ7SS06$ )Nr  Tr  rY  s     r7  r   r   #  s    ;E;d;;r9  c                 @    U R                  UR                  5       5      $ rF  )r   r;  r  r  s     r7  r   r   (  s    <<

%%r9  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 dimensionsrR  z`shifts` requiredz*shifts and dimensions must align. shifts: z, dims: Nr5  )rp  r  r2  r=  r   r  r   r  rU  r)  rs  rd  r   r   r  rV  r  r6  rM   r   )r  r  rB  
len_shiftslen_dimstail_shifts	tail_dimsfirst_dim_rolledr  r;  r  r\  s               r7  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<==r9  r   rR  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`.r1  z2expected total rotation dims == 2, but got dims = z/expected total dims >= 2, but got total dims = r   rR  z7expected rotation dims to be different, but got dim0 = z and dim1 = ry  r  r  )
rU  rs  r2  rp  r  rd  r   r   r   r?  )r  r  rB  s      r7  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$q'47KKwwU%<%<w==r9  c                     U S   R                   n[        S[        U 5      5       H1  nX   R                   U:X  a  M   SU SX   R                    SU 35       e   g )Nr   rR  z4stack expects each tensor to be equal size, but got z at entry 0 and z
 at entry )rV  rb  rU  )r  entry_shaper-  s      r7  _check_stack_inputsr  }  si    !*""K1c'l#z;. 	
B;- P:##$Jqc3	
. $r9  c                    [        U 5      S:  d   S5       e[        R                  " U S   R                  S-   U5      nX S   R                  :  ae  [	        U 5        [        U S   R                  5      nUR                  U[        U 5      5        [        R                  " X5      nUR                  U5      $ [        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 TensorListrR  )rU  rp  r  r2  r  rM  rV  insertrd  r   r  r  )r  r  wrapped_dimresult_sizesr  r   s         r7  r   r     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      $ )Nr   Tr  )	r  rp  r  r)   r  rA   r   r   r   )r  r  r  r  r  r  a_expa_maxs           r7  ro   ro     sz     #AGGL33LA	 	6BwwyA~BRd+BJ"E3u489< r9  c                     [         R                  " [        U 5      S:  S 5        [        U 6 nUS   R                  S:X  a  [        US5      $ [        US5      $ )Nr   c                      g)Nz%hstack expects a non-empty TensorListrN  rN  r9  r7  rP  hstack.<locals>.<lambda>  r  r9  rR  )rd  re  rU  r   r2  r   r  s     r7  r   r     sQ    	LLW!#RS '*Oq!#?A&&""r9  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%vstack expects a non-empty TensorListrN  rN  r9  r7  rP  vstack.<locals>.<lambda>  r  r9  )rd  re  rU  r   r   r  s     r7  r  r    r  r9  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-emptyrN  rN  r9  r7  rP  unflatten.<locals>.<lambda>  s    *Nr9  rR  )	rp  r  r2  rd  re  rU  r  r^  rV  )r  r  r@  s      r7  r  r    so    

 
 
-C	LLUq"NO66%&u5aggcAgi>P8QQRRr9  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      $ )Nr   rC  c                      g)Nz5Dimension specified as 0 but tensor has no dimensionsrN  rN  r9  r7  rP  unbind.<locals>.<lambda>  s    Gr9  rN  c              3   R   >#    U  H  n[         R                  " UT5      v   M     g 7frF  )rd  r   )rI  sr  s     r7  rK  unbind.<locals>.<genexpr>  s#      
+SaEMM!S!!+Ss   $')r]  rD  rp  r  r2  rd  _check_indexrU  rV  r^  r   )r   r  rD  s    ` r7  r  r    s    J

 
 
-C	AGGqG AGGCLA-.. 
+0+=+=as+S
 
 	
r9  r  r  c                 \    U R                  [        R                  S9R                  XU5      $ r  )r   rd  r?  rL   )rJ  r  r  r  s       r7  rK   rK     s+    77!8!879EEF r9  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        U R                  S:X  a  U R                  S5      OU n[        S 5      4U-  T4-   nX4U'   U $ )NrR  c                  $   > ST R                    S3$ Nz(Index should have dimension 1 or 0 (got r%  r  r  s   r7  rP  index_copy_.<locals>.<lambda>      :5::,aHr9  r   )rp  r  r2  rd  re  r  slice)rJ  r  r  r  r  r\  s     `   r7  rL   rL     sq    

!
!!&&#
.C	LL

aH
 &&A+A1A;.3
%
)CcFHr9  c                     [        XX#SS9$ )NFinplace_index_fillrJ  r  r  r  s       r7  rN   rN     s    
 quU;;r9  c                     [        XX#SS9$ )NTr  r   r"  s       r7  rO   rO     s     quT::r9  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	$ )NrR  c                  $   > ST R                    S3$ r  r  r  s   r7  rP  _index_fill.<locals>.<lambda>  r  r9  r   c                  $   > ST R                    S3$ )Nz<Only supports 0-dimensional value tensor. Got a tensor with r  r  r  s   r7  rP  r&    s     !!&L:r9  )r  r  r6  )rd  re  r2  r=  r%   r&  r  r  r6  r  rM  rV  r  r   rS  rL   rK   r   r   r7  r  copy_)rJ  r  r  r  r  zero_dimr  rV  rK   r  new_outs     ``       r7  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
r9  c                \    U R                  [        R                  S9R                  UUUUS9$ )Nr  rX  )r   rd  r?  
index_add_)rJ  r  r  r  rY  s        r7  rJ   rJ   )  s:     77!8!879DD	 E  r9  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        TR                  S:X  a  TR                  S5      mU R                  S:X  a6  [        R                  " U 5      R                  STU R                  T5      5      $ [        S 5      4U-  T4-   nX   $ )NrR  c                  $   > ST R                    S3$ r  r  r  s   r7  rP  index_select.<locals>.<lambda>A  r  r9  r   )
rp  r  r2  rd  re  r  r  rK   r   r  )rJ  r  r  r\  s     ` r7  rM   rM   ;  s     
!
!!&&#
.C	LL

aH zzQ"vv{ "--aE8JKK;.3
%
)C6Mr9  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   rC  c              3   :   #    U  H  u  pUS :X  d  M  Uv   M     g7fr\  rN  )rI  r\  r;  s      r7  rK  squeeze.<locals>.<genexpr>S  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r\  r+  )rI  dr  rD  s     r7  rK  r2  _  s'     JDq$8q$IDs   !1	1rR  T)r  )r]  rD  r^  ra  rV  r  r   rb  r2  rp  r  r=  r   rU  rM  r4  )r  r  rB  r2  	dims_listr-  rD  s   `     @r7  r   r   N  s   J
{J)AGG*<JJ)-u}}Q%C5==3CC66D

