
    N j|                    ~k   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	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  S SKrS SKJr  S SKJr  S SKJs  J r!  S SKJ"r"J#r#J$r$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/J0r0J1r1J2r2J3r3J4r4J5r5J6r6J7r7J8r8J9r9J:r:J;r;J<r<  S SK=J>r>J?r?J@r@JArAJBrBJCrC  / S	QrD\R                  rE\R                  R                  rG\R                  R                  R                  rJS
 rKS rLS rMSS.S jrNS SKOJPrP  \Q" 5       rR\RSSS.S\4S jjrSS rTS rU\S" \,R                  SS9S 5       rW\S" \,R                  5      S 5       rY\S" \,R                  5      S 5       rZ\S" \,R                  5      S 5       r[\S" \,R                  5      S 5       r\\S" \,R                  5      S 5       r]\S" \,R                  5      S 5       r^\S" \,R                  5      S 5       r`\S" \,R                  SS9S  5       ra\P" \JR                  5      S!\:4S" j5       rb\P" \JR                  5      \C" 5       S!\:4S# j5       5       rc\S" \,R                  5      S$ 5       rd\S" \,R                  5      S% 5       re\S" \,R                  5      S& 5       rf\S" \,R                  5      S' 5       rg\S" \,R                  5      S( 5       rh\S" \,R                  5      S) 5       ri\S" \,R                  5      S* 5       rj\S" \,R                  5      S+ 5       rk\S" \,R                  5      S, 5       rl\C" 5       \A" S-\,R                  S.9S/\:S0\4S\:4S1 j5       5       rnS/\:S0\4S\:4S2 jro\P" \JR                  5      \C" 5       S!\:S\:4S3 j5       5       rp\S" \,R                  SS9S4 5       rq\S" \,R                  SS9S5\:S\:4S6 j5       rrS/\:S\:4S7 jrs\S" \,R                  SS89S/\:S\:4S9 j5       ru\S" \,R                  5      S/\:S\:4S: j5       rv\S" \,R                  SS9S/\:S\:4S; j5       rw\S" \,R                  SS9S/\:S\:4S< j5       rx\S" \,R                  5      S/\:S\:4S= j5       ry\T" \R                  R                  S>5      r|\S" \,R                  SS89S/\:S\:4S? j5       r}\S" \,R                  \JR                  S89S@ 5       r~\S" \,R                  5      SA 5       r\S" \,R                  5      SB 5       r\S" \,R                  5      SC 5       r\S" \,R                  5      SD 5       r\S" \,R                  5      SE 5       r\C" 5        GSS/\:SF\SG\\GR
                     S\:4SH jj5       r\P" \JGR                  5      \C" 5       \A" SI\,R                  S.9 GSSJ\:SF\*SK\S\:4SL jj5       5       5       r\P" \JGR                  5      \C" 5          GSS/\:SM\\4   SN\\4   SO\\4   S\:4
SP jj5       5       rS/\:4SQ jr\S" \,R                  \SR9SS 5       rS/\:S\:4ST jrS/\:S\:4SU jr\S" \,R                  5      SV 5       r\P" \JGR                  5      \C" 5       \A" S-\,R                  S.9S SW.S/\:SX\S\:4SY jj5       5       5       r\S" \,R                  5      SZ 5       r\S" \,R                  5      S/\:S\:4S[ j5       r\S" \,R                  SS9S\ 5       r\S" \,R                  SS9S] 5       r\S" \,R                  SS9S^ 5       r\S" \,R                  5      S_ 5       r\S" \,R                  5      S` 5       r\S" \,R                  5      Sa 5       r\S" \,R                  5      Sb 5       r\S" \,GR2                  SS89S/\:S\:4Sc j5       r\S" \,R                  5      Sd 5       r\S" \,R                  5      Se 5       r\S" \,R                  SS9Sf 5       rSJ\:S\:4Sg jr\RSSSSSS4S\4Sh jjr\P" \JGR@                  5      \C" 5       \A" Si\,R                  S.9SSj.S/\\:\44   Sk\\:\44   Sl\\4   4Sm jj5       5       5       r\" \,R                  SSSn9So 5       r\" \,R                  Sp9S/\:Sk\:S\:4Sq j5       r\" \,R                  Sp9S/\:Sk\:S\:4Sr j5       r\" \,R                  Sp9S/\:Sk\:S\:4Ss j5       r\" \,R                  Sp9S/\:Sk\:S\:4St j5       r\" \,R                  Sp9S/\:Sk\:S\:4Su j5       r\" \,R                  SSv9S/\\:\44   Sk\\:\44   4Sw j5       r\P" \JGRP                  5      \C" 5       SSx.S/\\:\44   Sk\\:\44   Sy\\   4Sz jj5       5       r\" \,R                  SSv9S/\:Sk\:S\:4S{ j5       r\" \,GR2                  Sp9S/\\:\44   Sk\\:\44   S\:4S| j5       r\C" 5       S/\\:\44   Sk\\:\44   S\E4S} j5       r\" \RX                  R                  SSS~9S/\\:\44   Sk\\:\44   4S j5       rS/\ESk\ES\E4S jrS/\ESk\ES\E4S jr\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\P" \JGRf                  5      \C" SS5      SJ\:S\\:\:4   4S j5       5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSv9S/\:Sk\:S\:4S j5       r\" \,R                  SSv9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S!\:S\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       rS\S/\:Sk\:S\S\SS4S jr   GSS/\:Sk\:S\S\S\S\:4S jjr\" \,R                  SSSn9S/\:Sk\:4S j5       r\" \,R                  SSv9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  Sp9S/\:Sk\:4S j5       r\S" \,R                  5      S/\:4S j5       r\" \,R                  Sp9S/\:Sk\:4S j5       r\" \,R                  Sp9S/\:Sk\:4S j5       r\" \,R                  SSv9S/\:Sk\:S\:4S j5       r\" \,R                  Sp9S/\:Sk\:S\:4S j5       r\" \,R                  Sp9S/\:Sk\:S\:4S j5       r\" \,R                  SS9S/\:Sk\:S\:4S j5       r\" \,R                  SSv9S/\:Sk\:S\:4S j5       r\" \,R                  SSSn9S/\:Sk\:S\:4S j5       r\" \,R                  Sp9S/\:Sk\:S\:4S j5       r\P" \JGR                  5      \C" 5        GSS/\\:\44   Sk\\:\44   Sl\44S jj5       5       r\P" \JGR                  5      \C" 5       \A" Si\,R                  S.9SSj.S/\\:\44   Sk\\:\44   Sl\44S jj5       5       5       r\" \,R                  SSSS9S/\:Sk\:S\:4S j5       r\P" \JGR                  5      \C" 5       \A" Si\,R                  S.9S/\\:\44   Sk\\:\44   4S j5       5       5       r\" \RX                  R                  SSS9S/\\:\44   Sk\\:\44   4S j5       r\P" \JGR                  5      \C" 5       \A" S\,R                  S.9SS.SJ\:S\:S\:S0\4S\:4
S jj5       5       5       r\P" \JGR                  5      \C" 5       \A" S\,R                  S.9SS.SJ\:S\:S\:S0\4S\:4
S jj5       5       5       r\P" \JGR                  5      \C" 5       \A" S\,R                  S.9  GSS/\:S\\;   S\\;   S\:4S jj5       5       5       r\P" \JGR                  5      \C" 5        GSSJ\:S\\;   S\:4S jj5       5       r\P" \JGR                  5      \C" 5        GSSJ\:S\\;   S\:4S jj5       5       r\P" \JGR                  GR                  5      \P" \JGR                  GR                  5      \P" \JGR                  GR                  5      \P" \JGR                  GR                  5      \P" \JGR                  GR                  5      \C" SS9\A" Si\,R                  S.9  GSS\ES/\\;   Sk\\;   4S jj5       5       5       5       5       5       5       r\P" \JGR                  5      \C" 5       \GR                  S.S/\:S\GR                  S\:4S jj5       5       rSS.S/\ESk\E4S jjr\P" \JGR                  5      S/\:S\44S j5       r       GSS/\:S\\'   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\ES\S\S\\GR                     S\\\4   4
S jj5       rS/\ES\4S jrS/\:S\:4S jrSSSSSSS.S/\:S\S\S\S\\*   S\SG\\GR
                     S\\E   S\6S\:4S jjrGSS jr\P" \JGR                  5      \C" 5         GSS/\:SF\\*   SK\S\:4S jj5       5       r\P" \JGR                  5      \C" 5         GSS/\:SF\\*   SK\S\:4S jj5       5       r\P" \JGR                  GR                  \JGR                  GR                  /5        GSSSS.S/\:SF\\\   \\\      4   SK\SG\\GR
                     S\\E   S\:4S jjj5       rS/\ES\E4S jr\P" \JGR                  5        GSSSS.S/\:SF\\\   \\\      4   SK\S\\E   S\:4
S jjj5       r\P" \JGR                  5        GSSS.S/\:SF\\*   SK\S\\E   S\:4
S jjj5       r\P" \JGR                  5        GSSS.S/\:SF\\*   SK\S\\E   S\:4
S jjj5       rGSS jr\P" \JGR                  5      \C" 5          GSSS.S/\:SF\\*   S\\   SK\S\\4   S\:4S jjj5       5       r\P" \JGR                  5      \C" 5          GSSS.S/\:SF\\\   \\\      4   S\\   SK\S\\4   S\:4S jjj5       5       r\P" \JGR                  5        GSSSS.S/\:SF\\*   SK\S\:4S jjj5       r\P" \JGR                  5      \C" SS5       GSSSSS.S/\:SF\\*   S\\   SK\S\\4   4
S jjj5       5       r\P" \JGR                   5      \C" SS5         GSSS.S/\:SF\\*   S\\   SK\S\\4   4
S jjj5       5       Gr \P" \JGR                  5      \C" 5       \A" S\,R                  S.9SSS.SJ\:S\:S\:S\4Sl\4S\:4S jj5       5       5       GrS\\:\
\:   4   S\:S\\:\\:S4   4   4S jGrS\SF\S\:S\:4S jGrS\\:\
\:   4   S\:S\\:\\:S4   4   4S jGrS\\:\
\:   4   S\:S\\:\\:S4   4   4S jGr GSS/\:S\7GS \8GS\\   S\:4
GS jjGr\P" \JGR                  5      \C" 5        GSS!\:GS\:S\7GS \8GS\\   S\:4GS jj5       5       GrS\74GS jGr\JGR                  GR                  GR                  \GGR                  5      \JGR                  GR                  GR                  \GGR                  5      S\\:   4GS j5       5       Gr	S/\:S\7S\:4GS jGr\P" \JGR                  5      \C" 5       \A" GS\,R                  S.9GSGS	\<SF\S\:4GS
 jj5       5       5       Gr\C" 5       GS	\<S\:4GS j5       GrS!\:S\:4GS jGr\P" \JGR$                  5      \C" 5        GSS!\:GS\\   S0\4S\:4GS jj5       5       Gr\GR&                  S.S/\ES\GR                  S\E4GS jjGr\C" 5       GS	\<S\:4GS j5       Gr\P" \JGR,                  5      SGS.S/\EGS\S\E4GS jj5       GrS/\ESk\ES\E4GS jGrGSS/\:GS\SF\S\\:S4   4GS jjGrGSS/\:GS\GS\S\:4GS jjGr\P" \JGR4                  5      \C" 5       S/\:S\)S\:4GS j5       5       GrS/\:S\:4GS jGrS/\:S\:4GS jGrS/\:SF\GS\\\:4   GS\S\:4
GS jGrS/\EGS \*GS!\S\\E\E\E4   4GS" jGrS5\:GS#\\   S\:4GS$ jGr\P" \JGR@                  GR                  5      S!\EGS%\\E   GS&\\E   GS'\GS(\GS)\GS*\GS!\S\\E\E\E4   4GS+ j5       Gr \P" \JGRB                  5      \C" SSGS,5      S!\EGS-\7GS%\\E   GS&\\E   GS!\S\\E\E\E4   4GS. j5       5       Gr!\GRD                  GRF                  GRI                  \JGRB                  GR                  5      GS/ 5       Gr%\P" \JGRL                  5      S/\:S\:4GS0 j5       Gr&\P" \JGRN                  5      \C" 5       S!\:GS1\5SF\GS2\5S\:4
GS3 j5       5       Gr'\JGRP                  GRR                  GR                  \GGR                  5               GSS!\EGS4\GS5\\   GS6\\   GS7\\E   GS8\GS9\GS:\GS;\\   GS<\\   GS=\\   S\E4GS> jj5       Gr(\JGRT                  GR                  GR                  \GGR                  5              GSS!\EGS4\GS5\\   GS6\\   GS7\\E   GS8\GS:\GS;\\   GS\\   S\E4GS? jj5       Gr*GS@\7GSA\8GSB\S\GSC\4
GSD jGr+\P" \JGRX                  5      \C" 5       S/\ES\E4GSE j5       5       Gr,S/\:GSF\S\:4GSG jGr-S/\:GSF\S\:4GSH jGr.S/\:GSI\7S\:4GSJ jGr/SJ\:S\:S\:4GSK jGr0\P" \JGRb                  5      \C" 5       GSS/\:GSL\*S\*S\:4GSM jj5       5       Gr1\P" \JGRd                  5      \C" 5        GSS/\:GSO\S\)S\:4GSP jj5       5       Gr2GS	\<SS4GSQ jGr3\P" \JGRh                  5      \C" 5       GSGS	\<SF\S\:4GSR jj5       5       Gr4\C" 5        GSS/\:SF\SG\\GR
                     S\:4GSS jj5       Gr5\C" 5       GS	\<S\:4GST j5       Gr6\C" 5       GS	\<S\:4GSU j5       Gr7S/\:SF\GSV\7S\:4GSW jGr8\P" \JGRr                  5      GSGSX\:SF\S\<4GSY jj5       Gr9\C" 5       S5\9SF\GSZ\9GS[\94GS\ j5       Gr:S5\9SF\GSZ\9GS[\94GS] jGr;\P" \JGRx                  5      \C" 5       S5\9SF\GSZ\9S0\\4\94   4GS^ j5       5       Gr<\P" \JGRz                  5      S5\9SF\GSZ\9S0\\4\94   4GS_ j5       Gr=S5\9SF\GSZ\9S0\\4\94   GS`\4
GSa jGr>\C" 5       SSj.S5\9SF\GSZ\9GS[\9Sl\44
GSb jj5       Gr?\P" \JGR                  5      \C" 5       S5\9SF\GSZ\94GSc j5       5       Gr@\P" \JGR                  GR                  5      GSS/\:SF\\*   S\:4GSd jj5       GrA\P" \JGR                  5       GSSJ\EGSe\\   SF\S\\E   4GSf jj5       GrC GSS/\:GSg\\E\*4   SF\S\\:S4   4GSh jjGrDS/\:GSg\*S\\:S4   4GSi jGrES/\:GSg\*S\\:S4   4GSj jGrF\P" \JGR                  GR                  5      \C" 5        GSSJ\:GSk\S\:4GSl jj5       5       GrG\P" \JGR                  5      \C" 5          GSS!\:GS\:GSk\GSm\GSn\S\:4GSo jj5       5       GrI\P" \JGR                  5         GSSJ\:GSk\GSm\GSn\S\:4
GSp jj5       GrJ\P" \JGR                  5      \C" 5          GSGSX\:GSk\GSm\GSn\S\:4
GSq jj5       5       GrK\P" \JGR                  5      \C" 5       GS	\\:   S\:4GSr j5       5       GrMGS	\\:   S\:4GSs jGrLS/\:GSt\*S\<4GSu jGrN\P" \JGR                  GR                  5      S/\:4GSv j5       GrOS/\:S\:4GSw jGrP\P" \JGR                  5      S/\:S\:4GSx j5       GrQ\P" \JGR                  5      S/\:GSy\GSm\S\:4GSz j5       GrRG\RGrS\P" \JGR                  5      SJ\:GSB\S\GSC\S\:4
GS{ j5       GrT\P" \JGR                  5      \C" 5       SJ\:GSB\S\GSC\4GS| j5       5       GrUSSS.S/\:SF\SG\\GR
                     S\\E   S\:4
GS} jjGrV\P" \JGR                  5      SSS.S/\:SF\SG\\GR
                     S\\E   S\:4
GS~ jj5       GrW\P" \JGR                  5      SSS.S/\:SF\SG\\GR
                     S\\E   S\:4
GS jj5       GrX\P" \JGR                  5      S/\:SF\S\:4GS j5       GrY\P" \JGR                  GR                  5      S/\:GSI\7\\7   -  S\:4GS j5       GrZSJ\:S\:S\:4GS jGr[S/\:S\:4GS jGr\\C" 5        GSS/\R                  GS\R                  SF\\   S\R                  4GS jj5       Gr]\C" 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\:4GS jj5       Gr_\C" 5       S\GR                  SSS4SG\\GR
                     S\GR                  S\\'   GS\S\S\:4GS jj5       Gr`\P" \JGR                  5      \C" 5       SSSSGS.S/\:S\7SG\\GR
                     S\\GR                     S\\'   S\S\:4GS jj5       5       Gra\P" \JGR                  5      \C" 5       SSSSGS.S/\:S\7GS \8SG\\GR
                     S\\GR                     S\\'   S\S\:4GS jj5       5       Grb\P" \JGR                  GR                  5      \C" 5       S\GR                  SSSGS.SG\\GR
                     S\GR                  S\\'   S\GS\S\:4GS jj5       5       Grc\P" \JGR                  5      \C" 5       SSSSSGS.S/\:S\7SG\\GR
                     S\\GR                     S\\'   S\GS\S\:4GS jj5       5       Grd\P" \JGR                  GR                  5      \C" 5       S\GR                  SSSGS.SG\\GR
                     S\GR                  S\\'   S\GS\S\:4GS jj5       5       Gre\P" \JGR                  5      \C" 5       SSSSSGS.S/\:S\7SG\\GR
                     S\\GR                     S\\'   S\GS\S\:4GS jj5       5       Grf\P" \JGR                  5      \C" 5       SSSSGS.S/\:S\7GS\4SG\\GR
                     S\\GR                     S\\'   S\S\:4GS jj5       5       Grg\JGR                  GR                  GR                  \GGR                  5       GSS\:S\:S\\GR                     S\:4GS jj5       Grh\P" \JGR                  5      \C" 5       SSSSS\GR                  GS.S/\:SG\\GR
                     S\\'   S\\GR                     S\GS\S\GR                  S\:4GS jj5       5       Gri\P" \JGR                  GR                  \JGR                  GR                  /5      \C" 5          GS S\GR                  SSSGS.GS\4GS\\4   GSC\4SG\\GR
                     S\GR                  S\\'   S\GS\S\:4GS jjj5       5       Grj\P" \JGR                  5      \C" 5       \A" GS\,R                  S.9GS\EGS\EGS%\\E\44   4GS j5       5       5       Grm\P" \JGR                  5      \C" 5       SS\GR                  SSGS.GS\\4\:4   GS\\4\:4   GS\4SG\\GR
                     S\\'   S\GR                  S\GS\S\:4GS jj5       5       Grn\P" \JGR                  5      \C" 5        GSSS\GR                  SSGS.GS\\4\:4   GS\\4\:4   GS\4GS\4SG\\GR
                     S\\'   S\GR                  S\GS\S\:4GS jjj5       5       Gro\GS	\
\:   GS\4GS j5       Grp\GS	\:GS\4GS j5       Grp\P" \JGR                  5      GS	\\:\\:   \\:   4   GS\S\\:   4GS j5       GrpS!\:GS\\\)4   GS\\\)4   S\:4GS jGrq\P" \JGR                  5      \C" 5       SS\GR                  SSGS.GSI\\7\\7   4   GS\8SG\\GR
                     S\\'   S\GR                  GS\S\S\:4GS jj5       5       GrrGS\S\GR
                  4GS jGrs\P" \JGR                  5      \C" 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\:4GS jjj5       5       Grt\P" \JGR                  GR                  \JGR                  GR                  /5      \C" 5       S\GR                  SSSGS.GSI\7GS\4SG\\GR
                     S\GR                  S\\'   S\GS\S\:4GS jj5       5       GruSSSSS\GR                  GS.S/\:GS\4SG\\GR
                     S\\GR                     S\\'   S\GS\S\GR                  S\:4GS jjGrv\P" \JGR                  5      \C" 5       SSSSS\GR                  GS.S/\:SG\\GR
                     S\\GR                     S\\'   S\GS\S\GR                  S\:4GS jj5       5       Grw\P" \JGR                  5      \C" 5       SSSSS\GR                  GS.S/\:SG\\GR
                     S\\GR                     S\\'   S\GS\S\GR                  S\:4GS jj5       5       Grx\P" \JGR                  GR                  5      \C" 5       SSSSSGS.SG\\GR
                     S\\'   S\\GR                     GS\S\S\:4GS jj5       5       GryS\GR                  SSGS.S/\4SG\\GR
                     S\GR                  S\\'   S\S\:4GS jjGrz  GSGSI\7GS\\\\4   GS\\\\4   GS \7SG\GR
                  S\'S\:4GS jjGr{\P" \JGR                  5      \C" 5       S/\:GS\:S0\;4GS j5       5       Gr|\P" \JGR                  5      S/\:GS\:S0\;S\:4GS j5       Gr}   GSS/\:Sk\:S\S\S\S\4GS jjGr~S/\:Sk\:S\4GS jGr\P" \JGR                   5      \C" SS9   GSSGS.S!\:GS1\\\\4      SF\\*   SK\SG\\GR
                     S\:4GS jjj5       5       Gr\P" \JGR                  5      \C" 5       SJ\:S\:4GS j5       5       GrGS GrG\" \5      GrG\" \5      GrG\" \5      Gr\P" \JGR                  5      \C" 5       GSS/\:GS\S\:4GS jj5       5       Gr\P" \JGR                  5      \C" 5       GSS/\:GS\S\:4GS jj5       5       GrGS\GS\GSk\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\P" \JGR                  5      \C" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSk\SG\GR
                  S\GR                  S\'S\S\:4GS jjj5       5       GrGS\GS\GSk\S\\\\4   4GS jGr\P" \JGR                  5      \C" 5        GS\GR                  \GR                  GSSGS.GS\GS\GSk\SG\GR
                  S\GR                  S\'S\S\:4GS jjj5       5       Gr\P" \JGR                  5      \C" SS9SSGS.S/\;GS\:GS\GS\4GS jj5       5       Gr\P" \JGR                  5      \C" 5       \A" SI\,R                  S.9GSGS j5       5       5       Gr\P" \JGR                   5      \C" 5       \A" SI\,R                  S.9GSGS j5       5       5       Gr\P" \JGR"                  5      \C" 5       \A" SI\,R                  S.9GSGS j5       5       5       Gr\P" \JGR$                  5      \C" 5       \A" SI\,R                  S.9GSGS j5       5       5       Gr\P" \JGR&                  5      \C" 5       \A" GS\,R                  S.9   GSSSSSSGS.GS jj5       5       5       Gr\P" \JGR(                  5      GSNSGS.GS jj5       Gr\S" \,R                  5      SJ\:4GS j5       Gr\S" \,R                  5      SJ\:4GS j5       Gr\P" \JGR.                  5      \C" 5       GSSF\\*   4GS jj5       5       GrGS GrGS Gr\P" \JGR4                  5      \C" SS9G\\A" GS\,R                  S.9GS 5       5       5       5       Gr\P" \JGR6                  5      \C" SS9G\\A" GS\,R                  S.9GS 5       5       5       5       Gr\P" \JGR8                  5      \C" 5       S5\:GS\:SF\GSZ\4GS j5       5       Gr\U" \W5      Gr\U" \Y5      Gr\U" \Z5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \[5      Gr\U" \\5      Gr\U" \]5      Gr\U" \^5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \`5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \a5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \c5      Gr\U" \5      Gr\U" \d5      Gr\U" \e5      Gr\U" G\W5      Gr\U" G\X5      Gr\U" G\5      Gr\U" \f5      Gr\U" \5      Gr\U" \5      Gr\U" \g5      Gr\U" \i5      Gr\U" \h5      Gr\U" \j5      Gr\U" \l5      Gr\U" \k5      Gr\U" \5      Gr\U" \q5      Gr\U" \5      Gr\U" \5      Gr\U" \r5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \~5      Gr\U" \5      Gr\U" \5      Gr\U" G\m5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \|5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" G\5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" G\5      Gr\U" G\5      Gr\U" \5      Gr\U" \5      Gr\U" \5      Gr\U" G\5      Gr\U" G\5      Gr\U" G\5      Gr\U" G\5      Gr\U" \p5      Gr\" \JGR                  5      Gr\" \JGR                  5      Gr\" \JGR                  5      Gr\" \JGR,                  5      Gr\" \JGR:                  5      Gr \" \JGR                  5      Gr\" \JGRL                  5      Gr\" \JGR                  5      Gr\" \JGR                  5      Gr\" \JGRr                  SGS9Gr\" \JGR                  5      Gr\" \JGR                  5      GrGS GrGS Gr	GS Gr
GS\GR
                  GS\\;\<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)CallableIterableSequence)Enum)partialreducesingledispatchwraps)AnycastOptionaloverloadUnion)	sym_floatsym_intsym_maxsym_min)BoolLikeDeviceLikeTypeDimDimsSequenceTypeDimsTypedtype_to_typeELEMENTWISE_TYPE_PROMOTION_KIND	FloatLikeFloatWithoutSymFloatIntLike(is_contiguous_for_memory_format_or_falseis_contiguous_or_false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  $ )Nhputypedevices    e/root/GenerationalWealth/GenerationalWealth/venv/lib/python3.13/site-packages/torch/_refs/__init__.pyis_noncontiguous_supportedr:  p  s    T>1V[[E11    c                     S nSSK Jn  U  H!  n[        XC5      (       d  M  UR                  n  O   [	        U5      (       d  UR                  5       nU$ )Nr   )
FakeTensor)torch._subclasses.fake_tensorr=  
isinstancefake_devicer:  r   )input_tlistoutputr8  r=  r   s        r9  handle_noncontiguous_outputsrC  t  sK    F8a$$]]F 
 &f--""$Mr;  c            	        ^	^
^^ SSK JnJnJnJn  [
        R                  R                  R                  R                  n[        S [        S U 5       5       5      n[        U5      S:X  a  g U H$  m[        T[        5      (       a  M  [        ST5      e   S/[!        ["        S U 5       5      -  m
[%        U5       GH  u  m	m['        SS[        T5      -
  S5       GH^  mU" TT   5      (       a)  U" T
T   5      (       a  U" TT   T
T   :H  5      (       a  M<  OU(       a  U" TT   5      (       av  U" T
T   5      (       af  U" TT   5      nU" T
T   5      nUS:X  a"  US:w  a  [
        R(                  " TT   S:H  5        US:X  a"  US:w  a  [
        R(                  " T
T   S:H  5        U" TT   T
T   :H  5      (       a  M  U" T
T   S:H  5      (       a  TT   S:  a  [+        S	5      eTT   T
T'   U" TT   5      (       d  U" TT   S:H  5      (       a  GM7  [
        R(                  " T
T   TT   :H  U	U
UU4S
 j5        GMa     GM     T
$ )Nr   )guard_or_falsehas_hintis_nested_int	size_hintc              3   V   #    U  H  n[        U[        5      (       a  U4OUv   M!     g 7fNr?  r   .0xs     r9  	<genexpr>$_broadcast_shapes.<locals>.<genexpr>  s*      9A 1g&&A-9s   ')c                 
    U S L$ rJ   rN  s    r9  <lambda>#_broadcast_shapes.<locals>.<lambda>  s    !4-r;  zMInput shapes should be of type ints, a tuple of ints, or a list of ints, got    c              3   8   #    U  H  n[        U5      v   M     g 7frJ  len)rM  shapes     r9  rO  rP    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 rR  )arg_idxcommon_shapeidxrZ  s   r9  rT  rU    s:    LUSVZLX\]`\a b55<IU5' J22>Ar;  )%torch.fx.experimental.symbolic_shapesrE  rF  rG  rH  torchfxexperimental_configbacked_size_oblivioustuplefilterrY  r?  r   RuntimeErrorr   max	enumeraterange_check
ValueError)_shapesrE  rF  rG  rH  	backed_soshapesabr^  r_  r`  rZ  s            @@@@r9  _broadcast_shapesrt    sL     %%--CCI /9 F 6{a%**_   	
4s4V4546L $F+R#e*_b1CU3Z(( !c!233#J,s"339 9  %*!5!5(<PSCT:U:U!%*-A!,s"34AAv!q&U3Z1_5Av!q&\#%6!%;<!%*S0A"ABBl3/1455:>$S  %*#JS! s,,c
a1P1P  %s3AS 2 ,b r;  T)preserve_cpu_scalar_tensorsc                    ^ ^^^ [        S U 5       6 mS[        S[        S[        4S jmUU U4S jm[        UU4S jU 5       5      $ )Nc              3   h   #    U  H(  n[        U[        5      (       a  UR                  OS v   M*     g 7frJ  )r?  r'   rZ  rM  r   s     r9  rO  #_maybe_broadcast.<locals>.<genexpr>  s%     	G$QZ:..!''D
8$s   02rr  rs  returnc                 6   SSK JnJnJn  [	        U 5      [	        U5      :w  a  g[        X5       Hg  u  pVU" XV:g  5      (       a    gU" U" US:H  US:H  5      5      (       a  OU" U" US:H  US:H  5      5      (       a    g[        R                  " XV:H  S 5        Mi     g)Nr   )rE  sym_andsym_orTrV  c                      g)NzCsizes assumed to be the same due to unbacked broadcasting semanticsrR  rR  r;  r9  rT  9_maybe_broadcast.<locals>.should_expand.<locals>.<lambda>  s    ]r;  F)ra  rE  r|  r}  rY  ziprb  rm  )rr  rs  rE  r|  r}  rN  ys          r9  should_expand'_maybe_broadcast.<locals>.should_expand  s    	
 	
