Ë
    L²jÁü ã            !       óPy  — U d dl Z d dlZd dlZd dlZd dlZd dlmZmZ d dlm	Z	 d dl
mZ d dl mZmZ d dlmZmZ d dlmZmZ d dlZd dlZd dlmZ d dlmZ d dlmc mZ d dlmZm Z m!Z! d d	l"m#Z# d d
l$m%Z% d dlm&Z&m'Z'm(Z(m)Z)m*Z* d dl+m,Z,m-Z-m.Z.m/Z/ d dl0m1Z2 d dl3m4Z4 ejj                  jl                  Z6g Z7e8e9   e:d<   ejv                  jx                  jz                  Z= G d„ de«      Z>	 	 �d¬dedej~                  de@de@fd„ZA eeAej~                  j„                  d¬«      ZC eeAej~                  j„                  ¬«      ZD eeAej~                  j„                  d¬«      ZE eeAej~                  jŒ                  ¬«      ZGde!deHde!fd„ZI e#e=j”                  «       e/d «      eDd!e!d"e!fd#„«       «       «       ZJ e#e=j–                  «       e/d «      eDd!e!d"e!fd$„«       «       «       ZK e#e=j˜                  «       e/d «      eDd!e!de!d%eMd&eMfd'„«       «       «       ZL e#e=jœ                  «       e/d «      eDd(e!d)eMd*eMd+eMd,e@d-e!fd.„«       «       «       ZN e#e=jž                  j                   g«      d/„ «       ZQ e#e=jž                  jB                  g«      d0e!fd1„«       ZR e#e=j¦                  «       e/«       eDd2e!de!fd3„«       «       «       ZS e#e=j¨                  «       e/d «      eDd(e!d2e!fd4„«       «       «       ZT e#e=jª                  «       e/d «      d(e!d2e!d5eMd6eMfd7„«       «       ZU e#e=j¬                  «       e/«       eDd2e!de!fd8„«       «       «       ZV e#e=j®                  «       e/«       eDd(e!d2e!de!fd9„«       «       «       ZW e#e=j°                  «       e/d «      d(e!d2e!d&eMfd:„«       «       ZX e#e=j²                  «       e/d «      eDd(e!d2e!d;eMd<e@fd=„«       «       «       ZY e#e=j´                  «       e/d «      eD�d­d>e!d2e!d?e9fd@„«       «       «       ZZ e#e=j¶                  «      eDd(e!dAe!fdB„«       «       Z[ e#e=j¸                  «       e/«       eDd2e!de!fdC„«       «       «       Z\ e#e=jº                  «       e/d «      eDd(e!d2e!de!fdD„«       «       «       Z] e#e=j¼                  «      d2e!dEe!de!fdF„«       Z^ e#e=j¾                  «      d(e!d2e!dEe!de`e!e!f   fdG„«       Z_ e#e=jÂ                  «       e/«       eDd(e!d2e!dHe!dIeMdJeMdKe@d<e@de!fdL„«       «       «       Za e#e=jÄ                  «       e/d «      eDd(e!d2e!dMe!de!fdN„«       «       «       Zb e#e=jÆ                  «       e/«       d2e!dOe!de!fdP„«       «       ZcdQe!dReHfdS„ZddTejÊ                  fdU„Zf e#e=jÎ                  «       e/«       eDe>jÐ                  jÒ                  fd2e!dVe!dReHde!fdW„«       «       «       Zg e#e=jÔ                  «       e/d «      eDd(e!dAe!dVe!dReHfdX„«       «       «       Zj e#e=jÖ                  «      �d®dY„«       Zl e#e=jÚ                  «       e/«       eDe>jÐ                  jÒ                  dZfd2e!dVe!dReHd%eMfd[„«       «       «       Zm e#e=jÜ                  jÞ                  «      eDd(e!d2e!dVe!dReHd%eMf
d\„«       «       Zn e#e=jÜ                  jà                  «      eDd(e!d2e!dVe!dReHd%eMd e!fd]„«       «       Zq e#e=jä                  jÞ                  «      eDd(e!d2e!dVe!dReHd^eMf
d_„«       «       Zr e#e=jä                  jæ                  «      eDd(e!d2e!dVe!dReHd^eMd e!fd`„«       «       Ztd(e!d2e!dVe!dEe!dz  dReHdaeHdbe!de!fdc„Zu e#e=jì                  «       e/d «      eDd(e!d2e!deHde!fdd„«       «       «       Zv e#e=jî                  «       e/d «      d(e!d2e!dVe!dEe!dz  dReHdaeHdbe!de!fde„«       «       Zw e#e=jð                  «       e/d «      d(e!d2e!dVe!dEe!dz  dReHdaeHdbe!de!fdf„«       «       Zx e#e=jò                  «       e/«       eDde>jÐ                  jÒ                  fd2e!dVe!dEe!dz  dReHde!f
dg„«       «       «       Zy e#e=jô                  «       e/d «      eDde>jÐ                  jÒ                  fd(e!d2e!dVe!dEe!dz  dReHde!fdh„«       «       «       Zz e#e=jö                  «       e/«       eDe>jÐ                  jÒ                  fdAe!dVe!dReHde!fdi„«       «       «       Z{ e#e=jø                  «       e/d «      eDe>jÐ                  jÒ                  fd(e!d2e!dVe!dReHde!f
dj„«       «       «       Z| e#e=jú                  «       e/«       �d¯dAe!dOe!dkeMfdl„«       «       Z} e#e=jü                  «       e/«       dme!dne!de!fdo„«       «       Z~ e#e=jþ                  «       e/«       d(e!dpe8eH   deHdqeHdreHdseHfdt„«       «       Z e#e=�j                   jB                  «      	 	 	 	 �d°d2e!deHdqeHdz  dreHdz  dseHf
dv„«       Z�de!deHdqeHdz  dreHdz  de`eHeHf   f
dw„Z‚ e#e=�j                  «       e/«       	 	 	 	 �d°dAe!dxe!deHdqeHdz  dreHdz  dseHfdy„«       «       Zƒ e#e=�j                  «       e/«       d(e!dpe8eH   deHdzeHfd{„«       «       Z„ e#e=�j
                  «       e/«       d(e!dpe8eH   d|eHd}eHd~eHf
d„«       «       Z…d(e!d e!d€ejÊ                  fd�„Z† e#e=�j                  «       e/d «      eCd(e!d‚e!deHd€ejÊ                  fdƒ„«       «       «       Z‡ e#e=�j                  «       e/«       eCd(e!d‚e!deHd€ejÊ                  fd„„«       «       «       Zˆd…„ Z‰ e#e=�j                  «       e/«       dAe!d†e8eH   d‡e8eH   dˆe8eH   d‰e8eH   de!fdŠ„«       «       ZŠ e#e=�j                  «       e/«       eDdAe!d‹e8eH   d†e8eH   d‡e8eH   dˆe8eH   d‰e8eH   de!fdŒ„«       «       «       Z‹ e#e=�j                  «       e/«       d(e!d�e!d*eMfdŽ„«       «       ZŒ e#e=�j                  «       e/«       d>e!d�e8eH   d�eHd‘eHdseHde!fd’„«       «       Z� e#e=�j                  jÞ                  «      eD	 �d®d(e!d2e!d“eMdz  de!fd”„«       «       ZŽ e#e=�j                  «      e=�j                  jÞ                  �j!                  e6�j"                  «      e=�j                  jÞ                  �j!                  e6�j$                  «      dAe!dkeMd•e@dz  fd–„«       «       «       Z� e#e=�j&                  «       e/d—d˜«      dAe!dkeMd•e@dz  fd™„«       «       Z“ e#e=�j(                  «       e/«       de!deHdše@fd›„«       «       Z” e#e=�j*                  «       e/d¬œ«      de!deHdše@fd�„«       «       Z• e#e=�j,                  «       e/«       	 	 	 �d±dEe!dže!dŸeHd e@d¡e@de!fd¢„«       «       Z– e#e=�j.                  «       e/«       d(e!dže!d£eHdŸeHd e@f
d¤„«       «       Z—de8eH   fd¥„Z˜d¦e8e!   deHd§eHde8e!   fd¨„Z™d¦e8e!   fd©„Zšd¦e8e!   deHfdª„Z›d¦e8e!   deHd§eHfd«„Zœ e#e=�j:                  jÞ                  e=�j:                  jæ                  g«      	 �d®d¦e8e!   deHd§eHd¬e!dz  de!f
d­„«       Z� e#e=�j<                  jÞ                  e=�j<                  jæ                  g«      	 	 �d²d2e!d®e8eH   deHd¬e8e!   dz  de8e!   dz  f
d¯„«       Zž e#e=�j>                  jB                  «      �d³dAe!d°eHdeHde`e!d±f   fd²„«       ZŸ e#e=�j@                  jÞ                  «      	 �d³dAe!d®e8eH   deHde`e!d±f   fd³„«       Z  e#e=�jB                  jB                  «      �d³d2e!d°eHdeHde`e!d±f   fd´„«       Z¡e=�jD                  �jF                  �j!                  e6�j"                  «      	 �d³d2e!dµe!deHde`e!d±f   fd¶„«       Z¤ e#e=�jJ                  «       e/d¬œ«      eD�d´d2e!d·e!d¸e!d%eHd)eHf
d¹„«       «       «       Z¥ e#e=�jL                  «       e/«       eD	 	 	 �dµd2e!d·e!d¸e!d%eHd)eHdºe@fd»„«       «       «       Z¦ e#e=�jN                  «       e/d¬œ«      eD�d´d2e!d·e!d¼e!d%eHd)eHf
d½„«       «       «       Z§ e#e=�jP                  jÞ                  «      eDd(e!dAe!d¾e!d¿e!dÀe!dz  dÁeHdÂeHdÃeHdÄeHdÅe8e@   de`e!dz  e!dz  e!dz  f   fdÆ„«       «       Z¨ e#e=�jP                  jæ                  «      d(e!dAe!d¾e!d¿e!dÀe!dz  dÁeHdÂeHdÃeHdÄeHdÅe8e@   d—ejB                  d˜ejB                  dÇejB                  de`e!dz  e!dz  e!dz  f   fdÈ„«       Z©de!dz  de!dz  fdÉ„Zª e#e=�jV                  jÞ                  «      dÊe!dAe!dËe8eH   d¾e!d¿e!dEe!dz  dÌe!dz  dÅe8e@   de`e!dz  e!dz  e!dz  f   fdÍ„«       Z« e#e=�jV                  jæ                  «      dÊe!dAe!dËe8eH   d¾e!d¿e!dEe!dz  dÌe!dz  dÅe8e@   d—ejB                  d˜ejB                  dÇejB                  de`e!dz  e!dz  e!dz  f   fdÎ„«       Z¬ e#e=�jZ                  jÞ                  «      dAe!dËe8eH   dEe!dz  d“eMdz  de`e!e!f   f
dÏ„«       Z­ e#e=�j\                  jÞ                  «      dÊe!dAe!dËe8eH   d¿e!dEe!dz  dÅe8e@   de`e!dz  e!dz  f   fdÐ„«       Z®dAe!dEe!dz  dÌe!dz  dÑe!dz  dÒe!dz  dKe@dÓeMd“eMdÔe@de`e!e!e!e!dz  e!dz  f   fdÕ„Z¯ e#e=�j`                  «       e/d¬dÖd×«      dAe!dEe!dz  dÌe!dz  dÑe!dz  dÒe!dz  dKe@dÓeMd“eMde`e!e!e!f   fdØ„«       «       Z°e=�j`                  jÞ                  �j!                  e6�j$                  «      e=�j`                  jÞ                  �j!                  e6�j"                  «      dAe!dEe!dz  dÌe!dz  dÑe!dz  dÒe!dz  dKe@dÓeMd“eMde`e!e!e!f   fdÙ„«       «       Z±e=�jd                  jÞ                  �j!                  e6�j"                  «      �d³de8e!   fdÚ„«       Z³ e#e=�jh                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dÓeMd“eMde`e!e!e!f   fdÛ„«       Z´ e#e=�jj                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dKe@dÓeMd“eMde`e!e!e!f   fdÜ„«       Zµ e#e=�jj                  �jl                  «      dAe!dEe!dz  dÌe!dz  dKe@dÓeMd“eMde`e!e!e!f   fdÝ„«       Z· e#e=�jp                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dKe@dÓeMd“eMde`e!e!e!e!e!f   fdÞ„«       Z¸dAe!dEe!dz  dÌe!dz  dÑe!dÒe!d“eMdKe@de!fdß„Z¹ e#e=�jt                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dÓeMd“eMde`e!e!e!e!f   fdà„«       Zº e#e=�jv                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dÓeMd“eMde`e!e!e!e!e!e!f   fdá„«       Z» e#e=�jx                  jÞ                  «      dAe!dEe!dz  dÌe!dz  dÑe!dÒe!dÓeMd“eMde`e!e!e!e!f   fdâ„«       Z¼ e#e=�jz                  «       e/d—d˜«      eD�d®dã„«       «       «       Z¾ e#e=�j~                  «       e/«       dddddddäœde!e'z  dTejÊ                  dz  dåe�j€                  dz  dæe@dçe@dèe�j‚                  dz  fdé„«       «       Z¿ e#e=�j„                  e=�j†                  e=�jˆ                  g«       e/«       dê„ «       «       ZÅe=�jŒ                  jÞ                  �j!                  e6�j$                  «       e#e=�jŒ                  «       e/d—d˜dÇdë«      dAe!dEe!dÌe!dz  dÑe!dz  dÒe!dz  dKe@dìeMdíeMfdî„«       «       «       ZÆdï„ ZÇ e#e=�j�                  jÞ                  «      dÊe!dAe!dEe!dz  dÑe!dz  dÒe!dz  dÖe!dz  d×e!dz  d•e@d“eMdÅe8e@   dðe!de`e!e!dz  e!dz  f   fdñ„«       ZÈ e#e=�j’                  jÞ                  «      dÊe!dAe!dEe!dz  dÑe!dz  dÒe!dz  dÖe!dz  d×e!dz  d•e@d“eMdÅe8e@   de`e!e!dz  e!dz  f   fdò„«       ZÉ e#e=�j’                  jæ                  «      dÊe!dAe!dEe!dz  dÑe!dz  dÒe!dz  dÖe!dz  d×e!dz  d•e@d“eMdÅe8e@   d—ejB                  d˜ejB                  dÇejB                  de`e!e!dz  e!dz  f   fdó„«       ZÊ e#e=�j–                  «       e/d—d˜dÇ«      dAe!d(e!dEe!dÑe!dz  dÒe!dz  dÖe!dz  dôe!dz  díeMfdõ„«       «       ZË e#e=�j˜                  «       e/d—d˜dÇ«      dAe!d(e!dEe!dÑe!dz  dÒe!dz  dÖe!dz  dôe!dz  díeMdöe!fd÷„«       «       ZÌ e#e=�jš                  «       e/«       eDdAe!d‹e`eHeHf   fdø„«       «       «       ZÎd2e)dže)d‹e8eH   deHfdù„ZÏ e#e=�j                   «       e/«       d2e)dže)d‹e8eH   fdú„«       «       ZÐ e#e=�j¢                  «       e/«       dAe)dže)d‹e8eH   d‰e8eH   dˆe8eH   f
dû„«       «       ZÑ e#e=�j¤                  «      dudüœde)deHdze)dýe)d)e'f
dþ„«       ZÒ e#e=�j¦                  «       e/«       dudüœde)deHdze)dýe)d)e'f
dÿ„«       «       ZÓdudüœde)deHdze)dýe)�d e@d)e'f�d„ZÔ e#e=�jª                  jÞ                  «      e=�jª                  jÞ                  �j!                  e6�j"                  «      �d¶�d„«       «       ZÕ e#e=�j¬                  «      de)deHdze)dýe)f�d„«       ZÖ e#e=�j®                  «       e/«       de)deHdze)dýe)f�d„«       «       Z×de)deHdze)dýe)�d e@f
�d„ZØ e#e=�j²                  «       e/d‚dM«      eDd2e!de`e!e!f   f�d„«       «       «       ZÙ e#e=�j´                  «       e/«       	 	 	 �d·de!�de@eHz  eMz  �de@eHz  eMz  �d	e�j¶                  dz  f�d
„«       «       ZÚ e#e=�j¸                  «      �d¸�d„«       ZÜ�d„ ZÝ�d„ ZÞ e#e=�j¾                  �jÀ                  «       e#e=�jÂ                  �jÀ                  «       e#e=�jÄ                  �jÀ                  «      e=�j¾                  �jÀ                  �j!                  e6�j"                  «      e=�j¾                  �jÀ                  �j!                  e6�j$                  «      e=�jÂ                  �jÀ                  �j!                  e6�j"                  «      e=�jÂ                  �jÀ                  �j!                  e6�j$                  «      e=�jÄ                  �jÀ                  �j!                  e6�j"                  «      e=�jÄ                  �jÀ                  �j!                  e6�j$                  «      dAe!d‹e8eH   dz  �de8eM   dz  de!f�d„«       «       «       «       «       «       «       «       «       Zã e#e=�jÈ                  �jÀ                  «       e#e=�jÊ                  �jÀ                  «       e#e=�jÌ                  �jÀ                  «      e=�jÈ                  �jÀ                  �j!                  e6�j"                  «      e=�jÈ                  �jÀ                  �j!                  e6�j$                  «      e=�jÊ                  �jÀ                  �j!                  e6�j"                  «      e=�jÊ                  �jÀ                  �j!                  e6�j$                  «      e=�jÌ                  �jÀ                  �j!                  e6�j"                  «      e=�jÌ                  �jÀ                  �j!                  e6�j$                  «      dAe!d‹e8eH   dz  �de8eM   dz  de!f�d„«       «       «       «       «       «       «       «       «       Zç�d¹�d„Zè e#e=�j¾                  jÞ                  e=�j¾                  jæ                  g«      e=�j¾                  jÞ                  �j!                  e6�j"                  «      e=�j¾                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 �d®dAe!d‹e8eH   �deMdz  de!f�d„«       «       «       «       Zß e#e=�jÈ                  jÞ                  e=�jÈ                  jæ                  g«      e=�jÈ                  jÞ                  �j!                  e6�j"                  «      e=�jÈ                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 �d®dAe!d‹e8eH   �deMdz  de!f�d„«       «       «       «       Zé e#e=�jÂ                  jÞ                  e=�jÂ                  jæ                  g«      e=�jÂ                  jÞ                  �j!                  e6�j"                  «      e=�jÂ                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 	 �dºdAe!d‹e8eH   �deMdz  �deMdz  de!f
�d„«       «       «       «       Zá e#e=�jÊ                  jÞ                  e=�jÊ                  jæ                  g«      e=�jÊ                  jÞ                  �j!                  e6�j"                  «      e=�jÊ                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 	 �dºdAe!d‹e8eH   �deMdz  �deMdz  de!f
�d„«       «       «       «       Zå e#e=�jÄ                  jÞ                  e=�jÄ                  jæ                  g«      e=�jÄ                  jÞ                  �j!                  e6�j"                  «      e=�jÄ                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 	 	 �d»dAe!d‹e8eH   �deMdz  �deMdz  �deMdz  de!f�d„«       «       «       «       Zâ e#e=�jÌ                  jÞ                  e=�jÌ                  jæ                  g«      e=�jÌ                  jÞ                  �j!                  e6�j"                  «      e=�jÌ                  jÞ                  �j!                  e6�j$                  «       e/dd�¬«      	 	 	 �d»dAe!d‹e8eH   �deMdz  �deMdz  �deMdz  de!f�d„«       «       «       «       ZæeD	 �d¹dAe!d‹e8eH   �de8eMdz     �de@de!f
�d„«       Zê�d„ Zë�d „ Zì�d!„ Zí�d"„ Zî	 �d¹�d#„Zï�d$„ Zð�d%„ Zñ�d¹�d&„Zò�d¹�d'„Zó�d(„ Zô e#e=�jê                  �jì                  «      e=�jê                  �jì                  �j!                  e6�j"                  «      e=�jê                  �jì                  �j!                  e6�j$                  «      �d)„ «       «       «       Z÷ e#e=�jð                  �jì                  «      e=�jð                  �jì                  �j!                  e6�j"                  «      e=�jð                  �jì                  �j!                  e6�j$                  «      �d*„ «       «       «       Zù e#e=�jð                  �jô                  «      e=�jð                  �jô                  �j!                  e6�j"                  «      e=�jð                  �jô                  �j!                  e6�j$                  «      �d+„ «       «       «       Zû e#e=�jê                  �jô                  «      e=�jê                  �jô                  �j!                  e6�j"                  «      e=�jê                  �jô                  �j!                  e6�j$                  «      �d,„ «       «       «       Zü�d-„ Zý�d¹�d.„Zþ�d¹�d/„Zÿ�d0„ �Z  e#e=�j                  �jì                  «      e=�j                  �jì                  �j!                  e6�j"                  «      e=�j                  �jì                  �j!                  e6�j$                  «      �d1„ «       «       «       �Z e#e=�j                  �jô                  «      e=�j                  �jô                  �j!                  e6�j"                  «      e=�j                  �jô                  �j!                  e6�j$                  «      �d2„ «       «       «       �Z�d3„ �Z�d4„ �Z e#e=�j                  �jô                  «      e=�j                  �jô                  �j!                  e6�j"                  «      e=�j                  �jô                  �j!                  e6�j$                  «      �d5„ «       «       «       �Z e#e=�j                  �jì                  «      e=�j                  �jì                  �j!                  e6�j"                  «      e=�j                  �jì                  �j!                  e6�j$                  «      �d6„ «       «       «       �Z e#e=�j                  �jÀ                  «      e=�j                  �jÀ                  �j!                  e6�j"                  «      e=�j                  �jÀ                  �j!                  e6�j$                  «      �d7„ «       «       «       �Z