!
!$
,CS))C6sDqy4yA~--}}Q JDJJD
4yA~}}Q
4yA~}}Q%%T
Iy$/IAqM Hr9  split_sizesc                   ^ ^^ [        [        T5      5       H  n[        R                  " TU   S 5        M      [        R                  " [
        [        R                  " T5      T R                  T   :H  UU U4S j5        / nT R                  5       nT He  n[        T R                  5      nXgT'   UR                  T R                  UT R                  5       U5      5        UT R                  5       T   U-  -   nMg     U$ )Nc                      g)NzCsplit_with_sizes expects split_sizes have only non-negative entriesrN  rN  r9  r7  rP  "split_with_sizes.<locals>.<lambda>t  s    Yr9  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   rV  )r  r  r6  s   r7  rP  r9  y  s,    (k)B(CCabfblblmpbqarsr9  )rb  rU  rd  _check_is_sizer(  rc  r<  r   rV  r=  rM  r  r   r7  )r  r6  r  r-  splitsr  
split_sizer  s   ```     r7  r   r   k  s     3{#$NY	
 %
 
[!TZZ_4s F  "F!
$	## 	dooiGH$++-,z99 " Mr9  indices_or_sectionsc                    [         R                  " U R                  U5      nU R                  S:X  a  Sn[        U5      e[	        U[
        5      (       al  UR                  R                  S:X  d  SUR                   3n[        U5      eUR                  [        R                  :w  a  SUR                   3n[        U5      e[	        U[        5      (       d%  [	        U[
        5      (       a  UR                  S:X  a  [	        U[        5      (       a  UOUR                  5       nUS::  a  SU 3n[        U5      eU R                  U   n[        R                   " Xe-  5      nXe-  n/ n	[#        U5       H   n
X:  a  US-   OUnU	R%                  U5        M"     ['        [(        R+                  X	US95      $ 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!rz  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 rR  r  zntensor_split: non-scalar indices_or_sections tensors must have only one dimension, but received a tensor with re  )rp  r  r2  rc  r=  r%   r6  r4  r  rd  longr   r   r   rV  r#  rG   rb  r  r^  r  r   tolistrM  rU  )r  r>  r  _dimr  sectionsr  min_split_sizenum_splits_one_extrar6  	split_idxr=  indicesr-  s                 r7  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      $ )NrR  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.hsplit requires a tensor with at least 1 dimension, but got a tensor with  dimensions!rt  r2  r  s   r7  rP  hsplit.<locals>.<lambda>      ^!&&kr9  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 ro  rP  )r  r  r=  s   r7  rP  rM    sS    Bc(45 aggcl#$ 9	9
 j/" r9  c                      > S[        T 5       3$ )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 r3  r>  s   r7  rP  rM         !4568r9  
rd  re  r2  r=  r   rV  r   _check_typerM  r^  )r  r>  r6  r  r=  s   `` @@r7  r   r     s     
LL	!	
 vv{!C%w//(
1_?
!:a!?	
 Az3//	&u6	
 &K;,,r9  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      $ [         R                  " [        T[        [        45      U4S j5        Tn[        T US5      $ )Nr1  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.vsplit requires a tensor with at least 2 dimension, but got a tensor with rK  rL  r  s   r7  rP  vsplit.<locals>.<lambda>  rN  r9  r   c                  0   > ST R                   S    ST S3$ )NzQtorch.vsplit attempted to split along dimension 0, but the size of the dimension r   rP  ro  r+  )r  r=  s   r7  rP  rX    s%    3771:,6,r9  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 r3  rR  s   r7  rP  rX    rS  r9  rT  )r  r>  r6  r=  s   `` @r7  r
  r
    s     
LL	!	
 %w//(
1_=j!8A!=
	
 Az1--	&u6	
 &K;**r9  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)rR  r1  c                     > ST  S3$ )Nz'diag(): Supports 1D or 2D tensors. Got DrN  r  s   r7  rP  diag.<locals>.<lambda>,  s    "I$q Qr9  rR  )r  rd  re  r   r   )r  r  r2  s     @r7  r   r   $  sQ     88:D	LLQ qy--""400r9  r  dim2c                    ^^ [         R                  " U 5      nUR                  X#U5      m[        R                  " TR
                  TR
                  :H  UU4S j5        [        TT5        U$ )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   r7  rP  "diagonal_scatter.<locals>.<lambda>A  s"     yyk24::,@r9  )rp  clone_preserve_stridesr   rd  re  rV  r   )r  r  r  r  r_  r  r   s    `    @r7  r   r   4  sX     
&
&u
-C<<d+D	LL

cii	@
 D#Jr9  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$ s  snnf s  snnf )z,
Reference implementation of torch.diagonal
)r\  rankc                     > ST  ST 3$ Nz(diagonal dimensions cannot be identical r$  rN  r  r_  s   r7  rP  diagonal.<locals>.<lambda>W       HbQUPVWr9  r   )r;  r7  r=  )r  rp  r  rd  re  r=  r`  r  r;  r7  ra  r  r   )r  r  r  r_  num_dimsr=  	diag_sizer-  r  r@  r  r  s     ``        r7  r   r   H  s    xxzH!!d:D!!d:D	LLW ((*N{DIIK-tyy{4/@6/IJAN	DIIK-6		D8IJAN	1}Q;t{{}T':::Nt{{}T':::N$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       $ s  snf )
z.
Reference implementation of torch.diag_embed
rR  )re  r\  c                     > ST  ST 3$ rg  rN  rh  s   r7  rP  diag_embed.<locals>.<lambda>  rj  r9  rX  r   Fr  r6  r  r@  r6  r  )r2  rp  r  rd  re  r;  rM  rV  r<  r/   r(  r  r6  r   r  r   r  rQ  rb  rU  r   mask_tensorr   )r   r  r  r_  re  r  t_shapezpaira_rangeb_rangecondr-  
cond_shapes     ``          r7  r   r   r  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
rR  rX  c              3   >   #    U  H  oR                   S    v   M     g7fr\  r+  )rI  r  s     r7  rK  '_block_diag_iterable.<locals>.<genexpr>  s     BzVazs   r   r1  c                  2   > ST  STR                  5        S3$ )Nz5Input tensors must have 2 or fewer dimensions. Input z has re  r@  )r-  r  s   r7  rP  &_block_diag_iterable.<locals>.<lambda>  s      CuVZZ\N+7r9  c                  0   > ST  ST STR                    S3$ )NzCInput tensors must all be on the same device. Input 0 is on device z and input z is on device rn  r5  )r6  r-  r  s   r7  rP  r~    s&     $$*8;qcVWYr9  rq  r@  )r  r  r<  r   r6  ra  rd  re  rV  r(  r  r   )r  r  
tensors_2dncolsr  	col_startrowcolr  rightr6  r-  s    `        @@r7  _block_diag_iterabler    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      $ )z
This is used as an input to PythonRefInfo. `torch.block_diag`
expects arguments splatted, but `aten.block_diag` expects only
one argument that is a list of Tensors.
)r  r  s    r7  r   r     s      ((r9  rD  c                    U R                   S:  a  [        SU R                    S35      e[        U[        5      (       a>  US:X  d  U R                  S   U-  S:w  a"  [        SSU R                  S    SU S	3-   5      e[        XS5      $ )
Nr  zPtorch.dsplit requires a tensor with at least 3 dimension, but got a tensor with rK  r   r1  z3torch.dsplit attempted to split along dimension 2, zbut the size of the dimension rP  ro  )r2  rs  r=  r   rV  r   )r  rD  s     r7  r   r     s    vvz^_`_e_e^ffrs
 	