 q6SVIDAaf%%
 ga1fa1f566qAvqAv 677 LL] ( r;  c                 H  > U c  g [        U [        5      (       a  U $ [        U [        5      (       aO  T(       a  [        R                  " U 5      (       a  U $ T" U R
                  T5      (       a  U R                  T5      $ U $ [        S[        [        U 5      5      -   S-   5      e)Nz#Unexpected type when broadcasting: !)
r?  r!   r'   utilsis_cpu_scalar_tensorrZ  r   ri  strr6  )rN  rZ  r_  ru  r  s     r9  __maybe_broadcast+_maybe_broadcast.<locals>.__maybe_broadcast  s    96""H:&&*u/I/I!/L/LQWWl33xx--H5DGDsJ r;  c              3   6   >#    U  H  nT" UT5      v   M     g 7frJ  rR  )rM  rN  r  r_  s     r9  rO  ry    s     BT"1l33Ts   )rt  r%   boolrg  )ru  argsr  r_  r  s   ` @@@r9  _maybe_broadcastr    sH    $	G$	GL y T @$ BTBBBr;  )register_decompositionF)aten_op
extra_metaexact_dtyperz  c                0   ^ ^^^ S[         4UUUU 4S jjnU$ )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$ )Nr  rr  type_promoting_argstype_promotion_kindrr  rz  c                 D   > Tb  T" U 5        T" U 5      n[        U /U5      $ rJ  )rC  )rr  rB  r  r  s     r9  _ref>_make_elementwise_unary_reference.<locals>.inner.<locals>._ref&  s*     %1!WF/V<<r;  )
r
   r0   r/   r.   r(   infer_aten_opr  get_aten_op__name__r  )r  r  r  r  r  r  s   ` r9  inner0_make_elementwise_unary_reference.<locals>.inner#  s     
t		-	)	+ & 3

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

 
* 
. 
	= m#''dmm<G"7+D1r;  r   )r  r  r  r  r  s   ```` r9  !_make_elementwise_unary_referencer    s    H  0 Lr;  c                    ^  U 4S jnXl         [        R                  " 5       R                  R                  S   Ul        U$ )a  
This function defines an alias of another function and sets its __name__ argument.
It also sets its __module__ argument to the module of the caller.
Note that when naively doing `alias = fn`, we have that `alias.__name__ == "fn"`, and
`alias.__module__ == fn.__module__`.
c                     > T" U 0 UD6$ rJ  rR  )r  kwargsfns     r9  _fn_make_alias.<locals>._fnF  s    4"6""r;  r  )r  inspectcurrentframef_back	f_globals
__module__)r  namer  s   `  r9  _make_aliasr  >  s5    # L))+22<<ZHCNJr;  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$ )NoutrR  )rr  r  r  r  s      r9  r  _make_inplace.<locals>._fnU  s    !,d,,V,,r;  _r   )	getmodule)	r
   r  r  getattratenr  r  __all__append)r  r  inplace_namer  _alls   `    r9  _make_inplacer  N  ss     2Y- - kk]!$LL
 |!<
=c
BC "R=  DL!Jr;  r  c                 .    [         R                  " U 5      $ rJ  )primsr1   r  s    r9  r1   r1   g  s    
 99Q<r;  c                 .    [         R                  " U 5      $ rJ  )r  r2   r  s    r9  r2   r2   o      ::a=r;  c                 .    [         R                  " U 5      $ rJ  )r  r3   r  s    r9  r3   r3   t      ;;q>r;  c                 .    [         R                  " U 5      $ rJ  )r  r5   r  s    r9  r5   r5   y  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r4   r  s    r9  r4   r4   ~  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r6   r  s    r9  r6   r6     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r7   r  s    r9  r7   r7     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r8   r  s    r9  r8   r8     s    Qr;  c                 .    [         R                  " U 5      $ rJ  )r  r9   r  s    r9  r9   r9         
 ::a=r;  inputc                 B    [         R                  " U R                  5      $ rJ  )r  is_complex_dtypedtyper  s    r9  r/  r/    s    !!%++..r;  c                 |    [         R                  " U R                  5      (       d  U $ [        R                  " U 5      $ rJ  )r  r  r  r  r:   r  s    r9  r:   r:     s/     !!%++..u%%r;  c                 .    [         R                  " U 5      $ rJ  )r  r;   r  s    r9  r;   r;         99Q<r;  c                 .    [         R                  " U 5      $ rJ  )r  r<   r  s    r9  r<   r<     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r?   r  s    r9  r?   r?         ==r;  c                 .    [         R                  " U 5      $ rJ  )r  r@   r  s    r9  r@   r@     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  erf_invr  s    r9  rA   rA     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rB   r  s    r9  rB   rB     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rC   r  s    r9  rC   rC     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rD   r  s    r9  rD   rD     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rF   r  s    r9  rF   rF     r  r;  r  r  rr  valuec                    [        U [        5      (       d  [        S[        U 5       35      e[        U[        5      (       d  [        S[        U5       35      e[
        R                  " U R                  5      n[
        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        R                  " X5      $ )Na must be TensorLike, got zvalue must be Number, got value argument of type  cannot be safely cast to type r  )r?  r'   AssertionErrorr6  r!   r  r   r  r    rn  r  rG   )rr  r  python_typemsgs       r9  rG   rG     s     a$$9$q'CDDeV$$9$u+GHH%%agg.K&&tE{K@@'U}4ST_S``abo::ar;  c                 ^    [         R                  " X5      n[         R                  " X5        U $ rJ  )r  rG   r   )rr  r  rs      r9  rH   rH     s!    

1A	MM!Hr;  c                 .    [         R                  " U 5      $ rJ  )rb  r+  r  s    r9  r)  r)    s     E""r;  c                 .    [         R                  " U 5      $ rJ  )r  rI   r  s    r9  rI   rI         
 ;;q>r;  rN  c                     [         R                  " [         R                  " [         R                  " U 5      5      [         R                  " U 5      5      n[         R
                  " X5      $ rJ  )rb  r   rI   r1   rl   r   )rN  trunc_xs     r9  rJ   rJ     s<    
 iiEIIaL15::a=AG99Q  r;  c                     [        U [        5      (       d  [        S[        U 5       35      e[        R
                  " [        R                  " U R                  5      S 5        [        R                  " U 5      $ )Nr  c                      g)Nz#imag only supports complex tensors.rR  rR  r;  r9  rT  imag.<locals>.<lambda>  s    1Vr;  )r?  r'   r  r6  rb  rm  r  r  r  r  r   r  s    r9  r   r     sW    a$$9$q'CDD	LLqww')V ::a=r;  )r  c                     [         R                  " U R                  5      (       d%  [         R                  " U R                  5      (       a  [        R
                  " U 5      $ [        U [        R                  S9$ )Nr  )	r  is_float_dtyper  r  r  rR   r&  rb  r  r  s    r9  rR   rR     sM    
 AGG$$(>(>qww(G(G~~a  Qejj))r;  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$ )Ninfr  )r  r  r  rb  r   rS   r   r   r  r1   floatr+  r  r  s    r9  rS   rS     s    agg&&ejjm 4eEJJqM6JKKAGG$$yy|uU|++AUZZ00r;  c                 ,  ^  [         R                  " [        R                  " T R                  5      (       + U 4S j5        [        R
                  " T R                  5      (       a  T [        S5      :H  $ [         R                  " T [         R                  S9$ )Nc                  "   > ST R                    3$ )Nz7Complex dtype is not supported for isposinf, got dtype r  r  s   r9  rT  isposinf.<locals>.<lambda>+      I!''Sr;  r  r  	rb  rm  r  r  r  r  r  r+  r  r  s   `r9  rT   rT   $  sf    
 
LL""177++S AGG$$E%L  AUZZ00r;  c                 ,  ^  [         R                  " [        R                  " T R                  5      (       + U 4S j5        [        R
                  " T R                  5      (       a  T [        S5      :H  $ [         R                  " T [         R                  S9$ )Nc                  "   > ST R                    3$ )Nz7Complex dtype is not supported for isneginf, got dtype r  r  s   r9  rT  isneginf.<locals>.<lambda>9  r  r;  z-infr  r  r  s   `r9  rU   rU   2  sf    
 
LL""177++S AGG$$E&M!!AUZZ00r;  c                 .    [         R                  " X 5      $ rJ  r  r   r  s    r9  rV   rV   @  s    88A>r;  ra   c                     [         R                  " U R                  5      (       a  [        R                  " U 5      S:H  $ [        R
                  " U [        R                  S9$ )Nr   r  )r  r  r  rb  r   r&  r  r  s    r9  rW   rW   I  sA    
 agg&&zz!}!!??1EJJ//r;  c                 .    [         R                  " U 5      $ rJ  )r  	bessel_i0r  s    r9  rX   rX   T  s     ??1r;  c                 .    [         R                  " U 5      $ rJ  )r  rZ   r  s    r9  rZ   rZ   [  s    <<?r;  c                 .    [         R                  " U 5      $ rJ  )r  r[   r  s    r9  r[   r[   `  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r\   r  s    r9  r\   r\   e  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r]   r  s    r9  r]   r]   j  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  r^   r  s    r9  r^   r^   o  r  r;  dimr  c           	          U=(       d    U R                   n[        R                  " U5      n[        X5      n[        U[	        XQSS9-
  U5      $ )NTkeepdim)r  r  get_computation_dtyper+   r   )rr  r  r  result_dtypecomputation_dtypea_s         r9  r`   r`   u  sF     #AGGL33LA	 	6B"2	"4(H#H,WWr;  selfr  r  c                 X   [        U[        5      (       d  U4nU R                  5       S:X  a9  [        R                  " [        R
                  " U 5      X5      R                  5       $ [        R                  " [        R                  " U 5      USS9n[        R                  " X3R                  5       [        S5      :H  S5      nU(       a  UO[        R                  " X15      n[        R                  " [        R
                  " X-
  5      X5      nUR                  5       R                  U5      $ )Nr   Tr
  r  )r?  r   numelrb  r   rC   r[   r   r   r   r1   r  r   rx   )r  r  r  maxesmaxes_squeezedresults         r9  r   r     s     c8$$fzz|qyy4#7;;==JJuzz$'d;EeYY[E%L%@!DE%U5==+DNYYuyy.=F::<N++r;  nanposinfneginfc                    [        U [        5      (       d  [        S[        U 5       35      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$5      nU$ )Nr          )r?  r'   r  r6  r  is_boolean_dtyper  is_integer_dtyper   rb  finforj  minr   rV   rU   rT   )rr  r  r  r  r  s        r9  rd   rd     s     a$$9$q'CDDagg&&%*@*@*I*Iwwy
{~QWW%))~QWW%))[[Q0F[[*F;F[[*F;FMr;  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.rR  rR  r;  r9  rT  _neg_meta.<locals>.<lambda>  s     r;  )rb  rm  r  r  r  s    r9  	_neg_metar#    s#    	LL	uzz!	
r;  )r  c                 .    [         R                  " U 5      $ rJ  )r  re   r  s    r9  re   re     s     99Q<r;  c                     [        U [        5      (       d  [        S[        U 5       35      eU R                  [
        R                  L a  Sn[        U5      eU $ )Nr  z'positive does not support bool tensors.)r?  r'   r  r6  r  rb  r  ri  )rr  r  s     r9  rf   rf     sK    a$$9$q'CDDww%**73Hr;  c                     [        U [        5      (       d  [        S[        U 5       35      e[        R
                  " U R                  5      (       a  [        R                  " U 5      $ U $ )Nr  )	r?  r'   r  r6  r  r  r  r  r   r  s    r9  r   r     sN    a$$9$q'CDDagg&&zz!}Hr;  c                 .    [         R                  " U 5      $ rJ  )r  rh   r  s    r9  rh   rh     s    Ar;  )decimalsr(  c                    US:X  a  [         R                  " U 5      $ SU-  nSU* -  n[         R                  " [         R                  " [         R                  " X5      5      U5      $ )Nr   
   )r  ri   r   )rr  r(  ten_powten_neg_pows       r9  ri   ri     sQ     1}{{1~h,hY'yyUYYq%:;[IIr;  c                 .    [         R                  " U 5      $ rJ  )r  r   r  s    r9  r   r     r  r;  c                 R    [        S[        S[        [        U 5      5      5      5      $ NrV  )r   rx   rC   re   r  s    r9  rj   rj     s    q#aSV-..r;  c                     [         R                  " U R                  5      (       a-  U R                  5       n[        R
                  " US:H  SX-  5      $ U R                  5       $ Nr   )r  r  r  r1   rb  r   rl   )rr  a_abss     r9  rk   rk     sH    
 agg&&{{5A:q!)44vvxr;  c                 .    [         R                  " U 5      $ rJ  )r  rl   r  s    r9  rl   rl     r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rm   r  s    r9  rm   rm     s    
 ==r;  c                 .    [         R                  " U 5      $ rJ  )r  rn   r  s    r9  rn   rn     r  r;  c                     [         R                  U -  n [        R                  " U S:H  S[        R                  " U 5      U -  5      $ Nr   rV  )mathpirb  r   rn   r  s    r9  ro   ro     s3    !A;;qAvq%))A,"233r;  c                 .    [         R                  " U 5      $ rJ  )r  rp   r  s    r9  rp   rp   "  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rr   r  s    r9  rr   rr   '  r  r;  c                     [        X 5      $ rJ  )r   r  s    r9  rs   rs   ,  s    
 q9r;  c                 .    [         R                  " U 5      $ rJ  )r  rt   r  s    r9  rt   rt   4  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  ru   r  s    r9  ru   ru   9  r  r;  c                 .    [         R                  " U 5      $ rJ  )r  rw   r  s    r9  rw   rw   >  r  r;  c                   ^ U R                   m[        R                  " [        R                  " T5      U4S j5        U R                  5       n[        R                  " [        U5      S:g  S 5        [        R                  " US   S:H  S 5        U R                  5       n[        R                  " US   S:H  S 5        US S n[        R                  " [        R                  " S	 U 5       5      S
 5        [        R                  " U R                  5       S-  S:H  S 5        [        R                  " U [        R                  " T5      5      R                  S5      $ )Nc                     > ST  3$ )Nz^view_as_complex is only supported for floating pointtensors, but got a tensor of scalar type: rR  )input_dtypes   r9  rT  !view_as_complex.<locals>.<lambda>K  s     55@MCr;  r   c                      g)Nz-Input tensor must have one or more dimensionsrR  rR  r;  r9  rT  rC  Q      ?r;  r\     c                      g)Nz+Tensor must have a last dimension of size 2rR  rR  r;  r9  rT  rC  U      =r;  rV  c                      g)Nz/Tensor must have a last dimension with stride 1rR  rR  r;  r9  rT  rC  [      Ar;  c              3   0   #    U  H  oS -  S:H  v   M     g7f)rF  r   NrR  )rM  strides     r9  rO  "view_as_complex.<locals>.<genexpr>_  s     84aZ1_4s   c                      g)NzCTensor must have a stride divisible by 2 for all but last dimensionrR  rR  r;  r9  rT  rC  `  s    Ur;  c                      g)Nz0Tensor must have a storage_offset divisible by 2rR  rR  r;  r9  rT  rC  d  s    Br;  )r  rb  rm  r  r  sizerY  rL  builtinsr   storage_offsetr  view_element_typecorresponding_complex_dtyper   )r  sizesold_stridesdimsrB  s       @r9  r  r  G  s   **K	LL[)	C
 IIKE	LLE
a? 
LLb	Q=
 ++-K	LLB1A sD	LL8488U 
LL!Q&B ""e//<gbkr;  c           	      @   ^ ^^^^^^^ S[         4UUUUUUUU 4S jjnU$ )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$ )Nrr  rs  r  rr  rs  rz  c                   > [         R                  " T=(       d    [        U [        5      (       + U4S j5        [         R                  " T=(       d    [        U[        5      (       + U4S j5        [         R                  " T=(       d,    [        U [        5      =(       a    [        U[        5      (       + U4S j5        [	        X5      u  pT" X5      n[        X/U5      $ )Nc                     > T  S3$ )Nzc: Received a lhs Python scalar to an elementwise binary operation that does not accept lhs scalars!rR  r  s   r9  rT  Q_make_elementwise_binary_reference.<locals>.inner.<locals>._ref.<locals>.<lambda>      4& !> >r;  c                     > T  S3$ )Nzc: Received a rhs Python scalar to an elementwise binary operation that does not accept rhs scalars!rR  r]  s   r9  rT  r^    r_  r;  c                     > T  S3$ )Nz?: Receive two Number inputs to an elementwise binary operation!rR  r]  s   r9  rT  r^    s    4& _`r;  )rb  _check_valuer?  r!   r  rC  )rr  rs  rB  r  r  supports_lhs_python_scalarsupports_rhs_python_scalarsupports_two_python_scalarss      r9  r  ?_make_elementwise_binary_reference.<locals>.inner.<locals>._refz  s     *G*Q2G.G>
 *G*Q2G.G>
 + I"1f-G*Q2GH`
 $A)DA!ZF/??r;  )r  r
   r.   r   Tensorr"   r0   r  r  r  r  )
r  r  r  has_outr  should_register_decompositionrc  rd  re  r  s
   ` r9  r  1_make_elementwise_binary_reference.<locals>.inneru  s    <==D	t	+ * 3