 e#e=�j                  �jÀ                  «      e=�j                  �jÀ                  �j!                  e6�j"                  «      e=�j                  �jÀ                  �j!                  e6�j$                  «      �d8„ «       «       «       �Z e#e=�j                  �jÀ                  «      e=�j                  �jÀ                  �j!                  e6�j"                  «      e=�j                  �jÀ                  �j!                  e6�j$                  «      �d9„ «       «       «       �Z e#e=�j                  �jÀ                  «       e#e=�j                   �jÀ                  «      e=�j"                  �jÀ                  �j!                  e6�j"                  «      e=�j"                  �jÀ                  �j!                  e6�j$                  «      e=�j                  �jÀ                  �j!                  e6�j"                  «      e=�j                  �jÀ                  �j!                  e6�j$                  «      e=�j                   �jÀ                  �j!                  e6�j"                  «      e=�j                   �jÀ                  �j!                  e6�j$                  «      �d:„ «       «       «       «       «       «       «       «       �Z e#e=�j"                  jÞ                  e=�j"                  jæ                  g«       e/«       	 �d®dAe!d‹e8eH   �d;e@�deMdz  de!f
�d<„«       «       �Z e#e=�j                  jÞ                  e=�j                  jæ                  g«      e=�j                  jÞ                  �j!                  e6�j$                  «       e/«       	 	 �dºdAe!d‹e8eH   �d;e@�deMdz  �deMdz  de!f�d=„«       «       «       �Z e#e=�j                   jÞ                  e=�j                   jæ                  g«       e/«       	 	 	 �d»dAe!d‹e8eH   �d;e@�deMdz  �deMdz  �deMdz  de!f�d>„«       «       �Z�d®�d?„�Z�d@„ �Zdxee!   �dAee!   �dBe!de!f�dC„�Z�dAe*de!f�dD„�ZeDdAe!d‹e8eH   �d;e@�de8eMdz     de!f
�dE„«       �Z e#e=�j0                  jÞ                  «      �dFe!�dGe!de@f�dH„«       �Z e#e=�j2                  e=�j4                  g«       e/«       �dI„ «       «       �Z e#e=�j6                  g«      �dJ„ «       �Z e#e=�j8                  g«      �d¹�dK„«       �Z e#e=�j:                  g«      �dL„ «       �Z e#e=�j<                  g«      �dM„ «       �Zd2e!dVe!dEe!dz  dReHdaeHde`e!e!f   f�dN„�Z e#e=�j@                  «       e/d‚db«      d2e!dVe!dEe!dz  dReHdaeHde`e!e!f   f�dO„«       «       �Z  e#e=�jB                  «       e/d‚db«      d2e!dVe!dEe!dz  dReHdaeHde`e!e!f   f�dP„«       «       �Z!de!�dQeMde!f�dR„�Z"de!�dQeMde!f�dS„�Z#�dTe!de*f�dU„�Z$�dVe*�dWe!de!f�dX„�Z%�dWee!   de!f�dY„�Z&�dZeH�d;e@dTejÊ                  dåe�j€                  f�d[„�Z'�d\e!�d]eH�d^eH�d;e@f�d_„�Z(�d\e!�d`eH�d]eH�d^eH�d;e@f
�da„�Z)�d\e!d‘e8eH   �d;e@f�db„�Z*�d\e!d‘e8eH   �d;e@f�dc„�Z+ e#e=�jX                  «       e/«       eD�d\e!d‘e8eH   �d;e@f�dd„«       «       «       �Z,	 	 	 	 �d¼�dFe!�dee!�dfeH�dgeH�d;e@�dhe@de!f�di„�Z- e#e=�j\                  «       e/«       eD	 	 	 �d½�dFe!�dee!�dfeH�dgeH�d;e@de!f�dj„«       «       «       �Z. e#e=�j^                  «       e/d¬œ«      eD�dk„ «       «       «       �Z/ e#e=�j`                  «       e/«       dde>jÐ                  jÒ                  f�dl„«       «       �Z0�dmejB                  �dnejB                  �doe@de@f�dp„�Z1e=�jd                  jÞ                  �j!                  e6�j"                  «      e=�jd                  jæ                  �j!                  e6�j"                  «       e/d�¬q«      d�drœ�ds„«       «       «       �Z2 e#e=�jf                  jÞ                  e=�jf                  jæ                  g«      e=�jf                  jÞ                  �j!                  e6�j$                  «       e/«       eD	 	 �dºdAe!d‹e`eHeHf   �d;e@�dteMdz  �dueMdz  de!f�dv„«       «       «       «       �Z4 e#e=�jf                  �jÀ                  «      e=�jf                  �jÀ                  �j!                  e6�j"                  «      e=�jf                  �jÀ                  �j!                  e6�j$                  «       e/«       eD	 �d®�dFe!d‹e`eHeHf   dz  �d;e@�de`eMeMf   dz  de!f
�dw„«       «       «       «       «       �Z5 e#e=�jl                  «       e#e=�jn                  «       e#e=�jp                  «      eD e/«       �dFe!dˆe`eHd±f   de!f�dx„«       «       «       «       «       �Z9 e#e=�jt                  «       e#e=�jv                  «       e#e=�jx                  «      eD e/«       �dFe!dˆe`eHd±f   de!f�dy„«       «       «       «       «       �Z=�dFe!dˆe`eHd±f   �dzeeHeHeHge!f   de!f�d{„�Z> e#e=�j~                  «       e#e=�j€                  «       e#e=�j‚                  «       e/d «      �d|„ «       «       «       «       �ZB e#e=�j†                  «       e/�d}�d~«      dd�dœ�d€„«       «       �ZC e#e=�jˆ                  «       e/«       �d¾d�d�œ�d‚„«       «       �ZD e#e=�jŠ                  jÞ                  e=�jŠ                  jæ                  g«       e/«       de�jŒ                  dd�dƒœdre'dTejÊ                  dz  �d„e�jŽ                  dåe�j€                  dz  dæe@f
�d…„«       «       �ZH e#e=�jŠ                  �j’                  g«      de�jŒ                  dd�dƒœdqe'dre'dTejÊ                  dz  �d„e�jŽ                  dåe�j€                  dz  dæe@f�d†„«       �ZJ e#e%«      �d‡„ «       �ZK e#e=�j˜                  «      e=�j˜                  jÞ                  �j!                  e6�j$                  «       e/«       dudude>jÐ                  jÒ                  fdAe!dVe!dke'�dˆe'dEe!dz  dReHde!f�d‰„«       «       «       �ZL e#e=�jš                  «      e=�jš                  jÞ                  �j!                  e6�j$                  «       e/d‚�dŠ«      dAe!dVe!dReHde`e!e!f   f�d‹„«       «       «       �ZM e#e=�jœ                  jÞ                  «      	 	 �d¿dd�dŒœ�d�e!�dŽe!d0e!�d�eM�d�e@�d‘e!dz  d*eMdz  de`e!e!f   f�d’„«       �ZO�d“„ �ZP e#e=�j¢                  g«       e/d¬œ«      eD�d´�d”„«       «       «       �ZQ e#e=�j¤                  «       e/«       �d•„ «       «       �ZR e#e=�j¦                  «      �d–„ «       �ZS e#e=�j¨                  jÞ                  e=�j¨                  jæ                  g«      dd�d—œd2e!dTejÊ                  dz  d¬e!dz  de!f�d˜„«       �ZU e#e=�j¬                  jÞ                  e=�j¬                  �j®                  g«      �d®d2e!deHdz  f�d™„«       �ZX e#ejx                  jz                  �j²                  «      �d³�dš„«       �ZY e#e=�j´                  «       e/«       dd�d›œ�dœ„«       «       �ZZ e#e=�j¶                  jÞ                  «      d�d�œd2ejB                  �d	e�j¶                  dz  dejB                  f�dž„«       �Z[d�dŸœ�d „�Z\dd�d›œ�d¡„�Z] e#e=�j¼                  «       e/«       �d¢„ «       «       �Z^ e#e=�j¾                  «      �d®�d£„«       �Z_ e#e=�jÀ                  «      d(e!d2e!�d¤e@dže!f�d¥„«       �Z` e#e=�jÂ                  jÞ                  e=�jÂ                  jæ                  g«       e/«       dddd�dƒœ�d¦eHdTejÊ                  dz  �d„e�jŽ                  dz  dåe�j€                  dz  dæe@dz  de!f�d§„«       «       �Za e#e=�jÂ                  �jÄ                  e=�jÂ                  �jÆ                  g«       e/«       	 �dÀdddd�dƒœ�d¦eH�d¨e@dTejÊ                  dz  �d„e�jŽ                  dz  dåe�j€                  dz  dæe@dz  de!f�d©„«       «       �Zd �ePe=�jÊ                  e=�jÌ                  «        �ePe=�jÎ                  e=�jJ                  «        �ePe=�jÐ                  e=�jN                  «        �ePe=�jÒ                  e=�j¢                  «        �ePe=�jÔ                  e=jž                  «        �ePe=�jÖ                  e=�jØ                  «        �ePe=�jÚ                  e=j¬                  «        �ePe=�jÜ                  e=�jÞ                  «        �ePe=�jà                  e=j¦                  «        �ePe=�jâ                  e=�jä                  «        �ePe=�jæ                  e=�jè                  «        �ePe=�jê                  e=�jì                  «        �ePe=�jî                  e=�jð                  «        �ePe=�jò                  e=�jô                  «        �ePe=�jö                  e=�jø                  «        �ePe=�jú                  e=�jü                  «        �ePe=�jþ                  e=jÆ                  «        �ePe=�j                   e=�j                  «        �ePe=�j                  e=�j                  «        �ePe=�j                  e=�j
                  «        �ePe=�j                  e=�j                  «        �ePe=�j                  e=�j                  «        �ePe=�j                  e=�j                  «        �ePe=�j                  e=�j                  «        �ePe=�j                  e=�j                  «        �ePe=�j                   e=j¸                  «       e=�j"                  jÞ                  �j!                  e6�j"                  «      �dÁd2e!�dªeHde!f�d«„«       �Z‘y(Â  é    N)ÚCallableÚIterable)Únullcontext)ÚEnum)ÚpartialÚreduce)ÚchainÚproduct)ÚAnyÚcast)Ú	sym_floatÚsym_intÚTensor©Úregister_decomposition)Ú	out_dtype)ÚIntLikeÚ
NumberTypeÚsuggest_memory_formatÚ
TensorLikeÚTensorSequenceType)Ú_maybe_convert_to_dtypeÚ_maybe_resize_outÚ_safe_copy_outÚout_wrapper)Ú_pytree)Útree_mapÚ__all__c                   ó   — e Zd ZdZdZdZy)Ú	Reductionr   é   é   N)Ú__name__Ú
__module__Ú__qualname__ÚNONEÚMEANÚSUM© ó    ú[/var/www/html/ia-enhanced/venv/lib/python3.12/site-packages/torch/_decomp/decompositions.pyr    r    1   s   „ Ø€DØ€DØ
�Cr*   r    FÚfÚtype_promotionÚcompute_dtype_onlyÚinclude_non_tensor_argsc                 óN   ‡ ‡‡‡— t        j                  ‰ «      ˆˆ ˆˆfd„«       }|S )Nc                  ó\  •‡‡	— ‰r t         t        j                  j                  fnt         f}t	        j
                  | i |¤ŽD �cg c]  }t        ||«      r|‘Œ }}t        j                  |d‰iŽ\  ŠŠ	ˆfd„}ˆ	fd„} ‰t        || «      i t        ||«      ¤Ž}‰
r|S t        ||«      S c c}w )NÚtype_promotion_kindc                 óJ   •— t        | t        «      r| j                  ‰«      S | S ©N©Ú
isinstancer   Úto)ÚxÚcomputation_dtypes    €r+   Úincrease_precz0type_casts.<locals>.inner.<locals>.increase_precO   s"   ø€ Ü˜!œVÔ$Ø—t‘tÐ-Ó.Ð.à�r*   c                 óJ   •— t        | t        «      r| j                  ‰«      S | S r4   r5   )r8   Úresult_dtypes    €r+   Údecrease_precz0type_casts.<locals>.inner.<locals>.decrease_precU   s!   ø€ Ü˜!œVÔ$Ø—t‘t˜LÓ)Ð)à�r*   )
r   ÚtorchÚtypesÚ_NumberÚpytreeÚarg_tree_leavesr6   ÚutilsÚelementwise_dtypesr   )ÚargsÚkwargsÚallowed_typesr8   Ú	flat_argsr:   r=   Úrr9   r<   r.   r,   r/   r-   s           @@€€€€r+   Úinnerztype_casts.<locals>.inner@   sÂ   ú€ ñ .EŒV”U—[‘[×(Ñ(Ñ)Ì6È)ð 	ô
 ×+Ñ+¨TÐ<°VÑ<ö
àÜ˜!˜]Ô+ò ð
ˆ	ð 
ô
 +0×*BÑ*BØð+
Ø,:ñ+
Ñ'Ð˜<ô
	ô	ñ Œx˜ tÓ,ÐP´¸ÈÓ0OÑPˆÙØˆHä˜M¨1Ó-Ð-ùò5
s   ÁB))Ú	functoolsÚwraps)r,   r-   r.   r/   rJ   s   ```` r+   Ú
type_castsrM   :   s(   û€ ô ‡_�_�QÓö.ó ð.ð@ €Lr*   T)r-   r.   )r-   )r-   r/   r8   ÚdimÚreturnc                 ój   — t        || j                  «       z
  «      D ]  }| j                  d«      } Œ | S ©Néÿÿÿÿ)ÚrangerN   Ú	unsqueeze)r8   rN   Ú_s      r+   Ú_unsqueeze_to_dimrV   w   s2   € Ü�3˜Ÿ™›‘=Ó!ò ˆØ�K‰K˜‹O‰ðà€Hr*   Ú
grad_inputÚout_gradÚyc                 ó4   — | d||z  z
  j                  «       z  S ©Nr!   ©Úconj_physical©rX   rY   s     r+   Útanh_backwardr_   }   s    € ð �q˜1˜q™5‘y×/Ñ/Ó1Ñ1Ð1r*   c                 ó4   — | |d|z
  z  j                  «       z  S r[   r\   r^   s     r+   Úsigmoid_backwardra   „   s    € ð �q˜A ™E‘{×1Ñ1Ó3Ñ3Ð3r*   ÚbetaÚ	thresholdc                 ót   — ||z  j                  «       }t        j                  ||z  |kD  | | |z  |dz   z  «      S ©Nç      ð?)Úexpr>   Úwhere)rX   r8   rb   rc   Úzs        r+   Úsoftplus_backwardrj   ‹   s=   € ð 
ˆT‰�‰Ó€AÜ�;‰;˜˜D™ IÑ-¨x¸ÀA¹ÈÈSÉÑ9QÓRÐRr*   Úgrad_outputÚalphaÚscaleÚinput_scaleÚ	is_resultÚself_or_resultc                 óÜ   — ||z  }|}|}|r&t        j                  |dk  | |z  ||z   z  | |z  «      S t        j                  |dk  | |z  |z  t        j                  ||z  «      z  | |z  «      S ©Nr   )r>   rh   rg   )	rk   rl   rm   rn   ro   rp   ÚnegcoefÚposcoefÚ
negiptcoefs	            r+   Úelu_backwardrv   “   s�   € ð �e‰m€GØ€GØ€JÙÜ�{‰{Ø˜aÑØ˜*Ñ$¨¸Ñ(@ÑAØ˜'Ñ!ó
ð 	
ô �{‰{Ø˜aÑØ˜*Ñ$ wÑ.´·±¸>ÈJÑ;VÓ1WÑWØ˜'Ñ!ó
ð 	
r*   c                 ó.   — t        j                  | |«      S r4   )r>   Ú	full_like©ÚselfÚvalues     r+   Úfill_scalarr|   ¯   s   € ä�?‰?˜4 Ó'Ð'r*   r{   c                 ó„   ‡— t        j                  ‰j                  «       dk(  ˆfd„«       t        j	                  | ‰«      S )Nr   c                  ó,   •— d‰ j                  «       › d�S )Nz@fill only supports 0-dimension value tensor but got tensor with z dimensions©rN   )r{   s   €r+   ú<lambda>zfill_tensor.<locals>.<lambda>¸   s   ø€ ÐRÐSX×S\ÑS\ÓS^ÐR_Ð_jÐk€ r*   )r>   Ú_checkrN   ÚatenÚcopyry   s    `r+   Úfill_tensorr„   ´   s3   ø€ ä	‡L�LØ�	‰	‹�qÑÛkôô �9‰9�T˜5Ó!Ð!r*   rz   c                 óf   — t        j                  t        j                  | dz   d¬«      d¬«      dz  S ©Né   r   ©Úminé   ©Úmax©r>   Úclamp©rz   s    r+   Úhardsigmoidr�   ½   s)   € ô �;‰;”u—{‘{ 4¨!¡8°Ô3¸Ô;¸aÑ?Ð?r*   c                 óH   — t        j                  |dkD  |dk  z  | dz  d«      S )Ng      Àg      @gUUUUUUÅ?ç        ©r>   rh   ©rk   rz   s     r+   Úhardsigmoid_backwardr•   Ä   s0   € ô �;‰;Ø	�‰˜ ™Ñ$Ø�yÑ!Øóð r*   Úmin_valÚmax_valc                 óB   — t        j                  ||k  ||k\  z  d| «      S )Nr’   r“   )rk   rz   r–   r—   s       r+   Úhardtanh_backwardr™   Ï   s$   € ô
 �;‰;˜ ™¨D°G©OÑ<¸cÀ;ÓOÐOr*   c                 ól   — | t        j                  t        j                  | dz   d¬«      d¬«      z  dz  S r†   r�   r�   s    r+   Ú	hardswishr›   ×   s.   € ð ”%—+‘+œeŸk™k¨$°©(¸Ô:ÀÔBÑBÀQÑFÐFr*   c           
      óx   — t        j                  |dk  dt        j                  |dk  | |dz  dz   z  | «      «      S )Néýÿÿÿr’   r‡   ç      à?r“   r”   s     r+   Úhardswish_backwardrŸ   Þ   sA   € ô �;‰;Ø�‰
ØÜ�‰�D˜1‘H˜k¨d°Q©h¸#Ñ-=Ñ>ÀÓLóð r*   c                 ó6   — t        j                  ||k  d| «      S rr   r“   )rk   rz   rc   s      r+   Úthreshold_backwardr¡   é   s   € ô �;‰;�t˜yÑ(¨!¨[Ó9Ð9r*   Únegative_slopeÚself_is_resultc                 ó<   — t        j                  |dkD  | | |z  «      S rr   r“   )rk   rz   r¢   r£   s       r+   Úleaky_relu_backwardr¥   ï   s    € ô �;‰;�t˜a‘x ¨k¸NÑ.JÓKÐKr*   ÚgradÚapproximatec                 óŒ  — d}d}d}|dk(  ri||z  dz  }d}||z  }||z  }	||||	z  z   z  }
t        j                  |
«      }d|z  }d|z   }d|z  }d||z  z
  }|dd|z  |z  z   z  }||z  |z  }| ||z   z  S |}||z  dz  }ddt        j                  ||z  «      z   z  }|t        j                  ||z  d	z  «      z  }| |||z  z   z  S )
NgÍ;fž ö?gÍ;fž æ?gm›BP×ò?Útanhrž   g÷Hmâä¦?r!   r‡   ç      à¿)r>   r©   Úerfrg   )r¦   rz   r§   ÚM_SQRT2Ú	M_SQRT1_2Ú
M_2_SQRTPIÚkBetaÚkKappaÚx_sqÚx_cuberJ   Ú
tanh_innerÚleftÚrightÚleft_derivativeÚtanh_derivativeÚinner_derivativeÚright_derivativeÚkAlphaÚcdfÚpdfs                        r+   Úgelu_backwardr½   ø   s'  € ð %€GØ&€IØ'€JØ�fÒØ˜*Ñ$ sÑ*ˆØˆØ�d‰{ˆØ˜‘ˆØ˜ ¨¡Ñ/Ñ0ˆÜ—Z‘Z Ó&ˆ
à�T‰zˆØ�J‘ˆà ™+ˆà˜j¨:Ñ5Ñ5ˆØ  A¨¨F©
°TÑ(9Ñ$9Ñ:ÐØ /Ñ1Ð4DÑDÐà�Ð)9Ñ9Ñ:Ð:àˆØ˜YÑ&¨Ñ,ˆØ�QœŸ™ 4¨&¡=Ó1Ñ1Ñ2ˆØ”e—i‘i  t¡¨dÑ 2Ó3Ñ3ˆØ�s˜T C™ZÑ'Ñ(Ð(r*   Úinputc                 ó¨   — t        j                  t        j                  |«      «      }t        j                  |«      }||z  d||z  z
  z  }| ||z   z  S r[   )r>   r©   ÚFÚsoftplusÚsigmoid)rk   r¾   Úinput_tanh_softplusÚinput_sigmoidÚouts        r+   Úmish_backwardrÆ     sV   € ô  Ÿ*™*¤Q§Z¡Z°Ó%6Ó7ÐÜ—M‘M %Ó(€MØ
�-Ñ
 1Ð':Ð=PÑ'PÑ#PÑ
Q€CØÐ-°Ñ3Ñ4Ð4r*   c                 ó2   — | t        j                  | «      z  S r4   )r>   rÂ   r�   s    r+   ÚsilurÈ   "  s   € ð ”%—-‘- Ó%Ñ%Ð%r*   c                 ó\   — ddt        j                  | «      z   z  }| |z  d|d|z
  z  z   z  S r[   )r>   rg   )rk   rz   rÂ   s      r+   Úsilu_backwardrÊ   )  s<   € ð �1”u—y‘y $ Ó'Ñ'Ñ(€GØ˜Ñ  A¨°°G±Ñ(<Ñ$<Ñ=Ð=r*   Úweightc                 ó<   — t        j                  | dkD  | || z  «      S rr   r“   )rz   rË   s     r+   Ú_prelu_kernelrÍ   1  s   € ä�;‰;�t˜a‘x  v°¡}Ó5Ð5r*   c                 ó~   — t        j                  |dkD  | || z  «      }t        j                  |dkD  d|| z  «      }||fS )Nr   r’   r“   )rk   rz   rË   Ú
input_gradÚweight_grads        r+   Ú_prelu_kernel_backwardrÑ   6  sE   € ô —‘˜T A™X {°F¸[Ñ4HÓI€JÜ—+‘+˜d Q™h¨¨T°KÑ-?Ó@€KØ˜Ð$Ð$r*   ÚnoiseÚlowerÚupperÚtrainingc                 óh   — |r| j                  |«      S ||z   dz  }t        j                  | |||«      S ©Nr"   )Úmulr‚   r¥   )rk   rz   rÒ   rÓ   rÔ   rÕ   r£   r¢   s           r+   Úrrelu_with_noise_backwardrÙ   A  s@   € ñ Ø�‰˜uÓ%Ð%à %™-¨1Ñ,ˆÜ×'Ñ'Ø˜˜~¨~ó
ð 	
r*   Úbufferc                 ó  — |dk  }t        j                  |dd«      }t        j                  |dd«      }|j                  «       dkD  r|n(t        j                  t        j                  |«       «      }| |||d|z   z  z  z
  z  S )Nr   r!   rR   )r>   rh   Únumelrg   Úabs)rk   rz   rÚ   Úin_negativeÚ	max_derivÚsignri   s          r+   Úlog_sigmoid_backwardrá   V  sx   € ð ˜‘(€KÜ—‘˜K¨¨AÓ.€IÜ�;‰;�{ A rÓ*€Dð —,‘,“. 1Ò$‰¬%¯)©)´U·Y±Y¸t³_Ð4DÓ*E€AØ˜) d¨a°1°q±5©kÑ&:Ñ:Ñ;Ð;r*   Úotherc                 ó  — t        j                  | j                  «      st        j                  | j                  «      rt        j
                  n| j                  }| j                  dd|¬«      }| t	        j                  ||«      z  S )Nr)   ç       @©Údtype)rC   Úis_integer_dtyperæ   Úis_boolean_dtyper>   Úfloat32Únew_fullÚpow)rz   râ   Ú	two_dtypeÚ
two_tensors       r+   Úldexprî   c  sh   € ô
 ×!Ñ! $§*¡*Ô-´×1GÑ1GÈÏ
É
Ô1Sô 	�Šà�Z‰Zð ð
 —‘˜r 3¨i�Ó8€JØ”%—)‘)˜J¨Ó.Ñ.Ð.r*   ÚlossÚ	reductionc                 óÎ   — |t         j                  j                  k(  rt        j                  | «      S |t         j