 (G$$(a-1771:;PTU;UA.qwwqzl:^_g^hhijk
 	
 Q''r9  c                     U R                   S:  a  [        SU R                    S35      e[        R                  " U SU R                   S:  a  S5      $ S5      $ )Nr1  z7t() expects a tensor with <= 2 dimensions, but self is r]  r   rR  )r2  rs  rd  r   r  s    r7  r   r     sS     	vvzEaffXQO
 	
 ??1aaffqj88a88r9  c                 l    [         R                  " U R                  S;   S 5        U R                  5       $ )N)r   r1  c                      g)NzcThe use of `x.T` on tensors of dimension other than 0 or 2 to reverse their shape is not supported.rN  rN  r9  r7  rP  T.<locals>.<lambda>   s    7r9  )rd  re  r2  r   r  s    r7  r   r     s,    	LL	&	
 335Lr9  c                 .    [         R                  " U 5      $ rF  )r  rb  r  s    r7  r   r     r  r9  r  c                 ,   [         R                  " U R                  X45      u  p4U R                  S::  d  X:X  a  [        R                  R                  U 5      $ [        [        SU R                  5      5      nXEU'   X5U'   [        R                  " X5      $ )NrR  r   )
rp  r  r2  r  r   defaultrM  rb  rd  r   )r  r  r  _dim0_dim1r\  s         r7  r   r     st    **166D<@LEvv{dlzz!!!$$a()L==))r9  c                 t    [        U R                  U R                  5       XU5      u  pEU R                  XE5      $ rF  )r  rV  r7  r   )r  r  r;  r  rV  r  s         r7  r  r    s4     .

DKKM9DNE ??5**r9  c                 \    U R                  XU5      R                  [        R                  S9$ r  )r  r   rd  r?  )r  r  r;  r  s       r7  r  r  (  s0     ;;y-33-- 4  r9  c                   UR                   n[        R                  " Xc5      nUS:X  a  U " UR                  S5      SXES9$ 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  rR  r5  rX  )
r2  rp  r  r  rd  r  rV  r6  rb  r   )rX  initr  r  r  r  r2  rgr  r  masked_as              r7  _cumsumprod_commonr  0  s     66D

 
 
+CqyAKKN@@	C!GA	aggcl188	4B<<?b D4:>"~~b! #{{4D)H88r9  c          	      "    [        [        SXX#S9$ )Nr   rX  r  r  r  r  r  )r  r   r  r  r  r  s       r7  r   r   H  s     3Q!ESSr9  c          	      "    [        [        SXX#S9$ )NrR  r  )r  r   r  s       r7  r   r   S  s     4a1UTTr9  c                 x    U R                   S-   n[        R                  " X!5      n[        R                  " X4US9$ )NrR  r  )r2  rp  r  r  expand_dims)r  r  r2  s      r7  r  r  _  s6     66A:D

 
 
+CQT22r9  c                      [        U /UQ7SS06$ )Nr  Fr  rY  s     r7  r  r  l  s    <E<e<<r9  c                 @    U R                  UR                  5       5      $ rF  )r  r;  r  s     r7  r  r  r  s    99UZZ\""r9  c                     [        U S5      $ )N)rX  )r   r  s    r7  r   r   w  s    1er9  rH  c                   ^ ^ [         R                  " T R                  TR                  :H  U U4S j5        [         R                  " [        R                  " TR
                  5      U4S j5        Uc6  [         R                  " T R                  S5      STR                  S5      5      $ [        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  rH  s   r7  rP   take_along_dim.<locals>.<lambda>  s%    --.VVH4O||n35r9  c                  $   > ST R                    S3$ )Nz?torch.take_along_dim(): dtype of indices should be int but got z insteadr  )rH  s   r7  rP  r    s    M}}oX'r9  rX  r   )rd  re  r2  rp  r	  r  gatherr  rM  rV  r;  infer_size_shapesr   )r  rH  r  
self_sizesbroadcast_shapeindices_broadcastindices_sizesself_broadcasts   ``      r7  r   r   }  s    
LL	',,	
 
LLw}}-	
 {||AFF2J7<<+;<<!'']
!,,s+
11*gllnM(/BW]]+VVC[11-J%a9||N1BCCr9  r  r  r6  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$ )Nc                      g)Nz8torch.empty: the Preserve memory format is not supportedrN  rN  r9  r7  rP  empty.<locals>.<lambda>  s    Jr9  c                     > ST  S3$ )Nz/torch.empty: received an unknown memory format ro  rN  r  s   r7  rP  r    s    Em_TUVr9  r  r  r6  r  r  )rd  re  r  rp  r_  r?  r  channels_last_3d!make_channels_last_3d_strides_forchannels_last!make_channels_last_2d_strides_forr  )r  r  r6  r  r  r  rV  r  s        `  r7  r  r    s     
LL...J
 ,,U3E///33E:	%00	099%@U000V	
 99%@# r9  c                 2    [         R                  " U UUUUS9$ )Nrp  )r  r  )rV  physical_layoutr  r  r6  r  r  s          r7  r  r    s&     # r9  r  r  r6  r  c                    Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UUUUUS9$ )Nr  r6  r  r  )r  r  r6  rd  r  )r  r;  r  r  r6  r  s         r7  r  r    sQ     }AGG%EQXXVFQXXVF;; r9  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$ )z<
Reference implementation of torch.Tensor.new_empty_strided
r  )r  r  r6  rd  r  )r  r;  r7  r  r  r6  r  s          r7  r  r    sV      }AGG%EQXXVFQXXVF r9  r  c           
          [         R                  " U5      nU c  [        R                  " 5       n [        R                  " UU [        R
                  :X  a  SOSU UUUUS9$ NFr   r  rp  r_  rd  r  r  r  r  r  r6  r  r  r;  s         r7  r(  r(    sZ     ++D1D}'')::%**$!# r9  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  r6  rd  r  r  r  r;  r  r  r6  r  r  s          r7  r"  r"  ,  sm     }AGG%EQXXVFQXXVF::"177uzz1q# r9  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$ NTrR  r  r  r  s         r7  r#  r#  G  sZ     ++D1D}'')::## r9  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  s          r7  r!  r!  a  sm     }AGG%EQXXVFQXXVF::!!''ejj0a# r9  
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$ )Nr  )r  r  r6  rd  r  )r  r;  r  r  r  r6  r  s          r7  r   r   |  sT     }AGG%EQXXVFQXXVF:: r9  c                     U$ rF  rN  )r;  r  r  s      r7  	empty_outr    s	     Jr9  )r  r6  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$ )Nr  r  )
r  r  r6  rd  r  r  rV  rp  3compute_elementwise_output_logical_to_physical_permr  )r  r  r6  r  r  r  r  logical_to_physical_perms           r7  r  r    s     }AGG%EQXXVFQXXVF---{{GG'!'
 	