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

 

	@. =&Dm#''d3G#@"7+D1r;  r  )	r  r  r  rh  rc  rd  re  ri  r  s	   ```````` r9  "_make_elementwise_binary_referencerk  k  s    *H * *X Lr;  rZ  alphars  rm  c                   [        X5      u  pUb  [        U [        5      (       a  U R                  OUR                  n[        R
                  " U5      nU[        L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  r  )r  r?  r'   r  r  r   r  r    r6  rn  r  r   rx   rC  rr  rs  rm  r  r  r  rB  s          r9  rx   rx     s      A!DA%a44!''))%0d"5+F+FK,
 ,
 ,DK=8WXcWddefCS/!a$$		!#A	AYYq_F'77r;  )r  rc  rd  c                 .    [         R                  " X5      $ rJ  )r  ry   rZ  s     r9  ry   ry          ;;qr;  )r  c                 .    [         R                  " X5      $ rJ  )r  rz   rZ  s     r9  rz   rz          Q""r;  c                 .    [         R                  " X5      $ rJ  )r  
shift_leftrZ  s     r9  r{   r{          A!!r;  c                 .    [         R                  " X5      $ rJ  )r  r|   rZ  s     r9  r|   r|     rw  r;  c                 .    [         R                  " X5      $ rJ  )r  shift_right_arithmeticrZ  s     r9  r}   r}     s     ''--r;  c                 .    [         R                  " X5      $ rJ  )r  r~   rZ  s     r9  r~   r~     rt  r;  )r  rc  c                    [        U[        5      (       a4  [        U [        5      (       a  [        XR                  U R
                  S9nOl[        U [        5      (       aW  [        U[        5      (       aB  U R
                  UR
                  :w  a(  SU R
                   SUR
                   S3n[        U5      e[        [        U5      [        [        U 5      5      [        U 5      5      $ )Nr  r8  /Expected divisor (b) to be on the same device (&) as dividend (a), but it is found on r  )r?  r!   rg  r(  r  r8  ri  r   rm   re   r1   )rr  rs  r  s      r9  r   r     s     !VAv!6!6!77188<	Av		:a#8#8QXX=Q?zIopqpxpxoyyz{3SQ[#a&11r;  )rounding_moder  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
rw   rI   zLdiv expected rounding_mode to be one of None, 'trunc', or 'floor' but found .)r   r   r   rn  )rr  rs  r  r  s       r9  r   r     sV     1  	'	!A!!	'	!A!!\]j\kklmor;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r         
 88A>r;  c                 l   [        U [        5      (       d   [        U[        5      (       d  [        S5      e[        U[        5      (       a=  US:X  a  U R	                  5       $ 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      $ )Nz-at least one of a or b must be TensorLikeType      ?g       @      ?T)r?  r(   r  r!   r   rb  rr   rG   r  r  r  r  rF   r  r   rZ  s     r9  r   r   &  s     q.))Z>-J-JLMM!V8779#X5L#X::a=  	Av		8::a&&8  ))U-C-CAGG-L-L::a= 99Q?r;  c                    [        U [        5      (       a   [        U[        5      (       a  [        S5      e[        R                  " X5      nUc  [        S5      e[        R                  " U5      (       a  [        R                  nO[        R                  n[        X5      n [        X5      n[        X5      u  p[        X5      $ )Nz=Receive two Number inputs to an elementwise binary operation!z/dtype should not be None after get_higher_dtype)r?  r!   rn  r  get_higher_dtyper  r  rb  
complex128float64r+   r  r   rr  rs  r  s      r9  r   r   D  s    
 !VAv!6!6K
 	

 ""1(E}NOOe$$  
 	 )A)AA!DAq9r;  )r  re  ri  c                 Z  ^ [        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  [        S5      eU R                  m[        R                  " T5      (       a  [        X5      $ [        R                  " T5      (       a  [        X5      $ [        R                   " SU4S	 j5        g )
Nr}  cpur~  r  r  r7  z*a and b must both be Tensors at this pointFc                     > T  S3$ )Nz not supported for floor_dividerR  r  s   r9  rT  floor_divide.<locals>.<lambda>  s    ug-L$Mr;  )r?  r!   r(  rg  r  r8  rb  ri  r  
device_putr  r  r  _floor_divide_floatr  _floor_divide_integerrm  )rr  rs  r  r  s      @r9  r   r     s    !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q&!!jF&;&;IJJGGEE"""1((				&	&$Q**UMNr;  c                 |   [        X5      u  pU R                  R                  (       d  [        R                  " X5      $ [
        R                  " U 5      [
        R                  " U5      :g  R                  [
        R                  " X5      S:g  5      n[        R                  " X5      [        X R                  5      -
  $ r1  )
r  r  	is_signedr  r   rb  rm   r   r   r+   )rr  rs  offsets      r9  r  r    s~    A!DA77yy mmA%--"22??

1@PTU@UVF99Q?4VWWEEEr;  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      $ )Nr   rV  r  r}  )r   r   r   r~   r   r   rz   r   rI   r   rx   r(  r  r8  r   )
rr  rs  modr   different_signed_inputsnon_zero_remaindermask	floor_div	basic_divzero_tensors
             r9  r  r    s    
q*C
c!k1
%C *"Q(Bq!H=C)CD
c#qk3
'C c
Ic#!3'DdC	1-y9IA!IAQAQRK baj)Xk-MNI Aq900r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r          ::ar;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  mantissaexponentc                 h    [         R                  R                  [        R                  " U 5      5      $ rJ  )rb  return_typesfrexpr  r  s    r9  r  r    s$     ##EKK$566r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     s     99Q?r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  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$ r7  )rb  r   r   r   rV   r   )r  r  input_eq_zeroinput_lt_zerozeros_and_onesrB  s         r9  r   r     sa     HHUA&M$$UXXeQ%7U9KLM[[15N[[?FMr;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     rr  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     s     <<r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r   "  s     ==r;  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 r  r  )rr  rs  r  s   r9  rT  #_check_close_args.<locals>.<lambda>4  s'    4&LQWWIUZ[\[b[bZccder;  r   c                     > T  ST S3$ )Nz6: rtol must be greater than or equal to zero, but got r  rR  )r  r  s   r9  rT  r  8      4&NtfTUVr;  c                     > T ST  S3$ )Nz6: atol must be greater than or equal to zero, but got r  rR  )r  r  s   r9  rT  r  <  r  r;  )rb  rb  r  rm  r  rr  rs  r  r  s   `````r9  _check_close_argsr  +  sV     
	177e 
LL	V 
LL	Vr;  	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   r  r  r  r  r   r   rV   r  convert_element_typerb  get_default_dtyperx   r1   r   r   rR   r   )	rr  rs  r  r  r  closeallowed_erroractual_errorr  s	            r9  r   r   A  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 Mr;  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$ [        R
                  " XR5      $ r7  )r  rb  int8int16r  r  int32r   r   r1   r   )rr  rs  r  promote_to_intgress         r9  r   r   l  s     GGE uzz5;;77N&&q%++6&&q%++6		!AAFAq!A
))EIIaOa'
(C$3P%*D*DS*PPr;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  c                    [         R                  " U 5      [         R                  " U5      :  n[         R                  " X U5      n[         R                  " X!U 5      n[         R                  " [         R                  " [         R
                  " [         R                  " U 5      5      5      [         R                  " U 5      [         R                  " U5      :H  5      n[        R                  " U R                  5      (       d%  [        R                  " UR                  5      (       a  [         R                  " U5      S:  n[         R                  " Xd[         R                  " [         R                  " U5      [         R                  " U5      -   5      5      n[         R                  " XWU[         R                  " [         R                  " XC-
  5      5      -   5      n[         R                  " U5      n	[         R                  " U	[        [        S5      [        S5      5      U5      $ [         R                  " XPU[         R                  " [         R                  " XC-
  5      5      -   5      $ )Nr   r  )rb  r   r   r   r   rR   r  r  r  r[   rC   r\   rV   complexr  )
rr  rs  r  max_min_inf_maskneg_min_maskinf_valsnon_nan_valsnan_masks
             r9  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Sr;  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 dtypesrR  rR  r;  r9  rT  logaddexp2.<locals>.<lambda>      ;r;  r  rF  )rb  rm  r  r  r  r   r   rS   r8  r[   r\   rF   )rr  rs  r  r  r  r  	inv_log_2r  s           r9  r   r     s     
LL##AGG,O0F0Fqww0OP;
 6D;;t"D;;t"D  Q8Hdhhqk!IEKK

4; 789DDF;;xF++r;  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r1  r  r  r  rZ  s     r9  r   r     G     !!!''**F!!!''**F5Lr;  c                 \    [         R                  " U R                  5      (       d  U S:H  $ U ) $ r1  r  r  s    r9  r   r     s'    !!!''**Av2Ir;  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  n[        X5      $ r1  )r  r  r  r|   rZ  s     r9  r   r     sK     !!!''**F!!!''**Far;  c                     [         R                  " U R                  5      (       d  U S:g  n [         R                  " UR                  5      (       d  US:g  nX-  $ r1  r  rZ  s     r9  r   r     r  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r          ==r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     r  r;  )r  re  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     s    
 99Q?r;  c                 .    [         R                  " X5      $ rJ  r  rZ  s     r9  r   r     r  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r   	  s     ??1  r;  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r     s     ??1  r;  rV  c                 p    [        U [        5      (       a  Sn[        U5      e[        R                  " XUS9$ )Nz?Received a Number for the first argument, but expected a Tensorrl  )r?  r!   rn  rb  r   )rr  rs  rm  r  s       r9  r   r     s1     !VOo99Q''r;  c                   [        X5      u  p[        U [        5      (       a|  [        U[        5      (       ag  [        R                  " [
        R                  " U R                  5      (       + =(       a%    [
        R                  " UR                  5      (       + S 5        US:w  a  [        U [        5      (       a  U R                  OUR                  n[
        R                  " U5      n[
        R                  " [        U5      U5      (       d  S[        U5       SU S3n[        U5      e[        U[        R                  5      (       a  [        R                  " X5      nOX-  n[        R                  " X5      n[!        X/U5      $ )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.rR  rR  r;  r9  rT  sub.<locals>.<lambda>?  s    Cr;  rV  ro  r  r  )r  r?  r'   rb  rm  r  r  r  r   r    r6  rn  rg  r  r   r   rC  rp  s          r9  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7r;  r   )r  r  r  re  c                 .    [         R                  " X5      $ rJ  )r  r   rZ  s     r9  r   r   W  s     99Q?r;  c           
      d   [         R                  " [        U [        5      =(       d    [        U[        5      S 5        [        U[        5      (       a4  [        U [        5      (       a  [        XR                  UR                  S9n OH[        U [        5      (       a3  [        U[        5      (       a  [        XR                  U R                  S9n[        U [        5      (       d  [        S[        U 5       35      e[        U[        5      (       d  [        S[        U5       35      e[         R                  " [         R                  " U S5      S[         R                  " U [         R                  " U5      5      5      n[         R                  " [         R                  " U5      [        S5      U5      $ )Nc                      g)Nz/Expected either argument a or b to be a Tensor"rR  rR  r;  r9  rT  xlogy.<locals>.<lambda>j  rJ  r;  r}  r  zb must be TensorLike, got r   r  )rb  rm  r?  r'   r!   r(  r  r8  r  r6  r   r   r   r[   rV   r  )rr  rs  rhss      r9  r   r   a  s    
LL1j!>Z:%>A !Z  Z6%:%:!77188<	Az	"	"z!V'<'<!77188< a$$9$q'CDDa$$9$q'CDD
++ehhq!na1eiil)C
DC;;u{{1~uU|S99r;  )r  r  re  c                     [         R                  " U 5      n[         R                  " U5      (       a  [        R                  " X5      $ [        [        R                  " X5      5      $ rJ  )r  	get_dtyper  r  r   rw   r  s      r9  r   r   ~  sD     OOAEe$$yy1!!r;  )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-  -   $ )z+
Reference implementation of torch.addcdiv
c                  (   > S[        T5       ST  S3$ Nr  r  r  r5  r  r  s   r9  rT  addcdiv.<locals>.<lambda>      -d5k]:YZeYffghr;  r  r  r   rb  rb  r    r6  r  r  r  r  r  r  s      ` @r9  r   r     _      

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

 %'/G+++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-  -   $ )z+
Reference implementation of torch.addcmul
c                  (   > S[        T5       ST  S3$ r  r5  r  s   r9  rT  addcmul.<locals>.<lambda>  r  r;  r  r  s      ` @r9  r   r     r  r;  )rr  r  rj  r  rj  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 $ )Nz+clamp called but both min and max are none!)rn  rb  rV   r|   r   r   r   )rr  r  rj  r  a_isnan	conditions         r9  r   r     s     {s{;o
++a.$$UXXa%5w?	
 KK	c*
++a.$$UXXa%5w?	KK	c*Hr;  c                 *    [         R                  " XS9$ )N)r  rb  r   )r  r  s     r9  r   r          ;;t%%r;  c                 *    [         R                  " XS9$ )N)rj  r  )r  rj  s     r9  r   r     r  r;  predc                    ^  Ub  Uc  [         e[        R                  " T XSS9  [        R                  " T R
                  [        R                  L U 4S j5        [        T X5      u  m p[        R                  " T X5      $ ) Tallow_cpu_scalar_tensorsc                  "   > ST R                    3$ )Nz#expected predicate to be bool, got r  )r
  s   r9  rT  where.<locals>.<lambda>  s    5djj\Br;  )
NotImplementedErrorr  check_same_devicerb  rm  r  r  r  r  r   )r
  rr  rs  s   `  r9  r   r     sh    " 	yAI!!	D!F	LL

ejj B
 "$-JD!;;tQ""r;  memory_formatr  c                .    [         R                  " XS9nU$ Nr  )r  r   )rr  r  r  s      r9  r   r   "  s    
 [[8FMr;  )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      $ )NzAttempting to copy from device z to device z*, but cross-device copies are not allowed!)r8  ri  r  r   )rr  rs  r  r  s       r9  r   r   +  sK    !((ahh"6/zQXXJNxy3==r;  c                     U R                  5       S:w  a  SU R                  5        S3n[        U5      e[        R                  " U R                  5      nU" [
        R                  " U 5      5      $ )NrV  zCan't convert a tensor with z elements to a number!)r  rn  r  r   r  r  r   )rr  r  number_types      r9  r   r   3  sW    wwyA~,QWWYK7MNo %%agg.Kuzz!}%%r;  r8  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  )r8  r  r  rb  preserve_formatr  is_contiguous_for_memory_format)rr  r8  r  r  r  r  r  r  s           r9  _to_will_aliasr"  @  s      
	
t^1qxx61
	
d].agg.
	
 t^1qxx61
	
 T! U 5 55U44QTr;  c                      [         erJ  )r  )r  r  s     r9  _to_dispatchr$  Y  s    
r;  c                     U UUUUS.nU$ N)r8  r  r  r  r  rR  r8  r  r  r  r  r  s         r9  
_to_devicer(  ^  s!     $&F Mr;  c                 >    [         R                  " U 5      UUUUS.nU$ r&  )rb  r8  r'  s         r9  _to_device_strr*  p  s*     ,,v&$&F Mr;  c                     U UUUS.nU$ )N)r  r  r  r  rR  )r  r  r  r  r  s        r9  	_to_dtyper,    s     $&	F Mr;  otherc                 `    U R                   nU R                  nU R                  nUUUUUUS.nU$ )N)r8  r  r  r  r  r  )r8  r  r  )r-  r  r  r  r8  r  r  r  s           r9  	_to_otherr/    sA     \\FKKE\\F $&F Mr;  	to_kwargsc                    / SQnSU;   a4  [        US   [        5      (       a  [        R                  " US   5      US'   U H  nX1;   d  M
  US:X  a  X   [        R                  L dy  US:X  a_  X   R
                  U R                  R
                  :X  a9  X   R                  (       a:  X   R                  U R                  R                  :X  d  [        XS 5      X   :X  d  M  UR                  U5        M     g )N)r  r8  r  r  r8  r  )	r?  r  rb  r8  r   r6  indexr  pop)rr  r0  options_to_checkkws       r9  _canonicalize_to_argumentsr6    s    E9Ih,?!E!E#ll9X+>?	(?&9=E<Q<Q+Q(N!**ahhmm;%M//9=3F3F!((..3X A4(IM9 b! r;  c                 4   [        U5      S:w  a  [        U0 UD6nSU;   a  [        S5      e[        X5        [	        U 40 UD6(       a  U $ 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  z#pin_memory is not supported in refsr  Fr  r  r  r8  r  )rY  r$  r  r6  r"  r3  getr  r  r  rb  r  r   )rr  r  r  r  r  r  s         r9  r   r     s    
4yA~t.v. vBCCq)a"6"!'6!16::fuD1?61I6::n-uL 
&**Wagg.!''9F*V#V# ))!ZZ-IJJa*6*FFMr;  )has_identityaccepts_dim_tuplerW  keepdimsr  r  r  r9  r:  rW  r;  r  output_dtype_kindc                  ^  [        T [        5      (       d  [        S[        T 5       35      eT R                  S:  a  [        ST R                   S35      eUbI  [        U[        5      (       d  [        S[        U5       35      eUb  XgR                  :w  a  [        S5      eU(       d/  Ub,  [        U[        5      (       d  [        S[        U5       35      e[        U[        5      (       a  U4n[        R                  " T R                  U5      nU(       dC  SS	KJn	  T R                  S:H  =(       d    U	" U 4S
 jU 5       6 n
[        R                  " U
S 5        [        R                  " T X5      u  p[!        T U5      m U" T U5      nU(       a|  [#        T R                  5       Vs/ s H  oU;  a  T R                  U   OSPM     nn[#        T R                  5       Vs/ s H  oU;  d  M
  UPM     nn[$        R&                  " XU5      nUbI  Uc  [        S5      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 )Nr  @   zReceived a tensor with z? dimensions, but only tensors with up to 64 dims are supported!out must be TensorLike, got z4dtype argument and out dtype must match in reductionzdims must be None or Dim, got r   )r|  c              3   H   >#    U  H  nTR                   U   S :  v   M     g7fr   NrZ  rM  irr  s     r9  rO  _reduction.<locals>.<genexpr>	  s     .Lt!qwwqzA~ts   "c                      g)NzJreducing over zero-size dimension for reduction operation without identityrR  rR  r;  r9  rT  _reduction.<locals>.<lambda>	  s    `r;  rV  z4result_dtype should not be None when out is providedz7Expected the dtype of reduction result and out to match	copy_fromr   )r?  r'   r  r6  ndimri  r  r   r  reduction_dimsrZ  ra  r|  rb  rm  reduction_dtypesr+   rl  r  broadcast_in_dimr,   r-   r  )rr  r  r9  r:  rW  r;  r  r  r<  r|  valid_shaper  r  r  rD  output_shapebroadcast_dimss   `                r9  
_reductionrQ    sA    a$$9$q'CDDvv{%affX-lm
 	
 #z** #?S	{!KLL		!"J  
4 5 5 #A$t*!NOO$w.DAffkMW.Lt.L%M`	

 ',&<&<	'# 	 #45A!T]FDI!&&MRMqtm
:MR%*166]D]tm!]D''nM
 !WXX!:I   \\2<<|||#(@++FAM# SDs   ( J!	J	.J	c                 F  ^ ^ [        [        T R                  5      n[        T S0 5      n[        SS9" U5      m [	        T 5      SS.U U4S jj5       nT R                   S3nXTl        UR
                  R                  U5        [        [        [        U5      5      " U5        U$ )zc
Given a view function (e.g. torch.diagonal) generates its copy variant (e.g. torch.diagonal_copy)
__annotations__Tr  Nr  c                 h   > T" USU 0UD6nT(       a  U b  g U b  U$ [         R                  " S U5      $ )Nr  c                 <    U R                  [        R                  S9$ r  )r   rb  contiguous_formatrS  s    r9  rT  3_make_copy_from_view.<locals>._fn.<locals>.<lambda>C	  s    aggE,C,CgDr;  )pytreetree_map)r  r  r  r  r  return_none_on_out_variants       r9  r  !_make_copy_from_view.<locals>._fn:	  sB    T-s-f-%#/?MD
 	
r;  _copy)r  r  r  r0   r
   rS  updater  )r  r[  aten_fnannotationsr  	copy_names   ``    r9  _make_copy_from_viewrb  0	  s     dBKK(G"/4K 
	&w	/B
2Y 