                  j                  k(  rt        j                  | «      S | S r4   )r    r'   r{   r>   Úmeanr(   Úsum)rï   rð   s     r+   Úapply_loss_reductionrô   o  sH   € Ø”I—N‘N×(Ñ(Ò(Ü�z‰z˜$ÓÐØ	”i—m‘m×)Ñ)Ò	)Ü�y‰y˜‹Ðàˆr*   ræ   c                 óÖ   — | t         j                  k(  rt         j                  S | t         j                  k(  rt         j                  S | t         j
                  k(  rt         j                  S y r4   )r>   Ú	complex32Úfloat16Ú	complex64ré   Ú
complex128Úfloat64rå   s    r+   Úto_real_dtyperû   x  sK   € Ø”—‘ÒÜ�}‰}ÐØ	”%—/‘/Ò	!Ü�}‰}ÐØ	”%×"Ñ"Ò	"Ü�}‰}Ðð 
#r*   Útargetc                 ó*   — | |z
  dz  }t        ||«      S r×   )rô   )rz   rü   rð   rï   s       r+   Úmse_lossrþ   ‡  s   € ð �6‰M˜aÑ€DÜ  iÓ0Ð0r*   c                 ó|   — |t         j                  j                  k(  rd|j                  «       z  nd}|||z
  z  | z  S )Nrä   )r    r'   r{   rÜ   )rk   r¾   rü   rð   Únorms        r+   Úmse_loss_backwardr  ‘  s;   € ð #,¬y¯~©~×/CÑ/CÒ"Cˆ3�—‘“ÒÈ€DØ�5˜6‘>Ñ" [Ñ0Ð0r*   c                 óî   — t        j                  | ||¬«      }| j                  t        d«      «      }t        j                  ||d¬«      }t        j
                  |«      }t        j                  |||«      S )N)rN   ræ   z-infT©rN   Úkeepdim)r>   ÚsoftmaxÚeqÚfloatÚallÚ
zeros_likerh   )rz   rN   ræ   rÅ   ÚmaskedÚmasked_rowsÚzeross          r+   Úsafe_softmaxr  ›  s[   € ä
�-‰-˜ #¨UÔ
3€CØ�W‰W”U˜6“]Ó#€FÜ—)‘)˜F¨°TÔ:€KÜ×Ñ˜SÓ!€EÜ�;‰;�{ E¨3Ó/Ð/r*   rf   c                 ó’   — | |z
  j                  «       }t        j                  ||k  d|dz  z  |z  |d|z  z
  «      }t        ||«      S )Nrž   r"   )rÝ   r>   rh   rô   )rz   rü   rð   rb   rï   s        r+   Úsmooth_l1_lossr  ¤  sO   € ð �6‰M×ÑÓ €Dä�;‰;�t˜d‘{ C¨$°©'¡M°DÑ$8¸$ÀÀtÁÑ:KÓL€DÜ  iÓ0Ð0r*   c                 ó  — |t         j                  j                  k(  rd|j                  «       z  nd}||z
  }t	        j
                  |«      }|| z  }t	        j                  ||k  ||z  |z  |t	        j                  |«      z  «      S re   )r    r'   r{   rÜ   r>   rÝ   rh   rà   )	rk   rz   rü   rð   rb   r   r8   Úabs_xÚ	norm_grads	            r+   Úsmooth_l1_loss_backwardr  ³  s{   € ð
 "+¬i¯n©n×.BÑ.BÒ!Bˆ3�—‘“ÒÈ€DØˆv‰€AÜ�I‰I�a‹L€EØ�{Ñ"€IÜ�;‰;Ø�‰Ø�A‰˜ÑØ”E—J‘J˜q“MÑ!óð r*   c                 óh   — t        | ||||«      }t        ||j                  «       t        ||d¬«      S ©NT©Ú	copy_fromÚcopy_toÚexact_dtype)r  r   Úshaper   )rk   rz   rü   rð   rb   rW   Úresults          r+   Úsmooth_l1_loss_backward_outr  Ã  s3   € ô % [°$¸À	È4ÓP€FÜ�j &§,¡,Ô/Ü F°JÈDÔQÐQr*   Údeltac           
      óü   — |t         j                  j                  k(  rd|j                  «       z  nd}||z
  }t	        j
                  || k  | | z  |z  t	        j
                  ||kD  || z  |z  ||z  | z  «      «      S re   )r    r'   r{   rÜ   r>   rh   )rk   rz   rü   rð   r  r   r8   s          r+   Úhuber_loss_backwardr  Ò  s€   € ð
 "+¬i¯n©n×.BÑ.BÒ!Bˆ3�—‘“ÒÈ€DØˆv‰€AÜ�;‰;Ø	ˆUˆF‰
Ø	ˆ�Ñ˜eÑ#Ü�‰�A˜‘I˜t kÑ1°EÑ9¸4À!¹8ÀkÑ;QÓRóð r*   c                 óh   — t        | ||||«      }t        ||j                  «       t        ||d¬«      S r  )r  r   r  r   )rk   rz   rü   rð   r  rW   r  s          r+   Úhuber_loss_backward_outr!  á  s3   € ô ! ¨d°F¸IÀuÓM€FÜ�j &§,¡,Ô/Ü F°JÈDÔQÐQr*   Úignore_indexÚtotal_weightc                 óØ  — |j                  «       dk  rdnd}|t        j                  j                  k(  r| |z  } |j                  «       dk(  r|j                  «       dkD  r|d   }|j	                  |«      }t        j                  ||k7  |d«      }t        j                  |«      }	t        j                  |	||d«      }	|	j                  «       | j                  «       cxkD  rdkD  rn n| j	                  |«      } |�Nt        |j                  «       «      D �
cg c]  }
d‘Œ }}
|j                  d   ||<   |j                  |«      }| |z  } t        j                  ||k7  | d«      } |	| z  S c c}
w )Nr"   r   r!   g      ð¿)rN   r    r'   r{   rT   r>   rh   r	  ÚscatterrS   r  Úreshape)rk   rz   rü   rË   rð   r"  r#  Úchannel_dimÚsafe_targetrW   rU   Ú	new_shapes               r+   Ú_nll_loss_backwardr*  ð  sC  € ð —x‘x“z A’~‘!¨1€KØ”I—N‘N×(Ñ(Ò(Ø! LÑ0ˆð
 ‡x�xƒz�Q‚˜6Ÿ:™:›<¨!Ò+Ø˜‘ˆà×Ñ˜kÓ*€FÜ—+‘+˜f¨Ñ4°f¸aÓ@€KÜ×!Ñ! $Ó'€JÜ—‘˜z¨;¸ÀTÓJ€Jà‡~�~Ó˜+Ÿ/™/Ó+Ô/¨aÕ/Ø!×+Ñ+¨KÓ8ˆàÐÜ % d§h¡h£jÓ 1Ö2˜1’QÐ2ˆ	Ð2Ø!'§¡¨a¡ˆ	�+ÑØ—‘ 	Ó*ˆØ! FÑ*ˆä—+‘+˜f¨Ñ4°kÀ1ÓE€Kà˜Ñ#Ð#ùò 3s   Ä	E'c                 ó²  — |j                  «       dk  rt        d«      ‚t        j                  |j                  «       |«      }|j	                  |«      }|dz  dk7  rt        d|› d|› �«      ‚|dz  }|j                  |d|«      }|j                  |||«      }t        j                  |«      }d|z
  |z  |z  | z  }	|| z  }t        j                  ||	g|¬«      S )Nr   z*glu does not support 0-dimensional tensorsr"   z.Halving dimension must be even, but dimension z	 is size rf   r   )	rN   ÚAssertionErrorrC   Úcanonicalize_dimÚsizeÚnarrowr>   rÂ   Úcat)
rk   rz   rN   Úwrap_dimÚnInÚ	inputSizeÚ	firstHalfÚ
secondHalfÚgradInputFirstHalfÚgradInputSecondHalfs
             r+   Úglu_backwardr8    sí   € ð ‡x�xƒz�Q‚ÜÐIÓJÐJÜ×%Ñ% d§h¡h£j°#Ó6€HØ
�)‰)�HÓ
€CØ
ˆQ�w�!‚|ÜØ<¸X¸JÀiÐPSÈuÐUó
ð 	
ð �q‘€IØ—‘˜H a¨Ó3€IØ—‘˜X y°)Ó<€JÜŸ™ zÓ2Ðà	Ð!Ñ	!Ð%7Ñ7¸)ÑCÀkÑQð ð ,¨kÑ9ÐÜ�9‰9Ð(Ð*=Ð>ÀHÔMÐMr*   c           	      ó^  — d|j                  «       cxk  rdk  sn t        d|j                  «       › d�«      ‚|j                  «       dkD  rt        d|j                  «       › d�«      ‚|j                  «       dk(  xr |j                  «       dk(  }|sE|j                  d   |j                  d   k(  s&t        d|j                  › d|j                  › d	�«      ‚|j                  «       dk7  r*t        d
|j                  › d|j                  «       › d�«      ‚|�+|j                  «       |j                  d   k7  rt        d«      ‚|t        j
                  j                  k(  r�|j                  «       dk(  rn| j                  «       dk(  r| j                  d   |j                  d   k(  szt        d|j                  d   › d| j                  «       › d| j                  d   › �«      ‚| j                  «       dk  r| j                  «       dk(  st        d| j                  › �«      ‚t        | ||||||«      S )Nr   r"   ú%input tensor should be 1D or 2D, got ÚDr!   úA0D or 1D target tensor expected, multi-target not supported, got úsize mismatch (got input: ú
, target: ú)ú:expected total_weight to be a single element tensor, got: z (z
 elements)rR   z<weight tensor should be defined either for all or no classesz7Expected a tensor of dimension 1 and tensor.size[0] == z but got: dimension z and tensor.size[0] == z7Expected a single element grad_output tensor, but got: )rN   r,  r  rÜ   r    r&   r{   r*  )rk   rz   rü   rË   rð   r"  r#  Úno_batch_dims           r+   Únll_loss_backwardrB  -  s+  € ð �—‘“Ô ˜qÔ ÜÐDÀTÇXÁXÃZÀLÐPQÐRÓSÐSØ‡z�zƒ|�aÒÜØOÐPV×PZÑPZÓP\È~Ð]^Ð_ó
ð 	
ð —8‘8“: ‘?Ò8 v§z¡z£|°qÑ'8€LÙ˜TŸZ™Z¨™]¨f¯l©l¸1©oÒ=ÜØ(¨¯©¨°J¸v¿|¹|¸nÈAÐNó
ð 	
ð ×ÑÓ˜qÒ ÜØHØ×!Ñ!Ð" " \×%7Ñ%7Ó%9Ð$:¸*ðFó
ð 	
ð
 Ð˜fŸl™l›n°·
±
¸2±Ò>ÜØJó
ð 	
ð ”I—N‘N×(Ñ(Ò(¨T¯X©X«Z¸1ª_Ø—‘Ó! QÒ&¨;×+<Ñ+<¸QÑ+?À4Ç:Á:ÈaÁ=Ò+PÜ ØIÈ$Ï*É*ÐUVÉ-Èð Y"Ø"-§/¡/Ó"3Ð!4Ð4KÈK×L]ÑL]Ð^_ÑL`ÐKaðcóð ð
 —‘Ó! QÒ&¨;×+<Ñ+<Ó+>À!Ò+CÜ ØIÈ+×J[ÑJ[ÐI\Ð]óð ô Ø�T˜6 6¨9°lÀLóð r*   c           	      ó^  — |j                  «       dk7  rt        d|j                  «       › �«      ‚|j                  «       dk7  rt        d|j                  «       › �«      ‚|j                  d   |j                  d   k(  r>|j                  d   |j                  d   k(  r|j                  d   |j                  d   k(  s%t        d|j                  › d	|j                  › �«      ‚|j                  «       dk7  r*t        d
|j                  › d|j                  «       › d�«      ‚t	        | ||||||«      S )Né   zSonly batches of spatial inputs supported (4D tensors), but got input of dimension: r‡   zUonly batches of spatial targets supported (3D tensors) but got targets of dimension: r   r"   r!   r=  r>  r@  z ( z, elements))rN   r,  r  rÜ   r*  )rk   rz   rü   rË   rð   r"  r#  s          r+   Únll_loss2d_backwardrE  `  s;  € ð ‡x�xƒz�Q‚ÜØaÐbf×bjÑbjÓblÐamÐnó
ð 	
ð ‡z�zƒ|�qÒÜØcÐdj×dnÑdnÓdpÐcqÐró
ð 	
ð
 	�
‰
�1‰˜Ÿ™ a™Ò(Ø�J‰J�q‰M˜VŸ\™\¨!™_Ò,Ø�J‰J�q‰M˜VŸ\™\¨!™_Ò,äØ(¨¯©¨°J¸v¿|¹|¸nÐMó
ð 	
ð ×ÑÓ˜qÒ ÜðØ ×&Ñ&Ð' s¨<×+=Ñ+=Ó+?Ð*@ÀðMó
ð 	
ô
 Ø�T˜6 6¨9°lÀLóð r*   c           	      ó"  — |dz
  t        j                  t        j                  |  «      | j                  dd«      «      z  |t        j                  t        j                  | «      | j                  dd«      «      z  z
  }|�||z  }t        ||«      S )Nr!   r)   iœÿÿÿ)r>   ÚmaximumÚlog1prê   Úlogrô   )rz   rü   rË   rð   rï   s        r+   Úbinary_cross_entropyrJ  ‰  s‚   € ð �Q‰Jœ%Ÿ-™-Ü�‰�T�EÓ˜DŸM™M¨"¨dÓ3óñ à”—‘œuŸy™y¨›°·±¸bÀ$Ó0GÓHÑHñI€Dð ÐØ�f‰}ˆÜ  iÓ0Ð0r*   c                 óÄ   — d}| ||z
  z  t        j                  |d|z
  z  |¬«      z  }|�||z  }|t        j                  j                  k(  r||j                  «       z  }|S )Ngê-�™—q=r!   rˆ   )r>   rŽ   r    r'   r{   rÜ   )rk   rz   rü   rË   rð   ÚEPSILONr  s          r+   Úbinary_cross_entropy_backwardrM  Ÿ  sg   € ð €GØ˜D 6™MÑ*¬U¯[©[¸ÀÀTÁÑ9JÐPWÔ-XÑX€FØÐØ˜&‘ˆØ”I—N‘N×(Ñ(Ò(Ø˜$Ÿ*™*›,Ñ&ˆØ€Mr*   c                 ór   — t        j                  t        j                  |  |z  «      «      }t        ||«      S r4   )r>   rH  rg   rô   )r¾   rü   rð   rï   s       r+   Úsoft_margin_lossrO  ²  s.   € ô �;‰;”u—y‘y % ¨&¡Ó1Ó2€DÜ  iÓ0Ð0r*   c                 ó¨   — || z  t        j                  ||z  «      dz
  z  }|t        j                  j                  k(  r||j                  «       z  }|S r[   )r>   rÂ   r    r'   r{   rÜ   )rk   rz   rü   rð   rW   s        r+   Úsoft_margin_loss_backwardrQ  ¾  sM   € ð ˜+Ñ%¬¯©°vÀ±}Ó)EÈÑ)IÑJ€JØ”I—N‘N×(Ñ(Ò(Ø $§*¡*£,Ñ.ˆ
ØÐr*   Úpc                 ó6   — t         j                  | |z
  |¬«      S )N)rR  )r‚   r   )r¾   râ   rR  s      r+   ÚdistrT  Í  s   € ô �9‰9�U˜U‘] aˆ9Ó(Ð(r*   Úx1Úx2c                 ó  — | j                  d«      j                  dd«      }t        j                  |t        j                  ¬«      }|j                  d«      j                  dd«      }t        j                  |t        j                  ¬«      }t        j
                  | j                  d«      ||gd«      }t        j
                  |||gd«      }|j                  |j                  «      }|j                  d«      j                  «       S )Nr"   rR   T©Úmemory_formatéþÿÿÿr   )rë   ró   r>   Ú	ones_likeÚcontiguous_formatr0  rØ   ÚmatmulÚmTÚ	clamp_minÚsqrt)	rU  rV  Úx1_normÚx1_padÚx2_normÚx2_padÚx1_Úx2_r  s	            r+   Ú_euclidean_distrg  Ó  sÂ   € ð �f‰f�Q‹i�m‰m˜B Ó%€GÜ�_‰_˜W´E×4KÑ4KÔL€FØ�f‰f�Q‹i�m‰m˜B Ó%€GÜ�_‰_˜W´E×4KÑ4KÔL€FÜ
�)‰)�R—V‘V˜B“Z ¨&Ð1°2Ó
6€CÜ
�)‰)�R˜ Ð)¨2Ó
.€CØ�Z‰Z˜Ÿ™Ó€FØ×Ñ˜AÓ×#Ñ#Ó%Ð%r*   Úinput_sizesÚstartÚendÚstepc                 óX   — | j                  |«      }t        j                  || ||||«      S r4   )Ú	new_zerosr>   Úslice_scatter)rk   rh  rN   ri  rj  rk  rW   s          r+   Úslice_backwardro  à  s/   € ð ×&Ñ& {Ó3€JÜ×Ñ˜z¨;¸¸UÀCÈÓNÐNr*   r!   c                 óÚ  — ddl m} | j                  «       }|dk(  rt        d«      ‚t	        j
                  | j                  «       |«      }t        | j                  «       «      }t        | j                  «       «      }|dk  rt        d«      ‚|�|nd}	|�|nt        j                  }
|	dk  r|	||   z  }	|
dk  r|
||   z  }
|	dk  rd}	n|	||   kD  r||   }	 ||
t        j                  k(  «      r||   }
n|
|	k  r|	}
n|
||   kD  r||   }
| j                  «       |	||   z  z   }|
|	z
  }||z   dz
  |z  ||<   ||xx   |z  cc<   | j                  rt        d«      ‚| j                  |||«      S )Nr   ©Ústatically_known_truez,slice() cannot be applied to a 0-dim tensor.zslice step must be positiver!   z<Slice decomposition for quantized tensors aren't implemented)Ú%torch.fx.experimental.symbolic_shapesrr  rN   ÚRuntimeErrorrC   r-  Úlistr.  ÚstrideÚsysÚmaxsizeÚstorage_offsetÚis_quantizedÚNotImplementedErrorÚ
as_strided)rz   rN   ri  rj  rk  rr  ÚndimÚsizesÚstridesÚ	start_valÚend_valry  Úlens                r+   Úslice_forwardrƒ  î  s‹  € õ Là�8‰8‹:€DØˆq‚yÜÐIÓJÐJÜ
×
 Ñ
  §¡£¨SÓ
1€CÜ�—‘“Ó€EÜ�4—;‘;“=Ó!€Gàˆq‚yÜÐ8Ó9Ð9àÐ*‘°€IØ�_‰c¬#¯+©+€Gà�1‚}Ø�U˜3‘ZÑˆ	à�‚{Ø�5˜‘:Ñˆà�1‚}Ø‰	Ø	�U˜3‘ZÒ	Ø˜#‘Jˆ	á˜W¬¯©Ñ3Ô4Ø˜‘*‰Ø	�9Ò	Ø‰Ø	�5˜‘:Ò	Ø˜‘*ˆà×(Ñ(Ó*¨Y¸À¹Ñ-EÑE€NØ
�IÑ
€CØ˜‘*˜q‘. TÑ)€Eˆ#�JØˆCƒL�DÑƒLà×ÒÜ!ØJó
ð 	
ð �‰˜u g¨~Ó>Ð>r*   c                 ón   ‡— | j                   |   Šdt        fˆfd„} ||d‰d«      } |||‰‰«      }||fS )zn
    Normalize start and end such that both are in the range
    [0, x.get_size()[dim]] and start <= end.
    rO   c                 óL   •— | €|S | dk  r| ‰z   } t        t        | |«      |«      S rr   ©r‰   rŒ   )ÚvalrÓ   rÔ   ÚdefaultÚdim_sizes       €r+   Ú
clamp_wrapz(_normalize_start_end.<locals>.clamp_wrap.  s0   ø€ Øˆ;ØˆNØ�Š7Ø˜‘.ˆCÜ”3�s˜E“? EÓ*Ð*r*   r   )r  Úint)r8   rN   ri  rj  rŠ  r‰  s        @r+   Ú_normalize_start_endrŒ  %  sJ   ø€ ð �w‰w�s‰|€Hð+´#õ +ñ �u˜a ¨1Ó-€EÙ
�S˜% ¨8Ó
4€CØ�#ˆ:Ðr*   Úsrcc           	      ó|  — t        j                  | j                  |«      }| j                  |   }t	        | |||«      \  }}t        | j                  «      }||z
  |dz
  z   |z  ||<   |j                  |«      }|dk(  r||k(  r|dk(  r|j                  «       S d g| j                  «       z  }t        j                  || j                  ¬«      }	|	|z
  |z  ||<   t        j                  || j                  t        j                  ¬«      }
|dk7  rt        j                  |
|	|k\  «      }
||k7  rt        j                  |
|	|k  «      }
|dk7  rt        j                  |
|	|z
  |z  dk(  «      }
dg| j                  «       z  }d||<   |
j                  |«      }
t         j#                  |
t         j%                  ||
|d«      | «      S )Nr!   r   ©Údevice©r�  ræ   rR   )rC   r-  r}  r  rŒ  ru  ÚexpandÚclonerN   r>   Úaranger�  ÚonesÚboolÚlogical_andÚviewr‚   rh   Ú_unsafe_masked_index)r¾   r�  rN   ri  rj  rk  r‰  Úsrc_sizeÚindicesÚidxÚmaskÚ
mask_shapes               r+   rn  rn  <  s’  € ô ×
 Ñ
  §¡¨SÓ
1€CØ�{‰{˜3Ñ€HÜ% e¨S°%¸Ó=�J€Eˆ3ä�E—K‘KÓ €HØ˜5‘[ D¨1¡HÑ-°$Ñ6€HˆS�MØ
�*‰*�XÓ
€Cà�‚z�c˜X’o¨$°!ª)Ø�y‰y‹{Ðà$( 6¨E¯I©I«KÑ#7€GÜ
�,‰,�x¨¯©Ô
5€CØ˜%‘K DÑ(€GˆC�Lä�:‰:�h u§|¡|¼5¿:¹:ÔF€DØ�‚zÜ× Ñ   s¨e¡|Ó4ˆà
ˆh‚Ü× Ñ   s¨S¡yÓ1ˆàˆq‚yÜ× Ñ  ¨¨e©°tÑ';¸qÑ'@ÓAˆà��u—y‘y“{Ñ"€JØ€Jˆs�OØ�9‰9�ZÓ €DÜ�:‰:�dœD×5Ñ5°c¸4ÀÈ!ÓLÈeÓTÐTr*   Úindexc                 óT   — | j                  |«      }t        j                  || ||«      S r4   )rm  r>   Úselect_scatter)rk   rh  rN   rŸ  rW   s        r+   Úselect_backwardr¢  e  s+   € ð ×&Ñ& {Ó3€JÜ×Ñ 
¨K¸¸eÓDÐDr*   ÚoffsetÚdim1Údim2c                 óV   — | j                  |«      }t        j                  || |||«      S r4   )rm  r>   Údiagonal_scatter)rk   rh  r£  r¤  r¥  rW   s         r+   Údiagonal_backwardr¨  l  s-   € ð
 ×&Ñ& {Ó3€JÜ×!Ñ! *¨k¸6À4ÈÓNÐNr*   Úinput_dtypec                 óF   — | j                   |k7  r|j                  |«      }|S r4   )ræ   r7   )rk   rW   r©  s      r+   Ú_cast_grad_to_input_dtyper«  u  s&   € ð ×Ñ˜KÒ'Ø—]‘] ;Ó/ˆ
ØÐr*   Úoutputc                 ó~   — | |z  }||t        j                  ||d¬«      z  z
  }t        | ||«      j                  «       S ©NTr  )r>   ró   r«  Ú
contiguous)rk   r¬  rN   r©  Únew_grad_outputrW   s         r+   Ú_softmax_backward_datar±  }  sK   € ð " FÑ*€OØ  6¬E¯I©IØ˜S¨$ô-ñ $ñ €Jô % [°*¸kÓJ×UÑUÓWÐWr*   c                 ó~   — | t        j                  |«      t        j                  | |d¬«      z  z
  }t        | ||«      S r®  )r>   rg   ró   r«  )rk   r¬  rN   r©  rW   s        r+   Ú_log_softmax_backward_datar³  �  sA   € ð œuŸy™y¨Ó0´5·9±9Ø˜ dô4ñ  ñ €Jô % [°*¸kÓJÐJr*   c                 óì   — | |dz  z   ||dz
  z  z
  }t        t        j                  t        j                  |¬«      } |d||«      j	                  d«      } |d||z  |«      j	                  d«      }	||	z   S )z/Utility function to implement im2col and col2imr"   r!   ©ræ   r�  r   rR   )r   r>   r”  Úint64rT   )
Úinput_dÚkernel_dÚ
dilation_dÚ	padding_dÚstride_dr�  Úblocks_dÚ	arange_kwÚblocks_d_indicesÚkernel_grids
             r+   Ú _im2col_col2im_indices_along_dimrÀ  ›  s   € ð ˜ Q™Ñ&¨°xÀ!±|Ñ)DÑD€HäœŸ™¬E¯K©KÀÔG€Iñ !  H¨hÓ7×AÑAÀ!ÓDÐñ ˜A˜x¨*Ñ4°jÓA×KÑKÈBÓO€Kð ˜kÑ)Ð)r*   Úkernel_sizeÚdilationÚpaddingrv  c           
      óî  ‡‡‡‡‡‡— t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       dd„} |‰d«        |‰d«        |‰d	d
¬«        |‰d«       | j                  Št        ‰«      }t        j                  |dv xr t	        d„ ‰dd  D «       «      ˆfd„«       t        d„ t        ‰dd  ‰‰‰‰«      D «       «      Št        j                  t	        d„ ‰D «       «      ˆˆˆˆˆˆfd„«       |dk(  }|s| j                  d«      } | j                  \  }}	}
}‰\  }}‰\  }}‰\  }}‰\  }}t        |
||||| j                  «      }t        |||||| j                  «      }t        j                  | ||||f«      }|j                  d«      j                  d«      }|d d …d d …||f   }|j                  dddddd«      }|j                  d«      }|j                  d«      }|j                  ||	|z  |z  ||z  «      }|s|j                  d«      }|S )Nr"   c                   ó   — y)Nz"im2col(): only 2D kernel supportedr)   r)   r*   r+   r€   zim2col.<locals>.<lambda>·  ó   � r*   c                   ó   — y)Nz$im2col(): only 2D dilation supportedr)   r)   r*   r+   r€   zim2col.<locals>.<lambda>¸  rÆ  r*   c                   ó   — y)Nz#im2col(): only 2D padding supportedr)   r)   r*   r+   r€   zim2col.<locals>.<lambda>¹  rÆ  r*   c                   ó   — y)Nz"im2col(): only 2D stride supportedr)   r)   r*   r+   r€   zim2col.<locals>.<lambda>º  rÆ  r*   c                 óˆ   ‡ ‡— |rt        d„ ‰ D «       «      nt        d„ ‰ D «       «      }t        j                  |ˆ ˆfd„«       y )Nc              3   ó&   K  — | ]	  }|d kD  –— Œ y­w©r   Nr)   ©Ú.0rR  s     r+   ú	<genexpr>z1im2col.<locals>.check_positive.<locals>.<genexpr>½  ó   è ø€ Ò(˜Q�1�q•5Ñ(ùó   ‚c              3   ó&   K  — | ]	  }|d k\  –— Œ y­wrÌ  r)   rÍ  s     r+   rÏ  z1im2col.<locals>.check_positive.<locals>.<genexpr>½  ó   è ø€ Ò;RÀq¸AÀ½FÑ;RùrÑ  c                  ó   •— ‰› d‰ › �S ©Nz& should be greater than zero, but got r)   ©ÚparamÚ
param_names   €€r+   r€   z0im2col.<locals>.check_positive.<locals>.<lambda>¿  ó   ø€ ˜Z˜LÐ(NÈuÈgÐV€ r*   ©r  r>   r�   ©r×  rØ  ÚstrictÚconds   ``  r+   Úcheck_positivezim2col.<locals>.check_positive¼  ó4   ù€ Ù,2ŒsÑ( %Ô(Ô(¼Ñ;RÈEÔ;RÓ8RˆÜ�‰ØÔVõ	