 	AA!D  	 # r9  r  c          	         ^ ^^ [         R                  " U5        [         R                  " U5        [        R                  " [         R
                  " U5      5      n[        T [        5      (       a   e[        T[        5      (       a   e[        T[        5      (       a   eTc  T mSm [        R                  " TS:g  S 5        TS:  a  [        R                  " TT :  S 5        O!TS:  a  [        R                  " TT :*  S 5        S n[        R                  " U" T 5      =(       a    U" T5      UU 4S j5        [        R                  " U" T5      U4S j5        T TT4n	[        R                  " S U	 5       5      n
Uc,  U
(       a  [        R                  O[        R                  " 5       n[         R                  " U5      nU(       d  U
(       a!  [        T 5      n[        T5      n[        T5      nU[        R                  :X  d  U
(       a,  [        WS:  5      [        US:  5      -
  nWW-
  U-   U-
  U-  nO[         R"                  " TT -
  T-  5      nU(       a  [$        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$ )Nr   c                      g)Nzstep must be nonzerorN  rN  r9  r7  rP  arange.<locals>.<lambda>  s    $:r9  c                      gNz7upper bound and lower bound inconsistent with step signrN  rN  r9  r7  rP  r        Mr9  c                      gr  rN  rN  r9  r7  rP  r    r  r9  c                 f    [        U [        5      (       + =(       d    [        R                  " U 5      $ rF  )r=  r   r#  rP   rO  s    r7  	is_finitearange.<locals>.is_finite  s!    a!566J$--:JJr9  c                     > ST ST  3$ )Nzunsupported range: r  rN  )r  r  s   r7  rP  r    s    %eWD6r9  c                     > ST  3$ )Nzstep must be finite but got rN  r  s   r7  rP  r    s    .tf5r9  c              3   B   #    U  H  n[        U[        5      v   M     g 7frF  rG  rI  r  s     r7  rK  arange.<locals>.<genexpr>  s     IDS
3 8 8D   )r  r  r  r6  r  rR  FT)rp  check_layoutcheck_pin_memoryrd  r6  device_or_defaultr=  r  re  r<  r   rQ  r  r	  r   r  r#  r7   r  iotarA  get_acc_typer)   requires_grad_)r  r  r  r  r  r6  r  r  r  rx  integer_args
is_integerxstartxendxstepri   r
  r  r  r  s   ```                 r7  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$VU3Fd#Mr9  )r  r  r6  c                    X/n[        U[        5      (       a  U R                  SU5      nOUR                  U5        [        U[        5      (       d   eUR                  5       S:  n[        R                  " XBS-
  U5      n[        R                  " XAU 5      nXQU -
  -  U-   n[        R                  " [        U6 6 nUR                  5       U:w  a  [        R                  " Xx5      n[        X75      $ )NrN  rs  rR  )r=  r   r   r  rS  r/   rd  r   rp  "compute_elementwise_output_stridesry  r7  r  copy_stridedrA  )	r  r  r6  r  r  coeffbaser@  r7  s	            r7  rW   rW   /  s     \F&&!!F+fff%%%% ::<3DKKqj&1E;;t%(DEk"T)F557G7PQF}}& ##F3'77r9  )r  r6  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      $ )Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsrN  rN  r9  r7  rP  linspace.<locals>.<lambda>^  r  r9  c                      gr  rN  rN  r9  r7  rP  r  d  r  r9  c              3   B   #    U  H  n[        U[        5      v   M     g 7frF  r=  r  r  s     r7  rK  linspace.<locals>.<genexpr>h       L8KJsG,,8Kr  c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype rN  )default_complex_dtyper  s   r7  rP  r  q  s    56K5LLrsxryzr9  c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (r$  r%  )r4  r  )r  r  r  s   r7  rP  r  z  sB     u+r$s),,-RU0D0D/EQHr9  c                      g)Nz$number of steps must be non-negativerN  rN  r9  r7  rP  r  ~  s    %Kr9  )r  r6  r  r  r  rR  r  r1  )r  r   )r=  r&   rd  re  r  r)   rw  r<  r   rp  r?  r  r  r  rU  r   r  r  opsr  r  r  r  r  r	  rQ  r4  r"   rR  r   r   )r  r  r  r  r6  r  r  r  factory_kwargsempty_tensorr  	dtype_redr  r  cast_rgr  r  r  s   ````             @r7  r  r  N  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..r9  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 tensorsrN  rN  r9  r7  rP  logspace.<locals>.<lambda>      Tr9  c                      gr  rN  rN  r9  r7  rP  r    r  r9  c              3   B   #    U  H  n[        U[        5      v   M     g 7frF  r  r  s     r7  rK  logspace.<locals>.<genexpr>  r  r  r  )rd  r  r  rp  r	  r=  r   r   r&   re  r  r)   r<  r   r?  rw  r  r  r  r   )r  r  r  r  r  r6  r  r  r  r  _dtyperets               r7  r  r    so    }'') {{##E**eY''ENE~..LL		q T ,E9Ec9%%#,C^,,LL	QT *#5C||LU8KLLL % A A##%!
 &$((((ax!!
..#	C #599T#7??r9  indexingc                     g rF  rN  )r  r  s     r7  r   r         r9  c                     g rF  rN  )r  r  s     r7  r   r     r  r9  c                   ^ ^ [        US   [        [        45      (       a  [        U5      S:X  d   e[        US   5      n[        R
                  " [        R                  " S U 5       5      S 5        [        R
                  " [        U5      S:  S 5        [        [        U5      S-
  5       Ho  n[        R
                  " X   R                  XS-      R                  :H  S 5        [        R
                  " X   R                  XS-      R                  :H  S 5        Mq     SnT S	:X  a&  [        U5      S
:  nU(       a  US   US   /US
S  Q7nO[        R
                  " T S:H  U 4S j5        / nU Hw  m[        T[        5      (       d   e[        R
                  " TR                  S:H  =(       d    TR                  S:H  U4S j5        UR                  TR                  5       5        My     / n[        U5       He  u  nm[        T[        5      (       d   eTR                  S:X  a  TR!                  S5      mUR                  ["        R$                  " TXB45      5        Mg     U(       a  US   US   sUS'   US'   U$ )Nr   rR  c              3   B   #    U  H  n[        U[        5      v   M     g 7frF  r=  r%   r  s     r7  rK  meshgrid.<locals>.<genexpr>  s     @1Z:..r  c                      g)Nz)meshgrid expects its inputs to be tensorsrN  rN  r9  r7  rP  meshgrid.<locals>.<lambda>  r  r9  c                      g)Nz'meshgrid expects a non-empty TensorListrN  rN  r9  r7  rP  r     s    +Tr9  c                      g)Nz3meshgrid expects all tensors to have the same dtyperN  rN  r9  r7  rP  r    s    Ir9  c                      g)Nz4meshgrid expects all tensors to have the same devicerN  rN  r9  r7  rP  r  	  s    Jr9  Fxyr1  ijc                     > ST  3$ )NzDtorch.meshgrid: indexing must be one of "xy" or "ij", but received: rN  )r  s   r7  rP  r    s    !!)
,r9  c                     > ST  3$ )NzEtorch.meshgrid: Expected 0D or 1D tensor in the tensor list but got: rN  )r   s   r7  rP  r    s    [\][^_r9  r  )r=  rM  r^  rU  rd  re  r<  r   rb  r  r6  r%   r2  r  r  ra  r  r  r5  )r  r  r-  swap_first_and_second_tensorsresult_shapegridsr   s   `     @r7  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%(Lr9  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)rM  )r   r  s   r7  rP  movedim.<locals>.<lambda>C  s)    V~ ''+K'8&9Ar9  )re  rH  c                  "   > S[        T 5       S3$ )Nz#movedim: repeated dim in `source` (r%  r#  )r  s   r7  rP  r$  T  s    5d6l^1Er9  c                  "   > S[        T 5       S3$ )Nz(movedim: repeated dim in `destination` (r%  r#  )r   s   r7  rP  r$  X  s    :4;L:MQOr9  r   rR  )r4  r  rd  re  rU  r2  r^  rp  r  setdictr  rb  r#  r  r   )r  r  r   re  ssdssssdssr  rB  sidir  r  s    ``           r7  r   r   2  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Mr9  )r  r6  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$ )Nrz  rp  )	rp  r  r  r_  rd  r  r6  r  r  )rV  r  r  r6  r  r  r  s          r7  r  r  q  sz     
v	:&,,U3E).E##%EE$*NU\\% F# r9  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$ )Nz%n must be greater or equal to 0, got rN  )r0  s   r7  rP  eye.<locals>.<lambda>      #H!Lr9  c                     > ST  3$ )Nz%m must be greater or equal to 0, got rN  )r  s   r7  rP  r3    r4  r9  Frp  rX  r  r  )rd  re  r  rQ  r  r  r#  r   )r0  r  r  r  r6  r  r  range_nrange_mrx  ones   ``         r7  r  r    s     	y	LLaLM	LLaLMll1EKKeTGll1EKKeTGR G+D