 

 

 ;;-u%IL{+7434S9Jr;  c                     [         R                  " [         R                  " [         R                  " U 5      XS95      nU R                  [         R                  :X  a  UR                  [         R                  S9nU$ )Nr
  r  )rb  r   r   r  uint8r   )rr  r  r  r  s       r9  r   r   N	  sS     uyy):):1)=sTUFww%++-Mr;  c                 p   [        U [        R                  5      n[        U[        [
        45      (       a   [        U5      S:X  a  UR                  5       nOUR                  XS9R                  S5      nU R                  [        R                  L a%  [        R                  " U[        R                  5      $ U$ )Nr   )r  r  F)r+   rb  r  r?  listrg  rY  r   r   r   r  rd  r  r  )rr  r  r  r  r  s        r9  r   r   ]	  s     
!EJJ	/B#e}%%#c(a-C144U; 	ww%++))&%++>>Mr;  )r  r  c          
      h   Ucw  Ub  UR                   nOg[        R                  " U R                   5      (       d%  [        R                  " U R                   5      (       a  [        R
                  nOU R                   nUS:X  d  U/ :X  a  S n[        U [        R                  UUUU[        R                  S9$ NrR  rW  r;  r  r  r<  )r  r  r  r  rb  int64rQ  r  r   r$   SAMErr  r  r  r  r  s        r9  r   r   q	  s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I			499 r;  c           
        ^ ^^ [         R                  " TSS9m[        R                  " [         R                  " TT R
                  5      U U4S j5        [         R                  " TT R
                  5      (       a%  [        T5      S:  a  [        R                  " T 5      $ 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 ""rB  rr  rZ  s   r9  rT  sum_to_size.<locals>.<lambda>	  s    %eW,I!''RSTr;  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rV  NrB  )rM  rD  rr  leading_dimsrZ  s     r9  rO  sum_to_size.<locals>.<genexpr>	  s@      50A\!"a' 	
,-GGAJ!O 	
0s   55	5T)r  r  r  )r  extract_shape_from_varargsrb  rm  is_expandable_torZ  is_same_shaperY  r  view_ofrJ  rg  rl  r   )rr  rZ  reduce_dimsrv  s   `` @r9  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Br;  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$ rh  )r  r  r  r  rb  rj  rQ  r  r   r$   rk  rl  s        r9  r   r   	  s     }?IIE##AGG,,0F0Fqww0O0OKKEGGE
byC2I	

499 r;  rT  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ NrR  FrW  r;  r  r  r9  r<  )rQ  r  r   r$   rk  rr  r  r  r  s       r9  r   r   	  E     byC2I	

499	 	r;  c                v    US:X  d  U/ :X  a  S n[        U [        R                  UUS US[        R                  S9$ r  )rQ  r  r   r$   rk  r  s       r9  r   r   	  r  r;  c                 @    Uc  [        U [        5      (       a  U nS n X4$ rJ  )r?  r  )r  unbiaseds     r9  _dim_var_dispatchr  	  s(     JsD11=r;  
correctionr  r  c                    [        X5      u  p[        R                  " X$5      nUS:X  d  U/ :X  a  S n[        U [	        [
        R                  US9UUS S S[        R                  S9nU$ )NrR  r  Tr  )	r  r  set_correctionrQ  r   r  r   r$   COMPLEX_TO_FLOAT)rr  r  r  r  r  r  s         r9  r   r   	  sl     &c4MC%%h;J
byC2I			j14EE	F Mr;  c                4   [        X5      u  p[        R                  " X$5      n[        R                  " U [        R
                  5      u  pV[        X5      n [        R                  " XXCS9n[        R                  " U5      nUc  [        S5      e[        X5      $ N)r  r  z/dtype should not be None after reduction_dtypes)r  r  r  rL  r$   r  r+   rb  r   rr   r  )	rr  r  r  r  r  opmath_dtyper  a_vara_stds	            r9  r   r   
  s     &c4MC%%h;J00	%66L 	 0AIIaEEJJuE}NOO"500r;  c          
        ^ ^^	 US:X  d  U/ :X  a  S nTm	Tc  T R                   m[        T [        R                  UUTS [        R
                  S9n[        R                  " [        R                  " T5      =(       d    [        R                  " T5      UU	4S j5        [        U[        5      (       a  U4n[        R                  " T R                  U5      nT R                  S:X  a  SO$[!        ["        R$                  U 4S jU 5       S5      n['        XW5      nTc  T R                   OTn[)        XX5      nUbJ  [        U[*        5      (       d  [-        S[/        U5       35      e[1        XER                  5      n[3        XTS9$ U$ )	NrR  ri  c                     > STc  SOS ST  3$ )Nz&mean(): could not infer output dtype. Inputr   z> dtype must be either a floating point or complex dtype. Got: rR  )r  
orig_dtypes   r9  rT  mean.<locals>.<lambda>L
  s"    4$,w*= >77<g?r;  r   rV  c              3   B   >#    U  H  nTR                   U   v   M     g 7frJ  rB  rC  s     r9  rO  mean.<locals>.<genexpr>U
  s     7QDq
Ds   r?  rH  )r  rQ  r  r   r$   KEEP_PROMOTED_TYPErb  rm  r  r  r  r?  r   rK  rZ  rJ  r   operatorr   r   r+   r'   r  r6  r,   r-   )
rr  r  r  r  r  r  rW  nelemr  r  s
   `  `     @r9  r   r   2
  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** #?S	{!KLL\\2<<Mr;  out0out1)r  r  r  c                f   [        X5      u  p[        R                  " X$5      n[        R                  " U [        R
                  5      u  pVU R                  n[        X5      n [        R                  " XXCS9u  p[        R                  " U5      n
Uc  [        S5      e[        X5      [        X5      4$ r  )r  r  r  rL  r$   r  r  r+   rb  r   rr   r  )rr  r  r  r  r  r  r  original_dtyper  a_meanr  s              r9  r   r   a
  s     &c4MC%%h;J00	%66L WWN0ANN1jRMEJJuE}NOO-7 r;  c                P    [        X5      u  p[        XX#US9n[        XU5      nXV4$ )Nr  )r  r   r   )rr  r  r  r  r  vms          r9  r   r   |
  s1     &c4MCAH*=AQWA4Kr;  )r  vec1vec2)betarm  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      -  $ TT -  T[         R                  " TT5      -  -   $ )NrV  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec1, but got -DrJ  )r  s   r9  rT  addr.<locals>.<lambda>
      <TYYKrJr;  c                  $   > ST R                    S3$ )Nz*addr: Expected 1-D argument vec2, but got r  r  )r  s   r9  rT  r  
  r  r;  rm  r  c                     > ST  S3$ )NzBoolean z$ only supported for Boolean results.rR  )arg_names   r9  rT  r  
  s    (8*,PQr;  r   c                      > S[        T 5       3$ )Nzexpected bool/int beta but got r5  )r  s   r9  rT  r  
  s    5d4j\Br;  c                      > S[        T 5       3$ )Nz expected bool/int alpha but got r5  rl  s   r9  rT  r  
  s    6tE{mDr;  Fc                  :   > S[        T 5       STR                   3$ Nzcannot safely convert z to r6  r  )r  r  s   r9  rT  r  
  s    ,T$ZLTZZLIr;  c                  :   > S[        T 5       STR                   3$ r  r  )rm  r  s   r9  rT  r  
  s    ,T%[Mdjj\Jr;  )rb  rm  rJ  r?  r  r  r  r  r   rZ  r    r6  intouterr  r   r   )r  r  r  r  rm  argr  s   ````` @r9  r   r   
  s    
LL		QJ 
LL		QJ !'*T6N;Xc4  LL&&tzz2 7**4::67**4::6Q	 < ;;tzz!}djjm4Ddjj))!$t*c2B	
 	!$u+s3D	
 .35;;tT*Uu9UU##+0D$' 6;oodE6R 
 	!$t*mDJJ.GHI	
 	!$u+}TZZ/HIJ	
 195;;tT222$;T4)@!@@@r;  r  r  .c                 ,   U(       d,  [        U [        R                  R                  5      (       a  U nO:[        U [        R                  R                  5      (       a  [	        S5      eU 4U-   n[        S U 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_1d`.2arg should not be a Sequence when args is providedc              3   \   #    U  H"  oR                   S :  a  UO[        US5      v   M$     g7f)rV  r   N)rJ  r  rM  rr  s     r9  rO  atleast_1d.<locals>.<genexpr>
  s#     Eu!VVq[i1o5us   *,rV  r   )r?  collectionsabcr   r  rg  rY  )r  r  args_r  s       r9  r   r   
  sy     JsKOO$<$<==c;??3344 !UVV
EuE
ECc(Q,3*CF*r;  at_least_fnc                     U " U5      n[        U[        5      (       d  [        S[        U5       35      e[	        X15      $ )Nz(at_least_fn must return TensorLike, got )r?  r'   r  r6  r  )r  r  r  arg_s       r9  _unsqueeze_atleastr  
  s=     sDdJ''GT
|TUUTr;  c                 ^  ^ U(       d,  [        U [        R                  R                  5      (       a  U nO:[        U [        R                  R                  5      (       a  [	        S5      eU 4U-   n[        [        [        S5      m[        U4S jU 5       5      n[        U5      S:  a  U$ US   $ )z5Reference implementation of :func:`torch.atleast_2d`.r  r   c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)rF  Nr  )rM  rr  unsqueeze_atleast_1ds     r9  rO  atleast_2d.<locals>.<genexpr>
  $     Mu!VVq[&:1&==u   &)rV  )
r?  r  r  r   r  r   r  r   rg  rY  )r  r  r  r  r  s       @r9  r   r   
  s     JsKOO$<$<==c;??3344 !UVV"#5z1E
MuM
MCc(Q,3*CF*r;  c                 ^  ^ U(       d,  [        U [        R                  R                  5      (       a  U nO:[        U [        R                  R                  5      (       a  [	        S5      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`.r  r\  c              3   V   >#    U  H  oR                   S :  a  UOT" U5      v   M      g7f)   Nr  )rM  rr  unsqueeze_atleast_2ds     r9  rO  atleast_3d.<locals>.<genexpr>  r  r  rV  r   )
r?  r  r  r   r  r   r  r   rg  rY  )r  r  r  r  r  s       @r9  r   r   
  s     JsKOO$<$<==c;??3344 !UVV"#5z2F
MuM
MCc(Q,3*CF*r;  rP  rL  rR  c                 Z    Ub  UOU R                  5       n[        R                  " XX$5      $ rJ  )rR  r  r   )rr  rP  rL  rR  storage_offset_ints        r9  r   r     s1     )4!:J:J:L  AV@@r;  srcc                 @    Uc  SOUn[         R                  " XX#U5      $ r1  )r  r   )r  r  rP  rL  rR  r  s         r9  r   r     s'     -4.##E>PQQr;  c                  :    [         R                  " [        U 6 5      $ rJ  )rb  Sizert  )rq  s    r9  r   r     s    ::'011r;  c                      [        U 5      S:X  a  [        U S   [        5      (       d  U S   n [        [	        U SS065      $ )NrV  r   ru  F)rY  r?  rg  rf  r  tensorss    r9  r   r   #  s?     7|qGAJ!?!?!* 'MuMNNr;  c                     [        U5      [        U R                  5      -
  n[        [        U[        U R                  5      U-   5      5      n[        R
                  " XU5      $ rJ  )rY  rZ  rg  rl  r  rM  )rr  rP  startrW  s       r9  r   r   ,  sI    IAGG$Euc!''lU234D!!!400r;  r  r  c                 T  ^
^^^ S n[        U 5      S:X  a  Sn[        U5      eU  H/  n[        U[        5      (       a  M  [	        S[        U5       35      e   [        R                  " U SS06  SSKJ	n  S m
[        U 5       He  u  mmT
c  TR                  S:w  a  Tm
M  M  TR                  S:w  d  M1  [        R                  " TR                  T
R                  :H  U
UU4S	 j5        Mg     T
c  U S   m
T
R                  n/ n[        U 5       H  u  mn[        U5      [        UR                  5      :w  a\  UR                  S:w  a  [	        S
UR                   35      e[        R                  " U" UR                  S   S:H  5      U
U4S j5        M  UR                  S:X  a  U" UR                  S   S:H  5      (       a  M  UR                  U5        M     U" U 5      n[        U5      S:X  aB  U S   m [!        [#        S U  5       5      5      n	['        STR(                  TR*                  U	US9$ [        R,                  " US   R                  U5      n[        R.                  " US   R                  U5        [0        R2                  " Xq5      R5                  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  [	        S5      eU$ )Nz,format should not be None if len(inputs) > 0)r  suggest_memory_formatrb  rW  r  )inputsformatr   fs       r9   cat_compute_output_memory_format-cat.<locals>.cat_compute_output_memory_format9  sg    A++A.AE+++!fk...F  > !OPPr;  r   z3cat expects at least one tensor, but received zero!ztensor must be TensorLike, got r  FrE  rV  c                  D   > ST R                    STR                    ST S3$ )N6Number of dimensions of tensors must match.  Expected z-D tensors, but got z-D for tensor number  in the listr  )examplerD  r   s   r9  rT  cat.<locals>.<lambda>l  s.       '~-A!&& J%%&C|5r;  z+tensor.ndim should be 1 at this point, got c                  *   > ST R                    ST S3$ )Nr  z*-D tensors, but got 1-D for tensor number r  r  )r  
tensor_idxs   r9  rT  r    s"     #LL> *!!+L:r;  c              3   8   #    U  H  oR                   v   M     g 7frJ  )requires_gradrL  s     r9  rO  cat.<locals>.<genexpr>  s     $Fg__gr[  r   r  r8  r  r  r  )rY  rn  r?  r'   r  r6  r  r  ra  rE  rk  rJ  rb  rm  rZ  r  r  r   	Exceptionr  r  r8  canonicalize_dimvalidate_idxr  r   r   )r  r  r  r  tensorrE  rZ  filteredr  r  r  rD  r   r  s             @@@@r9  r   r   2  si    7|qCo&*-- #B4<.!QRR  
WEuED$ G'"1?vv{  vv{FFgll*5 #  !*MMEH'0
Fu:V\\**{{a$A&++O  LL v||A!34:$ {{aN6<<?a3G$H$HOOF#9 1< 5W=M
8}AJ	" !$Fg$F!FGM ''88''
 	
 
 
 !!1!13
7C	x{''-99X#)))FF  	"!M	"s   1J J'&J'c                 >    [        S U  5       5      n[        US5      $ )Nc              3      #    U  H7  oR                   S :  a  UO UR                  UR                  5       S 45      v   M9     g7fru  )rJ  r   r  rL  s     r9  rO  column_stack.<locals>.<genexpr>  s3      @G1VVaZQYY	1~66s   ?ArV  )rg  r   r  aligned_tensorss     r9  r   r     s(     @G O ""r;  c                     [         R                  " U R                  5      (       d  U $ U R                  (       a  [        R
                  " U 5      $ [        R                  " U 5      $ rJ  )r  r  r  	is_sparserb  r:   r  r   r  s    r9  r   r     sC    !!%++..""5))::er;  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$ )
NrF  r   c                      > S[        T 5       3$ )Nz1Length of pad must be even but instead it equals rX  )r  s   r9  rT  !constant_pad_nd.<locals>.<lambda>  s    CCH:Nr;  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.rX  )l_inpr  s   r9  rT  r    s      225c(;P'r;  rV  c              3   *   #    U  H	  oS :  v   M     g7frA  rR  )rM  ps     r9  rO  "constant_pad_nd.<locals>.<genexpr>  s     '3aE3s   c            	      F   > STTT -       STT    STTS-       STT -    S3	$ )NzThe input size z, plus negative padding r  rV  zG resulted in a negative output size, which is invalid. Check dimension z of your input.rR  )rD  input_sizesl_diffr  pad_idxs   r9  rT  r    sE    ok&1*&=%>>V7|nE#gk"2!3 4117!OMr;  r  F)rb  rm  rY  rZ  rl  r   rQ  r   r   rf  r  r  r  r  r  r8  r  r  rG   r  r   )r  r  r  l_padc_input	new_shapenew_dimr  rB  c_outputrD  r  r  r  r  s    `        @@@@@r9  r   r     s   
 
LLC1N
 ++KEHMEU]F	LL	 G65!uqy1}%w<!nnQWw}}Q7G#g,7VWGw{annQ7==+;c'A+>N+NOG "" ||'3'''}}[&)*I5\c(q1uk*fqj)CL83w{;KKqLM M	
 	!  //6M[[kk||))#F zekkUZZ/ZZ&FH65!uqy1}%w<13w<!2S\!AH w{q q!X^^A->Wq[AQ-QRH " 
MM($Mr;  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 operatorrR  rR  r;  r9  rT  contiguous.<locals>.<lambda>   s    Rr;  r  )rb  rm  r   r   r   )rr  r  s     r9  r   r     s?     
LL...R 0O;;q66r;  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%dstack expects a non-empty TensorListrR  rR  r;  r9  rT  dstack.<locals>.<lambda>,      +Rr;  rF  )rb  rm  rY  r   r   r  s     r9  r   r   *  1    	LLW!#RS '*O""r;  )implicitr  c                  ^^ SSK JnJnJnJn  [
        R                  R                  R                  R                  n[        U5      S:X  a&  [        US   [        5      (       a  [        US   5      n[
        R                  " [        U5      [        U R                  5      :  S 5        [        U5      [        U R                  5      -
  n[!        U5      n	[#        U R                  5       H  u  n
mX-   nX+   mU" TS:H  5      (       a  TX'   M$  U(       aO  U" T5      (       aB  U" T5      (       a5  U" T5      nU" T5      nUS:X  a  US:w  a  [
        R                  " TS:H  5        [
        R                  " U" TS:H  TT:H  5      UU4S j5        [
        R                  " TS:  5        TX'   M     [$        R&                  " U	5        [(        R*                  " X	[        [-        U[        U R                  5      U-   5      5      5      $ )Nr   )rE  rF  rH  r}  rV  c                      g)Nz3expand: the requested shape has too few dimensions!rR  rR  r;  r9  rT  expand.<locals>.<lambda>D  s    Er;  r\  c                     > ST ST  S3$ )Nz3expand: attempting to expand a dimension of length  -> r  rR  )requested_lengthrN  s   r9  rT  r  j  s    MaSPTUeTffghr;  )ra  rE  rF  rH  r}  rb  rc  rd  re  rf  rY  r?  r   rg  rm  rZ  rf  rk  r  validate_shaper  rM  rl  )rr  r  rZ  rE  rF  rH  r}  rp  r  shape_r`  
offset_idxx_hintrequested_hintr  rN  s                 @@r9  r   r   1  s     %%--CCI
 5zQ:eAh99eAh	LLE
c!''l"E
 Z#agg,&F%[FAGG$Q\
 , *b011!"F Xa[[X6F-G-G"1!*+;!<Q;>Q#6LLa(LLqAv/145h LL)Q./!1FI %N 
 !!	5vs177|f'<=> r;  c                 8    U R                  UR                  5      $ rJ  )r   rZ  rZ  s     r9  r   r   x  s    88AGGr;  chunksc           	         US::  a  SU S3n[        U5      e[        R                  " U R                  U5      nU R                  U   n[
        R                  " XA-  5      n[
        R                  " XE-  5      nXE-  n[        U5       Vs/ s H  n[        XX-  U5      PM     n	nUS:w  a  U	R                  [        XXe-  U5      5        [        U	5      $ s  snf )Nr   z%Expected at least one chunk, but got r  )rn  r  r  rJ  rZ  r8  r9   rI   rl  r   r  rg  )
rr  r#  r  r  length
chunk_sizefull_chunkstail_chunk_sizerD  r  s
             r9  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                 F   [         R                  " U R                  U5      n[         R                  " U R                  U5      nX:X  a  U R                  S:w  a  U $ [        R                  " XUS S9u  p4Ub  [        R
                  " XU5      $ [        R                  " XU5      $ )Nr   must_be_valid)r  r  rJ  r  _collapse_view_helpercollapse_viewcollapse)rr  r)  r*  r  _new_stridess        r9  r   r     s    &&qvvy9I$$QVVW5G !
 $99	gTI ""199 >>!00r;  c                    [        U[        5      (       d   [        U[        5      (       d  [        S5      e[        R
                  " U R                  U5      n[        R                  " U5        [        R                  " X5      $ )Nz!dims has to be a sequence of ints)
r?  rg  rf  rn  r  canonicalize_dimsrJ  validate_no_repeating_dimsr  rev)rr  rW  s     r9  r   r     s\     dE"":dD+A+A<==""16640D	$$T*99Qr;  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )NrF  zInput must be >= 2-d.rV  rJ  ri  r   r  s    r9  r   r     %    vvz2334=r;  c                 P    U R                   S:  a  [        S5      e[        U S5      $ )NrV  zInput must be >= 1-d.r  r8  r  s    r9  r   r     r9  r;  r  r%  c                 t  ^^^ [        T[        5      (       a`  [        R                  " TR	                  5       S:H  =(       a     [
        R                  " TR                  5      S 5        TR                  5       m[        [        T5      m[        R                  " U R	                  5       S:  S 5        [        R                  " TS:  S 5        [
        R                  " U R                  U5      nU R                  U5      m[        R                  " [        T* T:*  =(       a    TT:*  UU4S j5        TS:  a  TT-   m[        R                  " TTT-
  :*  UUU4S j5        [!        U R"                  5      nTXA'   U R%                  X@R'                  5       U R)                  5       U R'                  U5      T-  -   5      $ )Nr   c                      g)Nz'start must be an 0-dim integral Tensor.rR  rR  r;  r9  rT  narrow.<locals>.<lambda>  s    =r;  c                      g)Nz-narrow() cannot be applied to a 0-dim tensor.rR  rR  r;  r9  rT  r=    s    &Ur;  c                      g)Nz&narrow(): length must be non-negative.rR  rR  r;  r9  rT  r=    s    &Nr;  c                     > ST *  ST  ST S3$ )Nz0start out of range (expected to be in range of [, z], but got )rR  )
dim_lengthr  s   r9  rT  r=    s#    BJ;-rR\Q]]hinhoopqr;  c                     > ST ST ST  S3$ )Nzstart (z) + length (z) exceeds dimension size (z).rR  )rC  r%  r  s   r9  rT  r=    s    '%VH4NzlZ\]r;  )r?  r'   rb  rm  r  r  r  r  r   r   r  r  rJ  rP  _check_with
IndexErrorrf  rZ  r   rL  rR  )rr  r  r  r%  r  rC  s     `` @r9  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 r;  	norm_dimsepsc                 h   [         R                  " U R                  U5      n[         R                  " U R                  5      n[        X5      n[        U[        5      (       d  [        S[        U5       35      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.
za_acc must be TensorLike, got FTr  r  r  )r  r3  rJ  r  r  r+   r?  r'   r  r6  rb  r   r   )	rr  rG  rH  r  a_acc
biased_varr   rstdr  s	            r9  
_normalizerN    s    $ ''	:I33AGG<#A9EeZ((=d5k]KLL~~udJ ;;z'(D<4
Cd?r;  
dimensionsc                 V    [        U5       H  n[        R                  " X5      n M     U $ rJ  )sortedrb  r  )rN  rO  r  s      r9  _unsqueeze_multiplerR    s$    j!OOA# "Hr;  weightbias
batch_sizenum_channelsflattened_inner_size
num_groupsc                 x  ^ ^ [         R                  " T R                  S:  U 4S j5        [         R                  " UT-  S:H  U U4S j5        [        R                  " T R
                  5      n[        T U5      n	SS/n
[         R                  " U	UTUT-  U/5      n[        R                  " UR                  U
5      n
[         R                  " XSSS9u  p[         R                  " X-   5      nT R                  R                  S	:X  a  Ub  [         R                  " US
TUT-  S
/5      nX-  nU* U-  nUb#  [         R                  " US
TUT-  S
/5      nUU-   nUR                  5       R                  X4/US
/5      nUR                  5       R                  X4/US
/5      n[        [!        ST R                  5      5      n[#        UU5      n[#        UU5      nU	U-  U-   nOmX-
  U-  nUR%                  T R&                  5      nS/[        [!        ST R                  5      5      -   nUb  [#        UU5      nUU-  nUb  [#        UU5      nUU-   n[        UT R
                  5      n[        UT R
                  5      n[        UT R
                  5      n[         R(                  " X5      n[         R(                  " X5      nUX4$ )NrF  c                  "   > ST R                    3$ )Nz=Expected at least 2 dimensions for input tensor but received r  r  s   r9  rT  #native_group_norm.<locals>.<lambda>  s    OPUPZPZ|\r;  r   c                  .   > SST R                    ST 3-   $ )NzDExpected number of channels in input to be divisible by num_groups, zbut got input of shape z and num_groups = rB  )r  rX  s   r9  rT  r[    s!    V#EKK=0B:,
OPr;  r  FTrJ  r  rV  )rb  rm  rJ  r  r  r  r+   r   r3  r   r   r8  r6  r   r   rf  rl  rR  r	  rZ  r   )r  rS  rT  rU  rV  rW  rX  rH  r  	input_accrK  input_reshapedrL  r   rM  weight_reshapedwrs  bias_reshapedrP  unsqueeze_wunsqueeze_br  unsqueeze_weightunsqueeze_biass   `     `                  r9  r   r   
  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$89926>J((C0~FN&C
!#u{{
3C"45D"45D ==.D==.Dr;  out2normalized_shapec                   ^ ^^^ SSK Jn  [        T5      n[        R                  " US:  U4S j5        [        R                  " TS L =(       d    U" TR
                  [        T5      5      UU4S j5        [        R                  " TS L =(       d    U" TR
                  [        T5      5      UU4S j5        [        R                  " T R                  U:  =(       a,    U" T R
                  T R                  U-
  S  [        T5      5      U U4S j5        [        T 5      m Tb  [        T5      mTb  [        T5      mT R                  U-
  n[        [        UT R                  5      5      n[        T X5      u  pnTc	  Tb  U	T-   n	OTb	  Tc  U	T-  n	OTb  Tb  U	T-  T-   n	[        U	T R                  5      n	T R                  R                  S;   a,  [        U
T R                  5      n
[        UT R                  5      nXU4$ )	Nr   sym_eqrV  c                      > S[        T 5      -   $ )NzzExpected normalized_shape to be at least 1-dimensional, i.e., containing at least one element, but got normalized_shape = )r  )rg  s   r9  rT  #native_layer_norm.<locals>.<lambda>`  s     I