r*   rÁ  rÂ  rÃ  F©rÜ  rv  ©r‡   rD  c              3   ó&   K  — | ]	  }|d k7  –— Œ y­wrÌ  r)   ©rÎ  Úds     r+   rÏ  zim2col.<locals>.<genexpr>Ê  ó   è ø€ Ò:¨!˜q A�vÑ:ùrÑ  r�   c                  ó    •— dt        ‰ «      › �S )NzmExpected 3D or 4D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: ©Útuple©r  s   €r+   r€   zim2col.<locals>.<lambda>Ë  ó   ø€ ð -Ü-2°5«\¨Nð<€ r*   c              3   ó\   K  — | ]$  \  }}}}}d |d|z  z   ||d z
  z  z
  d z
  |z  z   –— Œ& y­w)r!   r"   Nr)   )rÎ  rÅ   ÚpadÚdilÚkerÚsts         r+   rÏ  zim2col.<locals>.<genexpr>Î  sF   è ø€ ò á"ˆC��c˜3 ð 	
ˆS�1�s‘7‰]˜S C¨!¡G™_Ñ,¨qÑ0°RÑ7Õ7ñùs   ‚*,rZ  c              3   ó&   K  — | ]	  }|d kD  –— Œ y­wrÌ  r)   )rÎ  Úcs     r+   rÏ  zim2col.<locals>.<genexpr>Õ  s   è ø€ Ò'�aˆA��EÑ'ùrÑ  c                  óF   •— dt        ‰dd  «      › d‰› d‰ › d‰› d‰› d‰› d�S )	Nz!Given an input with spatial size rZ  ú, kernel_size=ú, dilation=ú
, padding=ú	, stride=z9, the calculated shape of the array of sliding blocks is z*, but its components must be at least one.rç  )rÂ  rÁ  Úoutput_sizerÃ  r  rv  s   €€€€€€r+   r€   zim2col.<locals>.<lambda>Ö  sL   ø€ Ð3´E¸%ÀÀ¸*Ó4EÐ3Fð GØ"�m ;¨x¨jð 9Ø�)˜9 V Hð -àˆ]ÐDð	F€ r*   rD  r   rR   r!   r‡   é   ©T)r>   r�   r‚  r  r  rè  ÚziprT   rÀ  r�  rÀ   rì  Úpermuter.  r&  Úsqueeze)r¾   rÁ  rÂ  rÃ  rv  rÞ  r}  Úbatched_inputÚ	batch_dimr'  Úinput_hÚinput_wÚstride_hÚstride_wÚ	padding_hÚ	padding_wÚ
dilation_hÚ
dilation_wÚkernel_hÚkernel_wÚblocks_row_indicesÚblocks_col_indicesÚpadded_inputr¬  Únum_blocks_rowÚnum_blocks_colr÷  r  s    ````                     @@r+   Úim2colr  ®  s~  ý€ ô 
‡L�L”�[Ó! QÑ&Ñ(TÔUÜ	‡L�L”�X“ !Ñ#Ñ%SÔTÜ	‡L�L”�W“ Ñ"Ñ$QÔRÜ	‡L�L”�V“ Ñ!Ñ#OÔPó
ñ �; Ô.Ù�8˜ZÔ(Ù�8˜Y¨uÕ5Ù�6˜8Ô$à�K‰K€EÜˆu‹:€DÜ	‡L�LØ�ˆÒ:œ3Ñ:¨u°R°S¨zÔ:Ó:ó	<ôô
 ñ ä&)Ø�"�#ˆJ˜ ¨;¸ó'
ôó €Kô 
‡L�LÜÑ'˜;Ô'Ó'÷	Fð 	Fôð ˜A‘I€MÙØ—‘ Ó"ˆà/4¯{©{Ñ,€Iˆ{˜G WàÑ€HˆhØ"Ñ€IˆyØ%Ñ€J�
Ø$Ñ€Hˆhä9Ø�˜: y°(¸E¿L¹LóÐô :Ø�˜: y°(¸E¿L¹LóÐô —5‘5˜ ¨I°yÀ)Ð LÓM€Là+×5Ñ5°bÓ9×CÑCÀBÓGÐØš!šQÐ 2Ð4FÐFÑG€FØ�^‰^˜A˜q ! Q¨¨1Ó-€FØ'×,Ñ,¨QÓ/€NØ'×,Ñ,¨QÓ/€NØ�^‰^Ø�; Ñ)¨HÑ4°nÀ~Ñ6Uó€Fñ Ø—‘ Ó"ˆØ€Mr*   r÷  c                 ó®  ‡‡‡‡‡‡!‡"— t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       t        j                  t        ‰«      dk(  d„ «       dd„} |‰d	«        |‰d
«        |‰dd¬«        |‰d«        |‰d«       | j                  Š"t        ‰"«      }t        j                  |dv xr t	        d„ ‰"dd  D «       «      ˆ"fd„«       ‰d   ‰d   z  }t        j                  ‰"d   |z  dk(  ˆˆ"fd„«       t        ‰‰‰‰‰«      D �	�
���cg c]"  \  }	}
}}}d|	d|
z  z   ||dz
  z  z
  dz
  |z  z   ‘Œ$ }}}}
}	}|d   |d   z  Š!t        j                  ‰"d   ‰!k(  ˆ!ˆˆˆˆˆ"ˆfd„«       t        j                  ‰!dkD  ˆ!ˆˆˆˆˆ"ˆfd„«       |dk(  }|s| j                  d«      } | j                  Š"‰\  }}‰\  }}‰\  }}‰\  }}‰\  }}| j                  ‰"d   ‰"d   |z  g‰z   |z   «      } | j                  dddddd«      } t        |||||| j                  «      }t        |d«      }t        |||||| j                  «      }t        ‰‰«      D ��cg c]  \  }}|d|z  z   ‘Œ }}}| j                  ‰"d   ‰"d   t        ‰«      z  g|z   «      }d d ||f} t        j                  || | d¬«      }t!        j"                  || | | | f«      }|s|j%                  d«      }|S c c}}}}
}	w c c}}w )Nr"   c                   ó   — y)Nzonly 2D output_size supportedr)   r)   r*   r+   r€   zcol2im.<locals>.<lambda>  rÆ  r*   c                   ó   — y)Nzonly 2D kernel supportedr)   r)   r*   r+   r€   zcol2im.<locals>.<lambda>  rÆ  r*   c                   ó   — y)Nzonly 2D dilation supportedr)   r)   r*   r+   r€   zcol2im.<locals>.<lambda>  rÆ  r*   c                   ó   — y)Nzonly 2D padding supportedr)   r)   r*   r+   r€   zcol2im.<locals>.<lambda>  rÆ  r*   c                   ó   — y)Nzonly 2D stride supportedr)   r)   r*   r+   r€   zcol2im.<locals>.<lambda>  rÆ  r*   Tc                 óˆ   ‡ ‡— |rt        d„ ‰ D «       «      nt        d„ ‰ D «       «      }t        j                  |ˆ ˆfd„«       y )Nc              3   ó&   K  — | ]	  }|d kD  –— Œ y­wrÌ  r)   rÍ  s     r+   rÏ  z1col2im.<locals>.check_positive.<locals>.<genexpr>  rÐ  rÑ  c              3   ó&   K  — | ]	  }|d k\  –— Œ y­wrÌ  r)   rÍ  s     r+   rÏ  z1col2im.<locals>.check_positive.<locals>.<genexpr>  rÓ  rÑ  c                  ó   •— ‰› d‰ › �S rÕ  r)   rÖ  s   €€r+   r€   z0col2im.<locals>.check_positive.<locals>.<lambda>  rÙ  r*   rÚ  rÛ  s   ``  r+   rÞ  zcol2im.<locals>.check_positive  rß  r*   rÁ  rÂ  rÃ  Frà  rv  r÷  )r"   r‡   c              3   ó&   K  — | ]	  }|d k7  –— Œ y­wrÌ  r)   rã  s     r+   rÏ  zcol2im.<locals>.<genexpr>   rå  rÑ  rZ  c                  ó    •— dt        ‰ «      › �S )NzmExpected 2D or 3D (batch mode) tensor for input with possible 0 batch size and non-zero dimensions, but got: rç  ré  s   €r+   r€   zcol2im.<locals>.<lambda>!  rê  r*   r   r!   c                  ó   •— d‰d   › d‰ › �S )Nz|Expected size of input's first non-batch dimension to be divisible by the product of kernel_size, but got input.shape[-2] = rZ  z and kernel_size=r)   )rÁ  r  s   €€r+   r€   zcol2im.<locals>.<lambda>'  s#   ø€ ð =Ø=BÀ2¹Y¸Kð HØ"�mð%€ r*   rR   c                  ó:   •— d‰› d‰› d‰› d‰› d‰› d‰ › d‰d   › d	�S ©
NzGiven output_size=ró  rô  rõ  rö  z , expected input.size(-1) to be ú	 but got rR   ú.r)   ©ÚLrÂ  rÁ  r÷  rÃ  r  rv  s   €€€€€€€r+   r€   zcol2im.<locals>.<lambda>4  óF   ø€ Ð$ [ M°À¸}ð MØ�:˜Z¨ y°	¸&¸ð B)Ø)*¨¨9°U¸2±Y°K¸qðB€ r*   c                  ó:   •— d‰› d‰› d‰› d‰› d‰› d‰ › d‰d   › d	�S r  r)   r   s   €€€€€€€r+   r€   zcol2im.<locals>.<lambda>:  r"  r*   r‡   rD  rø  ©Ú
accumulaterù  )r>   r�   r‚  r  r  rú  rT   r&  rû  rÀ  r�  rV   rm  Úprodr‚   Ú_unsafe_index_putrÀ   rì  rü  )#r¾   r÷  rÁ  rÂ  rÃ  rv  rÞ  r}  Úprod_kernel_sizerÅ   rì  rí  rî  rï  Úcolrý  Úout_hÚout_wr  r  r  r  r  r  r  r  Úindices_rowÚindices_colÚorR  Úoutput_padded_sizer¬  rœ  r!  r  s#    `````                           @@r+   Úcol2imr0     s�  þ€ ô 
‡L�L”�[Ó! QÑ&Ñ(OÔPÜ	‡L�L”�[Ó! QÑ&Ñ(JÔKÜ	‡L�L”�X“ !Ñ#Ñ%IÔJÜ	‡L�L”�W“ Ñ"Ñ$GÔHÜ	‡L�L”�V“ Ñ!Ñ#EÔFó
ñ �; Ô.Ù�8˜ZÔ(Ù�7˜I¨eÕ4Ù�6˜8Ô$Ù�; Ô.à�K‰K€EÜˆu‹:€DÜ	‡L�LØ�ˆÒ:œ3Ñ:¨u°R°S¨zÔ:Ó:ó	<ôð
 # 1‘~¨°A©Ñ6ÐÜ	‡L�LØˆb‰	Ð$Ñ$¨Ñ)ô	%ôô '*Ø˜ (¨K¸ó'
÷ò á"ˆC��c˜3 ð 	
ˆS�1�s‘7‰]˜S C¨!¡G™_Ñ,¨qÑ0°RÑ7Ó7ð€Cô ð 	ˆA‰��Q‘‰€AÜ	‡L�LØˆb‰	�Q‰÷	Bñ 	Bôô 
‡L�LØ	ˆA‰÷	Bñ 	Bôð ˜A‘I€MÙØ—‘ Ó"ˆà�K‰K€Eà�L€Eˆ5ØÑ€HˆhØ"Ñ€IˆyØ%Ñ€J�
Ø$Ñ€Hˆhð �M‰M˜5 ™8 U¨1¡XÐ1AÑ%AÐBÀ[ÑPÐSVÑVÓW€EØ�M‰M˜!˜Q  1 a¨Ó+€Eä2Øˆx˜ Y°¸%¿,¹,ó€Kô $ K°Ó3€KÜ2Øˆx˜ Y°¸%¿,¹,ó€Kô 14°KÀÓ0I×J©¨¨1˜!˜a !™e›)ÐJÐÑJØ�_‰_Ø	ˆq‰�5˜‘8œt KÓ0Ñ0Ð1Ð4FÑFó€Fð ��{ KÐ
0€CÜ×#Ñ# F¨C°À4Ð#ÓH€FÜ�U‰U�6˜Y˜J¨¨
°Y°JÀÀ
ÐKÓL€FáØ—‘ Ó"ˆØ€MùökùóV Ks   Å6'MÊ9Mr�  c                 óz   — | |j                  | «      |z  z  j                  t        j                  | «      ¬«      }|S ©NrX  )Útype_asr“  rC   r   )rk   r�  rm   rI   s       r+   Únative_dropout_backwardr4  c  sB   € ð 
˜Ÿ™ [Ó1°EÑ9Ñ	:×AÑAÜ×1Ñ1°+Ó>ð 	Bó 	€Að €Hr*   Ú
input_sizeÚ	dimensionr.  c                 ó  — t        |«      dk(  rt        j                  | d«      S t        j                  t        |«      |«      }t        j
                  ||   | j                  t        j                  ¬«      }|j                  d||«      j                  «       }| j                  d|dz   «      j                  ||dz   «      } | j                  |«      }d|z  |fz   }t        j                  ||| d¬«      j                  «       S )Nr   r‘  rR   r!   r4   Tr$  )r‚  r>   Úsqueeze_copyrC   r-  r”  r�  Úint32ÚunfoldÚflattenÚmovedimrm  r‚   r'  r¯  )	r¦   r5  r6  r.  rk  rN   rœ  rW   rŸ  s	            r+   Úunfold_backwardr=  r  sÚ   € ô
 ˆ:ƒ˜!ÒÜ×!Ñ! $¨Ó*Ð*Ü
×
 Ñ
 ¤ Z£°)Ó
<€CÜ
�,‰,�z #‘¨t¯{©{Ä%Ç+Á+Ô
N€CØ
�*‰*�Q˜˜dÓ
#×
+Ñ
+Ó
-€CØ�<‰<˜˜C !™GÓ$×,Ñ,¨S°#¸±'Ó:€Dð —‘ 
Ó+€JØ�c‰M˜S˜FÑ"€EÜ×!Ñ! *¨e°TÀdÐ!ÓK×VÑVÓXÐXr*   Úepsc           
      ó.  — |�A|}d|z
  }t        j                  t        j                  ||k\  ||k  «      | |d|z
  z  z  d«      S t        j                  t        j                  |dk\  |dk  «      | |d|z
  z  z  |j                  dt	        d«      «      «      S )Nrf   r’   r)   Únan)r>   rh   r—  rê   r  )rk   rz   r>  ÚloÚhis        r+   Úlogit_backwardrC  …  s¢   € ð
 €ØˆØ�2‰XˆÜ�{‰{Ü×Ñ˜d b™j¨$°"©*Ó5Ø˜4 3¨¡:Ñ.Ñ/Øó
ð 	
ô �{‰{Ü×Ñ˜d c™k¨4°3©;Ó7Ø˜4 3¨¡:Ñ.Ñ/Ø�M‰M˜"œe E›lÓ+ó
ð 	
r*   Útrainc                 ód   — |r|dk7  rt         j                  | ||«      d   S | j                  «       S rr   )r‚   Únative_dropoutr“  )r¾   rR  rD  s      r+   ÚdropoutrG  š  s3   € ñ ��a’Ü×"Ñ" 5¨!¨UÓ3°AÑ6Ð6à�{‰{‹}Ðr*   Úout0Úout1c                 ó„  — |r˜|dk7  r“|dk(  r:t        j                  | «      t        j                  | t         j                  ¬«      fS | j                  j                  st        d«      ‚t        j                  | «      |kD  }|| z  t        dd|z
  z  «      z  }||fS | t        j                  | t         j                  ¬«      fS )Nr   r!   rå   z?result type Float can't be cast to the desired output type Longrf   )	r>   r	  r–  ræ   Úis_floating_pointrt  Ú	rand_liker  r[  )r¾   rR  rD  Ú	bool_maskÚress        r+   rF  rF  ¤  s®   € ñ ��a’Ø�Š6Ü×$Ñ$ UÓ+¬U×-=Ñ-=¸eÌ5Ï:É:Ô-VÐWÐWØ�{‰{×,Ò,ÜØQóð ô —O‘O EÓ*¨QÑ.ˆ	Ø˜%Ñ¤%¨¨s°Q©w©Ó"8Ñ8ˆØ�YÐÐà”u—‘ u´E·J±JÔ?Ð@Ð@r*   Úhalf_to_floatc                 óB  — ddl m} | j                  «       } |r6| j                  t        j
                  k7  rt        d| j                  › d�«      ‚t        j                  | t        j                  j                  ¬«      \  }}| j                  |«      }  || j                  «       dk(  «      rt	        j                  | «      }n0t	        j                  | |d¬«      }t	        j                  | |z
  «      }|t	        j                  ||d¬«      z  }|s|j                  |«      }|S ©Nr   ©Úguard_or_falsez%half_to_float is True but x.dtype is z, expected torch.half©r2   T)r  )rs  rS  r¯  ræ   r>   Úhalfr,  rC   rD   ÚELEMENTWISE_TYPE_PROMOTION_KINDÚDEFAULTr7   rÜ   rg   Úamaxró   )	r8   rN   rO  rS  r9   r<   ÚunnormalizedÚx_maxr  s	            r+   Ú_softmaxr[  µ  sð   € õ Eð 	
�‰‹€AÙØ�7‰7”e—j‘jÒ Ü Ø7¸¿¹°yÐ@UÐVóð ô ',×&>Ñ&>Ø	œu×DÑD×LÑLô'Ñ#Ð�|ð 	
�‰ÐÓ€AÙ�a—g‘g“i 1‘nÔ%Ü—y‘y “|‰ä—
‘
˜1˜c¨4Ô0ˆÜ—y‘y  U¡Ó+ˆØœEŸI™I l°CÀÔFÑF€FÙØ—‘˜<Ó(ˆØ€Mr*   )r  c                 óF  — ddl m} | j                  «       } |r6| j                  t        j
                  k7  rt        d| j                  › d�«      ‚t        j                  | t        j                  j                  ¬«      \  }}| j                  |«      }  || j                  «       dk(  «      r| }nt	        j                  | |d¬«      }| |z
  }t	        j                  t	        j                  t	        j                   |«      |d¬«      «      }||z
  }	|s|	j                  |«      }	|	S rQ  )rs  rS  r¯  ræ   r>   rU  r,  rC   rD   rV  rW  r7   rÜ   rX  rI  ró   rg   )
r8   rN   rO  rS  r9   r<   ÚshiftedrZ  Úshifted_logsumexpr  s
             r+   Ú_log_softmaxr_  Ñ  sø   € õ Eð 	
�‰‹€AÙØ�7‰7”e—j‘jÒ Ü Ø7¸¿¹°yÐ@UÐVóð ô ',×&>Ñ&>Ø	œu×DÑD×LÑLô'Ñ#Ð�|ð 	
�‰ÐÓ€AÙ�a—g‘g“i 1‘nÔ%Ø‰ä—
‘
˜1˜c¨4Ô0ˆØ�e‘)ˆÜŸ	™	¤%§)¡)¬E¯I©I°gÓ,>ÀÈTÔ"RÓSÐØÐ(Ñ(€FÙØ—‘˜<Ó(ˆØ€Mr*   r›  Úpadding_idxÚscale_grad_by_freqÚsparsec                 óò   — | j                  «       dk7  rt        d| j                  «       › d�«      ‚|j                  dk  r4| j                  d|«      }|j                  dk(  r|j	                  d«      }|S | |   S )Nr"   z'weight' must be 2-D, got z-Dr!   r   )rN   r,  r}  Úindex_selectrü  )rË   r›  r`  ra  rb  rÅ   s         r+   Ú	embeddingre  î  ss   € ð ‡z�zƒ|�qÒÜÐ9¸&¿*¹*»,¸ÀrÐJÓKÐKà‡|�|�qÒà×!Ñ! ! WÓ-ˆØ�<‰<˜1ÒØ—+‘+˜a“.ˆCØˆ
à�g‰Ðr*   Únum_weightsc                 ót  — t        j                  | t         j                  j                  ¬«      \  }}| j	                  |«      } t        |t        j                  «      }|rZ|j                  |f«      }t        j                  |«      }t        j                  ||g|d¬«      }||   }	| |	j                  d«      z  } t        ||k(  | j                  «      }
| j                  |
d«      }| j                  |f| j                   |j                  d  z   «      }t        j                  ||g|d¬«      j	                  |«      S )NrT  Tr$  rR   r   )rC   rD   rV  rW  r7   r   r>   Úlongrm  r[  r‚   r'  rT   rV   r}  Úmasked_fillr  )rk   r›  rf  r`  ra  r9   r<   Úcountsr•  Úgrad_weights_scaler�  r¦   Úgrad_weights                r+   Úembedding_dense_backwardrm    s,  € ô ',×&>Ñ&>Ø¬×)NÑ)N×)VÑ)Vô'Ñ#Ð�|ð —.‘.Ð!2Ó3€KÜ% g¬u¯z©zÓ:€GÙØ×"Ñ" K >Ó2ˆÜ�‰˜wÓ'ˆÜ×'Ñ'¨°°	¸4ÈDÐ'ÓQˆØ# G™_ÐØ!Ð$6×$@Ñ$@ÀÓ$DÑDˆä˜W¨Ñ3°[×5EÑ5EÓF€DØ×"Ñ" 4¨Ó+€DØ×'Ñ'Ø	ˆ˜×*Ñ*¨7¯<©<¨>Ð:Ñ:ó€Kô ×!Ñ! +°¨y¸$È4Ð!ÓP×SÑSØóð r*   c                 ó"   — d}| D ]  }||z  }Œ	 |S r[   r)   )r8   rI   Úis      r+   r&  r&  #  s$   € Ø	€AØò ˆØ	ˆQ‰‰ðà€Hr*   ÚtensorsÚ
num_chunksc                 óZ  — g }| D ]£  }|j                  «       }||   |z   dz
  |z  |z  }|||   k7  r;dgdz  |j                  |z
  dz
  z  d|||   z
  gz   }t        j                  ||d«      }|d | t	        j
                  |dg«      z   }|j                  |j                  |«      «       Œ¥ |S )Nr!   r   r"   rR   )r.  r}  r‚   Úconstant_pad_ndr>   ÚSizeÚappendr&  )	rp  rN   rq  Úpadded_tensorsÚtensorÚtensor_sizeÚpad_along_dimrì  Ú	view_sizes	            r+   Ú
_pad_chunkr{  *  sÚ   € ð
 €NØò 9ˆØ—k‘k“mˆØ$ SÑ)¨JÑ6¸Ñ:¸zÑIÈJÑVˆØ˜K¨Ñ,Ò,à�#˜‘'˜VŸ[™[¨3Ñ.°Ñ2Ñ3ØØ ¨CÑ 0Ñ0ð7ñ ˆCô ×)Ñ)¨&°#°qÓ9ˆFØ  Ð%¬¯
©
°JÀÐ3CÓ(DÑDˆ	Ø×Ñ˜fŸn™n¨YÓ7Õ8ð9ð Ðr*   c                 óR   — | d   j                   }| D ]  }|j                   |k7  sŒ y y)Nr   FT©r}  )rp  r}  rw  s      r+   Úhave_same_ndimsr~  ?  s2   € Ø�1‰:�?‰?€DØò ˆØ�;‰;˜$ÓÙðð r*   c                 ó”   — | d   j                  «       d | }| D ]-  }t        j                  |j                  «       d | |k(  d„ «       Œ/ y )Nr   c                   ó   — y)NzG_chunk_cat expects same sizes of 0,...,dim-1 dimensions for all tensorsr)   r)   r*   r+   r€   z+leading_dimension_matches.<locals>.<lambda>L  rÆ  r*   )r.  r>   r�   )rp  rN   Úleading_dim_sizesrw  s       r+   Úleading_dimension_matchesr‚  G  sN   € Ø ™
Ÿ™Ó)¨$¨3Ð/ÐØò 
ˆÜ�‰Ø�K‰K‹M˜$˜3ÐÐ#4Ñ4Ù]õ	
ñ
r*   c                 ó²  — t        j                  |dk\  d„ «       t        j                  t        | «      dkD  d„ «       | d   j                  }| d   j                  }| D ]r  }t        j                  |j                  «       dkD  d„ «       t        j                  |j                  |k(  d„ «       t        j                  |j                  |k(  d„ «       Œt t        | «      r(t        j                  | d   j                  «       |«      }nEt        j                  |dk\  d„ «       | D ]&  }t        j                  ||j                  k  d	„ «       Œ( t        | |«       |S )
Nr!   c                   ó   — y)Nz&_chunk_cat expects positive num_chunksr)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>U  rÆ  r*   r   c                   ó   — y)Nz0_chunk_cat expects a non-empty input tensor listr)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>W  rÆ  r*   c                   ó   — y)Nz#_chunk_cat expects non-empty tensorr)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>\  rÆ  r*   c                   ó   — y)Nz8_chunk_cat expects all input tensors with the same dtyper)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>_  rÆ  r*   c                   ó   — y)Nz8_chunk_cat expects all inputs tensors on the same devicer)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>c  rÆ  r*   c                   ó   — y)NzK_chunk_cat expects non-negative dim when input tensors have different ndimsr)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>j  rÆ  r*   c                   ó   — y)Nz3_chunk_cat expects dim < ndim for all input tensorsr)   r)   r*   r+   r€   z._preprocess_chunk_cat_inputs.<locals>.<lambda>o  rÆ  r*   )r>   r�   r‚  ræ   r�  rÜ   r~  rC   r-  rN   r}  r‚  )rp  rN   rq  Úexpected_dtypeÚexpected_devicerw  s         r+   Ú_preprocess_chunk_cat_inputsr�  P  s-  € ô
 
‡L�L�˜q‘Ñ"RÔSÜ	‡L�LÜˆG‹�qÑÑTôð ˜Q‘Z×%Ñ%€NØ˜a‘j×'Ñ'€OØò 	
ˆÜ�‰�V—\‘\“^ aÑ'Ñ)VÔWÜ�‰Ø�L‰L˜NÑ*ÙNô	
ô 	�‰Ø�M‰M˜_Ñ,ÙNõ	
ð	
ô �wÔÜ×$Ñ$ W¨Q¡Z§^¡^Ó%5°sÓ;‰ä�‰Ø�1‰HÙaô	
ð ò 	ˆFÜ�L‰LØ�f—k‘kÑ!ÙMõð	ô
 ˜g sÔ+Ø€Jr*   rÅ   c                 ó¦   — t        | ||«      }t        | ||«      }|€t        j                  ||dz   «      S t        j                  ||dz   |¬«       |S )Nr!   )rÅ   )r�  r{  r>   r0  )rp  rN   rq  rÅ   rv  s        r+   Ú
_chunk_catr�  u  sS   € ô ' w°°ZÓ
@€CÜ ¨¨jÓ9€NØ
€{Ü�y‰y˜¨¨q©Ó1Ð1ä�	‰	�. #¨¡'¨sÕ3Øˆ
r*   Úsplit_sizesc                 ó  — t         j                  | ||¬«      }|€.|D �cg c]"  }|j                  t        j                  ¬«      ‘Œ$ c}S t        ||«      D ])  \  }}t        ||j                  «       t        ||d¬«       Œ+ y c c}w )Nr   rX  Tr  )	r‚   Úsplit_with_sizesr“  r>   r\  rú  r   r  r   )rz   r�  rN   rÅ   ÚsplitsÚsr¬  Úsplits           r+   Úsplit_with_sizes_copyr–  †  sƒ   € ô ×"Ñ" 4¨¸#Ð"Ó>€FØ
€{ØHNÖOÀ1�—‘¤e×&=Ñ&=�Õ>ÒOÐOä   fÓ-ò 	N‰MˆF�EÜ˜f e§k¡kÔ2Ü U°FÈÖMð	Nð ùò Ps   Ÿ'BÚ
split_size.c                 óD   — t         j                  j                  | ||«      S r4   )r‚   r•  r   )r¾   r—  rN   s      r+   Úunsafe_splitr™  ™  s   € ä�:‰:×Ñ˜U J°Ó4Ð4r*   c                 óD   — t         j                  j                  | ||«      S r4   )r‚   r’  rˆ  )r¾   r�  rN   s      r+   Úunsafe_split_with_sizesr›  ž  s   € ô × Ñ ×(Ñ(¨°¸SÓAÐAr*   c                 ó.  — | j                   }||   }|dk(  r%|dk7  rt        d|› d�«      ‚| j                  «       fS ||z   dz
  |z  }ddlm}  ||«      }t        |«      D �cg c]  }|‘Œ }}|||z  |z
  z
  |d<   t        j                  | ||«      S c c}w )Nr   z split_size is 0 but dim_size is z, expected 0r!   )Ú	guard_intrR   )r  r,  Údetachrs  r�  rS   r>   r•  )	rz   r—  rN   rh  r‰  Úchunksr�  ro  r�  s	            r+   r•  r•  ¥  s¸   € à—*‘*€KØ˜3Ñ€HØ�Q‚Ø�qŠ=Ü Ø2°8°*¸LÐIóð ð —‘“ÐÐØ˜Ñ# aÑ'¨JÑ6€Fõ @á�vÓ€FÜ',¨V£}Ö5 !’:Ð5€KÐ5Ø  J°Ñ$7¸(Ñ$BÑC€K��OÜ�;‰;�t˜[¨#Ó.Ð.ùò 6s   Á"	BÚtensor_indices_or_sectionsc                 ó  ‡	— |j                   j                  dk7  rt        d|j                   › �«      ‚|j                  t        j