jj!
 {{4a((r9  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      $ )Nrz  r  )	rp  r  r  type_to_dtyper4  rd  r6  r  rE   )rV  r  r  r  r6  r  r  es           r7  r  r    s~     
v	:&&EE,?,?Z@P,QE)Vu||E/BF#	A ::a$$r9  r  r  r6  r  r  r  c          
      L    [         R                  " U UUUUUUS9n[        X5      $ )Nr<  )rd  r  rE   )	r  r  r  r  r6  r  r  r  r;  s	            r7  r  r    s6     		##	A r9  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NFr   r<  rd  r  r  r  r  r  r  r6  r  r  r  s          r7  r)  r)    sC     ??	"177uzz1q##	 	r9  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NTrR  r<  r?  r@  s          r7  r$  r$    sC     ??	!!''ejj0a##	 	r9  c           	          [         R                  " U5        [         R                  " U5      n[         R                  " U 5      n [         R                  " U5      n[
        R                  " USSU UUS9$ )Nr  rr  )r   r   r  r6  r  )rp  r  r_  dtype_or_defaultr  r  ra   )r  r6  r  r  r  rV  r  s          r7  r%  r%    se     
:&--e4F""5)E$$V,F<<# r9  c                   [         R                  " U5        [         R                  " U5        Ub  UO[         R                  " [	        U 5      5      nUb  UO[
        R                  " S5      n[        R                  " XUS9$ )Nrz  ri  )	rp  r  r  r:  r4  rd  r6  r  r&  )r  r  r  r6  r  s        r7  r&  r&  7  sc     
v	:&&EE,?,?Q,HE)Vu||E/BFqf==r9  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$ )N)rE  rF  r  r6  )
rp  r  r=  r   r   rd  r  canonicalize_devicer  _uniform_helper)rV  rE  rF  r  r6  s        r7  rI  rI  K  s     
c6""""dF####
C.CT?DeU[[))))&&v.F  dPVWWr9  r  c                 *  ^^ [         R                  " U R                  5      m[        U[        5      (       a  [        U5      nOUR                  m[        R                  " TS:H  U4S j5        U R                  R
                  SSS[        R                  R                  5       S4;   =(       a    UR                  R
                  S:H  n[        R                  " U=(       d    UR                  U R                  :H  S 5        [         R                  " UR                  5      nU[        L a0  [        R                  " [         R                  " UT5      U4S	 j5        [        X R                  5      n[        R                  " XU 5      nUR!                  5       $ )
Nr   c                     > ST  S3$ )Nz@only supports a 0-dimensional value tensor, but got tensor with z
 dimensionrN  )
value_ndims   r7  rP  masked_fill.<locals>.<lambda>l  s    VWaVbblmr9  cudaxpumpsr2  rz  c                      g)Nz,Expected `value` to be on same device as `a`rN  rN  r9  r7  rP  rM  v  s    Br9  c                     > ST  S3$ )Nzcould not convert to type z without overflowrN  )r  s   r7  rP  rM    s    0=NOr9  )rp  r   r  r=  r   r4  r2  rd  re  r6  _C_get_privateuse1_backend_namer  r   r)   r   r   )r  r  r  
value_typeis_cpu_scalarr  r  rL  s         @@r7  r   r   `  s.    %%agg.K%  %[
 ZZ
!Om	
 HHMMuehh&L&L&NPUVW +!!U* 	
 	5U\\QXX5B	
 ((5
W
 	''
K@O	
 $E773ED#A <<>r9  c                 V    [         R                  " XU5      nU R                  U5        U $ rF  )rd  r   r(  )r  r  r  rF  s       r7  r   r     s&     	!5)AGGAJHr9  c                     [        SXX#S9  [        [        R                  " [        R                  " XX#US95      R                  5       5      $ )z,
Reference implementation of torch.allclose
ztorch.allcloser  )r  r  r  )r  r  rd  r   r   r   )r  rF  r  r  r  s        r7  r*  r*    s@     +qDL		%--4iPQVVX r9  c                 R   [         R                  " XSS9  [         R                  " X5        U R                  UR                  :w  a  g[	        U R
                  UR
                  5       H  u  p#X#:w  d  M    g   U R                  5       S:X  a  g[        [        [        X5      5      5      $ )NFr  r   T)
rp  r  check_same_dtyper2  r  rV  r  r   r   r   )r  rF  rJ  r  s       r7  r+  r+    s}    	A5A	1  	vvAGGQWW%6 &
 	wwyA~BqHr9  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fror1  r  )r=  r   rU  rt  r^  rb  r2  rd  rf  matrix_normrg  )r  r  r  r  r  s        r7  r`   r`     s     	
U
z#s';';s3x1}	
#se!S ;ejj)*C||''#e'LL||''#e'LLr9  c                     [         R                  " U R                  S:H  S 5        [         R                  " [         R                  " U S5      5      $ )Nr1  c                      g)Nz6expected a matrix, but got tensor with dim {self.ndim}rN  rN  r9  r7  rP  trace.<locals>.<lambda>  s     Xr9  r   )rd  re  r2  r   r   r  s    r7  rt   rt     s:     
LL		QX 99UZZa())r9  c                 p   ^  S[         [        [        4   S[         [        [        4   S[        4U 4S jjnU$ )Nr  rF  r~  c                    > T" X5      $ rF  rN  )r  rF  base_ops     r7  rop_make_r_binary_op.<locals>.rop  s     q}r9  )r   r&   r    )rc  rd  s   ` r7  _make_r_binary_oprf    s=    +,+, 
 Jr9  r   c                 r   [         R                  " U R                  S:  S 5        U R                  SS  u  p#[         R                  " X0R
                  S9R                  S5      [         R                  " X R
                  S9R                  S5      -
  U:  n[        R                  " X@5      R                  5       $ )Nr1  c                      g)Nz2triu: input tensor must have at least 2 dimensionsrN  rN  r9  r7  rP  triu.<locals>.<lambda>      Qr9  r  r5  rX  
rd  re  r2  rV  r  r6  r  rp  rr  r   r  r   hrC  r  s        r7  r  r         
LL	!Q 7723<DAQxx(2226
,,q
*
4
4R
8	9	D T%0022r9  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       $ )Nr1  c                      g)Nz2tril: input tensor must have at least 2 dimensionsrN  rN  r9  r7  rP  tril.<locals>.<lambda>  rj  r9  r  r5  rX  rk  rl  s        r7  r  r     rn  r9  r  r  c                    U S:X  d  US:X  a  gUS:  a  [        USU-   5      O[        X-   S:  5      n[        S[        XU-   5      5      n[        S[        X U-   5      5      nXC-
  S-   nX4-   U-  S-  nXV-
  n[        SX-  5      n	XyU4$ )Nr   r   r   r   rR  r1  )r  r  r`  )
r  r  r  m_first_row
m_last_row	n_row_alln_row_trapezoidtrapezoid_sizediff_rowrectangle_sizes
             r7  _get_tril_sizesr{    s    
ax3!8*01*#c1v:&#clQ>N:OKQCv./JAs3f-.I .2O "./AQFN*HHN+N;66r9  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$ )Nzrow must be non-negative, got rN  )r  s   r7  rP  _trilu_checks.<locals>.<lambda>0      %CC5#Ir9  c                     > ST  3$ )Nzcol must be non-negative, got rN  )r  s   r7  rP  r~  1  r  r9  c                     > ST ST  S3$ )NrX  z" not implemented for ''rN  )r  r  s   r7  rP  r~  4  s    "TF25';r9  )rd  re  r  rQ  )r  r  r  r  r  r  s   ````  r7  _trilu_checksr  (  sO     
LLIJ	LLIJ	LL%++u{{++;r9  rz  c                l   [        SXX4U5        [        XU5      u  pxn	[        SU* 5      n
[        [        R
                  XEUS9nU" SU[        R                  S9nU	S-
  n[        R                  " U* [        R                  " X-  SU-  -   5      -   5      n[        R                  " USU	-  S-
  U-   U-  S-  -
  5      n[        X-   U5      n[        X5      nU" SXS9nUU-  X-
  S-   U
-   -   nUU-  n[        R                  " [        R                  " UU45      [        R                  " UU45      45      $ )Nr  r   r  r6  r  r  rs  r1  rR  )r  r{  r`  r   rd  r  rw  rG   rp   r)   r   r   )r  r  r  r  r  r6  r  rx  rz  rt  
row_offset	arange_kwxs1rF  	row_inds1	col_inds1xs2	row_inds2	col_inds2s                      r7  r  r  9  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 r9  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$ )Nr   rs  rR  )r`  r  r{  )
r  r  r  rt  rz  trapezoid_size_trilrectangle_size_trilr  	triu_sizerx  s
             r7  _get_triu_sizesr  d  s    
ax3!8*01*#a&#K CW-34N 3B#FUVJ2W/a	0FGI/N;66r9  c                v   [        SXX4U5        [        XU5      u  pxn	[        SU5      n
[        [        R
                  XEUS9nU" SXS9nX-  nX-  nU" SU[        R                  S9nSU	-
  n[        R                  " U* [        R                  " UU-  SU-  -
  5      -
  5      n[        R                  " USU	-  S-
  U-
  U-  S-  -
  5      n[        UU5      n[        UU5      nU(       a  UX-  -   nUU
-   n[        R                  " [        R                  " UU45      [        R                  " UU45      45      $ )	Nr  r   r  r  g      r1  rR  rs  )r  r  r`  r   rd  r  rw  rG   rp   r)   r   r   )r  r  r  r  r  r6  r  rx  rz  rt  
col_offsetr  r  r  r  r  rF  r  r  s                      r7  r  r  u  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 r9  )	out_int32r  
boundariesr  r  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      $ [         R                  " U R                  U R                  [         R                  S9nXe-   nXgU-
  S-  -   nTU   n	U(       a  X:  n
OX:  n
[         R                  " XUS-   5      nUS:  a  [         R                  " U [         R                  S9n[        [         R"                  " U5      5      n[%        U5       Hs  n[         R                  " X-  X5      nXg:  n[         R                  " XXv-
  S-  -   S5      nTU   n	U(       a  X:  n
OX:  n
[         R                  " U
) U-  US-   U5      nMu     UR'                  US9$ )NrR  c                  ,   > ST R                  5        S3$ )Nz2boundaries tensor must be 1 dimension but got dim(r%  r@  )r  s   r7  rP  bucketize.<locals>.<lambda>  s    DZ^^EUDVVWXr9  rX  r   rq  r1  r  )rd  re  r  r=  rS  r  r  rQ  rV  r)  r(  r6  r   r$  r  r  r#  r[   rb  r   )r  r  r  r  	out_dtypen_boundariesr  r  midmid_valcond_midcond_updatenitersr  s    `            r7  r,  r,    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$$r9  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   r7  rP  cauchy.<locals>.<lambda>       ::>**Gr9  r  c                     > ST  3$ )Nz-cauchy_ expects sigma > 0.0, but found sigma=rN  )sigmas   r7  rP  r    s    ?wGr9  rs  )rd  re  rp  r  r  r	  r  rr   r#  r$  	rand_like)r  medianr  	generators   ` ` r7  r  r    s     	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLG EEIIdgg1F1L&MNNNNr9  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   r7  rP  exponential.<locals>.<lambda>  r  r9  r  c                     > ST  3$ )Nz4exponential_ expects lambda > 0.0, but found lambda=rN  )rates   r7  rP  r    s    FtfMr9  r1  rr  rX  )rd  re  rp  r  r  r	  r  r  r
  r+  r   rY   )r  r  r  uniform_valepsilonr  log_uniforms   ``     r7  rC   rC     s     	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLs
M
 //$'K kk+++,0014GsW},I++i599[3IJK9{""r9  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   r7  rP  geometric.<locals>.<lambda>  s    0=r9  r   rR  c                     > ST  3$ )Nz0geometric_ expects p to be in (0, 1), but got p=rN  )r  s   r7  rP  r  #  s    B1#Fr9  )
rd  re  rp  r  r  r  rG   rZ   r  r#  )r  r  r  s   `` r7  rI   rI     s     	LL""4::.. 	3&&tzz22=
 