 r;  c                  R   > S[        TR                  5      -   S-   [        T 5      -   $ )NzQExpected weight to be of same shape as normalized_shape, but got weight of shape  and normalized_shape = r  rZ  )rg  rS  s   r9  rT  rl  j  s3     
fll
 %% 
	 r;  c                  R   > S[        T R                  5      -   S-   [        T5      -   $ )NzMExpected bias to be of same shape as normalized_shape, but got bias of shape rn  ro  )rT  rg  s   r9  rT  rl  s  s2     
djj/ %% 
	 r;  c                  p   > S[        T5      -   S-   [        T5      -   S-   [        T R                  5      -   $ )NzGiven normalized_shape=z, expected input with shape z, but got input of size ro  )r  rg  s   r9  rT  rl    sI    )

 
() 
  %	%
 ekk
r;  )r  mtia)ra  rj  rY  rb  rm  rZ  rg  rJ  r   rf  rl  rN  r+   r  r8  r6  )r  rg  rS  rT  rH  rj  normalized_ndimaxisrK  r  r   rM  s   ````        r9  r   r   R  s    =*+O	LL1	  
LL$G&u5E/FG	  
LLCtzz51A+BC	  
LL

o% 	
KKo589"#
	 uEF#$::'D%ejj12N <OCt~$*Dj		Fl		 0FlT!
!#u{{
3C||O+&tU[[9&tU[[9tr;  c                     [        U6 $ rJ  )r   )	fake_modefuncr  r  s       r9  native_layer_norm_fakerx    s    d##r;  c                     [         R                  " U R                  [         R                  " U5      5      n[        R
                  " X5      $ rJ  )r  r3  rJ  extract_dims_from_varargsr  r  )rr  rW  _permutations      r9  r   r     s7    **	//5L ??1++r;  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       $ )Nc                      g)Nzrenorm: p must be real-valuedrR  rR  r;  r9  rT  renorm.<locals>.<lambda>  s    5Tr;  r   c                      g)Nz'renorm: non-positive norm not supportedrR  rR  r;  r9  rT  r    s     Ir;  c                      g)Nz#renorm: maxnorm must be real-valuedrR  rR  r;  r9  rT  r    s    2Wr;  c                     > ST  3$ )Nz,renorm: expected maxnorm to be >= 0 but got rR  )r|  s   r9  rT  r    s     LWIVr;  rV  c                     > ST  S3$ )Nz/renorm: input needs at least 2 dimensions, got  dimensionsrR  r  s   r9  rT  r    s    A${Sr;  T)r  r  r
  gHz>r  )rb  rm  r?  r  rJ  r  r  rf  rl  r  r  linalgvector_normr   r  r  r   )
r  r  r  r|  r|  acc_typerb   rH  norm_factorrJ  s
      `     @r9  r0  r0    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++--r;  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	c[  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-   $ )NzAstft input and window must be on the same device but got self on  and window on r7  r  r  s   r9  rT  stft.<locals>.<lambda>  s'    OPUP\P\~^/0r;  c                      g)Nz6stft only supports align_to_window for center = False.rR  rR  r;  r9  rT  r    s    Hr;     c                      g)Nzstft requires the return_complex parameter be given for real inputs, and will further require that return_complex=True in a future PyTorch release.rR  rR  r;  r9  rT  r    s    cr;  c                      g)Nz:stft expected a tensor of floating point or complex valuesrR  rR  r;  r9  rT  r    s    Lr;  rV  rF  c                      g)Nzstft expected a 1D or 2D tensorrR  rR  r;  r9  rT  r    s    /Pr;  r   r  c                     > ST  ST 3$ )Nzstft expected 0 < n_fft <= z, but got n_fft=rR  )r%  r  s   r9  rT  r    s    -fX5EeWMr;  c                     > ST  3$ )Nz0stft expected hop_length > 0 but got hop_length=rR  )hop_length_s   r9  rT  r    s    B;-Pr;  c                     > ST  3$ )Nz9stft expected 0 < win_length <= n_fft but got win_length=rR  )win_length_s   r9  rT  r    s    KK=Yr;  c                  0   > ST  S3STR                    3-   $ )Nz8expected a 1D window tensor of size equal to win_length=rA  zbut got window with size rB  )r  r  s   r9  rT  r  "  s#    F{mSUV)&,,89r;  r}  r\  )	dimensionrP  steporthoc                      g)Nz9Cannot have onesided output if window or input is complexrR  rR  r;  r9  rT  r  =      Or;  r  rb   )rb  rm  r8  r/  r  r  r  r  rJ  r  	itertoolsr   rZ  r  r  r	  rP  r%  r   r  fftrfft
transpose_squeeze_view_as_real)r  r  r  r  r  r  r  r  r  r  r  return_complex_original_ndim
extra_dims
pad_amountextended_shapeleftinput_pad_amountcomplex_fftrb   r  r  r%  r  s   ``  `                @@@r9  r1  r1    s    
LL$7&--5<<7	
 
LL
-o-H
 !+ 6*EQJK * 6*EK**, 
$G5#9#9&,,#G 	 		
 )	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#'>>r;  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      m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TU:g  nU(       a%  [         R                  " US	-  S-   T:H  U4S j5        O[         R                  " UT:H  U4S j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c@  [        R                  " T R
                  5      n[         R                  " XT 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:w  a   [)        ST R                  S	5       SU 35      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      R1                  SX45      UR                  S5      U4SUU
S9nUUR                  S5      :w  a!  [)        SU SUR                  S5       S35      eUUR                  S5      :w  a!  [)        SU SUR                  S5       S35      eU(       a  US	-  OSnUb  UU-   nOU(       a  XS	-  -
  nOUn[3        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R5                  S5      nUU:  a1  [6        R8                  " SS	S9  [        R                  USUU-
  4S5      nU$ ) Nc                  B   > ST R                    3STR                    3-   $ NzBistft input and window must be on the same device but got self on r  r7  r  s   r9  rT  istft.<locals>.<lambda>[  s(    PQVQ]Q]P^_/0r;  r  c                  @   > ST R                    STR                    3-   $ r  r7  r  s   r9  rT  r  f  s!    Pofmm_=>r;  r\  rV  r   c                      g)Nz"istft input tensor cannot be emptyrR  rR  r;  r9  rT  r  o  s    ,Pr;  rF  r  c                  "   > ST R                    3$ )Nz8istft expected a tensor with 2 or 3 dimensions, but got r  r  s   r9  rT  r  r  s    J5::,Wr;  c                     > SST  3-   $ )NMistft expected the frequency dimension (3rd to the last) of the input tensor z3to match n_fft / 2 + 1 when onesided=True, but got rR  fft_sizes   r9  rT  r  y  s    _GzRSr;  c                     > SST  3-   4$ )Nr  z,to match n_fft when onesided=False, but got rR  r  s   r9  rT  r    s    _@
KLr;  c                      g)Nz+istft expected 0 < hop_length <= win_lengthrR  rR  r;  r9  rT  r    rH  r;  c                      g)Nz&istft expected 0 < win_length <= n_fftrR  rR  r;  r9  rT  r    s    *Rr;  c                      g)NzDInvalid window shape. window has to be 1D and length of `win_length`rR  rR  r;  r9  rT  r    s    Vr;  r}  r  c                      g)Nz9cannot have onesided output if window or input is complexrR  rR  r;  r9  rT  r    r  r;  r  c                      g)Nz:Complex windows are incompatible with return_complex=FalserR  rR  r;  r9  rT  r        Pr;  )r  r  r%  z%Expected input.size(2) == n_fft, got z != )r  r  rP  r  zexpected_output_signal_len (z) != y.size(1) (rB  z) != window_envelop.size(1) (zThe length of signal is shorter than the length parameter. Result is being padded with zeros in the tail. Please check your center and hop_length settings
stacklevel)rb  rm  r8  r  r  r  rP  r  rJ  rZ  corresponding_real_dtyper%  r  r   r  r  r  ifftr   irfftr  r	  unfold_backwardr   r   rj  r   warningswarn)r  r  r  r  r  r  r  r  r%  r  r  r  n_framesexpected_output_signal_len	onesided_
real_dtypewindow_r  r  rb   y_tmpr  window_envelopr  endr  s   `   `                    @r9  r2  r2  L  s    
LL$7&--5<<7	
 !+ 6*EQJK * 6*EK	LLu{{+	
 zz"~Hzz"~H!&1)E!E	LL"$PQ	LL	UZZ1W %0h%6GIQJNh&	
 	X	
 
LL	K&&;&= 
LL	K  5 "R 
LL$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zz!}3EJJqM?$ugN
 	
 GLL!Q//EZZ]$>? 	 	A ))Aq(23ZZ]$>? * N "QVVAY.*+E*FFVWXW]W]^_W`Vaabc
 	
 "^%8%8%;;*+E*FFcdrdwdwxydzc{{|}
 	
 !EQJaEfn	(A:5(C%K F	QeF3A#**qf*MN	NAIIaL
''`	

   Q.H(H$I1MHr;  a_shapea_strider  r  c                   ^^^	^
 [        U 5      n[        R                  " XRSS9m	US:X  a  SOU T	   m
US:X  a  SOUT	   n[        R                  " TT
:*  U	U
U4S j5        [        R                  " TS:  U4S j5        [        U 5      n[        U5      nUR                  T5        UR                  U5        T	U:  a  UT	   T-
  T-  S-   UT	'   UT	==   T-  ss'   Xx4$ )NT)wrap_scalarr   rV  c                     > ST  ST ST 3$ )Nz%Maximum size for tensor at dimension z is z but size is rR  )r  max_sizerP  s   r9  rT  *_get_unfold_shape_stride.<locals>.<lambda>  s    7uD
-X\W]^r;  c                     > ST  S3$ )NzStep is z but must be > 0rR  r  s   r9  rT  r    s    (4& 01r;  )rY  r  r  rb  rm  rf  r  )r  r  r  rP  r  a_ndimlast_striderZ  stridesr  r  s      ``    @@r9  _get_unfold_shape_strider    s     \F

 
 
ECaKqWS\H{!K	LL^
 
LLq1
 ME8nG	LLNN;
V|Cj4'D014c
>r;  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      $ )
NFrn  c                      g)Nzbrepeat: Number of dimensions of repeat dims can not be smaller than number of dimensions of tensorrR  rR  r;  r9  rT  repeat.<locals>.<lambda>  s    tr;  r   rV  c              3   .   #    U  H  u  pX-  v   M     g 7frJ  rR  )rM  padded_sizerepeat_sizes      r9  rO  repeat.<locals>.<genexpr>  s      (G$K 	!(G   r  T)keyreverse)r  rx  rb  rm  rY  rZ  r   rJ  r  rg  r  r  r  r8  r  r  make_contiguous_strides_forrk  r  rj  rf  sortr  
itemgetterr   r   r   )rr  repeat_shapenum_new_dimensionspadded_shapedim_sizetarget_shapeurtensor_shapeurtensor_strider  enumerated_stridepermute_order_sorted_striderepeat_xtensorcloned_resultpermuted_results                  r9  r   r     s    33L5QL	LLLS\)t
 <A{{1~\*QVV33++LGGH%   (+L(G L 	L{{''88//55a8
 	
 "N77EO"<0*BSC!<L+
' 1 Y78x2215tD$'):$;!M XXn-N KK/M $++M:O ""<00r;  
allow_copyc                   ^
^ SmU m
U GHW  nTT
R                   :  aP  US:w  a  [        SU S35      eT
R                   S-
  n[        R                  " T
UT
R                  U   5      m
TS-   mMd  UT
R                  T   :X  a  TS-   mM~  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  aw  [        R
                  " T
TUS S9u  pxUcN  U(       a  [        R                  " X5      s  $ SU R                   SU R                  5        SU S	3n	[        U	5      e[        T
TU5      m
XS:w  a  [        R                  " T
TU5      m
TS-   mGMZ     TT
R                   :  aJ  [        R                  " T
R                  T   S:H  U
U4S
 j5        [        T
T5      m
TT
R                   :  a  MJ  T
U L a  [        R                  " U 5      $ T
$ )Nr   rV  z'Cannot unsqueeze dimension with length z, expected 1r,  z Cannot view a tensor with shape z and strides  as a tensor with shape r  c                  .   > ST ST R                   T    3$ )Nza.size(z) expected to be 1 but got rB  )r  r`  s   r9  rT  /_reshape_view_helper_core_alg.<locals>.<lambda>  s    gcU"=bhhsm_Mr;  )rJ  r  r  	split_dimrZ  r.  r   rL  rn  r   rb  rm  r   r{  )rr  rZ  r  r%  last_dimaccumr  r  r1  r  r  r`  s             @@r9  _reshape_view_helper_core_algr	  A  s   ( C	
B"''>{$=fX\R  ww{H Xrxx/ABB'C RXXc]"'Cn!1HCRXXc]"E n! #: ',&A&ACD'#I   ==228	qxxzlZrsxryyz{ o%S#&B ?S&1BAg_ d -HHSMQM	
 R - 
Qw}}Q	r;  c                6  ^ ^ [         R                  " TSS9m[         R                  " TT R                  5       5      mT R                  5       S:X  a!  [	        T T[         R
                  " T5      5      $ T R                  S:X  aH  T nT H#  nUS:w  a  [        SU 35      e[        US5      nM%     UT L a  [        R                  " T 5      $ U$ [        T5      S:X  aR  T nT R                   H#  nUS:w  a  [        SU 35      e[        US5      nM%     UT L a  [        R                  " T 5      $ U$ [        T 5      (       a  [        T5      S:X  a8  T R                  S:  a(  [        R                  " T T R                  5       /S/5      $ [        T5      S:X  a5  T R                  S:X  a%  TS   nTS   n[        R                  " T XV/US/5      $ [!        ["        R$                  TS5      n[        R&                  " T R                  5       U:H  U U4S	 j5        [)        T TU5      $ )
NFrn  r   rV  z<Cannot reshape 0-dim tensor: shape dimension must be 1, got r\  z?Cannot reshape to 0-dim tensor: shape dimension must be 1, got rF  c                  *   > ST R                    ST S3$ )Nz&Could not reshape a tensor with shape r  r  rB  rr  s   r9  rT  &_reshape_view_helper.<locals>.<lambda>  s    8	AYZ_Y``abr;  )r  rx  
infer_sizer  r   r  rJ  r  r  r  r{  rY  rZ  r   r   rb  r   r  r   rm  r	  )rr  r  rZ  _ar%  dim0dim1shape_numels   ` `     r9  _reshape_view_helperr    s   ,,UUCE UAGGI.E 	wwyA~!UE$E$Ee$LMM 	vv{F{$RSYRZ[  2r"B  7==##I 5zQggF{$UV\U]^  RB  7==##Ia  u:?qvvz##A	{QC88u:?qvv{8D8D##A|dAY??ua0K	LL		[ b )E:>>r;  rZ  c                      [        U /UQ7SS06$ )Nr  T)r  rr  s     r9  r   r     s    ;E;d;;r;  c                 @    U R                  UR                  5       5      $ rJ  )r   rP  r  r-  s     r9  r   r     s    <<

%%r;  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::  a  [!        SU 35      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      $ )z/Reference implementation of :func:`torch.roll`.r   zDimension specified as z but tensor has no dimensionsrV  z`shifts` requiredz*shifts and dimensions must align. shifts: z, dims: zExpected len_dims > 1, got Nr7  )r  r3  rJ  r?  r   r  r   r  rY  rF  ri  rb  r   r   r	  rZ  r  r  r8  rO   r   )rr  r  rW  
len_shiftslen_dimstail_shifts	tail_dimsfirst_dim_rolledr  rP  r  r`  s               r9  r   r     s   
 ""16640Dfh''dH%%w 	wwyA~wwy 	uuw!|D	A%d1gY.KL
 	
 VJ4yHQ(a-?233 q=Z1_::emmA.:??HH!<ZLQYPZ[  q= #>xj!IJJQRjH	 !::a)tAw?zz*CC
 q'C773<D1I%E
,,tHH
-C>>#uzz%+t<==r;  r   rV  kc                    [        U5      S:w  a  [        S[        U5       35      eU R                  S:  a  [        SU R                   35      e[        R                  " U R                  U5      nUS   US   :X  a  [        SUS    SUS    35      eUS-  nUS:X  a6  [
        R                  " [
        R                  " XS   45      US   US   5      $ 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$ )z0Reference implementation of :func:`torch.rot90`.rF  z2expected total rotation dims == 2, but got dims = z/expected total dims >= 2, but got total dims = r   rV  z7expected rotation dims to be different, but got dim0 = z and dim1 = r  r  r  )
rY  ri  rJ  r  r3  rb  r  r   r   rW  )rr  r  rW  s      r9  r   r     s9    4yA~@TL
 	
 	vvzLQVVHUVV ""16640DAw$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==r;  c                    ^ SSK Jn  U S   R                  m[        S[	        U 5      5       H1  n[
        R                  " U" X   R                  T5      U4S j5        M3     g )Nr   ri  rV  c                     > ST  S3$ )Nz4stack expects each tensor to be equal size, but got z at entry 0 rR  )entry_shapes   r9  rT  %_check_stack_inputs.<locals>.<lambda>B  s    J;-Wcdr;  )ra  rj  rZ  rl  rY  rb  rm  )r  rj  rD  r"  s      @r9  _check_stack_inputsr$  ;  sK    <!*""K1c'l#7:##[1d	
 $r;  c                    [        U 5      S:X  a  [        S5      e[        R                  " U S   R                  S-   U5      nX S   R                  :  ae  [        U 5        [        U S   R                  5      nUR                  U[        U 5      5        [        R                  " X5      nUR                  U5      $ [        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 TensorListrV  )rY  r  r  r  rJ  r$  rf  rZ  insertrb  r   r	  r  )r  r  wrapped_dimresult_sizesr  r   s         r9  r   r   F  s     7|qCDD((1)<cBKQZ__$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  r  r  r+   r  rC   r   r   r   )rr  r  r  r  r  r  a_expa_maxs           r9  rq   rq   Y  s{     #AGGL33LA	 	6BwwyA~BRd+BJ"E3u489 r;  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 TensorListrR  rR  r;  r9  rT  hstack.<locals>.<lambda>q  r  r;  rV  )rb  rm  rY  r   rJ  r   r  s     r9  r   r   o  sQ    	LLW!#RS '*Oq!#?A&&""r;  c                 r    [         R                  " [        U 5      S:  S 5        [        U 6 n[	        US5      $ )Nr   c                      g)Nz%vstack expects a non-empty TensorListrR  rR  r;  r9  rT  vstack.<locals>.<lambda>{  r  r;  )rb  rm  rY  r   r   r  s     r9  r  r  y  r  r;  rU  c                 *   [         R                  " U R                  U5      n[        R                  " [        U5      S:g  S 5        U R                  [        U R                  S U 5      [        U5      -   [        U R                  US-   S  5      -   5      $ )Nr   c                      g)Nz"unflatten: sizes must be non-emptyrR  rR  r;  r9  rT  unflatten.<locals>.<lambda>  s    *Nr;  rV  )	r  r  rJ  rb  rm  rY  r	  rg  rZ  )rr  r  rU  s      r9  r  r    so    