                  k7  rt        d|j                  › �«      ‚|j                  «       Š	t	        j                  ‰	dk(  xs ‰	dk(  ˆ	fd„«       ‰	dk(  rS|j                  «       }t        |t        «      s!t        dt        |«      j                  › �«      ‚| j                  ||«      S t        }t        j                  j                  «       x}r|j                   x}r|j"                  } |«       5  |D �cg c]  }|j                  «       ‘Œ }}d d d «       | j                  |«      S c c}w # 1 sw Y   Œ xY w)NÚcpuz/tensor_indices_or_sections must be on CPU, got z.tensor_indices_or_sections must be int64, got r!   r   c                  ó   •— d‰ › d�S )Nz{tensor_split expected tensor_indices_or_sections to be a zero-dimensional or one-dimensional tensor, but got a tensor with z dimsr)   )Ú	split_dims   €r+   r€   zAtensor_split_tensor_indices_or_sections_py_impl.<locals>.<lambda>Í  s   ø€ ð <Ø<E¸;ÀeðM€ r*   z%Expected sections to be IntLike, got )r�  Útyper,  ræ   r>   r¶  rN   r�   Úitemr6   r   r#   Útensor_splitr   Ú_guardsÚdetect_fake_modeÚ	shape_envÚignore_fresh_unbacked_symbols)
rz   r   rN   ÚsectionsÚctxÚ	fake_moderª  ro  r›  r¤  s
            @r+   Ú/tensor_split_tensor_indices_or_sections_py_implr¯  º  s‚  ø€ ð "×(Ñ(×-Ñ-°Ò6ÜØ=Ð>X×>_Ñ>_Ð=`Ðaó
ð 	
ð "×'Ñ'¬5¯;©;Ò6ÜØ<Ð=W×=]Ñ=]Ð<^Ð_ó
ð 	
ð +×.Ñ.Ó0€IÜ	‡L�LØ�Q‰Ò(˜) q™.ó	Môð
 �A‚~Ø-×2Ñ2Ó4ˆÜ˜(¤GÔ,Ü Ø7¼¸X»×8OÑ8OÐ7PÐQóð ð × Ñ  ¨3Ó/Ð/äˆÜŸ™×7Ñ7Ó9Ð9ˆIÐ9Ø"×,Ñ,Ð,ˆIÐ,à×9Ñ9ˆCñ
 ‹Uñ 	EØ)CÖD A�q—v‘v•xÐDˆGÐD÷	Eð × Ñ  ¨#Ó.Ð.ùò E÷	Eð 	Eús   Ä:E7Ä?E2ÅE7Å2E7Å7F Úmat1Úmat2c                 ó¾   — | j                  «       s&| j                  «       st        |«      }t        |«      }|t        j                  ||«      z  }|dk(  r|S ||| z  z   S rr   )rK  Ú
is_complexr‹  r>   Úmm)rz   r°  r±  rb   rl   rÅ   s         r+   Úaddmmrµ  ð  s]   € ð ×!Ñ!Ô#¨D¯O©OÔ,=Ü�4‹yˆÜ�E“
ˆØ
”%—(‘(˜4 Ó&Ñ
&€CØˆq‚yØˆ
ð �˜‘ÑÐr*   Úuse_geluc                 ó¾   — t        | ||||«      }|r8| j                  rt        j                  |d¬«      S t        j                  |«      S t        j	                  |«      S )Nr©   )r§   )rµ  Úis_cudar‚   ÚgeluÚrelu)rz   r°  r±  rb   rl   r¶  rÅ   s          r+   Ú_addmm_activationr»    sO   € ô ��d˜D $¨Ó
.€CÙØ�<Š<Ü—9‘9˜S¨f�9Ó5Ð5ä—9‘9˜S“>Ð!Ü�9‰9�S‹>Ðr*   Úvecc                 óî   — | j                  «       s&| j                  «       st        |«      }t        |«      }|t        j                  ||«      z  }|dk(  r|S |j                  «       dk(  r|| z  S ||| z  z   S rr   )rK  r³  r‹  r>   ÚmvrÜ   )rz   r°  r¼  rb   rl   rÅ   s         r+   Úaddmvr¿    ss   € ð ×!Ñ!Ô#¨D¯O©OÔ,=Ü�4‹yˆÜ�E“
ˆØ
”%—(‘(˜4 Ó%Ñ
%€CØˆq‚yØˆ
Ø
‡y�yƒ{�aÒØ�d‰{ÐØ�˜‘ÑÐr*   rò   ÚrstdÚgammaÚNÚCÚHxWÚgroupÚoutput_maskc
           	      óD  ‡‡‡‡‡‡— t        j                  | |‰|d¬«       t        j                  || d¬«       t        j                  ‰|d¬«       t        j                  |j                  «       ‰‰z  ‰z  k(  ˆˆˆfd„«       t        j                  ‰j                  ‰‰fk(  ˆˆˆfd„«       t        j                  ‰d u xs ‰j                  «       ‰k(  ˆˆfd„«       ‰‰z  }
t        j                  ‰|
‰z  k(  ˆˆfd„«       t        j                  | |«      j                  ‰‰‰«      j                  dg¬«      }| j                  ‰‰‰«      j                  dg¬«      }d }d }d }|	d	   �r*d
‰|
z  z  }‰�Át        j                  |‰j                  d	«      «      j                  ‰‰|
«      j                  d«      }t        j                  |‰j                  d	«      «      j                  ‰‰|
«      j                  d«      }t        j                  |j                  d«      ‰j                  d‰|
«      «      }n‹|j                  ‰‰|
«      j                  d«      }|j                  ‰‰|
«      j                  d«      }t        j                  |j                  d«      t        j                  d‰|
f|j                  ¬«      «      }|‰z  |z
  |z  |z  |z  |z  }| ‰z  ||z  |z  z
  }|j                  d«      }t        |d«      }t        |d«      }t        j                  | j                  ‰‰|
‰«      |«      t        j                  |j                  ‰‰|
‰«      |«      z   |z   }|j                  |j                  «      j                  |j                   «      }|	d   rk|j                  ‰‰|
«      |j                  ‰‰|
«      ‰j                  d«      z  z
  |j                  d«      z  j                  d	g¬«      j                  ‰«      }|	d   r|j                  d	g¬«      }|||fS )NF)Úallow_cpu_scalar_tensorsc                  ó   •— d‰‰ z  ‰z  › d�S )NzExpect input to have z	 elementsr)   )rÃ  rÄ  rÂ  s   €€€r+   r€   z,native_group_norm_backward.<locals>.<lambda><  s   ø€ Ð'¨¨A©°© }°IÐ>€ r*   c                  ó.   •— d‰ › d‰› d‰j                   › �S )NzExpect mean to have shape (ú, z
, but got ré  )rÂ  rÅ  rò   s   €€€r+   r€   z,native_group_norm_backward.<locals>.<lambda>@  s   ø€ Ð-¨a¨S°°5°'¸ÀDÇJÁJÀ<ÐP€ r*   c                  ó<   •— d‰ › d‰�‰j                  «       › �S d› �S )NzExpect gamma to have z elements but got rR   )rÜ   )rÃ  rÁ  s   €€r+   r€   z,native_group_norm_backward.<locals>.<lambda>D  s-   ø€ Ð'¨ sÐ*<ÈeÐN_¸U¿[¹[»]Ð<hÐi€ ÐegÐ<hÐi€ r*   c                  ó   •— d‰ › d‰› �S )NzExpect number of channels z, to be evenly-divisible by number of groups r)   )rÃ  rÅ  s   €€r+   r€   z,native_group_norm_backward.<locals>.<lambda>J  s   ø€ Ð,¨Q¨CÐ/[Ð\aÐ[bÐc€ r*   r"   r   r   rf   rR   r!   r�  rD  )rC   Úcheck_same_deviceÚcheck_same_shaper>   r�   rÜ   r  rØ   r˜  ró   rT   r&  r•  r�  rV   r7   ræ   )rk   r¾   rò   rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  ÚcpgÚdsÚdbÚd_inputÚd_gammaÚd_biasr”  Úds_valÚdb_valÚc1Úc2Úc3s     ` `````             r+   Únative_group_norm_backwardrÛ  '  sº  ý€ ô 
×ÑØ�U˜D $Àõô 
×Ñ˜5 +ÈÕNÜ	×Ñ˜4 ÀÕFÜ	‡L�LØ�‰‹˜˜Q™ ™Ñ$Ý>ôô 
‡L�LØ�
‰
�q˜%�jÑ ÝPôô 
‡L�LØ�ˆÒ+˜Ÿ™›¨!Ñ+Üiôð
 ˆu‰*€CÜ	‡L�LØ	ˆS�5‰[ÑÜcôô 
�‰�; Ó	&×	+Ñ	+¨A¨q°#Ó	6×	:Ñ	:À¸sÐ	:Ó	C€BØ	×	Ñ	˜!˜Q Ó	$×	(Ñ	(¨a¨SÐ	(Ó	1€Bà!€GØ!€GØ €FØ�1ƒ~Ø�3˜‘9ÑˆØÐÜ—Y‘Y˜r 5§?¡?°1Ó#5Ó6×>Ñ>¸qÀ%ÈÓM×QÑQÐRSÓTˆFÜ—Y‘Y˜r 5§?¡?°1Ó#5Ó6×>Ñ>¸qÀ%ÈÓM×QÑQÐRSÓTˆFÜ—‘Ø—‘˜rÓ"Ø—‘˜a ¨Ó,ó‰Bð
 —Z‘Z  5¨#Ó.×2Ñ2°1Ó5ˆFØ—Z‘Z  5¨#Ó.×2Ñ2°1Ó5ˆFÜ—‘Ø—‘˜rÓ"Ü—
‘
˜A˜u c˜?°4·;±;Ô?óˆBð �t‰m˜fÑ$¨Ñ,¨tÑ3°dÑ:¸QÑ>ˆØˆS�4‰Z˜& 4™-¨!Ñ+Ñ+ˆà�\‰\˜"ÓˆÜ˜r 1Ó%ˆÜ˜r 1Ó%ˆä�I‰I�k×)Ñ)¨!¨U°C¸Ó=¸rÓBÜ�i‰i˜Ÿ™ a¨°°SÓ9¸2Ó>ñ?àñð 	ð
 —/‘/ %§+¡+Ó.×1Ñ1°%·+±+Ó>ˆØ�1‚~ð —‘˜˜E 3Ó'¨"¯'©'°!°U¸CÓ*@À4Ç>Á>ÐRTÓCUÑ*UÑUØ—.‘. Ó$ñ%÷ ‰S�a�SˆS‹\ß‰W�Q‹Zð 	ð �1‚~Ø—‘˜Q˜C�“ˆà�W˜fÐ%Ð%r*   Úout2c
                ó¸   — t        | |||||||||	«
      }|
||f}t        |«      D ]2  \  }}|€Œ	t        ||   |j                  «       t	        |||   d¬«       Œ4 |S r  )rÛ  Ú	enumerater   r  r   )rk   r¾   rò   rÀ  rÁ  rÂ  rÃ  rÄ  rÅ  rÆ  rH  rI  rÜ  r  rW   ro  rI   s                    r+   Únative_group_norm_backward_outrß  €  sz   € ô" (Ø�U˜D $¨¨q°!°S¸%Àó€Fð ˜˜dÐ#€JÜ˜&Ó!ò Q‰ˆˆ1Ø‰=Ü˜j¨™m¨Q¯W©WÔ5Ü Q°
¸1±È4ÖPðQð
 Ðr*   c                 ó,   — | �| j                  |«      S | S r4   ©r7   )r8   ræ   s     r+   Ú_maybe_castrâ  �  s   € Ø€}Ø�t‰t�E‹{ÐØ€Hr*   Úgrad_outÚnormalized_shapeÚbiasc                 ó~  ‡"— |j                   }|j                  «       }	t        j                  |j                  «      Š"ˆ"fd„| |||fD «       \  }
}}}|
€t        d«      ‚|	t        |«      z
  }||d  }|d | }g }g }t        |	«      D ]*  }||k\  r|j                  |«       Œ|j                  |«       Œ, t        |«      }t        |«      }ddl
m}  ||dk(  «      s ||dk(  «      rN|d   r|j                  |«      nd |d   r|j                  ||d  «      nd |d   r|j                  ||d  «      fS d fS t        ||j                  «       «      }t        ||j                  «       «      }|€t        d«      ‚||z
  |z  }|�|
|z  }n|
}||z  }t        j                  ||d«      }t        j                   ||«      }t        j                  ||d«      }t        j                   ||«      }||z
  |z
  }d }d } d }!|d   r||z  |z  }|d   r0|�.t        |«      dkD  rt        j                  |
|z  |d	«      } n|
|z  } |d   r8|�6t        |«      dkD  rt        j                  |
|d	«      }!n|
j#                  «       }!t%        ||j                  «      t%        | |�|j                  nd «      t%        |!|�|j                  «      fS d «      fS )
Nc              3   óh   •K  — | ])  }|�!|j                  ‰t        j                  ¬«      n|–— Œ+ y ­wr2  )r7   r>   r\  ©rÎ  r8   r9   s     €r+   rÏ  z-native_layer_norm_backward.<locals>.<genexpr>²  s>   øè ø€ ò 9ð ð ˆ=ð 	
�‰Ð¬e×.EÑ.EˆÔFàó	ñ9ùs   ƒ/2ú grad_out_cast should not be Noner   rq  r!   r"   zinput_cast should not be NoneTF)r  rN   rC   Úget_computation_dtyperæ   r,  r‚  rS   ru  r&  rs  rr  rm  rV   r>   ró   rØ   r“  râ  )#rã  r¾   rä  rò   rÀ  rË   rå  rÆ  Úinput_shapeÚ
input_ndimÚgrad_out_castÚ
input_castÚweight_castÚ	bias_castÚaxisÚ
inner_dimsÚ
outer_dimsÚinner_dim_indicesÚouter_dim_indicesro  rÂ  ÚMrr  Úx_hatÚ
grad_x_hatÚaÚbrØ  rÙ  rÚ  rJ   rÓ  Úd_weightrÕ  r9   s#                                     @r+   Únative_layer_norm_backwardrü  ¤  s  ø€ ð —+‘+€KØ—‘“€JÜ×3Ñ3°E·K±KÓ@Ðó9ð ˜E 6¨4Ð0ô	9Ñ5€M�:˜{¨Ið ÐÜÐ?Ó@Ð@àœÐ,Ó-Ñ-€DØ˜T˜UÐ#€JØ˜U˜dÐ#€JØ#%ÐØ#%ÐÜ�:Óò (ˆØ�Š9Ø×$Ñ$ QÕ'à×$Ñ$ QÕ'ð	(ô 	ˆZÓ€AÜˆZÓ€AÝKá˜Q !™VÔ$Ñ(=¸aÀ1¹fÔ(Eà,7¸ªNˆE�O‰O˜KÔ(ÀØ3>¸q²>ˆE�O‰O˜K¨¨Ð.Ô/ÀtØ3>¸q²>ˆE�O‰O˜K¨¨Ð.Ó/ð
ð 	
ð HLð
ð 	
ô
 ˜T :§>¡>Ó#3Ó4€DÜ˜T :§>¡>Ó#3Ó4€DØÐÜÐ<Ó=Ð=Ø˜$Ñ $Ñ&€EØÐØ" [Ñ0‰
à"ˆ
Ø�Q‰€AÜ�	‰	�*Ð/°Ó6€AÜ	�‰�:˜uÓ	%€BÜ	�‰�2Ð(¨$Ó	/€BÜ	�‰�5˜"Ó	€Bà�‰E�B‰J€EØ!€GØ"€HØ €FØ�1‚~Ø˜!‘8˜uÑ$ˆà�1‚~˜+Ð1ÜÐ Ó! AÒ%Ü—y‘y °Ñ!6Ð8IÈ5ÓQ‰Hà$ uÑ,ˆHà�1‚~˜)Ð/ÜÐ Ó! AÒ%Ü—Y‘Y˜}Ð.?ÀÓG‰Fà"×(Ñ(Ó*ˆFô 	�G˜UŸ[™[Ó)Ü�H¨fÐ.@˜fŸlšlÀdÓKÜ�F¨$Ð*:˜DŸJ™JÓEðð ð AEÓEðð r*   c          
      ó´   — t        | |||||||«      }||	|
f}t        |«      D ]2  \  }}|€Œ	t        ||   |j                  «       t	        |||   d¬«       Œ4 |S r  )rü  rÞ  r   r  r   )rã  r¾   rä  rò   rÀ  rË   rå  rÆ  rH  rI  rÜ  r  rW   ro  rI   s                  r+   Únative_layer_norm_backward_outrþ  ú  sw   € ô (Ø�%Ð)¨4°°v¸tÀ[ó€Fð ˜˜dÐ#€JÜ˜&Ó!ò Q‰ˆˆ1Ø‰=Ü˜j¨™m¨Q¯W©WÔ5Ü Q°
¸1±È4ÖPðQð
 Ðr*   c                 ó&  — g }t        t        |«      «      D ]'  }|j                  | j                  «       |z
  dz
  «       Œ) t	        j
                  | j                  «      }| j                  |«      }|€~|t        j                  t        j                  fv r.t        j                  t        j                  «      j                  }n0t        j                  t        j                  «      j                  }n|}t        j                  t        j                  j                   j"                  j%                  t        j&                  |d«      j)                  |d¬«      |«      «      }	|j+                  |	«      }
|�|
j+                  |«      }
| j,                  xs |d uxr |j,                  }t	        j.                  | «      }|t        j0                  t        j2                  fv }|s"|s |
j5                  «       }
|	j5                  «       }	|
j7                  | «      }||	fS )Nr!   r"   Tr  )rS   r‚  ru  rN   rC   rê  ræ   r7   r>   ré   rø   Úfinfor>  rú   ÚrsqrtÚopsr‚   ÚaddÚScalarrë   rò   rØ   Ú	is_nestedr   Úchannels_lastÚchannels_last_3dr¯  r3  )r¾   rä  rË   r>  Údims_to_reducero  r9   Úupcasted_inputÚeps_valÚrqrst_inputÚupcasted_resultr  rY  Úis_channels_lastr  s                  r+   Ú_fused_rms_normr    s¿  € ð !#€NÜ”3Ð'Ó(Ó)ò 3ˆØ×Ñ˜eŸi™i›k¨A™o°Ñ1Õ2ð3ô ×3Ñ3°E·K±KÓ@ÐØ—X‘XÐ/Ó0€Nð €{Ø¤§¡´·±Ð @Ñ@Ü—k‘k¤%§-¡-Ó0×4Ñ4‰Gä—k‘k¤%§-¡-Ó0×4Ñ4‰Gàˆä—+‘+ô 	�	‰	�‰×Ñ×!Ñ!Ü�I‰I�n aÓ(×-Ñ-°.È$Ð-ÓOÐQXó	
ó€Kð %×(Ñ(¨Ó5€OàÐØ)×-Ñ-¨fÓ5ˆð —‘ÒL F°$Ð$6Ò$K¸6×;KÑ;K€IÜ×/Ñ/°Ó6€MØ$Ü×ÑÜ×Ñð)ð Ðñ
 Ñ-Ø)×4Ñ4Ó6ˆØ!×,Ñ,Ó.ˆð ×$Ñ$ UÓ+€Fà�;ÐÐr*   c                 óL  — |j                   }|j                  «       }t        j                  |j                  «      }| j                  |t        j                  ¬«      }	|j                  |t        j                  ¬«      }
|�!|j                  |t        j                  ¬«      nd }|	€t        d«      ‚|t        |«      z
  }||d  }|d | }g }g }t        |«      D ]*  }||k\  r|j                  |«       Œ|j                  |«       Œ, t        |«      }t        |«      }ddlm}  ||dk(  «      s ||dk(  «      r4|d   r|j                  |«      nd |d   r|j                  ||d  «      fS d fS t!        ||
j                  «       «      }|�|	|z  }n|	}d }d }|
|z  }|d   r)t        j"                  ||z  |d¬«      }|||z  |z  z
  |z  }|d   r0|�.|	|z  }t        |«      dkD  rt        j"                  ||d¬«      }n|}t%        ||j                  «      t%        ||j                  «      fS )	NrX  ré  r   rR  r!   Tr  F)r  rN   rC   rê  ræ   r7   r>   r\  r,  r‚  rS   ru  r&  rs  rS  rm  rV   ró   râ  )rã  r¾   rä  rÀ  rË   rÆ  rë  rì  r9   rí  rî  rï  rñ  rò  ró  rô  rõ  ro  rÂ  rö  rS  rø  rÓ  rû  r÷  Úsum_valÚd_weight_full_shapes                              r+   Ú_fused_rms_norm_backwardr  L  sa  € ð —+‘+€KØ—‘“€JÜ×3Ñ3°E·K±KÓ@Ðà—K‘KØ¬×)@Ñ)@ð  ó €Mð —‘Ð+¼5×;RÑ;R�ÓS€Jð Ðð 	�	‰	Ð#´5×3JÑ3Jˆ	ÔKàð ð
 ÐÜÐ?Ó@Ð@àœÐ,Ó-Ñ-€DØ˜T˜UÐ#€JØ˜U˜dÐ#€JØ#%ÐØ#%ÐÜ�:Óò (ˆØ�Š9Ø×$Ñ$ QÕ'à×$Ñ$ QÕ'ð	(ô 	ˆZÓ€AÜˆZÓ€AÝDá�a˜1‘fÔ¡°°Q±Ô!7à,7¸ªNˆE�O‰O˜KÔ(ÀØ3>¸q²>ˆE�O‰O˜K¨¨Ð.Ó/ð
ð 	
àGKð
ð 	
ô
 ˜T :§>¡>Ó#3Ó4€DØÐØ" [Ñ0‰
à"ˆ
à!€GØ"€Hà˜Ñ€Eà�1‚~Ü—)‘)˜E JÑ.Ð4EÈtÔTˆØ ¨¡¨gÑ 5Ñ5¸Ñ=ˆà�1‚~˜+Ð1Ø+¨eÑ3ÐÜÐ Ó! AÒ%Ü—y‘yØ#Ð):ÀEô‰Hð +ˆHô 	�G˜UŸ[™[Ó)Ü�H˜eŸk™kÓ*ðð r*   Úrunning_meanÚrunning_varÚmomentumÚ
functionalc	                 óD  — dgt        t        d| j                  «       «      «      z   }	t        j                  | j
                  «      }
|}|}|�r"t        j                  | j
                  «      }
| j                  |
¬«      }t        j                  ||	dd¬«      \  }}t        j                  ||z   «      }| |z
  |z  }t        j                  ||	«      }t        j                  ||	«      }|�!||z  d|z
  |z  z   }|s|j                  |«       |��;| j                  «       | j                  d   z  }t        j                  ||	«      }|||dz
  z  z  }||z  d|z
  |z  z   }|sê|j                  |«       nØ|�|€t        d«      ‚|j                  |
d¬«      }|}|j                  |
d¬«      }|}|}dt        j                  ||z   «      z  }| j                   j"                  d	k7  r|}|}n"| j%                  d
«      }| j%                  d
«      }t'        || j                  «       dz
  «      }t'        || j                  «       dz
  «      }| |z
  |z  }|�2|j)                  «       }t'        || j                  «       dz
  «      }||z  }|�2|j)                  «       }t'        || j                  «       dz
  «      }||z   }| j                   j"                  d	k(  r8|j                  | j
                  ¬«      }|j                  | j
                  ¬«      }|j                  | j
                  ¬«      ||||fS )Nr   r"   rå   T)rN   Ú
correctionr  r!   z:running_mean and running_var must not be None in eval mode)ræ   rƒ   r¢  ©r   )ru  rS   rN   rC   rê  ræ   r7   r>   Úvar_meanr  rü  Úcopy_rÜ   r  r,  r`  r�  r¥  rm  rV   r;  )r¾   rË   rå  r  r  rÕ   r  r>  r  Úreduction_dimsr9   Únew_running_meanÚnew_running_varÚ	input_accÚ
biased_varrò   rÀ  r¬  Ú	save_meanÚ	save_rstdÚnÚsqueezed_varÚunbiased_varÚinvstds                           r+   Únative_batch_norm_helperr'  ˜  s  € ð �Sœ4¤ a¨¯©«Ó 5Ó6Ñ6€NÜ×3Ñ3°E·K±KÓ@ÐØ#ÐØ!€OÚÜ!×7Ñ7¸¿¹ÓDÐØ—H‘HÐ#4�HÓ5ˆ	Ü Ÿ>™>Ø˜>°aÀô
Ñˆ
�Dô �{‰{˜:¨Ñ+Ó,ˆà˜$‘, $Ñ&ˆä—M‘M $¨Ó7ˆ	Ü—M‘M $¨Ó7ˆ	ØÐ#Ø'¨)Ñ3°q¸8±|À|Ñ6SÑSÐÙØ×"Ñ"Ð#3Ô4ØÑ"Ø—‘“ §¡¨A¡Ñ.ˆAô !Ÿ=™=¨°^ÓDˆLØ'¨1°°A±©;Ñ7ˆLØ&¨Ñ5¸¸X¹ÈÑ8TÑTˆOÙØ×!Ñ! /Õ2àÐ ;Ð#6Ü ØLóð ð $—‘Ð->ÀT�ÓJˆØ'ÐØ!—n‘nÐ+<À4�nÓHˆØ%ˆØˆØ”e—j‘j ¨sÑ!2Ó3Ñ4ˆà�<‰<×Ñ Ò%Ø$ˆIØ‰IàŸ™¨Ó-ˆIØŸ™¨Ó-ˆIÜ   u§y¡y£{°Q¡Ó7ˆÜ" 6¨5¯9©9«;¸©?Ó;ˆØ˜$‘, &Ñ(ˆàÐØ—‘Ó!ˆÜ" 6¨5¯9©9«;¸©?Ó;ˆØ˜&‘ˆàÐØ�|‰|‹~ˆÜ   u§y¡y£{°Q¡Ó7ˆØ˜$‘ˆà‡|�|×Ñ˜EÒ!Ø—L‘L u§{¡{�LÓ3ˆ	Ø—L‘L u§{¡{�LÓ3ˆ	à�	‰	˜Ÿ™ˆ	Ó$ØØØØðð r*   r!  Úsave_invstdc                 ó>   — t        | |||||||d«	      \  }}	}
}}||	|
fS ©NF©r'  ©r¾   rË   rå  r  r  rÕ   r  r>  r¬  r!  r"  rU   s               r+   Únative_batch_normr-  í  s=   € ô *BØˆv�t˜\¨;¸À(ÈCÐQVó*Ñ&€FˆI�y ! Qð �9˜iÐ'Ð'r*   c           
      óä   — |€|€t         j                  | |||||«      S |€t        d«      ‚|€t        d«      ‚|rt         j                  | |||||||«      S t         j                  | ||||||«      S )Nz`running_mean is None, but running_var is provided. They should both be None or both be provided.z`running_var is None, but running_mean is provided. They should both be None or both be provided.)r‚   Ú_native_batch_norm_legitrt  Ú$_native_batch_norm_legit_no_training)r¾   rË   rå  r  r  rÕ   r  r>  s           r+   Únative_batch_norm_decompositionr1  	  s±   € ð Ð Ð 3Ü×,Ñ,Ø�6˜4 ¨8°Só
ð 	
ð ÐÜð<ó
ð 	
ð ÐÜð<ó
ð 	
ñ ä×,Ñ,Ø�6˜4 ¨{¸HÀhÐPSó
ð 	
ô ×8Ñ8Ø�6˜4 ¨{¸HÀcó
ð 	
r*   c                 ó~  — | j                  |«      }||z   dz
  |z  }|dk(  rc|dk(  r^t        |«      D �cg c]  }|‘Œ }}|||z  |z
  z
  ||dz
  <   t        j                  j                  j
                  j                  | ||«      S t        j                  j                  j                  j                  | ||«      S c c}w ©Nr!   r   )	r.  rS   r>   r  r‚   r›  rˆ  r™  r   )rw  rŸ  rN   r‰  r—  rU   r�  s          r+   Úunsafe_chunk_py_implr4  .  s±   € à�{‰{˜3Ó€HØ˜VÑ# aÑ'¨FÑ2€Jà�Q‚˜8 qš=Ü+0°«=Ö9 a’zÐ9ˆÐ9Ø",°
¸VÑ0CÀhÑ0NÑ"Oˆ�F˜Q‘JÑÜ�y‰y�~‰~×5Ñ5×=Ñ=¸fÀkÐSVÓWÐWÜ�9‰9�>‰>×&Ñ&×-Ñ-¨f°jÀ#ÓFÐFùò :s   ´	B:c           
      óN   — t         j                  j                  | ||||d||«      S r*  )r‚   r/  rˆ  )r¾   rË   rå  r  r  r  r>  s          r+   r0  r0  :  s5   € ô ×(Ñ(×0Ñ0ØØØØØØØØó	ð 	r*   c                 ó>   — t        | |||||||d«	      \  }}	}
}}||	|
fS r*  r+  r,  s               r+   r/  r/  P  s=   € ô *BØˆv�t˜\¨;¸À(ÈCÐQVó*Ñ&€FˆI�y ! Qð �9˜iÐ'Ð'r*   c                 ó>   — t        | ||d d |||d«	      \  }}}}	}	|||fS r*  r+  )
r¾   rË   rå  rÕ   r  r>  r¬  r!  r"  rU   s
             r+   Ú!_native_batch_norm_legit_no_statsr8  a  s<   € ô *BØˆv�t˜T 4¨°8¸SÀ%ó*Ñ&€FˆI�y ! Qð �9˜iÐ'Ð'r*   c                 óv   — t        | |||||||d«	      \  }}	}
}}|€t        d«      ‚|€t        d«      ‚||	|
||fS )NTú#new_running_mean should not be Noneú"new_running_var should not be None)r'  r,  )r¾   rË   rå  r  r  rÕ   r  r>  r¬  r!  r"  r  r  s                r+   Ú#_native_batch_norm_legit_functionalr<  p  sl   € ô" 	!Øˆv�t˜\¨;¸À(ÈCÐQUó	ñØØØØØð ÐÜÐBÓCÐCØÐÜÐAÓBÐBØ�9˜iÐ)9¸?ÐJÐJr*   c           	      óT  — t         j                  j                  | ||||d|«      }d}|t         j                  j                  j                  k(  r t         j                  j                  | |«      }t        j                  |t         j                  | j                  | j                  ¬«      S )a©  
    Return a reserve tensor for batch norm, used only by cudnn to pass forward state to the
    backward pass. This is needed for `_batch_norm_with_update` and `_batch_norm_no_update`,
    which support a variety of backends including cudnn. We create this tensor here to get
    the correct shape in the traced graph if we detect that will call the cudnn kernel,
    and rely on DCE to avoid materializing this tensor.