LL	A!a%F ;;u{{EOOD$9#9:TZZ^KLqPPr9  c                   ^ ^ Ub   e[         R                  " [        R                  " T R                  5      (       + =(       aQ    [        R
                  " T R                  5      (       + =(       a%    [        R                  " T R                  5      (       + U 4S j5        [         R                  " ST:  U4S j5        [         R                  " T[         R                  " T 5      -  U-   5      $ )Nc                  "   > ST R                    3$ )Nzlog_normal not implemented for r  r  s   r7  rP  log_normal.<locals>.<lambda>4  s    1$**>r9  r   c                     > ST  3$ )Nz-log_normal_ expects std > 0.0, but found std=rN  r   s   r7  rP  r  8  s    ?uEr9  )	rd  re  rp  r  r  r	  r  rA   
randn_liker  r   r   r  s   ` ` r7  r]   r]   (  s     	LL""4::.. 	3&&tzz22	3&&tzz22>	 
LL	CE 99S5++D11D899r9  )r   r   )r  r  r  r6  r  c          
        ^ Ub  U[         R                  :X  d   e[        T[        5      (       d  [         R                  " TS:  U4S j5        Uc  [        S U T4 5       5      n[         R                  " [        U5      S:  S 5        [         R                  " US L =(       a    US L S 5        [        S U 5       6 nUS   R                  nUS   R                  nO|[         R                  " [        U [        5      (       + =(       a    [        T[        5      (       + S 5        Uc  [         R                  " 5       OUnUc  [         R                  " S5      OUn[        R                  " US	S
UUSUS9n	TU	-  U -   $ )Nr   c                     > ST  3$ )Nz)normal expects std >= 0.0, but found std rN  r  s   r7  rP  normal.<locals>.<lambda>W  s     I#Or9  c              3   T   #    U  H  n[        U[        5      (       d  M  Uv   M      g 7frF  r  rl  s     r7  rK  normal.<locals>.<genexpr>[  s     L;a*Q
2K;s   (	(c                      g)NzFnormal expects that either mean or std is a tensor, or size is definedrN  rN  r9  r7  rP  r  ^  s    \r9  c                      g)Nz.Cannot pass layout, or pin_memory without sizerN  rN  r9  r7  rP  r  b  s    Dr9  c              3   8   #    U  H  oR                   v   M     g 7frF  r+  rl  s     r7  rK  r  e  s     "<Gq77GrW  c                      g)Nz>normal expects mean and std to be scalars when size is definedrN  rN  r9  r7  rP  r  k  s    Tr9  rz  r  rr  F)r   r   r  r6  r  r  )rd  stridedr=  r%   re  r^  rU  rh  r  r6  r  r  ra   )
r   r   r;  r  r  r  r6  r  r  normal_sampless
    `        r7  ra   ra   ?  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 $&&r9  )r  c                ,    [        XU R                  XS9$ )N)r  r  )ra   rV  r  s       r7  normal_r  |  s    $TZZTGGr9  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-rad2deg is not supported for complex tensors.rN  rN  r9  r7  rP  rad2deg.<locals>.<lambda>  r0  r9  gcܥL@rd  re  rp  r  r  )r  M_180_PIs     r7  re   re     s6    	LL""4::..? CH?r9  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-deg2rad is not supported for complex tensors.rN  rN  r9  r7  rP  deg2rad.<locals>.<lambda>  r0  r9  g9RFߑ?r  )r  M_PI_180s     r7  r<   r<     s6    	LL""4::..? EH?r9  c                 *    U S:g  R                  U5      $ r  )r   )r  r  s     r7  r;   r;     s     AI??3r9  c                 v  ^ ^ [         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        UU 4S jn[         R                  " T R	                  5       TR	                  5       :H  U5        g )NrR  c                  N   > STR                  5        ST R                  5        S3$ )Nz1D tensors expected, but got zD and z	D tensorsr@  r  r  s   r7  rP  _dot_check.<locals>.<lambda>  s!    /
|6%))+iXr9  c                  <   > STR                    ST R                    3$ )Nz:dot : expected both vectors to have same dtype, but found r  r  r  s   r7  rP  r    s    L::,eEKK=*r9  c            	         > STR                  5        ST R                  5        STR                  5        ST R                  5        S3	$ )Nz+inconsistent tensor size, expected tensor [z] and src [z.] to have thesame number of elements, but got r  z elements respectively)r  r  s   r7  numel_error_dot_check.<locals>.numel_error  sL    9$**,{SXS^S^S`Ra b004