 
 
-C	LLUq"NO66%&u5aggcAgi>P8QQRRr;  r   c                 8  ^ [         R                  " U R                  T5      m[        R                  " [        U R                  5      S:  S 5        U R                  T   S:X  a  g[        U4S j[        R                  " X R                  T   T5       5       5      $ )Nr   c                      g)Nz5Dimension specified as 0 but tensor has no dimensionsrR  rR  r;  r9  rT  unbind.<locals>.<lambda>  s    Gr;  rR  c              3   R   >#    U  H  n[         R                  " UT5      v   M     g 7frJ  )rb  r   )rM  sr  s     r9  rO  unbind.<locals>.<genexpr>  s#      
+SaEMM!S!!+Ss   $')	r  r  rJ  rb  _check_indexrY  rZ  rg  r  )r   r  s    `r9  r  r    s~    

 
 
-C	AGGqG 	wws|q 
+0+=+=as+S
 
 	
r;  r2  r  c                 \    U R                  [        R                  S9R                  XU5      $ r  )r   rb  rW  rN   )rN  r  r2  r  s       r9  rM   rM     s+    77!8!879EEF r;  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        U R                  S:X  a  U R                  S5      OU n[        S 5      4U-  T4-   nX4U'   U $ )NrV  c                  $   > ST R                    S3$ Nz(Index should have dimension 1 or 0 (got rB  r  r2  s   r9  rT  index_copy_.<locals>.<lambda>      :5::,aHr;  r   )r  r3  rJ  rb  rm  r  slice)rN  r  r2  r  r  r`  s     `   r9  rN   rN     sq    

!
!!&&#
.C	LL

aH
 &&A+A1A;.3
%
)CcFHr;  c                     [        XX#SS9$ )NFinplace_index_fillrN  r  r2  r  s       r9  rP   rP     s    
 quU;;r;  c                     [        XX#SS9$ )NTrE  rG  rI  s       r9  rQ   rQ     s     quT::r;  rF  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	$ )NrV  c                  $   > ST R                    S3$ r?  r  r@  s   r9  rT  _index_fill.<locals>.<lambda>  rB  r;  r   c                  $   > ST R                    S3$ )Nz<Only supports 0-dimensional value tensor. Got a tensor with r   r  r  s   r9  rT  rM    s     !!&L:r;  )r  r  r8  )rb  rm  rJ  r?  r'   r(  r  r  r8  r  rf  rZ  r  r   rg  rN   rM   r   r   rL  r  copy_)rN  r  r2  r  rF  zero_dimr  rZ  rM   r  new_outs     ``       r9  rH  rH    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
r;  c                \    U R                  [        R                  S9R                  UUUUS9$ )Nr  rl  )r   rb  rW  
index_add_)rN  r  r2  r  rm  s        r9  rL   rL     s:     77!8!879DD	 E  r;  c                   ^ [         R                  " U R                  U5      n[        R                  " TR                  S:*  U4S j5        TR                  S:X  a  TR                  S5      mU R                  S:X  a6  [        R                  " U 5      R                  STU R                  T5      5      $ [        S 5      4U-  T4-   nX   R                  5       $ )NrV  c                  $   > ST R                    S3$ r?  r  r@  s   r9  rT  index_select.<locals>.<lambda>  rB  r;  r   )r  r3  rJ  rb  rm  r  r  rM   r   rC  r   )rN  r  r2  r`  s     ` r9  rO   rO     s     
!
!!&&#
.C	LL

aH zzQ"vv{ "--aE8JKK;.3
%
)C6r;  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  a9  [        U5      S:X  d  US:X  d  [        SU 35      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   r  c              3   :   #    U  H  u  pUS :X  d  M  Uv   M     g7fru  rR  )rM  r`  rP  s      r9  rO  squeeze.<locals>.<genexpr>  s     J*<YS	SS*<s   	r  z8Expected dims to be empty or (0,) for 0-dim tensor, got c              3   f   >#    U  H&  nT" TR                   U   S :H  5      (       d  M"  Uv   M(     g7fru  rB  )rM  drr  rE  s     r9  rO  rY  (  s&     DDqN1771:?$CDs   !1	1rV  T)r  )ra  rE  rg  rk  rZ  r  r   r{  rJ  r  r3  r?  r   rY  r  rf  rQ  )rr  r  rW  rJ  	dims_listrD  rE  s   `     @r9  r   r     s*   D
{J)AGG*<JJ)-u}}Q%C5==3CC66D

!
!$
,CS))C6sDqyD	Q$$, J4&Q  }}Q DDDDD
4yA~}}Q
4yA~}}Q%%T
Iy$/IAqM Hr;  split_sizesc                   ^ ^^ [        [        T5      5       H!  n[        R                  " TU   S:  S 5        M#     [        R                  " [
        [        R                  " T5      T R                  T   :H  UU U4S j5        / nT R                  5       nT He  n[        T R                  5      nXgT'   UR                  T R                  UT R                  5       U5      5        UT R                  5       T   U-  -   nMg     U$ )Nr   c                      g)NzCsplit_with_sizes expects split_sizes have only non-negative entriesrR  rR  r;  r9  rT  "split_with_sizes.<locals>.<lambda>=  s    Yr;  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 )rQ  r   rZ  )r  r  r]  s   r9  rT  r`  B  s,    (k)B(CCabfblblmpbqarsr;  )rl  rY  rb  rm  rE  rn  rQ  r   rZ  rR  rf  r  r   rL  )r  r]  r  rD  splitsr  
split_sizer  s   ```     r9  r   r   4  s     3{#$NaY	
 %
 
[!TZZ_4s F  "F!
$	## 	dooiGH$++-,z99 " Mr;  indices_or_sectionsc                    [         R                  " U R                  U5      nU R                  S:X  a  Sn[        U5      e[	        U[
        5      (       al  UR                  R                  S:w  a  SUR                   3n[        U5      eUR                  [        R                  :w  a  SUR                   3n[        U5      e[	        U[        5      (       d%  [	        U[
        5      (       a  UR                  S:X  a  [	        U[        5      (       a  UOUR                  5       nUS::  a  SU 3n[        U5      eU R                  U   n[        R                   " Xe-  5      nXe-  n/ n	[#        U5       H   n
X:  a  US-   OUnU	R%                  U5        M"     ['        [(        R+                  X	US95      $ 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!r  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 rV  r  zntensor_split: non-scalar indices_or_sections tensors must have only one dimension, but received a tensor with r  )r  r  rJ  rn  r?  r'   r8  r6  r  rb  longr   r!   r   rZ  r8  rI   rl  r  rg  r  r   tolistrf  rY  )rr  rd  r  _dimr  sectionsr  min_split_sizenum_splits_one_extrar]  	split_idxrc  indicesrD  s                 r9  r  r  T  s|   
 !!!&&#.Dvv{ho %z22%%**e3'':'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      $ )NrV  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.hsplit requires a tensor with at least 1 dimension, but got a tensor with  dimensions!r  rJ  r  s   r9  rT  hsplit.<locals>.<lambda>      ^!&&kr;  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 r  ro  )rr  r  rc  s   r9  rT  rs    sS    Bc(45 aggcl#$ 9	9
 j/" r;  c                      > S[        T 5       3$ )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 r5  rd  s   r9  rT  rs         !4568r;  
rb  rm  rJ  r?  r   rZ  r  _check_typerf  rg  )rr  rd  r]  r  rc  s   `` @@r9  r   r     s     
LL	!	
 vv{!C%w//(
1_?
!:a!?	
 Az3//	&u6	
 &K;,,r;  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      $ [         R                  " [        T[        [        45      U4S j5        Tn[        T US5      $ )NrF  c                  :   > S[        T R                  5      -   S-   $ )NzPtorch.vsplit requires a tensor with at least 2 dimension, but got a tensor with rq  rr  r  s   r9  rT  vsplit.<locals>.<lambda>  rt  r;  r   c                  0   > ST R                   S    ST S3$ )NzQtorch.vsplit attempted to split along dimension 0, but the size of the dimension r   rv  r  rB  )rr  rc  s   r9  rT  r~    s%    3771:,6,r;  c                      > S[        T 5       3$ )Nzvsplit(): received an invalid combination of arguments. Expected indices_or_sections to be of type int, list of ints or tuple of ints but got type r5  rx  s   r9  rT  r~    ry  r;  rz  )rr  rd  r]  rc  s   `` @r9  r  r    s     
LL	!	
 %w//(
1_=j!8A!=	
 Az1--	&u6	
 &K;**r;  r  c                    ^ U R                  5       m[        R                  " TS;   U4S j5        TS:X  a  [        R                  " X5      $ [        R                  " X5      $ )N)rV  rF  c                     > ST  S3$ )Nz'diag(): Supports 1D or 2D tensors. Got DrR  r  s   r9  rT  diag.<locals>.<lambda>  s    "I$q Qr;  rV  )r  rb  rm  r   r   )r  r  rJ  s     @r9  r   r     sQ     88:D	LLQ qy--""400r;  r  dim2c                 `  ^^ SSK JnJn  [        R                  " U 5      nUR                  X#U5      m[        R                  " TR                  TR                  :H  =(       a5    U" U" S [        TR                  TR                  5       5       6 5      (       + UU4S j5        [        TT5        U$ )Nr   )rE  r}  c              3   .   #    U  H  u  pX:g  v   M     g 7frJ  rR  )rM  d1d2s      r9  rO  #diagonal_scatter.<locals>.<genexpr>  s     G,F&"RX,Fr  c                  <   > 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 rB  )r   r  s   r9  rT  "diagonal_scatter.<locals>.<lambda>  s"     yyk24::,@r;  )ra  rE  r}  r  clone_preserve_stridesr   rb  rm  rJ  r  rZ  r   )	r  r  r  r  r  rE  r}  r  r   s	    `      @r9  r   r     s     M

&
&u
-C<<d+D	LL		SXX 	
GC

CII,FGH
 
	@ D#Jr;  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:  aT  [        [        U R                  5       T   U R                  5       T   U-
  5      S5      nXQU R                  5       T   -  -  nOS[        [        U R                  5       T   U-   U R                  5       T   5      S5      n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 rA  rR  r  r  s   r9  rT  diagonal.<locals>.<lambda>*       HbQUPVWr;  r   )rP  rL  rR  )r  r  r  rb  rm  rR  r   r   rP  rL  rk  r  r   )r  r  r  r  num_dimsrR  	diag_sizerD  r9  rU  r  r  s     ``        r9  r   r     s    xxzH!!d:D!!d:D	LLW ((*N {GDIIK$5tyy{47H67QRTUV	4;;=#666GDIIK$5$>		D@QRTUV	4;;=#666$TYY[1K141QtTl5JQ1EK	LL&t{{}5O5TQ4,9Nq5GONN4;;=&t)<<=__%_WFM L Ps   5G G =G&G&c                 *  ^^ U R                   S-   n[        R                  " UTS9m[        R                  " UTS9mTT:  a  TTsmmU* n[        R                  " TT:g  UU4S j5        U R                  S5      nUS:w  a  [        U R                  5      n[        R                  " U5      US'   [        R                  " X`R                  U R                  SS9nUS:  a  Xp4OX4n[        R                  " USS9n U[        R                  " U5      -  nU R                  T5      R                  ST5      n [        R                   " XPR                  [        R"                  S	9n	[        R                   " XU-   U R                  [        R"                  S	9n
XR                  S5      :H  n[%        ['        U R                  5      5       Vs/ s H  oTT4;   a  UOSPM     nnUR)                  U5      n[        R*                  " X5      R-                  5       $ s  snf )
z.
Reference implementation of torch.diag_embed
rV  )r  r`  c                     > ST  ST 3$ r  rR  r  s   r9  rT  diag_embed.<locals>.<lambda>Y  r  r;  r\  r   Fr  r8  r  rf  r8  r  )rJ  r  r  rb  rm  rP  rf  rZ  rQ  r1   r*  r  r8  r   r  r   r  rj  rl  rY  r   mask_tensorr   )r   r  r  r  r  r  t_shapezpaira_rangeb_rangecondrD  
cond_shapes     ``          r9  r   r   B  s    66A:D!!t6D!!t6D d{4
d	LLW
 vvbzH{qww-ll6*KKwwqxxuU!v!IId#HLL(( 	
D!!"d+A ll8HHEKKHGll6!!((%++G
 ''++D@Ec!''l@ST@S1D$</(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$ s  snf )
z.
Reference implementation of torch.block_diag
rV  r\  c              3   >   #    U  H  oR                   S    v   M     g7fru  rB  )rM  r  s     r9  rO  '_block_diag_iterable.<locals>.<genexpr>  s     BzVazs   r   rF  c                  2   > ST  STR                  5        S3$ )Nz5Input tensors must have 2 or fewer dimensions. Input z has r  rf  )rD  r  s   r9  rT  &_block_diag_iterable.<locals>.<lambda>  s      CuVZZ\N+7r;  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 r  r7  )r8  rD  r  s   r9  rT  r    s&     $$*8;qcVWYr;  r  rf  )r  r	  rQ  r   r8  rk  rb  rm  rZ  r*  r  r   )r  r  
tensors_2dncolsr  	col_startrowcolr  rightr8  rD  s    `        @@r9  _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      $ )z
This is used as an input to PythonRefInfo. `torch.block_diag`
expects arguments splatted, but `aten.block_diag` expects only
one argument that is a list of Tensors.
)r  r  s    r9  r   r     s      ((r;  rj  c                    U R                   S:  a  [        SU R                    S35      e[        U[        5      (       a>  US:X  d  U R                  S   U-  S:w  a"  [        SSU R                  S    SU S	3-   5      e[        XS5      $ )
Nr  zPtorch.dsplit requires a tensor with at least 3 dimension, but got a tensor with rq  r   rF  z3torch.dsplit attempted to split along dimension 2, zbut the size of the dimension rv  r  )rJ  ri  r?  r   rZ  r  )rr  rj  s     r9  r   r     s    vvz^_`_e_e^ffrs
 	
 (G$$(a-1771:;PTU;UA.qwwqzl:^_g^hhijk
 	
 Q''r;  c                     U R                   S:  a  [        SU R                    S35      e[        R                  " U SU R                   S:  a  S5      $ S5      $ )NrF  z7t() expects a tensor with <= 2 dimensions, but self is r  r   rV  )rJ  ri  rb  r  r  s    r9  r   r     sS     	vvzEaffXQO
 	
 ??1aaffqj88a88r;  c                 l    [         R                  " U R                  S;   S 5        U R                  5       $ )N)r   rF  c                      g)NzcThe use of `x.T` on tensors of dimension other than 0 or 2 to reverse their shape is not supported.rR  rR  r;  r9  rT  T.<locals>.<lambda>  s    7r;  )rb  rm  rJ  r   r  s    r9  r   r     s,    	LL	&	
 335Lr;  c                 .    [         R                  " U 5      $ rJ  )r  r{  r  s    r9  r   r     r  r;  r  c                 *   [         R                  " U R                  X45      u  p4U R                  S::  d  X:X  a  [        R                  R                  U 5      $ [        [        U R                  5      5      nXEU'   X5U'   [        R                  " X5      $ r/  )
r  r3  rJ  r  r   defaultrf  rl  rb  r   )rr  r  r  _dim0_dim1r{  s         r9  r  r    sq    **166D<@LEvv{dlzz!!!$$aff&L==))r;  c                 t    [        U R                  U R                  5       XU5      u  pEU R                  XE5      $ rJ  )r  rZ  rL  r   )r  r  rP  r  rZ  r  s         r9  r  r    s4     .

DKKM9DNE ??5**r;  c                 \    U R                  XU5      R                  [        R                  S9$ r  )r  r   rb  rW  )r  r  rP  r  s       r9  r  r    s0     ;;y-33-- 4  r;  c                   UR                   n[        R                  " Xc5      nUS:X  a  U " UR                  S5      SXES9$ 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  rV  r7  r\  )
rJ  r  r  r  rb  r  rZ  r8  rl  r   )rw  initrr  r  r  r  rJ  rgr  r  masked_as              r9  _cumsumprod_commonr    s     66D

 
 
+CqyAKKN@@	C!GA	aggcl188	4B<<?b D4:>"~~b! #{{4D)H88r;  c          	      "    [        [        SXX#S9$ )Nr   rw  r  rr  r  r  r  )r  r   rr  r  r  r  s       r9  r   r     s     3Q!ESSr;  c          	      "    [        [        SXX#S9$ )NrV  r  )r  r   r  s       r9  r   r   $  s     4a1UTTr;  c                 x    U R                   S-   n[        R                  " X!5      n[        R                  " X4US9$ )NrV  r  )rJ  r  r  r  expand_dims)rr  r  rJ  s      r9  r  r  0  s6     66A:D

 
 
+CQT22r;  c                 0   SSK JnJn  [        R                  " [        [        [        [        [           4   U5      SS9n[        R                  R                  R                  R                  (       d  U" U U5      (       a  U" X5      $ [        U /UQ7SS06$ )Nr   )_view_has_unbacked_input_view_unbacked_metaFrn  r  )torch._subclasses.fake_implsr  r  r  rx  r   r   r%   rg  rb  rc  rd  re  rf  r  )rr  rZ  r  r  shape_tuples        r9  r	  r	  =  s     22U9eI../7%K xx$$::>V	? ? #122<E<e<<r;  c                 @    U R                  UR                  5       5      $ rJ  )r	  rP  r  s     r9  r
  r
  S  s    99UZZ\""r;  c                     [        U S5      $ )N)r\  )r   r  s    r9  r   r   X  s    1er;  rn  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      $ [        T R                  5      nTR                  U5      X2'   [        R                  " UTR                  5       5      n[        TU5      n[        TR                  5      nT R                  U5      Xb'   [        R                  " UT R                  5       5      n[        T U5      nUR                  U5      nXX-  n[         R                  " XrU5      $ )Nc                  >   > ST R                    STR                    S3$ )Nz]torch.take_along_dim(): input and indices should have the same number of dimensions, but got z dimensions for input, and z dimensions for indicesr  )rr  rn  s   r9  rT   take_along_dim.<locals>.<lambda>d  s%    --.VVH4O||n35r;  c                  $   > ST R                    S3$ )Nz?torch.take_along_dim(): dtype of indices should be int but got z insteadr  )rn  s   r9  rT  r  m  s    M}}oX'r;  r\  r   )rb  rm  rJ  r  r  r  gatherr	  rf  rZ  rP  infer_size_shapesr   )	rr  rn  r  
self_sizesbroadcast_shapeindices_broadcastindices_sizesself_broadcastr  s	   ``       r9  r   r   ^  s'    
LL	',,	
 
LLw}}-	
 {||AFF2J7<<+;<<!'']
!,,s+
11*gllnM(/BW]]+VVC[11-J%a9 "&&s+-8||N1BCCr;  r  r  r8  r  r  r  r  c           
        ^ [         R                  " T[         R                  :g  S 5        [        R                  " U5      nT[         R
                  :X  a  [        R                  " U5      nOmT[         R                  :X  a  [        R                  " U5      nOB[         R                  " T[         R                  :H  U4S j5        [        R                  " U5      n[         R                  " UUU UUUUS9$ )Nc                      g)Nz8torch.empty: the Preserve memory format is not supportedrR  rR  r;  r9  rT  empty.<locals>.<lambda>  s    Jr;  c                     > ST  S3$ )Nz/torch.empty: received an unknown memory format r  rR  r  s   r9  rT  r    s    Em_TUVr;  r  r  r8  r  r  )rb  rm  r   r  rx  rW  r  channels_last_3d!make_channels_last_3d_strides_forchannels_last!make_channels_last_2d_strides_forr  )r  r  r8  r  r  r  rZ  r  s        `  r9  r  r    s     
LL...J
 ,,U3E///33E:	%00	099%@U000V	

 99%@# r;  c                 2    [         R                  " U UUUUS9$ )Nr  )r  r  )rZ  physical_layoutr  r  r8  r  r  s          r9  r  r    s&     # r;  r  r  r8  r  c                    Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UUUUUS9$ )Nr  r8  r  r  )r  r  r8  rb  r  )rr  rP  r  r  r8  r  s         r9  r   r     sQ     }AGG%EQXXVFQXXVF;; 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US9$ )z<
Reference implementation of torch.Tensor.new_empty_strided
r  )r  r  r8  rb  r  )rr  rP  rL  r  r  r8  r  s          r9  r!  r!    sV      }AGG%EQXXVFQXXVF r;  r  c           
          [         R                  " U5      nU c  [        R                  " 5       n [        R                  " UU [        R
                  :X  a  SOSU UUUUS9$ NFr   r  r  rx  rb  r  r  r  r  r  r8  r  r  rP  s         r9  r*  r*    sZ     ++D1D}'')::%**$!# r;  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  r8  rb  r  r  rr  rP  r  r  r8  r  r  s          r9  r$  r$    sm     }AGG%EQXXVFQXXVF::"177uzz1q# 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$ NTrV  r  r  r  s         r9  r%  r%  .  sZ     ++D1D}'')::## r;  c          
          Uc  U R                   OUnUc  U R                  OUnUc  U R                  OUn[        R                  " UU=(       d    U R                   [        R
                  :X  a  SOSUUUUUS9$ r  r  r  s          r9  r#  r#  H  sm     }AGG%EQXXVFQXXVF::!!''ejj0a# r;  
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$ )Nr  )r  r  r8  rb  r  )rr  rP  r  r  r  r8  r  s          r9  r"  r"  c  sT     }AGG%EQXXVFQXXVF:: r;  c                     U$ rJ  rR  )rP  r  r  s      r9  	empty_outr  }  s	     Jr;  )r  r8  r  r  r  r  c          
      P   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      u  px[        R                  " U R                  UUUUUUS9$ )Nr  r  )
r  r  r8  rb  r   r  rZ  r  3compute_elementwise_output_logical_to_physical_permr  )	rr  r  r8  r  r  r  r  logical_to_physical_permr  s	            r9  r  r    s     }AGG%EQXXVFQXXVF---{{GG'!'
 	