    Tr   )ræ   Úlayoutr�  )
r>   Ú_CÚ_select_batch_norm_backendÚ_BatchNormBackendÚCudnnÚ(_get_cudnn_batch_norm_reserve_space_sizeÚemptyÚuint8r>  r�  )	r¾   rË   rå  r  r  r>  rÕ   ÚbackendÚreserve_sizes	            r+   Ú_get_batch_norm_reserve_tensorrH  ‹  s‡   € ô  �h‰h×1Ñ1Øˆv�t˜\¨;¸¸có€Gð €LØ”%—(‘(×,Ñ,×2Ñ2Ò2Ü—x‘x×HÑHØ�8ó
ˆô �;‰;ØœEŸK™K°·±ÀUÇ\Á\ôð r*   c                 ód   — t        | ||||d||d«	      \  }}}	}
}
t        | |||||d¬«      }|||	|fS )NTF©rÕ   ©r'  rH  ©r¾   rË   rå  r  r  r  r>  r¬  r!  r"  rU   Úreserves               r+   Ú_batch_norm_with_updaterN  ¨  sa   € ô *BØØØØØØØØØó
*Ñ&€FˆI�y ! Qô -Øˆv�t˜\¨;¸Àdô€Gð �9˜i¨Ð0Ð0r*   c                 óœ   — t        | ||||d||d«	      \  }}}	}
}t        | |||||d¬«      }|
€t        d«      ‚|€t        d«      ‚|||	||
|fS )NTrJ  r:  r;  )r'  rH  r,  )r¾   rË   rå  r  r  r  r>  r¬  r!  r"  Únew_rmÚnew_rvrM  s                r+   Ú"_batch_norm_with_update_functionalrR  Ã  s…   € ô  	!Øˆv�t˜\¨;¸¸hÈÈTó	ñØØØØØô -Øˆv�t˜\¨;¸Àdô€Gð €~ÜÐBÓCÐCØ€~ÜÐAÓBÐBØ�I˜y¨'°6¸6ÐBÐBr*   c                 ód   — t        | ||||d||d«	      \  }}}	}
}
t        | |||||d¬«      }|||	|fS )NFrJ  rK  rL  s               r+   Ú_batch_norm_no_updaterT  à  sa   € ô *BØØØØØØØØØó
*Ñ&€FˆI�y ! Qô -Øˆv�t˜\¨;¸Àeô€Gð �9˜i¨Ð0Ð0r*   c                 óÊ   — |�t        d|› �«      ‚t        j                  | «      |k  j                  t        j                  ¬«      }|j                  | «      | z  d|z  z  }||fS )Nz=generator must be None for _fused_dropout decomposition, got rå   rf   )r,  r>   rL  r7   rE  r3  )r¾   rR  Ú	generatorr�  rN  s        r+   Ú_fused_dropout_decompositionrW  û  sn   € ð ÐÜØKÈIÈ;ÐWó
ð 	
ô �O‰O˜EÓ" QÑ&×*Ñ*´·±Ð*Ó=€DØ
�,‰,�uÓ
 Ñ
%¨¨q©Ñ
1€CØ�ˆ;Ðr*   )ræ   r>  r�  Ú
pin_memoryÚnon_blockingrY  r�  rX  rY  rY  c                ó  — |r!|t         j                  k7  rt        d|› �«      ‚|rt        d«      ‚t        | t         j                  t
        t        t        t        f«      s!t        dt        | «      j                  › �«      ‚|€0|€.|€,t        | t         j                  «      r| j                  «       S | S d}t        | t         j                  «      r| }nt        j                  | «      }|�c||j                  k7  rT|�1|j                  dk(  r"t         j                  j                  ||«      }d}t         j                  j!                  |||«      }|�$|s"t         j                  j                  ||«      }d}|�t        j                  ||¬«      S |S )Nz*layout must be None or torch.strided, got z:pin_memory=True is not supported in _to_copy decompositionz x must be Tensor or scalar, got Fr¢  TrX  )r>   Ústridedr,  r6   r   r‹  r  r–  Úcomplexr¥  r#   r“  Úscalar_tensorr�  Ú_primsÚconvert_element_typeÚ
device_put)	r8   ræ   r>  r�  rX  rY  rY  Údtype_convertedÚx_tensors	            r+   Ú_to_copyrc  	  sZ  € ñ �&œEŸM™MÒ)ÜÐIÈ&ÈÐRÓSÐSÙÜØHó
ð 	
ô �aœ%Ÿ,™,¬¬U´D¼'ÐBÔCÜÐ?ÄÀQÃ×@PÑ@PÐ?QÐRÓSÐSØ€~˜%˜-¨MÐ,AÜ�aœŸ™Ô&Ø—7‘7“9ÐàˆHØ€Oä�!”U—\‘\Ô"Ø‰ä×&Ñ& qÓ)ˆàÐ˜f¨¯©Ò7àÐ §¡°Ò!5Ü—|‘|×8Ñ8¸À5ÓIˆHØ"ˆOÜ—<‘<×*Ñ*¨8°V¸\ÓJˆàÐ¡Ü—<‘<×4Ñ4°X¸uÓEˆØˆàÐ Ü�{‰{˜8°=ÔAÐAØ€Or*   c                 ó,   — t         j                  | «      S r4   )r‚   Úalias)r8   s    r+   Únop_decompositionrf  ;	  s   € ô �:‰:�a‹=Ðr*   Úout3Úexponential_average_factorÚepsilonc           
      ó  — t         j                  | |||||||«      \  }}	}
|r%||	|
| j                  dt        j                  ¬«      fS ||j                  d«      |j                  d«      | j                  dt        j                  ¬«      fS )Nr  rå   )r‚   r-  rm  r>   rE  )r¾   rË   rå  r  r  rÕ   rh  ri  rù  rú  rñ  s              r+   Úcudnn_batch_normrk  C	  s”   € ô ×$Ñ$ØØØØØØØ"Øó	�G€A€qˆ!ñ Ø�1�a˜Ÿ™¨´U·[±[˜ÓAÐBÐBà	Ø×Ñ˜ÓØ×Ñ˜ÓØ�‰˜¤E§K¡KˆÓ0ð	ð r*   c                 óž   — t        |«      D ]>  \  }}|dk(  sŒ|| j                  k  r| j                  |   |k(  rŒ.| j                  |«      } Œ@ | S r[   )rÞ  r}  r  rT   )r8   Úbroadcast_maskrñ  r�  s       r+   Ú_broadcast_batch_norm_backwardrn  e	  sO   € Ü Ó/ò "‰
ˆˆdØ�1‹9˜d Q§V¡Všm°·±¸±ÀÓ0EØ—‘˜DÓ!‰Að"ð €Hr*   rM  c                 ó*   — t        | |||||||||	«
      S r4   )Únative_batch_norm_backward)rã  r¾   rË   r  r  r!  r(  rD  r>  rÆ  rM  s              r+   Úbatch_norm_backwardrq  l	  s/   € ô &ØØØØØØØØØØóð r*   c
                 ó  ‡&— |j                   }
|�|j                   }n|
}t        j                  |j                   «      Š&ˆ&fd„| ||||||fD «       \  }}}}}}}|j                  }|j	                  «       }|dk  rt        d|› �«      ‚d}t        t        |«      «      ||   z  }|}|}|r|�|€4t        d«      ‚|�|€t        d«      ‚|}t        j                  ||z   «      }dg|z  }||   ||<   g }t        |«      D ]  }||k7  sŒ	|j                  |«       Œ t        ||«      }d|z  }t        j                  ||«      }t        j                  |||z
  z  |«      }t        ||z  |«      }t        t        j                  ||z  ||z  «      |«      } |€t        ||«      dz  }!nt        ||z  |«      }!|r||z
  | z  }"||"z
  |z
  |!z  }#n||!z  }#|	d   r||z  }$nd }$|	d   r|}%nd }%|#j                  |
«      t!        |$|«      t!        |%|«      fS )Nc              3   óH   •K  — | ]  }|�|j                  ‰«      n|–— Œ y ­wr4   rá  rè  s     €r+   rÏ  z-native_batch_norm_backward.<locals>.<genexpr>£	  s,   øè ø€ ò 	àð $% =ˆ�‰ÐÔ°aÓ7ñ	ùs   ƒ"r"   z*rank of the input must be at least 2, got r!   z1mean and invstd must not be None in training modezDrunning_mean_cast and running_var_cast must not be None in eval moderf   )ræ   rC   rê  r  rN   r,  r&  ru  r>   r  rS   ru  rn  ró   rØ   r7   râ  )'rã  r¾   rË   r  r  r!  r(  rD  r>  rÆ  r©  Úweight_dtyperí  rî  rï  Úrunning_mean_castÚrunning_var_castÚsave_mean_castÚsave_invstd_castrë  Ú
input_rankrñ  Únum_featuresrò   r&  rm  Úreduction_axesro  r   Úgrad_output_sumÚdot_pÚ	grad_meanÚ
proj_scaleÚ
grad_scaleÚprojrW   rl  Ú	grad_biasr9   s'                                         @r+   rp  rp  ˆ	  s�  ø€ ð —+‘+€KØÐØ—|‘|‰à"ˆÜ×3Ñ3°E·K±KÓ@Ðó	ð ØØØØØØð
ô	ñØØØØØØØð —+‘+€KØ—‘“€JØ�A‚~ÜÐIÈ*ÈÐVÓWÐWà€DÜœ˜[Ó)Ó*¨[¸Ñ->Ñ>€LØ€DØ€FÙØˆ<˜6˜>Ü Ð!TÓUÐUð Ð$Ð(8Ð(@Ü ØVóð ð !ˆÜ—‘Ð-°Ñ3Ó4ˆà!"  jÑ 0€NØ& tÑ,€N�4Ñà "€NÜ�:Óò %ˆØ�‹9Ø×!Ñ! !Õ$ð%ô *¨$°Ó?€DØ�Ñ€DÜ—i‘i ¨~Ó>€OÜ�I‰I�m z°DÑ'8Ñ9¸>ÓJ€Eä.¨ÀÑ/EÀ~ÓV€IÜ/Ü�	‰	�%˜$‘, ¨¡Ó0Øó€Jð
 ÐÜ3°F¸NÓKÈcÑQ‰
ä3Ø�[Ñ  .ó
ˆ
ñ Ø˜TÑ! ZÑ/ˆØ$ tÑ+¨yÑ8¸JÑF‰
à" ZÑ/ˆ
à�1‚~Ø˜f‘n‰àˆà�1‚~Ø#‰	àˆ	ð 	�‰�kÓ"Ü�K Ó.Ü�I˜|Ó,ðð r*   c
                ó¸   — t        | |||||||||	«
      }|
||f}t        |«      D ]2  \  }}|€Œ	t        ||   |j                  «       t	        |||   d¬«       Œ4 |S r  )rp  rÞ  r   r  r   )rã  r¾   rË   r  r  r!  r(  rD  r>  rÆ  rH  rI  rÜ  r  rW   ro  rI   s                    r+   Únative_batch_norm_backward_outr„  ö	  sƒ   € ô" (ØØØØØØØØØØó€Fð ˜˜dÐ#€JÜ˜&Ó!ò Q‰ˆˆ1Ø‰=Ü˜j¨™m¨Q¯W©WÔ5Ü Q°
¸1±È4ÖPðQð
 Ðr*   Úsave_varc                 óB   — t         j                  || |||||d|g d¢«
      S ©NT)TTT©r‚   rp  )r¾   rk   rË   r  r  r!  r…  ri  s           r+   Úmiopen_batch_norm_backwardr‰  
  s5   € ô ×*Ñ*ØØØØØØØØØÚóð r*   ÚreserveSpacec	                 óB   — t         j                  || |||||d|g d¢«
      S r‡  rˆ  )	r¾   rk   rË   r  r  r!  r…  ri  rŠ  s	            r+   Úcudnn_batch_norm_backwardrŒ  6
  s5   € ô ×*Ñ*ØØØØØØØØØÚóð r*   c                 óÊ  ‡‡‡‡‡— | j                   Š| j                  Št        ‰«      Št        j                  ‰dv ˆfd„«       | j                  dd  D ]  }t        j                  |dk7  ˆfd„«       Œ  ‰d   |d   z  dk(  rx‰d   |d   z  dk(  rjt        d„ t        ‰dd  |«      D «       «      }t        d„ t        ‰dd  ||«      D «       «      }t        j                  j                  j                  | ||«      S d	„ Šd
„ Šˆˆˆfd„} |‰d   |d   «      \  }}}}	 |‰d   |d   «      \  }
}}}| dt        |d«      |
f   }|	s|st        j                  |d¬«      S d„ } |||||	d¬«      \  }} |||||d¬«      \  }}d }t        t        |j                  d   «      t        |j                  d   «      «      D ]!  \  }}|€|d|d d …|f   }Œ||d|d d …|f   z   }Œ# |||z  z  S )Nrá  c                  ó   •— d‰ › �S )Nz9adaptive_avg_pool2d(): Expected 3D or 4D tensor, but got r)   r}  s   €r+   r€   z%adaptive_avg_pool2d.<locals>.<lambda>[
  s   ø€ ÐKÈDÈ6ÐR€ r*   rZ  r   c                  ó"   •— dt        ‰ «      › d�S )Nzjadaptive_avg_pool2d(): Expected input to have non-zero size for non-batch dimensions, but input has shape r  rç  ré  s   €r+   r€   z%adaptive_avg_pool2d.<locals>.<lambda>`
  s   ø€ ð 9Ü9>¸u»¸ÀaðI€ r*   rR   c              3   ó,   K  — | ]  \  }}||z  –— Œ y ­wr4   r)   )rÎ  ro  r.  s      r+   rÏ  z&adaptive_avg_pool2d.<locals>.<genexpr>f
  s   è ø€ ÒG¡$ ! Q�q˜A•vÑGùó   ‚c              3   ó:   K  — | ]  \  }}}||d z
  |z  z
  –— Œ y­w©r!   Nr)   )rÎ  ro  r.  r”  s       r+   rÏ  z&adaptive_avg_pool2d.<locals>.<genexpr>g
  s'   è ø€ ò 
Ù '  1 aˆA��Q‘˜!‘�Oñ
ùs   ‚c                 ó8   — t        j                  | |z  |d¬«      S )NÚtrunc©Úrounding_mode©r>   Údiv©rù  rú  rñ  s      r+   Ústart_indexz(adaptive_avg_pool2d.<locals>.start_indexl
  s   € Ü�y‰y˜˜Q™ °Ô9Ð9r*   c                 óJ   — t        j                  | dz   |z  |z   dz
  |d¬«      S )Nr!   r•  r–  r˜  rš  s      r+   Ú	end_indexz&adaptive_avg_pool2d.<locals>.end_indexo
  s&   € Ü�y‰y˜!˜a™% 1™ q™¨1Ñ,¨a¸wÔGÐGr*   c                 óô  •— t        j                  |‰t         j                  ¬«      } ‰||| «      }| |z  dz   }| |z  }|dk(  xs ||z  dk(   }|r|dz  }n
|dk(  r|dz  }t        j                  |‰t         j                  ¬«      }|j                  d«      |z   }|rUt        j                  | dz
  |j
                  |j                  ¬«      }	t        j                  ||	«      } ‰||| «      }
|
|z
  }n|}||||fS )Nr‘  r!   r   rR   rµ  )r>   r”  r¶  rT   r]  ræ   r�  Úminimum)Úin_sizeÚout_sizeÚorangeÚi0Ú	maxlengthÚin_size_modÚadaptiveÚ	range_maxrœ  ÚmaxvalÚi1Úlengthr�  r�  r›  s               €€€r+   Úcompute_idxz(adaptive_avg_pool2d.<locals>.compute_idxr
  s  ø€ Ü—‘˜h¨v¼U¿[¹[ÔIˆÙ˜ ¨7Ó3ˆð ˜xÑ'¨!Ñ+ˆ	Ø Ñ(ˆà# qÑ(ÒG¨H°{Ñ,BÀaÑ,GÐHˆÙØ˜‰N‰IØ˜AÒØ˜‰NˆIä—L‘L °6ÄÇÁÔMˆ	Ø�l‰l˜2Ó Ñ*ˆÙô ×(Ñ(Ø˜!‘ 3§9¡9°S·Z±ZôˆFô —-‘-  VÓ,ˆCñ ˜6 8¨WÓ5ˆBØ˜"‘W‰FàˆFØ�F˜I xÐ/Ð/r*   .rD  )r�   rR   r   c                 óê   — t        |t        «      r| |fS |dk\  rt        d|› �«      ‚||j                  d«      k\  }|dk(  rt	        |d«      }t        j                  | |d«      } t	        || «      }| |fS )Nr   z)dim should be negative when masking, got rR   rZ  rD  r’   )r6   r   r,  rT   rV   r>   ri  )Úvalsrª  r§  r¦  rN   r�  s         r+   Ú
maybe_maskz'adaptive_avg_pool2d.<locals>.maybe_maskš
  sˆ   € Ü�fœgÔ&Ø˜�<Ðð �aŠxÜ$Ð'PÐQTÐPUÐ%VÓWÐWà × 0Ñ 0°Ó 4Ñ4ˆDØ�bŠyÜ(¨¨qÓ1�Ü×$Ñ$ T¨4°Ó5ˆDä& v°¨tÓ4ˆFØ˜�<Ðr*   )r¦  rN   r�   )r�  r  r‚  r>   r�   rè  rú  Únnr  Ú
avg_pool2drV   rò   r
   rS   )r¾   r÷  rä  rv  Úkernelr«  ÚidxhÚlength_hÚrange_max_hÚ
adaptive_hÚidxwÚlength_wÚrange_max_wÚ
adaptive_wr­  r®  Úretro  Újr�  r�  r}  r  r›  s                      @@@@@r+   Úadaptive_avg_pool2dr¼  Q
  s.  ü€ ð
 �\‰\€FØ�K‰K€EÜˆu‹:€DÜ	‡L�LØ�ˆÛRôð �[‰[˜˜Ðò 
ˆÜ�‰Ø�‰FóIõ	
ð
ð ˆR�y�;˜r‘?Ñ" aÒ'¨E°"©I¸ÀB¹Ñ,GÈ1Ò,LÜÑG¬#¨e°B°C¨j¸+Ó*FÔGÓGˆÜñ 
Ü+.¨u°R°S¨z¸;ÈÓ+Oô
ó 
ˆô �x‰x×"Ñ"×-Ñ-¨e°V¸VÓDÐDò:òHö0ñ@ /:¸%À¹)À[ÐQSÁ_Ó.UÑ+€Dˆ(�K Ù.9¸%À¹)À[ÐQSÁ_Ó.UÑ+€Dˆ(�K à�Ô'¨¨aÓ0°$Ð6Ñ7€Dá™jÜ�z‰z˜$ HÔ-Ð-ò ñ   Øˆh˜¨j¸bô�N€Dˆ(ñ  Øˆh˜¨j¸bô�N€Dˆ(ð
 €CÜœ˜dŸj™j¨™nÓ-¬u°T·Z±ZÀ±^Ó/DÓEò +‰ˆˆ1Øˆ;Ø�s˜Ašq !�|Ñ$‰Cà˜˜S !¢Q¨˜\Ñ*Ñ*‰Cð	+ð
 �(˜XÑ%Ñ&Ð&r*   c                 óÞ  — t        j                  d|› d�«       t        | j                  d |  «      t        |«      z   }t	        d„ |D «       «      r| j                  |«      S t        t        j                  | j                  d |  «      }t        t        j                  |«      }dg| j                  z  }| j                  d |  |d |  |t        j                  || j                  ¬«      j                  |«      |z  z   j                  d«      }| j                  |«      }	t        j                  |	j                  d«      |g| j                  d«      d¬«      j                  |	j                  «      S )	NÚmax_unpoolingÚd_forward_outc              3   ó&   K  — | ]	  }|d k(  –— Œ y­wrÌ  r)   )rÎ  r”  s     r+   rÏ  z _max_unpoolnd.<locals>.<genexpr>Æ
  s   è ø€ Ò
(�aˆ1��6Ñ
(ùrÑ  r!   r�  rR   Fr$  )rC   Úalert_not_deterministicru  r  Úanyrm  r   ÚoperatorrØ   r}  r‚   r”  r�  r˜  r&  r'  )
rz   r›  r÷  rN   Úoutput_shapeÚncÚhwÚindices_nc_shapeÚindices_flatr¬  s
             r+   Ú_max_unpoolndrÉ  »
  s=  € ô 
×!Ñ! M°#°°mÐ"DÔEÜ˜Ÿ
™
 5 S DÐ)Ó*¬T°+Ó->Ñ>€LÜ
Ñ
(˜<Ô
(Ô(Ø�~‰~˜lÓ+Ð+Ü	”—‘˜dŸj™j¨¨3¨$Ð/Ó	0€BÜ	”—‘˜kÓ	*€BØ�s˜TŸY™Y‘ÐØ"Ÿj™j¨¨3¨$Ð/Ð�U�s�dÐà”$—+‘+˜b¨¯©�+Ó5×:Ñ:Ð;KÓLÈrÑQÑQß�gˆbƒkð ð �^‰^˜LÓ)€FÜ×!Ñ!Ø�‰�rÓ˜\˜N¨D¯L©L¸Ó,<Èð "ó ç
�dˆ6�<‰<Óðr*   c                 ó  ‡ ‡‡‡— t        j                  ‰j                  t         j                  k(  ˆfd„«       t        j                  t	        ‰«      dk(  ˆfd„«       t        j                  ‰ j
                  dv ˆ fd„«       t        j                  ‰ j                  ‰j                  k(  ˆˆ fd„«       t        d‰ j
                  «      D ].  Št        j                  ‰ j                  ‰«      dkD  ˆˆ fd	„«       Œ0 t        ‰ ‰‰d«      S )
Nc                  ó"   •— d‰ j                   › �S )Nz2elements in indices should be type int64 but got: rå   )r›  s   €r+   r€   zmax_unpool2d.<locals>.<lambda>ß
  s   ø€ ÐDÀWÇ]Á]ÀOÐT€ r*   r"   c                  ó"   •— dt        ‰ «      › d�S )NzMThere should be exactly two elements (height, width) in output_size, but got ú
 elements.©r‚  ©r÷  s   €r+   r€   zmax_unpool2d.<locals>.<lambda>ã
  ó   ø€ ðÜ˜;Ó'Ð(¨
ð4ð r*   rá  c                  ó$   •— d‰ j                   › d�S )NzLInput to max_unpooling2d should be a 3d or 4d Tensor, but got a tensor with ú dimensions.r}  r�   s   €r+   r€   zmax_unpool2d.<locals>.<lambda>ë
  s   ø€ ð%Ø%)§Y¡Y K¨|ð=ð r*   c                  ó<   •— d‰j                   › d‰ j                   › �S ©NzBExpected shape of indices to be same as that of the input tensor (z%) but got indices tensor with shape: ré  )r›  rz   s   €€r+   r€   zmax_unpool2d.<locals>.<lambda>ò
  s,   ø€ ØPÐQU×Q[ÑQ[ÐP\ð ]2Ø29·-±-°ðBð r*   r!   r   c                  ó*   •— d‰j                   › d‰ › d�S )NzZmax_unpooling2d(): Expected input to have non-zero size for non-batch dimensions, but got ú with dimension ú being empty.ré  )ro  rz   s   €€r+   r€   zmax_unpool2d.<locals>.<lambda>û
  s%   ø€ ðàŸ:™:˜,Ð&6°q°c¸ðHð r*   )
r>   r�   ræ   r¶  r‚  r}  r  rS   r.  rÉ  )rz   r›  r÷  ro  s   ```@r+   Úmax_unpool2drØ  Ö
  sÖ   û€ ô 
‡L�LØ�‰œŸ™Ñ$ÛTôô 
‡L�LÜˆKÓ˜AÑó	
ôô 
‡L�LØ�	‰	�VÐó	
ôô 
‡L�LØ�
‰
�g—m‘mÑ#ô	
ôô �1�d—i‘iÓ ò 
ˆÜ�‰Ø�I‰I�a‹L˜1Ñôõ	
ð
ô ˜˜w¨°QÓ7Ð7r*   c                 ó  ‡ ‡‡‡‡‡— t        j                  ‰j                  t         j                  k(  d„ «       t        j                  ‰ j                  dv ˆ fd„«       t        j                  t        ‰«      dk(  ˆfd„«       t        j                  t        ‰«      dk(  ˆfd„«       t        j                  t        ‰«      dk(  ˆfd„«       t        j                  ‰ j                  ‰j                  k(  ˆˆ fd„«       t        d	‰ j                  «      D ].  Št        j                  ‰ j                  ‰«      d
kD  ˆˆ fd„«       Œ0 t        j                  ‰d
   d
kD  xr ‰d	   d
kD  xr ‰d   d
kD  ˆfd„«       t        ‰ ‰‰d«      S )Nc                   ó   — y)Nz(elements in indices should be type int64r)   r)   r*   r+   r€   zmax_unpool3d.<locals>.<lambda>  rÆ  r*   ©rD  rø  c                  ó$   •— d‰ j                   › d�S )NzLInput to max_unpooling3d should be a 4d or 5d Tensor, but got a tensor with rÒ  r}  ©r¾   s   €r+   r€   zmax_unpool3d.<locals>.<lambda>  s   ø€ Ð^Ð_d×_iÑ_iÐ^jÐjvÐw€ r*   r‡   c                  ó"   •— dt        ‰ «      › d�S )NzVThere should be exactly three elements (depth, height, width) in output_size, but got rÍ  rÎ  rÏ  s   €r+   r€   zmax_unpool3d.<locals>.<lambda>  rÐ  r*   c                  ó"   •— dt        ‰ «      › d�S )NzRThere should be exactly three elements (depth, height, width) in stride, but got: rÍ  rÎ  ©rv  s   €r+   r€   zmax_unpool3d.<locals>.<lambda>  s   ø€ ÐdÔehÐioÓepÐdqÐq{Ð|€ r*   c                  ó"   •— dt        ‰ «      › d�S )NzSThere should be exactly three elements (depth, height, width) in padding, but got: rÍ  rÎ  )rÃ  s   €r+   r€   zmax_unpool3d.<locals>.<lambda>"  s   ø€ ÐeÔfiÐjqÓfrÐesÐs}Ð~€ r*   c                  ó<   •— d‰j                   › d‰ j                   › �S rÔ  ré  )r›  r¾   s   €€r+   r€   zmax_unpool3d.<locals>.<lambda>&  s,   ø€ ØPÐQV×Q\ÑQ\ÐP]ð ^2Ø29·-±-°ðBð r*   r!   r   c                  ó*   •— d‰j                   › d‰ › d�S )NzZmax_unpooling3d(): Expected input to have non-zero size for non-batch dimensions, but got rÖ  r×  ré  )ro  r¾   s   €€r+   r€   zmax_unpool3d.<locals>.<lambda>/  s%   ø€ ðà Ÿ;™;˜-Ð'7¸°s¸-ðIð r*   r"   c                  ó   •— d‰ › �S )Nz5strides should be greater than zero, but got stride: r)   rà  s   €r+   r€   zmax_unpool3d.<locals>.<lambda>8  s   ø€ ÐGÈÀxÐP€ r*   )
r>   r�   ræ   r¶  r}  r‚  r  rS   r.  rÉ  )r¾   r›  r÷  rv  rÃ  ro  s   `````@r+   Úmax_unpool3drå    sD  ý€ ô 
‡L�LØ�‰œŸ™Ñ$Ñ&Xôô 
‡L�LØ�
‰
�fÐÛwôô 
‡L�LÜˆKÓ˜AÑó	
ôô 
‡L�LÜˆF‹�qÑÛ|ôô 
‡L�LÜˆG‹˜ÑÛ~ôô 
‡L�LØ�‰�w—}‘}Ñ$ô	
ôô �1�e—j‘jÓ!ò 
ˆÜ�‰Ø�J‰J�q‹M˜AÑôõ	
ð
ô 
‡L�LØˆq‰	�A‰Ò9˜& ™) a™-Ò9¨F°1©I¸©MÛPôô
 ˜ ¨°aÓ8Ð8r*   )rl   rw  c                ó$   — t        | |||d|¬«      S )NT©Úinplacerl   ©Ú
_index_add©r8   rN   rŸ  rw  rl   s        r+   Ú
index_add_rì  >  s   € ô �a˜˜e V°TÀÔGÐGr*   c                ó$   — t        | |||d|¬«      S )NFrç  ré  rë  s        r+   Ú	index_addrî  J  s   € ô �a˜˜e V°UÀ%ÔHÐHr*   rè  c                ó6  ‡‡‡‡‡‡— t        j                  | j                  ‰«      Št        j                  ‰j                  dk  ˆfd„«       ‰j                  dk(  r‰j                  d«      ndŠ|j                  dkD  r|j                  ‰«      ndŠt        j                  ‰‰k(  ˆˆˆfd„«       ‰dk7  ret        j                  | j                  «      Št        j                  ‰t        u xs t        j                  t        ‰«      ‰«      ˆˆfd„«       |‰z  }| j                  dk(  }|r| j                  d«      n| }d‰z  ‰fz   }|rt        j                  nt        j                  }	 |	|||d¬«      }
|r| S |r|
j                  d«      S |
j!                  «       S )	Nr!   c                  ó$   •— d‰ j                   › d�S ©Nz(Index should have dimension 1 or 0 (got r?  r}  ©rŸ  s   €r+   r€   z_index_add.<locals>.<lambda>c  ó   ø€ Ð:¸5¿:¹:¸,ÀaÐH€ r*   r   c                  ó   •— d‰› d‰› d‰ ›�S )NzNumber of indices (z') should be equal to tensor.size(dim) (z), for dim=r)   )rN   Ú
index_sizerx  s   €€€r+   r€   z_index_add.<locals>.<lambda>i  s!   ø€ Ð% j \Ð1XÐYdÐXeÐeqÐmpÐlrÐs€ r*   c                  ó(   •— dt        ‰ «      › d‰› d�S )Nzalpha argument of type z cannot be safely cast to type ú!)r¥  )rl   Úpython_types   €€r+   r€   z_index_add.<locals>.<lambda>p  s   ø€ Ð-¬d°5«k¨]Ð:YÐZeÐYfÐfgÐh€ r*   r4   Tr$  )rC   Úcanonicalize_dimsr}  r>   r�   r.  Údtype_to_typeræ   r–  Úis_weakly_lesser_typer¥  rT   r‚   Ú