~U5;;=/Qgi	
r9  )rd  re  r  r  r  )r  r  r  s   `` r7  
_dot_checkr    sx    	LL
a,EIIK1,X
 
LL

ekk!	*
 
LL.<r9  c                 0   ^  [        T 5      U 4S j5       nU$ )Nc                 *   > [        X5        T" X5      $ rF  )r  )r  r  r  s     r7  wrapper#_dot_check_wrapper.<locals>.wrapper  s    4$r9  )r	   )r  r  s   ` r7  _dot_check_wrapperr    s     
2Y  Nr9  r  c                    U R                  5       (       a  U R                  5       (       a{  UR                  5       (       aA  [        R                  " U R	                  5       UR	                  5       5      R	                  5       $ [        R
                  " U R	                  5       U5      $ UR                  5       (       a%  [        R
                  " UR	                  5       U 5      $ X-  R                  5       $ rF  )r-  is_conjrd  r   r   r   r   r  s     r7  r   r     s     <<>>}}yyejjl;@@BBzz$))+u55]]__::ejjlD11Lr9  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       $ rF  )r-  rd  r   r  r   r   r8   r   r  s     r7  r   r     s     ??yy%%||~~==??::ejjlDIIK8899TYY[%00	yyzz|,1133  5(--//r9  c                    [         R                  " U R                  U5      nS/U R                  -  nSXB'   US:  a  X0R                  U   -   n[        R
                  " U R                  U   U R                  S9R                  U5      U:H  n[        R                  " X5      R                  U R                  5      n[        R                  " XQU 5      $ )NrR  rX  r   r5  )rp  r  r2  rV  rd  r  r6  r  r  r   r   )rJ  r  r  r  
mask_shaper  s         r7  select_scatterr    s     
 