 	AA!D   	 # r;  r  c          	      6  ^ ^^ [         R                  " U5        [         R                  " U5        [        R                  " [         R
                  " U5      5      n[        T [        5      (       a  [        S5      e[        T[        5      (       a  [        S5      e[        T[        5      (       a  [        S5      eTc  T mSm [        R                  " TS:g  S 5        TS:  a  [        R                  " TT :  S 5        O!TS:  a  [        R                  " TT :*  S 5        S n[        R                  " U" T 5      =(       a    U" T5      UU 4S	 j5        [        R                  " U" T5      U4S
 j5        T TT4n	[        R                  " S U	 5       5      n
Uc,  U
(       a  [        R                  O[        R                  " 5       n[         R                  " U5      nU(       d  U
(       a!  [        T 5      n[        T5      n[        T5      nU[        R                  :X  d  U
(       a,  [!        WS:  5      [!        US:  5      -
  nWW-
  U-   U-
  U-  nO["        R$                  " TT -
  T-  5      nU(       a  [&        R(                  " UWWUUUS9$ [&        R(                  " USS[        R                  USS9nU
(       a  [        R*                  O[         R,                  " X55      n[/        UU5      nT TU-  -   n[/        UU5      nU(       a  UR1                  S5        U$ )Nz%arange does not support complex startz#arange does not support complex endz$arange does not support complex stepr   c                      g)Nzstep must be nonzerorR  rR  r;  r9  rT  arange.<locals>.<lambda>  s    $:r;  c                      gNz7upper bound and lower bound inconsistent with step signrR  rR  r;  r9  rT  r        Mr;  c                      gr   rR  rR  r;  r9  rT  r    r  r;  c                 f    [        U [        5      (       + =(       d    [        R                  " U 5      $ rJ  )r?  r   r8  rR   rS  s    r9  	is_finitearange.<locals>.is_finite  s!    a!566J$--:JJr;  c                     > ST ST  3$ )Nzunsupported range: r  rR  )r  r  s   r9  rT  r    s    %eWD6r;  c                     > ST  3$ )Nzstep must be finite but got rR  r  s   r9  rT  r    s    .tf5r;  c              3   B   #    U  H  n[        U[        5      v   M     g 7frJ  rK  rM  r  s     r9  rO  arange.<locals>.<genexpr>  s     IDS
3 8 8D   )r  r  r  r8  r  rV  FT)r  check_layoutcheck_pin_memoryrb  r8  device_or_defaultr?  r  r  rm  rQ  r   rj  r  r  r   r  r8  r9   r  iotarg  get_acc_typer+   requires_grad_)r  r  r  r  r  r8  r  r  r  r  integer_args
is_integerxstartxendxsteprk   r%  r2  r  r  s   ```                 r9  r  r    s    
v	:&\\%11&9:F%!!DEE#wBCC$  CDD {	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$VU3Fd#Mr;  )r  r  rS  c                 
   X/n[        U[        5      (       a  U R                  SU5      nOUR                  U5        [        U[        5      (       d  [        S[        U5       35      eUR                  5       S:  n[        R                  " XBS-
  U5      n[        R                  " XAU 5      nXQU -
  -  U-   n[        R                  " [        U6 6 nUR                  5       U:w  a  [        R                  " Xx5      n[!        X75      $ )NrR  z)weight must be Tensor at this point, got r  rV  )r?  r!   r"  r  rg  r  r6  r1   rb  r   r  "compute_elementwise_output_stridesr  rL  r  copy_stridedrC  )	r  r  rS  r  r  coeffbaserB  rL  s	            r9  rY   rY     s     \F&&!!F+fff%%HfWXX ::<3DKKqj&1E;;t%(DEk"T)F557G7PQF}}& ##F3'77r;  )r  r8  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  [        S[        T5       35      e[        R                   " [        T["        5      UU U4S j5        [        T["        5      (       d  [        S[        T5       35      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$ [        R0                  " ST40 UD6n
[        R2                  " T5      (       d  [        R4                  " T5      (       a  [        R6                  OTn[        R8                  " U
[:        R<                  U5      u  p[?        [
        US9nTT -
  TS-
  -  n[        R@                  " U
TS-  :  T X" U
5      -  -   TX" TS-
  U
-
  5      -  -
  5      n[        UT5      $ )Nr   c                      gNz:linspace only supports 0-dimensional start and end tensorsrR  rR  r;  r9  rT  linspace.<locals>.<lambda>I  r  r;  c                      gr  rR  rR  r;  r9  rT  r   O  r  r;  c              3   B   #    U  H  n[        U[        5      v   M     g 7frJ  r?  r  r	  s     r9  rO  linspace.<locals>.<genexpr>S       L8KJsG,,8Kr  c                     > ST  ST 3$ )Nzlinspace(): inferred dtype z& can't be safely cast to passed dtype rR  )default_complex_dtyper  s   r9  rT  r   \  s    56K5LLrsxryzr;  dtype must be torch.dtype, got c                     > S[        T5      R                   S[        T 5      R                   S[        T5      R                   S3$ )Nz4received an invalid combination of arguments - got (rA  rB  )r6  r  )r  r  r  s   r9  rT  r   f  sB     u+r$s),,-RU0D0D/EQHr;  zsteps must be IntLike, got c                      g)Nz$number of steps must be non-negativerR  rR  r;  r9  rT  r   k  s    %Kr;  )r  r8  r  r  r  rV  r  rF  )r  r   )!r?  r(   rb  rm  r  r+   r  rQ  r   r  rT  r  r  r  r  r6  r{  r   r  r  opsr  r  r  r  r  r  rj  rL  r$   rk  r   r   )r  r  r  r  r8  r  r  r  factory_kwargsempty_tensorr  	dtype_redr  r  cast_rgr  r  r'  s   ````             @r9  r  r  9  s    %((IIK1P	
 (u}}=#~&&GGINP	
 &c5==9||LU8KLLL % A A##%!
 =)ELL&&u-z
 2002eU[[))>tE{mLMM 
5'"	H
 eW%%:4;-HII	LL!KL  &	N zzzAA.AAze^,, ;;xOuOOL99>>&&..|UCC::uhMUMnMM 
a	1.	1B
 ""5))U-C-CE-J-J 	 
 !11
&++Y -5FGG %KEAI&D
++
UQYwr{""dWeai2-...C
 #3..r;  r  c                   Uc  [         R                  " 5       n[        R                  R	                  U5      (       a  [        U [        5      (       a  [        U 5      n OI[        U [        5      (       a4  [         R                  " U R                  5       S:H  S 5        [        X5      n [        U[        5      (       a  [        U5      nOI[        U[        5      (       a4  [         R                  " UR                  5       S:H  S 5        [        X5      n[        R                  " S XU4 5       5      (       a.  [        R                  " [         R                  " 5       5      n	U	nS n
O[         R                  n
[        U[         5      (       a  [#        S[%        U5       35      eUS:  a  [&        e[         R(                  " U UUU
UUUUS9n[        [         R*                  " X;5      U5      $ )Nr   c                      gNz:logspace only supports 0-dimensional start and end tensorsrR  rR  r;  r9  rT  logspace.<locals>.<lambda>      Tr;  c                      gr2  rR  rR  r;  r9  rT  r3    r4  r;  c              3   B   #    U  H  n[        U[        5      v   M     g 7frJ  r#  r	  s     r9  rO  logspace.<locals>.<genexpr>  r%  r  zbase must not be complex, got r  )rb  r  r  r  r  r?  r   r   r(   rm  r  r+   rQ  r   rT  r  r  r  r6  r  r  r   )r  r  r  r  r  r8  r  r  r  r'  _dtyperets               r9  r  r    s    }'') {{##E**eY''ENE~..LL		q T ,E9Ec9%%#,C^,,LL	QT *#5C||LU8KLLL % A A##%!
 &$  =d4j\JKKax!!
..#	C #599T#7??r;  indexingc                     g rJ  rR  )r  r:  s     r9  r   r     s     	r;  c                     g rJ  rR  )r:  r  s     r9  r   r     s    r;  c                 v  ^ ^ [        US   [        [        45      (       a4  [        U5      S:w  a  [	        S[        U5       35      e[        US   5      n[
        R                  " [        R                  " S U 5       5      S 5        [
        R                  " [        U5      S:  S 5        [        [        U5      S-
  5       Ho  n[
        R                  " X   R                  XS-      R                  :H  S 5        [
        R                  " X   R                  XS-      R                  :H  S 5        Mq     S	nT S
:X  a&  [        U5      S:  nU(       a  US   US   /USS  Q7nO[
        R                  " T S:H  U 4S j5        / nU H  m[        T[        5      (       d  [	        S[        T5       35      e[
        R                  " TR                  S:H  =(       d    TR                  S:H  U4S j5        UR                  TR!                  5       5        M     / n[#        U5       Hz  u  nm[        T[        5      (       d  [	        S[        T5       35      eTR                  S:X  a  TR%                  S5      mUR                  [&        R(                  " TXB45      5        M|     U(       a  US   US   sUS'   US'   U$ )Nr   rV  z*Expected exactly 1 tensor list/tuple, got c              3   B   #    U  H  n[        U[        5      v   M     g 7frJ  r?  r'   r  s     r9  rO  meshgrid.<locals>.<genexpr>  s     @1Z:..r  c                      g)Nz)meshgrid expects its inputs to be tensorsrR  rR  r;  r9  rT  meshgrid.<locals>.<lambda>  r  r;  c                      g)Nz'meshgrid expects a non-empty TensorListrR  rR  r;  r9  rT  rB    s    +Tr;  c                      g)Nz3meshgrid expects all tensors to have the same dtyperR  rR  r;  r9  rT  rB    s    Ir;  c                      g)Nz4meshgrid expects all tensors to have the same devicerR  rR  r;  r9  rT  rB    s    Jr;  FxyrF  ijc                     > ST  3$ )NzDtorch.meshgrid: indexing must be one of "xy" or "ij", but received: rR  )r:  s   r9  rT  rB    s    !!)
,r;  zexpected TensorLike, got c                     > ST  3$ )NzEtorch.meshgrid: Expected 0D or 1D tensor in the tensor list but got: rR  )r   s   r9  rT  rB    s    [\][^_r;  r7  )r?  rf  rg  rY  r  rb  rm  rQ  r   rl  r  r8  r'   r6  rJ  r  r  rk  r	  r  rM  )r:  r  rD  swap_first_and_second_tensorsresult_shapegridsr   s   `     @r9  r   r     s^    '!*tUm,,w<1 <S\NK  
#	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(( #<T!WI!FGGFFaK&166Q;_	
 	AGGI&  #%E'"1!Z(( #<T!WI!FGG66Q;tAU++A|TBC # %"1XuQxa%(Lr;  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)rf  )rN  rM  s   r9  rT  movedim.<locals>.<lambda>8  s)    V~ ''+K'8&9Ar;  )r  rn  c                  "   > S[        T 5       S3$ )Nz#movedim: repeated dim in `source` (rB  rQ  )rM  s   r9  rT  rR  I  s    5d6l^1Er;  c                  "   > S[        T 5       S3$ )Nz(movedim: repeated dim in `destination` (rB  rQ  )rN  s   r9  rT  rR  M  s    :4;L:MQOr;  r   rV  )r6  r  rb  rm  rY  rJ  rg  r  r3  setdictr  rl  r8  r  r   )r  rM  rN  r  ssdssssdssr  rW  sidir9  r  s    ``           r9  r   r   '  sh    F|sKC"n 
LLFs;''	
 ::D	u&&D&A	BB	u&&D+F	GB
b'C
b'C 
LLB3s8E 
LLB3s8O
 	S[AD	
BDkEE"I=KKN )a )KKO!GB  ]]5%+.FMr;  )r  r8  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$ )Nr  r  )	r  r  r  rx  rb  r  r8  r  r  )rZ  r  r  r8  r  r  r  s          r9  r  r  f  sz     
v	:&,,U3E).E##%EE$*NU\\% F# r;  valc                     [         R                  [         R                  [         R                  4 H+  nU [         R                  " U5      R
                  ::  d  M)  Us  $    [         R                  $ rJ  )rb  rd  uint16r  iinforj  rj  )r^  possible_dtypes     r9  _strength_reduce_integerrc    sI     ;;ekkB%++n-111!! C ;;r;  nr  c          	        ^ ^ Tc  T m[         R                  " T S:  U 4S j5        [         R                  " TS:  U4S j5        [         R                  n[        T [        R
                  5      (       a4  [        T[        R
                  5      (       a  [        [        T T5      5      n[         R                  " T XtSS9n[         R                  " TXtSS9n	UR                  S5      U	:H  n
U[         R                  S4;   a4  U(       d-  U
R                  U=(       d    [         R                  " 5       5      $ [         R                  " SUUUUSS	9n[         R                  " XS5      $ )
z'
Reference implementation of torch.eye
Nr   c                     > ST  3$ )Nz%n must be greater or equal to 0, got rR  )rd  s   r9  rT  eye.<locals>.<lambda>      #H!Lr;  c                     > ST  3$ )Nz%m must be greater or equal to 0, got rR  )r  s   r9  rT  rg    rh  r;  Fr  r\  r7  r  )rb  rm  rj  r?  r  IntWithoutSymIntrc  rj  r  r  stridedr   r  r%  r   )rd  r  r  r  r8  r  r  range_dtyperange_nrange_mr  ones   ``          r9  r  r    s    	y	LLaLM	LLaLM++K!U++,,Au?U?U1V1V.s1ay9ll1KeTGll1KeTGR G+D%--&&zwwu9 7 7 9::jj!
 {{4a((r;  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      $ )Nr  r  )	r  r  r  type_to_dtyper6  rb  r8  r  rG   )rZ  r  r  r  r8  r  r  es           r9  r  r    s~     
v	:&&EE,?,?Z@P,QE)Vu||E/BF#	A ::a$$r;  r  r  r8  r  r  r  c          
      L    [         R                  " U UUUUUUS9n[        X5      $ )Nrs  )rb  r  rG   )	rr  r  r  r  r8  r  r  r  rr  s	            r9  r  r    s6     		##	A r;  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NFr   rs  rb  r  r  r  rr  r  r  r8  r  r  r  s          r9  r+  r+    sC     ??	"177uzz1q##	 	r;  c                    [         R                  " U U=(       d    U R                  [         R                  :X  a  SOSUUUUUUS9$ )NTrV  rs  rv  rw  s          r9  r&  r&    sC     ??	!!''ejj0a##	 	r;  c           	          [         R                  " U5        [         R                  " U5      n[         R                  " U 5      n [         R                  " U5      n[
        R                  " USSU UUS9$ )Nr  r  )r   r   r  r8  r  )r  r  rx  dtype_or_defaultr  r  rc   )r  r8  r  r  r  rZ  r  s          r9  r'  r'    se     
:&--e4F""5)E$$V,F<<# r;  c                   [         R                  " U5        [         R                  " U5        Ub  UO[         R                  " [	        U 5      5      nUb  UO[
        R                  " S5      n[        R                  " XUS9$ )Nr  r}  )	r  r  r  rq  r6  rb  r8  r  r(  )rr  r  r  r8  r  s        r9  r(  r(  6  sc     
v	:&&EE,?,?Q,HE)Vu||E/BFqf==r;  lowhighc          	         [         R                  " U 5        [        U[        5      (       d  [	        S[        U5       35      e[        U[        5      (       d  [	        S[        U5       35      e[        U5      n[        U5      n[        U[        R                  5      (       d  [	        S[        U5       35      e[         R                  " U5      n[        R                  " XX$XSS9$ )Nzlow must be Number, got zhigh must be Number, got r(  )r|  r}  r  r8  rL  )r  r  r?  r!   r  r6  r   rb  r  canonicalize_devicer  _uniform_helper)rZ  r|  r}  rL  r  r8  s         r9  r  r  J  s     
c6""7S	{CDDdF##8dEFF
C.CT?DeU[[))>tE{mLMM&&v.F  Tv r;  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
 dimensionrR  )
value_ndims   r9  rT  masked_fill.<locals>.<lambda>q  s    VWaVbblmr;  cudaxpumpsr4  r  c                      g)Nz,Expected `value` to be on same device as `a`rR  rR  r;  r9  rT  r  {  s    Br;  c                     > ST  S3$ )Nzcould not convert to type z without overflowrR  )r  s   r9  rT  r    s    0=NOr;  )r  r   r  r?  r!   r6  rJ  rb  rm  r8  _C_get_privateuse1_backend_namer  r    r+   r   r   )rr  r  r  
value_typeis_cpu_scalarr  r  r  s         @@r9  r   r   e  s.    %%agg.K%  %[
 ZZ
!Om	
 HHMMuehh&L&L&NPUVW +!!U* 	
 	5U\\QXX5B	
 ((5
W
 	''
K@O	
 $E773ED#A <<>r;  c                 V    [         R                  " XU5      nU R                  U5        U $ rJ  )rb  r   rO  )rr  r  r  rs  s       r9  r   r     s&     	!5)AGGAJHr;  c                     [        SXX#S9  [        [        R                  " [        R                  " XX#US95      R                  5       5      $ )z,
Reference implementation of torch.allclose
ztorch.allcloser  )r  r  r  )r  r  rb  r   r   r   )rr  rs  r  r  r  s        r9  r,  r,    s@     +qDL		%--4iPQVVX r;  c                 R   [         R                  " XSS9  [         R                  " X5        U R                  UR                  :w  a  g[	        U R
                  UR
                  5       H  u  p#X#:w  d  M    g   U R                  5       S:X  a  g[        [        [        X5      5      5      $ )NFr  r   T)
r  r  check_same_dtyperJ  r  rZ  r  r   r   r   )rr  rs  rN  r  s       r9  r-  r-    s}    	A5A	1  	vvAGGQWW%6 &
 	wwyA~BqHr;  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frorF  r  )r?  r   rY  r  rg  rl  rJ  rb  r  matrix_normr  )r  r  r  r  r  s        r9  rb   rb     s     	
U
z#s';';s3x1}	
#se!S ;ejj)*C||''#e'LL||''#e'LLr;  c                    ^  [         R                  " T R                  S:H  U 4S j5        [         R                  " [         R                  " T S5      5      $ )NrF  c                  "   > ST R                    3$ )Nz+expected a matrix, but got tensor with dim r  r  s   r9  rT  trace.<locals>.<lambda>  s    =dii[Ir;  r   )rb  rm  rJ  r   r   r  s   `r9  rv   rv     s;     
LL		QI 99UZZa())r;  c                 p   ^  S[         [        [        4   S[         [        [        4   S[        4U 4S jjnU$ )Nrr  rs  rz  c                    > T" X5      $ rJ  rR  )rr  rs  base_ops     r9  rop_make_r_binary_op.<locals>.rop  s     q}r;  )r   r(   r"   )r  r  s   ` r9  _make_r_binary_opr    s=    +,+, 
 Jr;  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       $ )NrF  c                      g)Nz2triu: input tensor must have at least 2 dimensionsrR  rR  r;  r9  rT  triu.<locals>.<lambda>      Qr;  r  r7  r\  
rb  rm  rJ  rZ  r  r8  r  r  r  r   rr  r   hr`  r  s        r9  r  r         
LL	!Q 7723<DAQxx(2226
,,q
*
4
4R
8	9	D T%0022r;  c                 r   [         R                  " U R                  S:  S 5        U R                  SS  u  p#[         R                  " X0R
                  S9R                  S5      [         R                  " X R
                  S9R                  S5      -
  U:*  n[        R                  " X@5      R                  5       $ )NrF  c                      g)Nz2tril: input tensor must have at least 2 dimensionsrR  rR  r;  r9  rT  tril.<locals>.<lambda>  r  r;  r  r7  r\  r  r  s        r9  r  r    r  r;  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$ )Nr   r   r   r   rV  rF  )r  r  rj  )
r  r  r  m_first_row
m_last_row	n_row_alln_row_trapezoidtrapezoid_sizediff_rowrectangle_sizes
             r9  _get_tril_sizesr    s    
ax3!8*01*#c1v:&#clQ>N:OKQCv./JAs3f-.I .2O "./AQFN*HHN+N;66r;  c                    ^ ^^^ [         R                  " TS:  U4S j5        [         R                  " TS:  U4S j5        [         R                  " T[         R                  [         R                  4;   UU 4S j5        g )Nr   c                     > ST  3$ )Nzrow must be non-negative, got rR  )r  s   r9  rT  _trilu_checks.<locals>.<lambda>7      %CC5#Ir;  c                     > ST  3$ )Nzcol must be non-negative, got rR  )r  s   r9  rT  r  8  r  r;  c                     > ST ST  S3$ )Nrq  z" not implemented for ''rR  )r  r  s   r9  rT  r  ;  s    "TF25';r;  )rb  rm  r  rj  )r  r  r  r  r  r  s   ````  r9  _trilu_checksr  /  sO     
LLIJ	LLIJ	LL%++u{{++;r;  r  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      $ )Nr  r   r  r8  r  r  r  rF  rV  )r  r  rj  r   rb  r  r  rI   rr   r+   r   r   )r  r  r  r  r  r8  r  r  r  r  
row_offset	arange_kwxs1rs  	row_inds1	col_inds1xs2	row_inds2	col_inds2s                      r9  r  r  @  s7    .#E:F2A#F2S/NKQJVzI
 A~U]]
;CcAQBAEAGO!<<=IC1{?Q#6#Bi"ORU"UUVI'	(>FI'	9I A~
3Cs
c/!3j@AIc	I;;	Iy)	*EIIy)6L,MN r;  c                     U S:X  d  US:X  a  gUS:  a  [        SX-
  5      OUn[        S[        X* 5      U-  5      n[        XUS-
  5      u  pVnX-  XV-   -
  nX-
  n	XU4$ )Nr   r  rV  )rj  r  r  )
r  r  r  r  r  trapezoid_size_trilrectangle_size_trilr  	triu_sizer  s
             r9  _get_triu_sizesr  k  s    
ax3!8*01*#a&#K CW-34N 3B#FUVJ2W/a	0FGI/N;66r;  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      rF  rV  r  )r  r  rj  r   rb  r  r  rI   rr   r+   r   r   )r  r  r  r  r  r8  r  r  r  r  
col_offsetr  r  r  r  r  rs  r  r  s                      r9  r  r  |  s:    .#E:F2A#F2S/NKQJVzI
 A~
3C
I	I A~U]]
;C{AQBAEAGO!<<=ICAOa$7)$Cy#PTW"WWXI'	59I'	59I
!67	J&I;;	Iy)	*EIIy)6L,MN r;  )	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      $ [         R                  " U R                  U R                  [         R                  S9nXe-   nXgU-
  S-  -   nTU   n	U(       a  X:  n
OX:  n
[         R                  " XUS-   5      nUS:  a  [         R                  " U [         R                  S9n[        [         R"                  " U5      5      n[%        U5       Hs  n[         R                  " X-  X5      nXg:  n[         R                  " XXv-
  S-  -   S5      nTU   n	U(       a  X:  n
OX:  n
[         R                  " U
) U-  US-   U5      nMu     UR'                  US9$ )NrV  c                  ,   > ST R                  5        S3$ )Nz2boundaries tensor must be 1 dimension but got dim(rB  rf  )r  s   r9  rT  bucketize.<locals>.<lambda>  s    DZ^^EUDVVWXr;  r\  r   r  rF  r  )rb  rm  r  r?  rg  r  r  rj  rZ  r+  r*  r8  r   r&  r  r  r8  r]   rl  r   )rr  r  r  r  	out_dtypen_boundariesr  r  midmid_valcond_midcond_updatenitersr  s    `            r9  r.  r.    s    
LLAX
 5<<((ell1oA(ekkI##B'Lq""
 KKDE