index_put_Ú	index_putrü  r¯  )r8   rN   rŸ  rw  rè  rl   Úzero_dimrU  rœ  rý  rÅ   rõ  rø  rx  s    ``  `     @@@r+   rê  rê  W  sM  ý€ ô ×
!Ñ
! !§&¡&¨#Ó
.€CÜ	‡L�LØ�
‰
�a‰ÛHôð #(§*¡*°¢/�—‘˜A”°q€JØ&,§k¡k°A¢o�&—+‘+˜cÔ"¸1€KÜ	‡L�LØ�zÑ!Ýsôð �‚zÜ×)Ñ)¨!¯'©'Ó2ˆÜ�‰Øœ4Ðò EÜ×*Ñ*¬4°«;¸ÓDÜhô	
ð
 ˜%‘ˆà�v‰v˜‰{€HÙ#ˆ�‰�QŒ¨€BØ
�C‰-˜5˜(Ñ
"€CÙ#*”—’´·±€IÙ
�B˜˜V°Ô
5€CÙØˆá!)ˆs�{‰{˜1‹~Ð?¨s¯~©~Ó/?Ð?r*   c           
      ó  — t        j                  t        | «      dkD  d„ «       t        | «      }| d   j                  «       }|dd  }t	        d„ | D «       «      }|r||f}n||f}||z   }| d   j                  ||«      }dt        |«      z  }	t        |«      D ]j  }
| |
   }t        j                  ||	d||j                  d«      z
  fz   |«      }|rt        j                  ||d|
¬«      }ŒRt        j                  ||d|
¬«      }Œl |S )Nr   c                   ó   — y)Nz#received an empty list of sequencesr)   r)   r*   r+   r€   zpad_sequence.<locals>.<lambda>‚  rÆ  r*   r!   c              3   ó>   K  — | ]  }|j                  d «      –— Œ y­wrÌ  ©r.  )rÎ  r8   s     r+   rÏ  zpad_sequence.<locals>.<genexpr>†  s   è ø€ Ò/ �!—&‘&˜—)Ñ/ùs   ‚)r   r   ©rN   rŸ  )
r>   r�   r‚  r.  rŒ   rê   rS   r‚   rs  r¡  )Ú	sequencesÚbatch_firstÚpadding_valueÚsequences_sizeÚmax_sizeÚtrailing_dimsÚmax_lenÚout_dimsrÅ   Údim_paddingsro  ÚcurrseqÚrows                r+   Úpad_sequencer    s#  € ô 
‡L�L”�Y“ !Ñ#Ñ%RÔSÜ˜“^€NØ˜‰|× Ñ Ó"€HØ˜Q˜R�L€MÜÑ/ YÔ/Ó/€GÙØ" GÐ,‰à˜^Ð,ˆØ˜-Ñ'€HØ
�A‰,×
Ñ
 ¨-Ó
8€CØœC Ó.Ñ.€LÜ�>Ó"ò @ˆØ˜A‘,ˆÜ×"Ñ"Ø�\ Q¨°'·,±,¸q³/Ñ(AÐ$BÑBÀMó
ˆñ Ü×%Ñ% c¨3°A¸QÐ%Ó?‰Cä×%Ñ% c¨3°A¸QÐ%Ó?‰Cð@ð €Jr*   c                 ó"   — t        | |||d¬«      S )NT©rè  ©Ú_index_copy©r8   rN   rŸ  rw  s       r+   Úindex_copy_r  š  s   € ä�q˜#˜u f°dÔ;Ð;r*   c                 ó"   — t        | |||d¬«      S )NFr  r  r  s       r+   Ú
index_copyr  Ÿ  s   € ô �q˜#˜u f°eÔ<Ð<r*   c                óÔ  ‡— t        j                  | j                  |«      }t        j                  ‰j                  dk  ˆfd„«       | j                  dk(  }|r| j                  d«      n| }‰j                  dk(  r‰j                  d«      n‰Šd|z  ‰fz   }|rt        j                  nt        j                  } ||||«      }	|r| S |r|	j                  d«      S |	j                  «       S )Nr!   c                  ó$   •— d‰ j                   › d�S rñ  r}  rò  s   €r+   r€   z_index_copy.<locals>.<lambda>«  ró  r*   r   r4   )rC   rù  r}  r>   r�   rT   r‚   rü  rý  rü  r¯  )
r8   rN   rŸ  rw  rè  rþ  rU  rœ  rý  rÅ   s
     `       r+   r  r  ¥  sÂ   ø€ ô ×
!Ñ
! !§&¡&¨#Ó
.€CÜ	‡L�LØ�
‰
�a‰ÛHôð
 �v‰v˜‰{€HÙ#ˆ�‰�QŒ¨€BØ"'§*¡*°¢/ˆE�O‰O˜AÔ°u€EØ
�C‰-˜5˜(Ñ
"€CÙ#*”—’´·±€IÙ
�B˜˜VÓ
$€CÙØˆá!)ˆs�{‰{˜1‹~Ð?¨s¯~©~Ó/?Ð?r*   c                 ó*  — t        j                  | j                  d«      | «      }t        j                  t        j                  | «       «      }| j
                  s| j                  r| j                  d«      }n|}|t        j                  |«      z
  |fS )Nr)   r  )r>   rŸ  rm  rg   rÝ   r¸  Úis_xpurH  )rz   r‰   ri   rÚ   s       r+   Úlog_sigmoid_forwardr  »  sn   € ô �-‰-˜Ÿ™ rÓ*¨DÓ
1€CÜ�	‰	”5—9‘9˜T“?Ð"Ó#€AØ‡|‚|�t—{’{Ø—‘ Ó%‰àˆØ”—‘˜Q“Ñ Ð'Ð'r*   ÚlowÚhighrV  c           	      ó¶   — t        j                  | j                  | j                  «       t	        |«      t	        |«      | j
                  | j                  |¬«      S )N)rv  r  r  ræ   r�  rV  )ÚprimsÚ_uniform_helperr  rv  r   ræ   r�  )r8   r  r  rV  s       r+   Úuniformr"  È  sF   € ô × Ñ Ø	�‰Ø�x‰x‹zÜ�c‹NÜ�t‹_Ø�g‰gØ�x‰xØôð r*   c                 ó<   — | j                  t        | |||«      «      S r4   )r  r"  )rz   r  r  rV  s       r+   Úuniform_r$  Û  s   € à�:‰:”g˜d C¨¨yÓ9Ó:Ð:r*   c                 ó"  — t        | «      dz
  }|�>t        j                  |d u d„ «       t        j                  t        |«      |k(  d„ «       |S |�¨t        j                  |d u d„ «       t        j                  t        |«      |k(  d„ «       g }t        |«      D ]Z  \  }}t	        |«      |k(  r$|j                  | |dz      t	        |«      z  «       Œ8|j                  t        | |dz      |z  «      «       Œ\ |S t        j                  dd„ «       y )Nr"   c                   ó   — y©Nz9Must specify exactly one of output_size and scale_factorsr)   r)   r*   r+   r€   z.upsample_compute_output_size.<locals>.<lambda>æ  rÆ  r*   c                   ó   — y©NÚ r)   r)   r*   r+   r€   z.upsample_compute_output_size.<locals>.<lambda>è  rÆ  r*   c                   ó   — yr'  r)   r)   r*   r+   r€   z.upsample_compute_output_size.<locals>.<lambda>î  rÆ  r*   c                   ó   — yr)  r)   r)   r*   r+   r€   z.upsample_compute_output_size.<locals>.<lambda>ð  rÆ  r*   Fc                   ó   — yr'  r)   r)   r*   r+   r€   z.upsample_compute_output_size.<locals>.<lambda>ù  rÆ  r*   )r‚  r>   r�   rÞ  r‹  ru  r   )r5  r÷  Úscale_factorsÚspatial_dimensionsro  r”  s         r+   Úupsample_compute_output_sizer0  á  s  € Ü˜Z›¨1Ñ,ÐØÐÜ�‰Ø˜TÐ!ÙOô	
ô 	�‰”S˜Ó%Ð);Ñ;¹ZÔHØÐØÐ ä�‰Ø˜4ÐÙOô	
ô 	�‰”S˜Ó'Ð+=Ñ=¹zÔJØˆÜ˜mÓ,ò 	C‰DˆAˆqÜ�1‹v˜Š{Ø×"Ñ" :¨a°!©eÑ#4´s¸1³vÑ#=Õ>à×"Ñ"¤7¨:°a¸!±eÑ+<¸qÑ+@Ó#AÕBð		Cð
 ÐÜ	‡L�LØÑRõr*   c                 ó   — | €y | |   S r4   r)   )Úscalesrœ  s     r+   Úget_scale_valuer3  ý  s   € Ø€~ØØ�#‰;Ðr*   r.  c                 óx   — t        | j                  «       ||«      }|r|nd gt        |«      z  }t        | ||«      S r4   ©r0  r.  r‚  Ú_upsample_nearest©r¾   r÷  r.  Úosizer2  s        r+   Ú_upsample_nearest_vecr9    s@   € ô )¨¯©«°{ÀMÓR€Eá&‰¨T¨F´S¸³ZÑ,?ð ô ˜U E¨6Ó2Ð2r*   c                 ó|   — t        | j                  «       ||«      }|r|nd gt        |«      z  }t        | ||d¬«      S ©NT©Úexactr5  r7  s        r+   Ú_upsample_nearest_exact_vecr>    sB   € ô )¨¯©«°{ÀMÓR€Eá&‰¨T¨F´S¸³ZÑ,?ð ô ˜U E¨6¸Ô>Ð>r*   c                 óÐ  — g }t        |«      }|rdnd}t        |«      D ]Ä  }||   }| j                  | |z      }	||   �||   dkD  r|	|	||   z  z  n|	|z  }
t        j                  |t        j
                  | j                  ¬«      }||z   |
z  j                  t        j                  «      }t        |dz
  |z
  «      D ]  }|j                  d«      }Œ |j                  |«       ŒÆ |S )Nrž   r’   r   rµ  r!   rR   )r‚  rS   r  r>   r”  ré   r�  r7   r¶  rT   ru  )r¾   r÷  r2  r=  r›  Únum_spatial_dimsr£  rä  r8  Úisizerm   Úoutput_indicesÚinput_indicesrU   s                 r+   Ú!_compute_upsample_nearest_indicesrD  -  s  € ð €GÜ˜;Ó'ÐÙ‰S˜s€FäÐ#Ó$ò &ˆð ˜A‘ˆØ—‘Ð-Ð-°Ñ1Ñ2ˆð
 �a‰yÐ$¨°©°Qªð �U˜V A™YÑ&Ò'à˜‘ð 	ô Ÿ™ e´5·=±=ÈÏÉÔVˆØ(¨6Ñ1°UÑ:×>Ñ>¼u¿{¹{ÓKˆÜÐ'¨!Ñ+¨aÑ/Ó0ò 	8ˆAØ)×3Ñ3°BÓ7‰Mð	8à�‰�}Õ%ð7&ð8 €Nr*   )Úpreserve_memory_formatr  r2  c                 ó   — t        | ||g«      S r4   ©r6  ©r¾   r÷  r2  s      r+   Úupsample_nearest1drI  S  s   € ô ˜U K°&°Ó:Ð:r*   c                 ó"   — t        | ||gd¬«      S r;  rG  rH  s      r+   Úupsample_nearest_exact1drK  _  s   € ô ˜U K°&°ÀÔFÐFr*   Úscales_hÚscales_wc                 ó    — t        | |||g«      S r4   rG  ©r¾   r÷  rL  rM  s       r+   Úupsample_nearest2drP  m  s   € ô ˜U K°(¸HÐ1EÓFÐFr*   c                 ó$   — t        | |||gd¬«      S r;  rG  rO  s       r+   Ú_upsample_nearest_exact2drR  z  s   € ô ˜U K°(¸HÐ1EÈTÔRÐRr*   Úscales_dc                 ó"   — t        | ||||g«      S r4   rG  ©r¾   r÷  rS  rL  rM  s        r+   Úupsample_nearest3drV  ‰  s   € ô ˜U K°(¸HÀhÐ1OÓPÐPr*   c                 ó&   — t        | ||||gd¬«      S r;  rG  rU  s        r+   Ú_upsample_nearest_exact3drX  —  s!   € ô Øˆ{˜X x°Ð:À$ôð r*   r=  c                 óD  — t        | |||¬«      }d d g|z   }t        j                  | |«      }|j                  dk(  rdt	        j
                  | «      }| j                  d   }| j                  j                  dk(  r|dk  rt        j                  }|j                  |¬«      }|S )Nr<  rD  r!   ÚcudarX  )rD  r‚   Ú_unsafe_indexr}  rC   r   r  r�  r¥  r>   r\  r¯  )	r¾   r÷  r2  r=  Úspatial_indicesr›  r  rY  Ú
n_channelss	            r+   r6  r6  ©  sŸ   € ô 8Øˆ{˜F¨%ô€Oð �Tˆl˜_Ñ,€GÜ×Ñ  wÓ/€Fà‡{�{�aÒä×3Ñ3°EÓ:ˆð —[‘[ ‘^ˆ
Ø�<‰<×Ñ Ò&¨:¸ª>Ü!×3Ñ3ˆMà×"Ñ"°Ð"Ó?ˆØ€Mr*   c           	      óî   — |r|rd}n|rd}n|rd}nd}t        | «      |z  dk7  rt        dt        | «      › d|› �«      ‚t        dt        | «      |«      D �cg c]  }t        | |||z    «      ‘Œ c}S c c}w )Nrø  rD  r‡   r"   r   zlen(params)=z  is not divisible by group_size=)r‚  r,  rS   rè  )ÚparamsÚ
has_biasesÚhas_projectionsÚ
group_sizero  s        r+   Úgather_paramsrc  Ä  s�   € Ù‘oØ‰
Ù	Ø‰
Ù	Ø‰
àˆ
ä
ˆ6ƒ{�ZÑ 1Ò$ÜØœ3˜v›;˜-Ð'GÈ
À|ÐTó
ð 	
ô 49¸¼CÀ»KÈÓ3TöØ./Œˆf�Q˜˜Z™Ð(Õ)òð ùò s   ÁA2c                 ó~   — |r'| d|z     |d|z     }}| d|z  dz      |d|z  dz      }}n| |   ||   }}d\  }}||||fS )Nr"   r!   ©NNr)   )r_  Úhiddensro  ÚbidirectionalÚ
cur_paramsÚ
cur_hiddenÚbidir_paramsÚbidir_hiddens           r+   Úparams_hiddensrl  ×  sk   € ÙØ!'¨¨A©¡°¸¸A¹±�Jˆ
Ø%+¨A°©E°A©IÑ%6¸ÀÀAÁÈÁ	Ñ8J�l‰à!'¨¡¨G°A©J�Jˆ
Ø%/Ñ"ˆ�là�z <°Ð=Ð=r*   c                 ó    — ||k  rt        d|› d|› d�«      ‚|j                  | j                  d|||z
  «      «       | j                  dd|«      S )Núlast_batch_size (z) must be > batch_size (r?  r   )r,  ru  r/  )ri  Úlast_batch_sizeÚ
batch_sizerf  s       r+   Úupdate_hidden_for_packedrq  â  sc   € Ø˜*Ò$ÜØ Ð0Ð0HÈÈÐTUÐVó
ð 	
ð ‡N�N�:×$Ñ$ Q¨
°OÀjÑ4PÓQÔRØ×Ñ˜Q  :Ó.Ð.r*   c           	      ó”   — ||k(  r| S ||k\  rt        d|› d|› d�«      ‚t        j                  | |j                  d|||z
  «      f«      S )Nrn  z) must be < batch_size (r?  r   )r,  r>   Úconcatr/  )ri  ro  rp  Ú
inp_hiddens       r+   Ú update_hidden_for_packed_reverseru  ë  sn   € ð ˜*Ò$ØÐØ˜*Ò$ÜØ Ð0Ð0HÈÈÐTUÐVó
ð 	
ô �<‰<àØ×Ñ˜a °*¸Ñ2NÓOð	
óð r*   c           	      óX  — |d   }|d   }|r|d   nd }	|r|d   nd }
g }g }|r|d   n|d   }|j                  dd|«      }t        j                  | t        |«      «      }|r|d d d…   }|D ]V  } | j                  d   }||k(  rn|rt        ||||«      }nt        ||||«      } || |||	||
«      }|}|j                  |«       ŒX |r|j                  «        n!|j                  |«       |j                  «        t        j                  |d«      }|st        j                  |d«      n|}||fS )Nr   r!   r"   r‡   rR   )
r/  r>   r•  ru  r  ru  rq  ru  Úreverser0  )ÚinpÚhiddenr_  r`  Ú	hidden_fnÚbatch_sizesrw  Ú	ih_weightÚ	hh_weightÚih_biasÚhh_biasÚstep_outputrf  ro  ri  Ú	split_inpro  rÅ   Ú
hidden_outs                      r+   Úone_layer_rnn_datarƒ  ü  sR  € ð �q‘	€IØ�q‘	€IÙ%ˆf�QŠi¨4€GÙ%ˆf�QŠi¨4€Gà€KØ"$€Gá)0�k "’o°kÀ!±n€OØ—‘˜q ! _Ó5€JÜ—‘˜C¤ kÓ!2Ó3€IÙØ™d ˜d‘Oˆ	Øò 'ˆØ�I‰I�a‰Lˆà˜aÒØáÜ9Ø˜O¨Q°ó‰Jô 2Ø˜O¨Q°óˆJñ ˜s J°	¸7ÀIÈwÓWˆ
ØˆØ×Ñ˜:Õ&ð#'ñ& Ø×ÑÕà�‰�zÔ"Ø�‰Ôä
�)‰)�K Ó
#€CÙ.5”—‘˜7 AÔ&¸:€JØ�
ˆ?Ðr*   c                 ó   ‡ — ˆ fd„}|S )Nc                 óD   •—  ‰t        j                  |||«      | z   «      S r4   ©rÀ   Úlinear©ro  ri  r|  r~  r}  r  Únonlinearitys         €r+   rJ   zrnn_cell.<locals>.inner+  s    ø€ ÙœAŸH™H Z°¸GÓDÀqÑHÓIÐIr*   r)   ©r‰  rJ   s   ` r+   Úrnn_cellr‹  *  s   ø€ ôJð €Lr*   c                 ó   ‡ — ˆ fd„}|S )Nc                 ór   •— t        j                  | ||«      }  ‰t        j                  |||«      | z   «      S r4   r†  rˆ  s         €r+   rJ   zrnn_cell_data.<locals>.inner2  s2   ø€ Ü�H‰H�Q˜	 7Ó+ˆÙœAŸH™H Z°¸GÓDÀqÑHÓIÐIr*   r)   rŠ  s   ` r+   Úrnn_cell_datarŽ  1  s   ø€ ôJð €Lr*   c           	      óx  — |d   }|d   }|r|d   nd }|r|d   nd }	t        j                  | ||«      }
|r|
j                  d«      n|
}
|j                  d«      }g }|
D ]   } |||||||	«      }|j	                  |«       Œ" |r|j                  «        t        j                  |d«      }||j                  d«      fS )Nr   r!   r"   r‡   )	rÀ   r‡  ÚfliprT   ru  rw  r>   r0  rü  )rx  ry  r_  r`  rz  rw  r|  r}  r~  r  Úprecomputed_inputri  r€  ro  rÅ   s                  r+   Úone_layer_rnnr’  9  sÕ   € Ø�q‘	€IØ�q‘	€IÙ%ˆf�QŠi¨4€GÙ%ˆf�QŠi¨4€GäŸ™  i°Ó9ÐÙ5<Ð)×.Ñ.¨qÔ1ÐBSÐØ×!Ñ! !Ó$€JØ€KØò 'ˆÙ˜q *¨i¸À)ÈWÓUˆ
Ø×Ñ˜:Õ&ð'ñ Ø×ÑÔä
�)‰)�K Ó
#€Cà�
×"Ñ" 1Ó%Ð%Ð%r*   c                 ó�  — |d   }|d   }|r|d   }|d   }nFt        j                  |j                  «       «      }t        j                  |j                  «       «      }|d   j                  d«      }	|d   j                  d«      }
g }d}|	j                  d«      }d}d}d}d}| j	                  «       } |	j	                  «       }	|
j	                  «       }
t         j
                  j                  j                  j                  | |||||	|
|||||||||«      }|d   |d   |d   }}}||j                  d«      |j                  d«      ffS )Nr   r!   r"   r‡   F)
r>   r  r.  rT   r¯  r  r‚   Úmkldnn_rnn_layerrˆ  rü  )rx  ry  r_  r`  rw  Úw0Úw1Úw2Úw3ÚhxÚcxr{  ÚmodeÚhidden_sizeÚ
num_layersrg  r  rD  ÚoutputsrY   ÚhyÚcys                         r+   Úmkldnn_one_layer_lstmr¡  O  sS  € Ø	�‰€BØ	�‰€BÙØ�A‰YˆØ�A‰Y‰ä�[‰[˜Ÿ™›Ó#ˆÜ�[‰[˜Ÿ™›Ó#ˆà	�‰×	Ñ	˜QÓ	€BØ	�‰×	Ñ	˜QÓ	€Bà€KØ€DØ—'‘'˜!“*€KØ€Jð €MØ€Kà€Eð �.‰.Ó
€CØ	�‰‹€BØ	�‰‹€BÜ�i‰i�n‰n×-Ñ-×5Ñ5ØØ
Ø
Ø
Ø
Ø
Ø
ØØØØØØØØØó!€Gð$ ˜‘
˜G A™J¨°©
ˆ2€r€AØˆr�z‰z˜!‹}˜bŸj™j¨›mÐ,Ð,Ð,r*   c
                 óü  — |r| j                  dd«      n| } g }
t        |«      D ]½  }t        ||||«      \  }}}}|r
||dz
  k  r|nd} |	| |||«      \  }}|
j                  |«       |r! |	| |||d¬«      \  }}|
j                  |«       |r*t	        j
                  |g|j                  «       dz
  «      } n|} |dk7  sŒš|sŒ�||dz
  k  sŒ¦t	        j                  | |d¬«      } Œ¿ |r| j                  dd«      n| } | |
fS )Nr   r!   r’   T)rw  )rD  )Ú	transposerS   rl  ru  r>   r0  rN   rG  )r¾   ry  r_  r`  r�  rG  rD  rg  r  Úlayer_fnÚfinal_hiddensro  rh  ri  rj  rk  Úfwd_inpÚ
fwd_hiddenÚbwd_inpÚ
bwd_hiddens                       r+   Ú_rnn_helperrª  �  s"  € ñ &1ˆE�O‰O˜A˜qÔ!°e€EØ€Mä�:Óò >ˆÜ=KØ�F˜A˜}ó>
Ñ:ˆ
�J ¨lñ $¨
°Q¸±UÒ(:‘'ÀˆÙ& u¨j¸*ÀjÓQÑˆ�Ø×Ñ˜ZÔ(áÙ"*Ø�| \°:Àtô#ÑˆG�Zð × Ñ  Ô,áÜ—I‘I˜w¨Ð0°'·+±+³-À!Ñ2CÓD‰EàˆEà�a‹<šE a¨*°q©.Ó&8Ü—M‘M %¨¸Ô=‰Eð)>ñ, &1ˆE�O‰O˜A˜qÔ!°e€EØ�-ÐÐr*   c	                 óè   — |j                  d«      }	t        ||d«      }t        | |	|||||||t        t        t        t        j                  «      ¬«      «
      \  }
}|
t        j                  |d«      fS ©Nr   F©rz  )	Úunbindrc  rª  r   r’  r‹  r>   r©   Ústack©r¾   r™  r_  r`  r�  rG  rD  rg  r  ry  rÅ   r¥  s               r+   Úrnn_tanh_inputr±  ª  ót   € ð �Y‰Y�q‹\€FÜ˜6 :¨uÓ5€FÜ$ØØØØØØØØØÜ”¬´%·*±*Ó)=Ô>óÑ€Cˆð ”—‘˜M¨1Ó-Ð-Ð-r*   c	                 óè   — |j                  d«      }	t        ||d«      }t        | |	|||||||t        t        t        t        j                  «      ¬«      «
      \  }
}|
t        j                  |d«      fS r¬  )	r®  rc  rª  r   r’  r‹  r>   rº  r¯  r°  s               r+   Úrnn_relu_inputr´  É  r²  r*   c	                 óê   — |j                  d«      }	t        ||d«      }t        | |	||||||dt        t        |t        t        j                  «      ¬«      «
      \  }
}|
t        j                  |d«      fS ©Nr   F©r{  rz  )	r®  rc  rª  r   rƒ  rŽ  r>   rº  r¯  ©Údatar{  r™  r_  r`  r�  rG  rD  rg  ry  rÅ   r¥  s               r+   Úrnn_relu_datarº  è  ó{   € ð �Y‰Y�q‹\€FÜ˜6 :¨uÓ5€FÜ$ØØØØØØØØØÜÜØ#Ü#¤E§J¡JÓ/ô	
óÑ€Cˆð  ”—‘˜M¨1Ó-Ð-Ð-r*   c	                 óê   — |j                  d«      }	t        ||d«      }t        | |	||||||dt        t        |t        t        j                  «      ¬«      «
      \  }
}|
t        j                  |d«      fS r¶  )	r®  rc  rª  r   rƒ  rŽ  r>   r©   r¯  r¸  s               r+   Úrnn_tanh_datar½    r»  r*   c                 ól  — t        j                  |||«      | z   }|j                  d|«      }|d   j                  «       }	|d   j                  «       }
|d   j	                  «       }|d   j                  «       }|
|z  |	|z  z   }||j	                  «       z  }|€|nt        j                  ||d «      }||fS )NrD  r   r!   r"   r‡   ©rÀ   r‡  ÚchunkrÂ   r©   )rx  r™  rš  r}  r  Ú	hr_weightÚ	chunk_dimÚgatesÚchunked_gatesÚin_gateÚforget_gateÚ	cell_gateÚout_gater   rŸ  s                  r+   Ú	lstm_cellrÉ  .  s»   € Ü�H‰H�R˜ GÓ,¨sÑ2€EØ—K‘K  9Ó-€MØ˜AÑ×&Ñ&Ó(€GØ Ñ"×*Ñ*Ó,€KØ˜aÑ ×%Ñ%Ó'€IØ˜QÑ×'Ñ'Ó)€HØ	�rÑ	˜W yÑ0Ñ	1€BØ	�B—G‘G“IÑ	€BØÐ ‰¤a§h¡h¨r°9¸dÓ&C€Bàˆrˆ6€Mr*   c           
      ó(  — |d   }|d   }|r|d   nd }|r|d   nd }t        |«      dk(  r|d   nt        |«      dk(  r|d   nd }	|d   j                  d«      }
|d   j                  d«      }t        j                  | ||«      }|r|j	                  d«      n|}g }|D ](  } t        | |
||||	d¬«      \  }
}|j                  |
«       Œ* |r|j                  «        t        j                  |d«      }||
j                  d«      |j                  d«      ffS )Nr   r!   r"   r‡   rø  rD  ©rÂ  )r‚  rT   rÀ   r‡  r�  rÉ  ru  rw  r>   r0  rü  )rx  ry  r_  r`  rw  r|  r}  r~  r  rÁ  r™  rš  r‘  r€  rÅ   s                  r+   Úone_layer_lstmrÌ  <  s*  € Ø�q‘	€IØ�q‘	€IÙ%ˆf�QŠi¨4€GÙ%ˆf�QŠi¨4€Gä˜“[ AÒ%ˆˆqŠ	¼¸F»ÀqÒ8H¨6°!ª9Èdð ð 
�‰×	Ñ	˜QÓ	€BØ	�‰×	Ñ	˜QÓ	€BäŸ™  i°Ó9ÐÙ5<Ð)×.Ñ.¨qÔ1ÐBSÐØ€KØ ò ˆÜ˜3  B¨	°7¸IÐQRÔS‰ˆˆBØ×Ñ˜2Õðñ Ø×ÑÔä
�)‰)�K Ó
#€Cà�—‘˜A“ §
¡
¨1£Ð.Ð.Ð.r*   c           
      ó¦  — |d   }|d   }|r|d   nd }|r|d   nd }	t        |«      dk(  r|d   nt        |«      dk(  r|d   nd }
g }g }|r|d   n|d   }t        j                  | t        |«      «      }|r|d d d…   }|d   }|d   }|j	                  dd|«      |j	                  dd|«      }}|D �]  } | j
                  d   }t        j                  | ||«      } ||k  ra|j                  |j	                  d|||z
  «      |j	                  d|||z
  «      f«       |j	                  dd|«      |j	                  dd|«      }}||kD  rXt        j                  ||j	                  d|||z
  «      fd«      }t        j                  ||j	                  d|||z
  «      fd«      }t        | ||||	|
d¬«      \  }}|}|j                  |«       �Œ |r|j                  «        ||f}nZ|j                  ||f«       |j                  «        t        |Ž \  }}t        j                  |d«      t        j                  |d«      f}t        j                  |d«      }||fS )	Nr   r!   r"   r‡   rø  rD  rR   rË  )r‚  r>   r•  ru  r/  r  rÀ   r‡  ru  rs  rÉ  rw  rú  r0  )rx  ry  r_  r`  r{  rw  r|  r}  r~  r  rÁ  r€  rf  ro  r�  Úorig_hxÚorig_cxr™  rš  ro  r‚  Úhidden0Úhidden1rÅ   s                           r+   Úone_layer_lstm_datarÒ  W  sy  € Ø�q‘	€IØ�q‘	€IÙ%ˆf�QŠi¨4€GÙ%ˆf�QŠi¨4€Gä˜“[ AÒ%ˆˆqŠ	¼¸F»ÀqÒ8H¨6°!ª9Èdð ð €KØ€Gá)0�k "’o°kÀ!±n€OÜ—‘˜C¤ kÓ!2Ó3€IÙØ™d ˜d‘Oˆ	à�Q‰i€GØ�Q‰i€Gà�‰�q˜!˜_Ó-Ø�‰�q˜!˜_Ó-ð 	€Bð
 ó ˆØ�I‰I�a‰LˆÜ�h‰h�s˜I wÓ/ˆð ˆÒØ�N‰Nà—I‘I˜a  O°aÑ$7Ó8Ø—I‘I˜a  O°aÑ$7Ó8ðôð —Y‘Y˜q ! QÓ'¨¯©°1°a¸Ó);�ˆBð ˆÒÜ—‘Ø�W—^‘^ A ¸¸OÑ8KÓLÐMÈqóˆBô —‘Ø�W—^‘^ A ¸¸OÑ8KÓLÐMÈqóˆBô ˜3  B¨	°7¸IÐQRÔS‰ˆˆBØˆØ×Ñ˜2Öð3ñ6 Ø×ÑÔØ˜"�X‰
à�‰˜˜B�xÔ Ø�‰ÔÜ ˜=Ñˆ�Ü—Y‘Y˜w¨Ó*¬E¯I©I°g¸qÓ,AÐAˆ
ä
�)‰)�K Ó
#€CØ�
ˆ?Ðr*   c                 ó4   — d„ } || ||«      rt         S t        S )a*  Check whether we could use decompose lstm with mkldnn_rnn_layer.
    All the below conditions need to be met:
        * ``torch._C._get_mkldnn_enabled()`` returns ``True``.
        * All the input args are on CPU.
        * The dtypes of args are either torch.float or torch.bfloat16.
        * Inference.
        * ``has_projections`` returns ``False``.