 
-CqvvJJOqy$<<QXX6;;JG5PD
//#
#
*
*177
3C;;t!$$r9  c                 V    [        U [        R                  [        R                  45      $ rF  )r=  rd  TypedStorageUntypedStorage)objs    r7  
_isStorager  c  s     cE..0D0DEFFr9  c                    Sn[        U 5      n/ n[        U [        [        45      (       a  [	        U 5      nU(       a  XQR
                  -  nUR                  U5        [	        U5      U:  a"  [        S[        U 5      R                   S35      eUS:X  a   U$  U S   nUn [        U [        [        45      (       a  M  U$ ! [         a#    [        S[        U 5      R                   S35      ef = f)N   ztoo many dimensions 'r  r   z.could not determine the shape of object type ')r  r=  rM  r^  rU  itemsizer  rc  r4  r  r  )seqscalar_typeMAX_DIMS
is_storager@  r
  handles          r7  _compute_sizesr  h  s    HCJE
S4-
(
(S+++FVu: 4T#Y5G5G4HJKKQ; L	VF
  S4-
(
(" L  	@cASAS@TTUV 	s   B= =-C*c                    [        U [        5      (       a  [        R                  " 5       $ [        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 'r  r   zCould not infer dtype of )r=  r   rd  r  r   r  rQ  r   r  r  cfloatdoublecdoublehalfchalfrs  rS  r  rt  	TypeErrorr4  r  rM  r^  rU  rb  _infer_scalar_typepromote_types)r  default_dtype
scalarTyper
  r-  cur_itemitem_scalarTypes          r7  r  r    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Hr9  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      $ s  snf )NrR  rz  T)r  r6  r  rN  r  r   )r=  rS  r  detachr   r  r   rd  r&  r  r   _recursive_build)r   r  r  r   s       r7  r  r    s     #v399;!#3zz|ZDINNrRR	C	 	  zz|ZDII	C	 	 ""399 C  	A [[M*:<MN Ns   (Dc                 B   [        U[        R                  5      (       an  [        R                  " U(       + S 5        UnU(       a  UR	                  5       nU(       a  UR
                  OUn	Ub  UOUR                  n
UR                  U
U	SUS9$ [        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$ )Nc                      g)Nz,Can't pin tensor constructed from a variablerN  rN  r9  r7  rP  )_internal_new_from_data.<locals>.<lambda>  s    $Rr9  F)r6  r  r	  r  __cuda_array_interface__r6  meta)r	  r  )r=  rd  rS  re  r  r  r6  r   hasattrNotImplementedr  r  r4  r  )optionsr  
device_optdatacopy_variables
copy_numpytype_inferencer  r   inferred_scalar_typer6  r  s               r7  _internal_new_from_datar    s    $%%NR	
 **,C,:syy)53::vv&	  
 	
 t/00 &1Zwx7HF7E-d3; $<<$$.!! ""6=6eRWX Mr9  )r  r6  r  r  c                $   [        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$ )NzTo copy construct from a tensor, it is recommended to use sourceTensor.detach().clone() or sourceTensor.detach().clone().requires_grad_(True), rather than torch.tensor(sourceTensor)r1  )
stacklevelr6  rz  T)r  r  r  r  )
r=  rd  rS  r  r  UserWarningr  r  detach_r  )r  r  r6  r  r  r  
new_tensors          r7  r  r  	  s    $%%l		
 d]N( 
5"(?(?(A%J !!-0r9  rF  )F)r  NN)gh㈵>g:0yE>Fr  )NN)NNNNNFF)FFN)NF)NNFr  )r   rX  )	NNNTreflectFNNN)NNNTFNNF)rN  )rR  r  )r   r   rR  )r   r  rX  )r   NrR  )r  )r  rr  )r\  NF)r   rR  Nr\  )rR  r1  N(  r<  r  r  r  r#  r  r  collections.abcr   r   enumr   	functoolsr   r   r   r	   typingr
   r   r   r   r   r   rd  torch._prims_primsr  torch._prims_common_prims_commonrp  torch.utils._pytree_pytreerA  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   torch._prims_common.wrappersr)   r*   r+   r,   r-   r.   r  rS  rS  DispatchKey_opsr  r  r8  rA  rh  ry  torch._decomprz  objectr  r  r  r  rr  r/   INT_TO_FLOATr0   r1   r3   r2   r4   r5   DEFAULTr6   r7   r-  r8   r9   r:   r=   r>   r?   r@   rA   rB   rD   	NO_OPMATHrE   rF   r'  rG   rH   r   ALWAYS_BOOLrP   rQ   rR   rS   rT   specialmultigammalnr_   rU   rV   rX   rY   rZ   r[   r\   r  r  r^   r   r  rb   r  rc   rd   r   rf   rg   r   rh   ri   rj   rk   rl   rm   rn   rp   BOOL_TO_LONGrq   rr   rs   ru   r  rW  rv   rw   rx   ry   rz   r{   r|   r   r   rt  r   r   r   r   r  r~  r   r   r   r  r^  r   r   r   r   r   r   r   r  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r}   r~   r   r   r  r  r   r   r  r  r  registerr6  r(  r  r  r  r  r!  r   r9  rI  r   r   r   dim_IntListIntList_outrM  r   r   r   r   rm  r   r   r   r   r   r   r   r  r   r   r   r   r   r   r  py_implCompositeImplicitAutogradMetar   r   r   r   r   r?  r   r   r   r   r   r   r   r   r   r   r1  r5  r   r   _subclasses
fake_implsregister_op_implrY  r   r.  r/  rn  r0  r  r   r  r  r   r   r   r   r  r   ro   r   r  r  r  rK   rL   rN   rO   r!  rJ   rM   r   rB  r   r   r   r
  r   r  r   r   r   r   r  r   r   r   r   r   r   r  r  r  r   r   r  r  r  r   r   r  r  r  r  r  r(  r"  r#  r!  r   r  r  r  
start_step	start_outrW   r  r  r   r   r  r  r  r  r)  r$  r%  r&  rI  r   r   r*  r+  r`   rt   rf  r   r   r   r  r  r{  r  r  rA  r  r  r,  r  rC   rI   r]   ra   r  re   r<   r;   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.specialrN  r9  r7  <module>r     sP          .  < < A A   # $ $ $      2 l\	 
hh""zz~~2%P 9= C8 1   D 2 ##44	 ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#J#JK  L  ##++	 (/n / )/ **+& &  ,& ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q ##B#O#OP Q #7AA	 N 	 : 	 . 	 	 
	 ^ J >  		"# #> #  ## ##++	 ##++!N !~ !	!N ~  ##//* *> *	* ##B#N#NO1^ 1 1 P1 ##//1 1> 1	1 ##//1 1> 1	1 ##B#N#NO^   P
 u}}11:> ##//0n 0 0	0 ##00$'' ##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vG# vG# vGn vG	  "vGt #, # # # >  ,,-?@PP $S	P2<PP  .Ph 8=7N7N77!&!4!477 #& #> # # $.f . . %.d F v ^ S s 5QTAT;U ,1~ 1# 1C 1 1$ 		"N "2 ~   #n  n  (-c>.A(BLOD").
666!"<> tCy ^  ..667DDVD 6
D 	D
 D D D 
D 666!"D 8DN ../VVV$AAA VA 6
	A
 
A 666!"A % 0AH ..t/E/E/M/MN$ O$ %,~ , , &, $#.#.,#.36#.AO#.#.  %#.N +??@ !% $##%)&*p?p?p? p? 	p?
 Vp? p? p? p? tnp? TNp? d^p? p? Ap?h 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MM*.MM`2?N 2? 2? 2?r<~ <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\\" ^$    '0 ==> 48
	 E//0 	 ? ( $('+%)).)>)>&& 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 

#* *> *  $* [)l+	 		"3N 3c 3. 3  #3 		"3N 3c 3. 3  #3(7 73 7 7c3m8L 7$
	 
 ;;	
 LL " ))* "
  ==""	"	" "
 ;;" LL" " " "  +"R7 73 7 7c3m8L 7" ))* &
  =="&	&	& &
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 7%7%7% 	7%
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