C ;1$
$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$$r;  c                   ^ ^ Ub  [        S5      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      -  -   $ )N"generator is not supported in refsc                  "   > ST R                    3$ )NzwCauchy distribution is a continuous probability distribution.         dtype must be a floating point but you specified r  r  s   r9  rT  cauchy.<locals>.<lambda>       ::>**Gr;  r  c                     > ST  3$ )Nz-cauchy_ expects sigma > 0.0, but found sigma=rR  )sigmas   r9  rT  r    s    ?wGr;  r  )r  rb  rm  r  r  r  r  r  rt   r8  r9  	rand_like)r  medianr  	generators   ` ` r9  r  r    s     ABB	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLG EEIIdgg1F1L&MNNNNr;  c                   ^ ^ Ub  [        S5      e[        R                  " [        R                  " T R
                  5      (       + =(       aQ    [        R                  " T R
                  5      (       + =(       a%    [        R                  " T R
                  5      (       + U 4S j5        [        R                  " TS:  U4S j5        [        R                  " T 5      n[        R                  " UR
                  5      R                  S-  nUSU-
  :  n[        R                  " XT* [        R                  " U5      5      nST-  U-  $ )Nr  c                  "   > ST R                    3$ )Nz|Exponential distribution is a continuous probability distribution.         dtype must be a floating point but you specified r  r  s   r9  rT  exponential.<locals>.<lambda>  r  r;  r  c                     > ST  3$ )Nz4exponential_ expects lambda > 0.0, but found lambda=rR  )rates   r9  rT  r    s    FtfMr;  rF  r  r\  )r  rb  rm  r  r  r  r  r  r  r  rH  r   r[   )r  r  r  uniform_valepsilonr  log_uniforms   ``     r9  rE   rE     s     ABB	LL""4::.. 	3&&tzz22	3&&tzz22	G	 
LLs
M
 //$'K kk+++,0014GsW},I++i599[3IJK9{""r;  c                   ^ ^ Ub  [        S5      e[        R                  " [        R                  " T R
                  5      (       + =(       a%    [        R                  " T R
                  5      (       + U 4S j5        [        R                  " ST:  =(       a    TS:  U4S j5        [        R                  " [        R                  " [        R                  " T 5      * 5      [        R                  " T* 5      -  5      S-   $ )Nr  c                  "   > ST R                    3$ )Nzgeometric not implemented for r  r  s   r9  rT  geometric.<locals>.<lambda>)  s    0=r;  r   rV  c                     > ST  3$ )Nz0geometric_ expects p to be in (0, 1), but got p=rR  )r  s   r9  rT  r  -  s    B1#Fr;  )r  rb  rm  r  r  r  r  rI   r\   r  r8  )r  r  r  s   `` r9  rK   rK     s     ABB	LL""4::.. 	3&&tzz22=
 
LL	A!a%F ;;u{{EOOD$9#9:TZZ^KLqPPr;  c                   ^ ^ Ub  [        S5      e[        R                  " [        R                  " T R
                  5      (       + =(       aQ    [        R                  " T R
                  5      (       + =(       a%    [        R                  " T R
                  5      (       + U 4S j5        [        R                  " ST:  U4S j5        [        R                  " T[        R                  " T 5      -  U-   5      $ )Nr  c                  "   > ST R                    3$ )Nzlog_normal not implemented for r  r  s   r9  rT  log_normal.<locals>.<lambda>?  s    1$**>r;  r   c                     > ST  3$ )Nz-log_normal_ expects std > 0.0, but found std=rR  r   s   r9  rT  r  C  s    ?uEr;  )
r  rb  rm  r  r  r  r  r  rC   
randn_liker  r   r   r  s   ` ` r9  r_   r_   2  s     ABB	LL""4::.. 	3&&tzz22	3&&tzz22>	 
LL	CE 99S5++D11D899r;  )r   r   )r  r  r  r8  r  c          
        ^ Ub"  U[         R                  :w  a  [        SU 35      e[        T[        5      (       d  [         R
                  " TS:  U4S j5        Uc  [        S U T4 5       5      n[         R
                  " [        U5      S:  S 5        [         R
                  " US L =(       a    US L S 5        [        S U 5       6 nUS   R                  nUS   R                  nO|[         R
                  " [        U [        5      (       + =(       a    [        T[        5      (       + S 5        Uc  [         R                  " 5       OUnUc  [         R                  " S	5      OUn[        R                  " US
SUUSUS9n	TU	-  U -   $ )Nz*layout must be None or torch.strided, got r   c                     > ST  3$ )Nz)normal expects std >= 0.0, but found std rR  r  s   r9  rT  normal.<locals>.<lambda>c  s     I#Or;  c              3   T   #    U  H  n[        U[        5      (       d  M  Uv   M      g 7frJ  r?  rx  s     r9  rO  normal.<locals>.<genexpr>g  s     L;a*Q
2K;s   (	(c                      g)NzFnormal expects that either mean or std is a tensor, or size is definedrR  rR  r;  r9  rT  r  j  s    \r;  c                      g)Nz.Cannot pass layout, or pin_memory without sizerR  rR  r;  r9  rT  r  n  s    Dr;  c              3   8   #    U  H  oR                   v   M     g 7frJ  rB  rx  s     r9  rO  r  q  s     "<Gq77Gr[  c                      g)Nz>normal expects mean and std to be scalars when size is definedrR  rR  r;  r9  rT  r  w  s    Tr;  r  r  r  F)r   r   r  r8  r  r  )rb  rk  r  r?  r'   rm  rg  rY  rt  r  r8  r  r  rc   )
r   r   rP  r  r  r  r8  r  r  normal_sampless
    `        r9  rc   rc   J  s^   ( f5I&RSSc:&&1HO	
 |LD#;LLL1\	
 	dN1zT1D	

 !"<G"<=
  ""4,,PZZ5P1PT	
 .3]'')(.e$F\\N $&&r;  )r  c                ,    [        XU R                  XS9$ )N)r  r  )rc   rZ  r  s       r9  normal_r     s    $TZZTGGr;  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-rad2deg is not supported for complex tensors.rR  rR  r;  r9  rT  rad2deg.<locals>.<lambda>  rE  r;  gcܥL@rb  rm  r  r  r  )r  M_180_PIs     r9  rg   rg     s6    	LL""4::..? CH?r;  c                     [         R                  " [        R                  " U R                  5      (       + S 5        SnX-  $ )Nc                      g)Nz-deg2rad is not supported for complex tensors.rR  rR  r;  r9  rT  deg2rad.<locals>.<lambda>  rE  r;  g9RFߑ?r  )r  M_PI_180s     r9  r>   r>     s6    	LL""4::..? EH?r;  c                 *    U S:g  R                  U5      $ r1  )r   )r  r  s     r9  r=   r=     s     AI??3r;  c                 v  ^ ^ [         R                  " T R                  5       S:H  =(       a    TR                  5       S:H  UU 4S j5        [         R                  " T R                  TR                  :H  UU 4S j5        UU 4S jn[         R                  " T R	                  5       TR	                  5       :H  U5        g )NrV  c                  N   > STR                  5        ST R                  5        S3$ )Nz1D tensors expected, but got zD and z	D tensorsrf  r-  r  s   r9  rT  _dot_check.<locals>.<lambda>  s!    /
|6%))+iXr;  c                  <   > STR                    ST R                    3$ )Nz:dot : expected both vectors to have same dtype, but found r  r  r  s   r9  rT  r    s    L::,eEKK=*r;  c            	         > STR                  5        ST R                  5        STR                  5        ST R                  5        S3	$ )Nz+inconsistent tensor size, expected tensor [z] and src [z.] to have thesame number of elements, but got r  z elements respectively)r  r  s   r9  numel_error_dot_check.<locals>.numel_error  sL    9$**,{SXS^S^S`Ra b004

~U5;;=/Qgi	
r;  )rb  rm  r  r  r  )r  r-  r  s   `` r9  
_dot_checkr    sx    	LL
a,EIIK1,X
 
LL

ekk!	*
 
LL.<r;  c                 0   ^  [        T 5      U 4S j5       nU$ )Nc                 *   > [        X5        T" X5      $ rJ  )r  )r  r-  r  s     r9  wrapper#_dot_check_wrapper.<locals>.wrapper  s    4$r;  )r
   )r  r  s   ` r9  _dot_check_wrapperr    s     
2Y  Nr;  r  c                    U R                  5       (       a  U R                  5       (       a{  UR                  5       (       aA  [        R                  " U R	                  5       UR	                  5       5      R	                  5       $ [        R
                  " U R	                  5       U5      $ UR                  5       (       a%  [        R
                  " UR	                  5       U 5      $ X-  R                  5       $ rJ  )r/  is_conjrb  r   r   r   r   r  s     r9  r   r     s     <<>>}}yyejjl;@@BBzz$))+u55]]__::ejjlD11Lr;  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       $ rJ  )r/  rb  r   r  r   r   r:   r   r  s     r9  r   r     s     ??yy%%||~~==??::ejjlDIIK8899TYY[%00	yyzz|,1133  5(--//r;  c                    [         R                  " U R                  U5      nS/U R                  -  nSXB'   US:  a  X0R                  U   -   n[        R
                  " U R                  U   U R                  S9R                  U5      U:H  n[        R                  " X5      R                  U R                  5      n[        R                  " XQU 5      $ )NrV  r\  r   r7  )r  r  rJ  rZ  rb  r  r8  r	  r  r   r   )rN  r  r  r2  
mask_shaper  s         r9  select_scatterr    s     
 
 
-CqvvJJOqy$<<QXX6;;JG5PD
//#
#
*
*177
3C;;t!$$r;  )r[  c                 V    [        U [        R                  [        R                  45      $ rJ  )r?  rb  TypedStorageUntypedStorage)objs    r9  
_isStorager#  o  s     cE..0D0DEFFr;  c                    Sn[        U 5      n/ n[        U [        [        45      (       a  [	        U 5      nU(       a  XQR
                  -  nUR                  U5        [	        U5      U:  a"  [        S[        U 5      R                   S35      eUS:X  a   U$  U S   nUn [        U [        [        45      (       a  M  U$ ! [         a#    [        S[        U 5      R                   S35      ef = f)N   ztoo many dimensions 'r  r   z.could not determine the shape of object type ')r#  r?  rf  rg  rY  itemsizer  rn  r6  r  r  )seqscalar_typeMAX_DIMS
is_storagerU  r%  handles          r9  _compute_sizesr,  t  s    HCJE
S4-
(
(S+++FVu: 4T#Y5G5G4HJKKQ; L	VF
  S4-
(
(" L  	@cASAS@TTUV 	s   B= =-C*c                    [        U [        5      (       a  [        R                  " 5       $ [        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   rb  r  r   r  rj  r   r  r  cfloatdoublecdoublehalfchalfri  rg  r  r  	TypeErrorr6  r  rf  rg  rY  rl  _infer_scalar_typepromote_types)r"  default_dtype
scalarTyper%  rD  cur_itemitem_scalarTypes          r9  r4  r4    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Hr;  r7  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      $ s  snf )NrV  r  T)r  r8  r  rR  r  r   )r?  rg  r  detachr   r	  r!   rb  r(  r  r   _recursive_build)r7  r"  r'  r   s       r9  r<  r<    s     #v399;!#3zz|ZDINNrRR	C	 	  zz|ZDII	C	 	 ""399 C  	A [[M*:<MN Ns   (Dc                 B   [        U[        R                  5      (       an  [        R                  " U(       + S 5        UnU(       a  UR	                  5       nU(       a  UR
                  OUn	Ub  UOUR                  n
UR                  U
U	SUS9$ [        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$ )Nc                      g)Nz,Can't pin tensor constructed from a variablerR  rR  r;  r9  rT  )_internal_new_from_data.<locals>.<lambda>  s    $Rr;  F)r8  r  r  r  __cuda_array_interface__r8  meta)r  r  )r?  rb  rg  rm  r;  r  r8  r   hasattrNotImplementedr4  r#  r6  r<  )optionsr(  
device_optdatacopy_variables
copy_numpytype_inferencer  r   inferred_scalar_typer8  r  s               r9  _internal_new_from_datarK    s    $%%NR	
 **,C,:syy)53::vv&	  
 	
 t/00 &1Zwx7HF7E-d3; $<<$$.!! ""6=6eRWX Mr;  )r  r8  r  r  c                $   [        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$ )NzTo copy construct from a tensor, it is recommended to use sourceTensor.detach().clone() or sourceTensor.detach().clone().requires_grad_(True), rather than torch.tensor(sourceTensor)rF  r  r8  r  T)rG  rH  rI  r  )
r?  rb  rg  r  r  UserWarningrK  r  detach_r  )rF  r  r8  r  r  rI  
new_tensors          r9  r  r    s    $%%l		
 d]N( 
5"(?(?(A%J !!-0r;  rJ  )F)r  NN)gh㈵>g:0yE>Fr7  )NN)NNNNNFF)FFN)NF)NNFr  )r   r\  )	NNNTreflectFNNN)NNNTFNNF)rR  )rV  r  )r   r   rV  )r   r  r\  )r   NrV  )r*  )r  r  )r  NF)r   rV  Nru  )rV  rF  N(  rQ  r  r  r  r8  r  r  collections.abcr   r   r   enumr   	functoolsr   r   r	   r
   typingr   r   r   r   r   rb  torch._prims_primsr  torch._prims_common_prims_commonr  torch.utils._pytree_pytreerY  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   torch._prims_common.wrappersr+   r,   r-   r.   r/   r0   r  rg  r  DispatchKey_opsr+  r  r:  rC  rt  r  torch._decompr  objectr  r  r  r  r  r1   INT_TO_FLOATr2   r3   r5   r4   r6   r7   DEFAULTr8   r9   r/  r:   r;   r<   r?   r@   rA   rB   rC   rD   rF   	NO_OPMATHrG   rH   r)  rI   rJ   r   ALWAYS_BOOLrR   rS   rT   rU   rV   specialmultigammalnra   rW   rX   rZ   r[   r\   r]   r^   r  r  r`   r   r  rd   r#  re   rf   r   rh   ri   r   rj   rk   rl   rm   rn   ro   rp   rr   BOOL_TO_LONGrs   rt   ru   rw   r  rk  rx   ry   rz   r{   r|   r}   r~   r   r   r  r   r   r   r   r  r  r   r   r   r  rg  r   r   r   r   r   r   r   r  r  r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  
ScalarSelfScalarOtherScalarself_outr   r   r  r   r   r  r"  r$  registerr8  rV  r(  r*  r,  r/  r6  r   rQ  rb  r   r   r   dim_IntListIntList_outrf  r   r   r   r   r  r   r   r   r   r   r   r   r  r   r   r   r   r   r   r  py_implCompositeImplicitAutogradMetar   r   r   r   r   rW  r   r   r   r   r   r   r   r   r   r   rN  rR  r   r   _subclasses
fake_implsregister_op_implrx  r   r0  r1  r  r2  r  r   r	  r  r   r   r   r   r$  r   rq   r   r  r  r  rM   rN   rP   rQ   rH  rL   rO   r   rW  r   r  r   r  r   r  r   r   r   r   r  r   r   r   r   r  r   r  r  r  r   r   r  r	  r
  r   r   rk  r  r  r   r!  r*  r$  r%  r#  r"  r  r  r  
start_step	start_outrY   r  r  r   r   r  rc  r  r  r  r+  r&  r'  r(  r  r   r   r,  r-  rb   rv   r  r   r   r   r  r  r  r  r  rg  r  r  r.  r  rE   rK   r_   rc   r   rg   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,  r4  r<  rK  r  torch._refs._conversionstorch._refs.ffttorch._refs.linalgtorch._refs.nn.functionaltorch._refs.specialrR  r;  r9  <module>r     sQ          8 8  < < 7 7   # $ $ 6 6      2 l\	 
hh""zz~~2Od 9= 8Cx 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 	
   )6  ##++	 > 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'( 6 ^Z'(^Z'(  t $==EE $"'
O^Z'(O-2>:3M-NO
OBFV F F6 F16 1f 1 12 $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 +/*.#
#&'# &'#	  - + 0 / )#. 

#?D?T?T).)<)<  $ 9= v &  		"&N &z & #& (,#'%)37!&^$ EKK  4.	
 U\\" E//0   
2    37LL;;  	
 E//0 
#s(^ "  37;;  	
 E//0 
#s(^ "  37	;;  E//0	
 
#s(^   37	  E//0	
 
#s(^ ."& "T "0 .  n  X "##' CC
C 	C
 C 8
C C EKK C 
&	C 2C CL< ! #

	(	
 
 	
  "
 ! #	(	  	  "$ --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, 		" #+
 ++	(	+ + + #+\ &VV #  $'+	(	 tn	
  $  '2 &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yG# yG# yGn yG	  "yGz #, # # # >  ,,-?@PP $S	P2<PP  .Ph 8=7N7N77!&!4!477 #& #> # # $/4 Bf B B B %BL 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$HHH VH 6
	H
 
H 666!"H % 0HV ..t/E/E/M/MN$ 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 !% $## ZZZ Z 	Z
 VZ Z Z tnZ SMZ Z CZ|",9<DGOR8 $51f 51 51  %51pRR*.RRj8?N 8? 8? 8?~<~ <y <^ <
&^ &N &~ & 		"8>N 8>H 8>H 8>n 8>  #8>v 

#<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 .  +B --.56
#Cy/2	&\ /D DFDFvx/0DF 
DF >3	DFP(-(-,4(-
>3(-X&+&+,4&+
>3&+R 		& 1
11 1  '1 --. 	  	
    /0 & 	#
## # 	#
 # '#L ( 	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i0@$@ =^ = +=*#. # #N #
^   AE%D||%D#ll%D19#%D
\\%D %DP  $( =='+).)@)@%EKK % LL% ^$	%
 % % &&% % %P  $( =='+ 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 $c
 $( =='+cc	*	c c
 EKK c LLc ^$c c c c  IcL 		"#27??8 8V 8U6:3E-F 8	  #84 & $('+ ==X/^+,X/	z>)	*X/ X/
 EKK X/ ^$X/ LLX/ X/ X/ X/  'X/v &
 	9@ $('+ ==9@^+,9@	z>)	*9@ 9@ 	9@ EKK 9@ ^$9@ LL9@ 9@ 9@ 9@  '9@x 
	h~. 	# 	 
	 
	~ 	 	 
	 &CND$8%:OOPCC 
.C 'CN;;#''(; s,,-; 	;~ **+
 $('+ ==E),,- EKK 	
 ^$ LL     ,6# %++  ! %) $( =='+%)
%)}%) EKK 	%)
 LL%) ^$%) %) %) %)  "%)V **DIIMM:;
 $( =='+%%% EKK 	%
 LL% ^$% % % %  <%> $(%)'+).)>)> EKK 	
 U\\" ^$   && . ( $(%)'+).)>)> EKK  U\\"	
 ^$   &&   ), ' $(%)'+).)>)> EKK  U\\"	
 ^$   &&   (, 

**+ $('+%)EKK  ^$ U\\"	
     ,8 $( =='+>> EKK > LL	>
 ^$> > >, $'$'	tS%	  c5 
!
  ;;  6 (()*> * *@V *  **Z ))*+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" ))* &
  =="&	&	& &
 ;;& LL& & & &  +&R '
 7%7%7% 	7%
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		2'
 
2'  %2'j %Hd H &H ##B#O#OP.  Q ##B#O#OP.  Q **+ Xh/    , =* !#)7??
 	   "
  		"#)7??0	   #0  ++,%n %> % %C %  -% Sd	u	S!!d	u	d	u		u	[)#$67 [)J'$%89 [)d	u	9%
9%
}-(#	Sd

!!!SBSd

Sd	u	[)	u	l+ddSBB9%
	u	

!BSBd

	u		u	dS[)[)J'[)BS(#	J'BS9%
S!J'9%
	u	S!dSddd

SSddd[)	u		u	

[)9%
J'd!$**-
&t7$T]]3"4;;/ #4;;/#DLL1#DLL1	dff	%%dnn5"4;;4P%dnn5 +	G
4/Ih"'(>@R(R"SH 5r tU  L       r;  