    Args:
        * input: the input sequence to LSTM
        * hx: a tuple of the input hidden state and cell state ``(h_0, c_0)`` to LSTM
        * params: the weight and bias tensors of LSTM
    c                 óN  — t         j                  j                  «       sy| gt        |«      z   t        t	        j
                  |«      «      z   }|D �ch c]  }|j                  ’Œ }}t        |«      dk7  ry|j                  «       }|t        j                  d«      k7  ry|D �ch c]  }|j                  ’Œ }}|D ]&  }|t         j                  t         j                  fvsŒ& y | j                  ry|d   j                  d«      |d   j                  d«      k7  }	|	ryyc c}w c c}w )NFr!   r¢  r   r"   T)r>   r?  Ú_get_mkldnn_enabledru  r	   Úfrom_iterabler�  r‚  Úpopræ   r  Úbfloat16Úrequires_gradr.  )
r¾   r™  r_  rp  ÚtÚdevicesr�  Údtypesræ   ra  s
             r+   Ú
use_mkldnnz2select_one_layer_lstm_function.<locals>.use_mkldnn¦  s   € Ü�x‰x×+Ñ+Ô-Øà�'œD ›HÑ$¤t¬E×,?Ñ,?ÀÓ,GÓ'HÑHˆØ%,Ö- �1—8“8Ð-ˆÐ-Üˆw‹<˜1ÒØà—‘“ˆØ”U—\‘\ %Ó(Ò(Øà#*Ö+˜a�!—'“'Ð+ˆÐ+Øò 	ˆEØœUŸ[™[¬%¯.©.Ð9Ò9Ùð	ð ×ÒØà˜Q™%Ÿ*™* Q›-¨2¨a©5¯:©:°a«=Ñ8ˆÙØàùò) .ùò ,s   ÁDÂ#D")r¡  rÌ  )r¾   r™  r_  rÝ  s       r+   Úselect_one_layer_lstm_functionrÞ  —  s!   € òñ: �%˜˜VÔ$Ü$Ð$äÐr*   c	                 óº  — t        |«      dk7  rt        dt        |«      › �«      ‚t        |||d   j                  d«      |d   j                  d«      k7  «      }t	        t        |d   |d   «      «      }	t        | ||«      }
t        | |	||||||||
«
      \  }}t	        t        |Ž «      }|t        j                  |d   d«      t        j                  |d   d«      fS )Nr"   ú$lstm expects two hidden states, got r   r!   )
r‚  r,  rc  r.  ru  rú  rÞ  rª  r>   r¯  )r¾   r™  r_  r`  r�  rG  rD  rg  r  ry  r¤  rÅ   r¥  s                r+   Ú	lstm_implrá  É  sä   € ô ˆ2ƒw�!‚|ÜÐCÄCÈÃGÀ9ÐMÓNÐNÜ˜6 :¨r°!©u¯z©z¸!«}ÀÀ1ÁÇ
Á
È1ÃÑ/MÓN€FÜ”#�b˜‘e˜R ™UÓ#Ó$€FÜ-¨e°R¸Ó@€HÜ$ØØØØØØØØØØóÑ€Cˆô œ˜mÐ,Ó-€MØ”—‘˜M¨!Ñ,¨aÓ0´%·+±+¸mÈAÑ>NÐPQÓ2RÐRÐRr*   c	                 ó¾  — t        |«      dk7  rt        dt        |«      › �«      ‚t        |||d   j                  d«      |d   j                  d«      k7  «      }t	        t        |d   |d   «      «      }	t        | |	||||||dt        t        |¬«      «
      \  }
}t	        t        |Ž «      }|
t        j                  |d   d«      t        j                  |d   d«      fS )Nr"   rà  r   r!   F)r{  )r‚  r,  rc  r.  ru  rú  rª  r   rÒ  r>   r¯  r¸  s               r+   Úlstm_data_implrã  ì  sÞ   € ô ˆ2ƒw�!‚|ÜÐCÄCÈÃGÀ9ÐMÓNÐNÜ˜6 :¨r°!©u¯z©z¸!«}ÀÀ1ÁÇ
Á
È1ÃÑ/MÓN€FÜ”#�b˜‘e˜R ™UÓ#Ó$€FÜ$ØØØØØØØØØÜÔ#°Ô=óÑ€Cˆô œ˜mÐ,Ó-€MØ”—‘˜M¨!Ñ,¨aÓ0´%·+±+¸mÈAÑ>NÐPQÓ2RÐRÐRr*   c                 ó&  — | j                  dd«      }t        j                  |||«      j                  dd«      }|d   |d   z   j                  «       }|d   |d   z   j                  «       }	|d   |d   |z  z   j	                  «       }
||
z
  |	z  |
z   S )Nr‡   r!   r"   r   )rÀ  rÀ   r‡  rÂ   r©   ©rx  ri  r|  r~  r}  r  Úchunked_igatesÚchunked_hgatesÚ
reset_gateÚ
input_gateÚnew_gates              r+   Úgru_cellrë    s¡   € Ø—Y‘Y˜q !“_€NÜ—X‘X˜j¨)°WÓ=×CÑCÀAÀqÓI€NØ  Ñ# n°QÑ&7Ñ7×@Ñ@ÓB€JØ  Ñ# n°QÑ&7Ñ7×@Ñ@ÓB€JØ˜qÑ! ^°AÑ%6¸Ñ%CÑD×JÑJÓL€HØ˜Ñ! ZÑ/°(Ñ:Ð:r*   c                 óP  — t        j                  | ||«      j                  dd«      }t        j                  |||«      j                  dd«      }|d   |d   z   j                  «       }|d   |d   z   j                  «       }	|d   |d   |z  z   j	                  «       }
||
z
  |	z  |
z   S )Nr‡   r!   r   r"   r¿  rå  s              r+   Úgru_cell_datarí    s±   € Ü—X‘X˜c 9¨gÓ6×<Ñ<¸QÀÓB€NÜ—X‘X˜j¨)°WÓ=×CÑCÀAÀqÓI€NØ  Ñ# n°QÑ&7Ñ7×@Ñ@ÓB€JØ  Ñ# n°QÑ&7Ñ7×@Ñ@ÓB€JØ˜qÑ! ^°AÑ%6¸Ñ%CÑD×JÑJÓL€HØ˜Ñ! ZÑ/°(Ñ:Ð:r*   c	                 óÀ   — t        ||d«      }t        | |j                  d«      ||||||dt        t        |t
        ¬«      «
      \  }	}
|	t        j                  |
d«      fS )NFr   r·  )rc  rª  r®  r   rƒ  rí  r>   r¯  )r¹  r{  r™  r_  r`  r�  rG  rD  rg  rÅ   r¥  s              r+   Úgru_impl_datarï     si   € ô ˜6 :¨uÓ5€FÜ$ØØ
�	‰	�!‹ØØØØØØØÜÔ"°Ä}ÔUóÑ€Cˆð ”—‘˜M¨1Ó-Ð-Ð-r*   c	                 ó¾   — t        ||d«      }t        | |j                  d«      |||||||t        t        t
        ¬«      «
      \  }	}
|	t        j                  |
d«      fS )NFr   r­  )rc  rª  r®  r   r’  rë  r>   r¯  )r¾   r™  r_  r`  r�  rG  rD  rg  r  rÅ   r¥  s              r+   Úgru_implrñ  >  sf   € ô ˜6 :¨uÓ5€FÜ$ØØ
�	‰	�!‹ØØØØØØØÜ”¬Ô2óÑ€Cˆð ”—‘˜M¨1Ó-Ð-Ð-r*   c                 óÂ   — t        | j                  «       ||«      }t        |d«      }t        |d«      }t        j                  j
                  j                  | ||||«      S ©Nr   r!   )r0  r.  r3  r>   r  r‚   Ú_upsample_bilinear2d_aa©r¾   r÷  Úalign_cornersr.  r8  Úscale_hÚscale_ws          r+   Úupsample_bilinear2d_aa_vecrù  \  sV   € ô )¨¯©«°{ÀMÓR€EÜ˜m¨QÓ/€GÜ˜m¨QÓ/€GÜ�9‰9�>‰>×1Ñ1Øˆu�m W¨góð r*   c                 óÂ   — t        | j                  «       ||«      }t        |d«      }t        |d«      }t        j                  j
                  j                  | ||||«      S ró  )r0  r.  r3  r>   r  r‚   Ú_upsample_bicubic2d_aarõ  s          r+   Úupsample_bicubic2d_aa_vecrü  h  óV   € ô )¨¯©«°{ÀMÓR€EÜ˜m¨QÓ/€GÜ˜m¨QÓ/€GÜ�9‰9�>‰>×0Ñ0Øˆu�m W¨góð r*   c                 óÂ   — t        | j                  «       ||«      }t        |d«      }t        |d«      }t        j                  j
                  j                  | ||||«      S ró  )r0  r.  r3  r>   r  r‚   Ú_upsample_lanczos2d_aarõ  s          r+   Úupsample_lanczos2d_aa_vecr   t  rý  r*   c                 óz   — t        | j                  «       ||«      }|r|nd gt        |«      z  }t        | |||«      S r4   )r0  r.  r‚  Ú_upsample_linear)r¾   r÷  rö  r.  r8  r2  s         r+   Ú_upsample_linear_vecr  €  s=   € ô )¨¯©«°{ÀMÓR€EÙ+‰]°$°¼#¸e»*Ñ1D€FÜ˜E 5¨-¸Ó@Ð@r*   rö  c                 ó    — t        | |||g«      S r4   ©r  )r¾   r÷  rö  rM  s       r+   Úupsample_linear1dr  Ž  s   € ô ˜E ;°À¸zÓJÐJr*   c                 ó"   — t        | ||||g«      S r4   r  )r¾   r÷  rö  rL  rM  s        r+   Úupsample_bilinear2dr  ™  s   € ô ˜E ;°ÀÈ(Ð?SÓTÐTr*   c                 ó$   — t        | |||||g«      S r4   r  )r¾   r÷  rö  rS  rL  rM  s         r+   Úupsample_trilinear3dr
  ¨  s!   € ô Øˆ{˜M¨H°hÀÐ+Ióð r*   c                 óL   — |r|dkD  r| dz
  |dz
  z  S dS |�
|dkD  rd|z  S | |z  S )Nr!   rf   r   r)   )r   r¡  rö  rm   s       r+   Ú_compute_scaler  ¹  sB   € ÙØ5=À²\�˜#‘ (¨S¡.Ñ1ÐHÀqÐHà#Ð/°E¸A²Iˆs�U‰{ÐUÀ7ÈXÑCUÐUr*   c                 ó&   — |r| |z  S | |dz   z  dz
  S ©Nrž   r)   )rm   Ú	dst_indexrö  s      r+   Ú_compute_source_indexr  À  s$   € ÙØ�yÑ Ð à˜	 C™Ñ(¨3Ñ.Ð.r*   ÚweightsÚweights_precisionc                 ó¾   — t        d„ t        | |«      D «       «      d|dz
  z  z   }||z	  }t        j                  |dd«      j	                  t        j
                  «      S )Nc              3   ó    K  — | ]F  \  }}|j                  t        j                  «      |j                  t        j                  «      z  –— ŒH y ­wr4   )r7   r>   r9  )rÎ  r”  rñ  s      r+   rÏ  z%_sum_tensors_uint8.<locals>.<genexpr>Ê  s8   è ø€ ò Ù26°!°Qˆ�‰ŒU�[‰[Ó˜AŸD™D¤§¡Ó-Õ-ñùs   ‚AAr!   r   éÿ   )Ú_sum_tensorsrú  r>   rŽ   r7   rE  )r�  r  r  r¬  s       r+   Ú_sum_tensors_uint8r  Ç  sd   € ô ñ Ü:=¸cÀ7Ó:Kôó à	
Ð  1Ñ$Ñ	%ñ'€Fð Ð(Ñ(€FÜ�;‰;�v˜q #Ó&×)Ñ)¬%¯+©+Ó6Ð6r*   c                 óÚ   — t        j                  | «      j                  «       }d}t        j                  ||j                  ¬«      }d|d|dz   z  z  z   }|dk\  }||j                  «       z
  S )Né   r�  rž   r!   i €  )r>   r¯  rŒ   r”  r�  ró   )r  Ú
max_weightÚmax_weight_precisionÚ
precisionsÚvaluesr�  s         r+   Ú_compute_weight_precisionr  Ñ  si   € Ü—‘˜WÓ%×)Ñ)Ó+€JØÐÜ—‘Ð2¸:×;LÑ;LÔM€JØ�:  z°A¡~Ñ!6Ñ7Ñ7€FØ�gÑ€DØ $§(¡(£*Ñ,Ð,r*   c                 óL  ‡ ‡‡— ‰ j                   d   }‰ j                   dd  }t        |«      }t        j                  ‰ t        j                  j
                  ¬«      \  }Šˆˆˆ fd„}t        t        |||«      «      D �	�
��cg c]  \  }	\  }
}} ||
|||dz
  |	z
  «      ‘Œ }}}
}	}t        t        |Ž «      \  }}}g }t        ddgg|z  Ž D ]c  }d d gt        |«      D �cg c]  }||   dk(  r||   n||   ‘Œ c}z   }t        j                  ‰ |«      }t        |‰«      }|j                  |«       Œe t        t        |«      «      D ]p  }	||	   ||	   z
  j!                  dd«      j#                  ‰«      }t        |d d d…   |dd d…   «      D ��cg c]!  \  }}|t%        j&                  ||z
  |«      z   ‘Œ# }}}Œr t        |«      dk7  rt)        dt        |«      › �«      ‚|d   }t        j*                  ‰ «      }‰ j,                  j.                  d	k(  r|d
k  rt$        j0                  }t3        |t$        j4                  «      s!t)        dt/        |«      j6                  › �«      ‚|j9                  |¬«      }‰ j;                  «       s|j=                  «       }|S c c}}}
}	w c c}w c c}}w )Nr!   r"   rT  c                 ó|  •— t        | |‰	|«      }t        j                  |‰j                  ¬«      j	                  ‰
¬«      }t        ||‰	«      j                  d¬«      } |j                  |j                  d   gdg|z  ¢­Ž }|j	                  t        j                  «      }|dz   j                  | dz
  ¬«      }|||fS )Nr�  rå   r’   rˆ   r   r!   r‹   )
r  r>   r”  r�  r7   r  rŽ   r&  r  r¶  )Úinp_sizer¡  r2  ÚnsqueezeÚscale_factorro  Úx_f32r8   Úxp1rö  ræ   r¾   s            €€€r+   Ú
get_valuesz$_upsample_linear.<locals>.get_valuesë  s®   ø€ ä% h°¸-ÈÓPˆô �L‰L˜¨%¯,©,Ô7×:Ñ:ÀÐ:ÓGˆä% l°A°}ÓE×KÑKÐPSÐKÓTˆØ�—‘˜eŸk™k¨!™nÐ@°¨s°hÑ/?Ò@ˆØ�H‰H”U—[‘[Ó!ˆØ�1‰u�m‰m ¨1¡ˆmÓ-ˆØ�a˜ˆ}Ðr*   r   r’   rf   z+Expected vs to have exactly 1 element, got rZ  é   z$Expected result to be a Tensor, got rX  )r  r‚  rC   rD   rV  ÚINT_TO_FLOATrÞ  rú  ru  r
   rS   r‚   r[  r   ru  ÚreversedrŽ   r7   r>   rØ   r,  r   r�  r¥  r\  r6   r   r#   r¯  rK  Úround)r¾   r÷  rö  r2  r]  Ú	inp_sizesÚn_dimsrU   r&  ro  r!  r¡  r  Úxs_f32ÚxsÚxp1sÚvsrù  Úkrœ  ÚvÚxscaleÚv1Úv2r  rY  ræ   s   ` `                       @r+   r  r  Ú  s¬  ú€ ð —‘˜Q‘€JØ—‘˜A˜B�€IÜ�‹^€Fä×'Ñ'ØÜ!×AÑA×NÑNô�H€A€uö
ô 09Ü�	˜;¨Ó/ó0
÷ñ á+ˆAÑ+�˜( Fñ 	�8˜X v¨v¸©z¸A©~Õ>ð€Fó ô œC ˜LÓ)Ñ€FˆB�à	€BÜ˜˜1�v�h Ñ'Ð(ò ˆØ�TˆlÄuÈVÃ}ÖUÀ! q¨¡t¨q¢y˜b še°d¸1±gÑ=ÒUÑUˆÜ×Ñ˜u cÓ*ˆÜ# A uÓ-ˆØ
�	‰	�!�ð	ô ”e˜F“mÓ$ò 
ˆØ˜‘)˜b ™eÑ#×*Ñ*¨3°Ó4×7Ñ7¸Ó>ˆô ˜b¡ 1 ™g r¨!¨$¨Q¨$¡xÓ0÷
ñ ��Bð ”—‘˜2 ™7 FÓ+Ó+ð
ˆò 
ð
ô ˆ2ƒw�!‚|ÜÐJÌ3ÈrË7È)ÐTÓUÐUØ�‰U€Fô ×/Ñ/°Ó6€Mð ‡|�|×Ñ˜FÒ" z°B¢Ü×/Ñ/ˆä�fœeŸl™lÔ+ÜØ2´4¸³<×3HÑ3HÐ2IÐJó
ð 	
ð ×Ñ¨]ÐÓ;€Fà×"Ñ"Ô$Ø—‘“ˆà€MùõYùò Vùó
s   ÂJ
ÃJÆ&J rù  rú  c                 ó4   — | j                   |j                   k(  S r4   ré  )rù  rú  s     r+   Úis_same_sizer7  (  s   € à�7‰7�a—g‘gÑÐr*   c                 ó.   — t         j                  | |«      S r4   )r‚   r˜  )r8   r  rE   s      r+   Ú_reshape_aliasr9  -  s   € ô �9‰9�Q˜ÓÐr*   c                 ó.   — t         j                  | |«      S r4   )r‚   rŸ  )r8   r›  s     r+   r[  r[  3  s   € ä�:‰:�a˜Ó!Ð!r*   c                 ó2   — t         j                  | |||«      S r4   )r‚   rý  )r8   r›  r{   r%  s       r+   r'  r'  8  s   € ä�>‰>˜!˜W e¨ZÓ8Ð8r*   c                 ó’  — |D ]F  }|€Œt        j                  |j                  t         j                  t         j                  fv d„ «       ŒH t        j                  |j                  t         j
                  k(  d„ «       ddlm}  || j                  «       dk(  «      r<t         j                  j                  | |«      }| j                  |j                  |«      S t        t        |«      «      D ]2  }||   }|€Œ|j                  d| j!                  |«      dz
  ¬«      ||<   Œ4 t"        j%                  | |«      j'                  | |«      S )Nc                   ó   — y©Nz3tensors used as indices must be long or int tensorsr)   r)   r*   r+   r€   z&_unsafe_masked_index.<locals>.<lambda>C  rÆ  r*   c                   ó   — y©Nz*tensors used as masks must be bool tensorsr)   r)   r*   r+   r€   z&_unsafe_masked_index.<locals>.<lambda>H  rÆ  r*   r   rR  r!   r†  )r>   r�   ræ   rh  r‹  r–  rs  rS  rÜ   Ú_meta_registrationsÚmeta_index_Tensorrê   r  rS   r‚  rŽ   r.  r‚   r[  ri  )r8   r�  r›  ÚfillrŸ  rS  Úmeta_resultro  s           r+   r™  r™  =  s  € àò ˆØÑÜ�L‰LØ—‘¤§
¡
¬E¯I©IÐ6Ð6ÙMõðô 
‡L�LØ�
‰
”e—j‘jÑ Ù<ôõ
 Eá�a—g‘g“i 1‘nÔ%Ü×/Ñ/×AÑAÀ!ÀWÓMˆØ�z‰z˜+×+Ñ+¨TÓ2Ð2ä”3�w“<Ó ò ?ˆØ˜‘
ˆØÑØŸ™¨°·±°q³	¸A±˜Ó>ˆG�AŠJð?ô
 ×Ñ˜a Ó)×5Ñ5°t°e¸TÓBÐBr*   c                 óL  — |D ]F  }|€Œt        j                  |j                  t         j                  t         j                  fv d„ «       ŒH t        j                  |j                  t         j
                  k(  d„ «       | j                  «       dk(  r| j                  «       S t        t        |«      «      D ]B  }||   }|€Œ|j                  | j                  |«       | j                  |«      dz
  ¬«      ||<   ŒD |j                  | d«      }t        j                  | ||d¬«      S )Nc                   ó   — yr>  r)   r)   r*   r+   r€   z5_unsafe_masked_index_put_accumulate.<locals>.<lambda>_  rÆ  r*   c                   ó   — yr@  r)   r)   r*   r+   r€   z5_unsafe_masked_index_put_accumulate.<locals>.<lambda>d  rÆ  r*   r   r!   r†  Tr$  )r>   r�   ræ   rh  r‹  r–  rÜ   r“  rS   r‚  rŽ   r.  ri  r‚   r'  )r8   r�  r›  r  rŸ  ro  Úmasked_values          r+   Ú#_unsafe_masked_index_put_accumulaterI  Y  s   € àò ˆØÑÜ�L‰LØ—‘¤§
¡
¬E¯I©IÐ6Ð6ÙMõðô 
‡L�LØ�
‰
”e—j‘jÑ Ù<ôð
 	‡w�wƒy�A‚~Ø�w‰w‹yÐä”3�w“<Ó ò HˆØ˜‘
ˆØÑØŸ™¨!¯&©&°«)¨¸¿¹À»ÀQ¹˜ÓGˆG�AŠJðHð
 ×%Ñ% t e¨QÓ/€LÜ×!Ñ! ! W¨lÀtÐ!ÓLÐLr*   c                 óÖ  — | j                  «       }d}|dk  rd}|�6|dkD  r*dg|z  }|j                  d   ||<   |j                  |«      }n|}| |z  } t        j                  ||k7  |d«      }	|	j                  |«      }
t        j                  | ||
«      j                  |«       }t        j                  ||k7  |d«      }|t        j                  j                  k(  r|dkD  r| j                  dd«      }||fS |�lj                  | j                  «      }t        j                  |||
«      j                  |«      }t        j                  ||k7  |d«      }|j                  «       }n"||k7  j                  «       j                  | «      }|t        j                  j                  k(  r|j                  «       }||fS |t        j                   j                  k(  r|j                  «       |z  }||fS )Nr!   r"   r   r)   r’   )rN   r  r˜  r>   rh   rT   Úgatherrü  r    r&   r{   rê   r’  ró   r7   r(   r'   )rz   rü   rË   rð   r"  r,  r'  r  Úwr(  Úsafe_target_r  r#  Úwsums                 r+   Ú_nll_loss_forwardrO  s  sÐ  € ð �X‰X‹Z€FØ€KØ�‚zØˆàÐØ�AŠ:àðàñˆEð "(§¡¨a¡ˆE�+ÑØ—‘˜EÓ"‰AàˆAØ�a‰xˆÜ—+‘+˜f¨Ñ4°f¸aÓ@€KØ×(Ñ(¨Ó5€Lô �l‰l˜4 ¨lÓ;×CÑCÀKÓPÐP€Fä�[‰[˜ <Ñ/°¸Ó;€Fà”I—N‘N×(Ñ(Ò(¨V°aªZØ—}‘} R¨Ó-ˆØ�|Ð#Ð#àÐà�H‰H�T—Z‘ZÓ ˆÜ�|‰|˜A˜{¨LÓ9×AÑAÀ+ÓNˆÜ�{‰{˜6 \Ñ1°4¸Ó;ˆØ—x‘x“z‰à ,Ñ.×3Ñ3Ó5×8Ñ8¸Ó>ˆà”I—M‘M×'Ñ'Ò'Ø—‘“ˆð �<ÐÐð 
”i—n‘n×*Ñ*Ò	*Ø—‘“ Ñ,ˆà�<ÐÐr*   c                 óp  ‡ ‡— ‰ j                  «       dkD  r‰ j                  «       dk  st        d‰ j                  «       › d�«      ‚‰j                  «       dkD  rt        d‰j                  «       › d�«      ‚‰ j                  «       dk(  xr ‰j                  «       dk(  }|s7t        j                  ‰ j                  d   ‰j                  d   k(  ˆ ˆfd„«       ‰ j                  d   }|�A|j                  «       dk(  r|j                  «       |k(  st        d	|› d
|j                  › �«      ‚t        ‰ ‰|||«      S )Nr   r"   r:  r;  r!   r<  c                  ó>   •— d‰ j                   › d‰j                   › d�S )Nr=  r>  r?  ré  )rz   rü   s   €€r+   r€   z"nll_loss_forward.<locals>.<lambda>½  s    ø€ Ð0°·±°¸JÀvÇ|Á|ÀnÐTUÐV€ r*   rR   z/weight tensor should be defined either for all z7 classes or no classes but got weight tensor of shape: )rN   r,  r>   r�   r  rÜ   rO  )rz   rü   rË   rð   r"  rA  Ú	n_classess   ``     r+   Únll_loss_forwardrS  ©  s#  ù€ ð �H‰H‹J˜ŠN˜tŸx™x›z¨QšÜÐDÀTÇXÁXÃZÀLÐPQÐRÓSÐSØ‡z�zƒ|�aÒÜØOÐPV×PZÑPZÓP\È~Ð]^Ð_ó
ð 	
ð —8‘8“: ‘?Ò8 v§z¡z£|°qÑ'8€LÙÜ�‰Ø�J‰J�q‰M˜VŸ\™\¨!™_Ñ,ÜVô	
ð
 —
‘
˜2‘€IàÐ 6§:¡:£<°1Ò#4¸¿¹»È9Ò9TÜØ=¸i¸[ð I/Ø/5¯|©|¨nð>ó
ð 	
ô
 ˜T 6¨6°9¸lÓKÐKr*   c                 ó    — t        | ||||«      S r4   )rO  )rz   rü   rË   rð   r"  s        r+   Únll_loss2d_forwardrU  Ë  s   € ô ˜T 6¨6°9¸lÓKÐKr*   ÚAc                 ó0   — |dz   | z  |dz   z
  | z  | z  dz   S )Nr"   r‡   r!   r)   ©r8   rV  s     r+   Ú_upsample_cubic_convolution1rY  Ù  s(   € Ø�‰U�a‰K˜1˜q™5Ñ! QÑ&¨Ñ*¨QÑ.Ð.r*   c                 ó<   — || z  d|z  z
  | z  d|z  z   | z  d|z  z
  S )Nrø  é   rD  r)   rX  s     r+   Ú_upsample_cubic_convolution2r\  Ý  s0   € Ø�‰U�Q˜‘U‰]˜aÑ ! a¡%Ñ'¨1Ñ,¨q°1©uÑ4Ð4r*   rÚ  c                 óÒ  — d}| j                   t        j                   d«      k(  r�t        j                  | d| z
  gd¬«      }t        j                  | dz   d| z
  gd¬«      }t        ||«      }t	        ||«      }t        j
                  |d¬«      \  }}t        j
                  |d¬«      \  }}	|||	|fS t        | dz   |«      t	        | |«      t	        d| z
  |«      t        d| z
  |«      fS )Ng      è¿r¢  rf   r   r   rä   )r�  r>   r¯  r\  rY  r®  )
rÚ  rV  Útt1Útt2Úw03Úw12r•  r˜  r–  r—  s
             r+   Ú _upsample_get_cubic_coefficientsrb  á  sß   € Ø€Aà‡x�x”5—<‘< Ó&Ò&Ü�k‰k˜1˜c A™g˜,¨AÔ.ˆÜ�k‰k˜1˜s™7 C¨!¡GÐ,°!Ô4ˆÜ*¨3°Ó2ˆÜ*¨3°Ó2ˆÜ—‘˜c qÔ)‰ˆˆBÜ—‘˜c qÔ)‰ˆˆBØ�2�r˜2ˆ~Ðô )¨¨S©°!Ó4Ü(¨¨AÓ.Ü(¨¨q©°!Ó4Ü(¨¨q©°!Ó4ð	
ð 	
r*   ÚcoeffsÚtsc                 óP   — t        |«      }t        d„ t        | |«      D «       «      S )Nc              3   ó,   K  — | ]  \  }}||z  –— Œ y ­wr4   r)   ©rÎ  rØ  rÙ  s      r+   rÏ  z+_upsample_cubic_interp1d.<locals>.<genexpr>÷  s   è ø€ ÒE¡H R¨˜˜R�ÑEùr‘  )rb  r  rú  )rc  rd  Úcoeffs2s      r+   Ú_upsample_cubic_interp1dri  õ  s$   € Ü.¨rÓ2€GÜÑE´°F¸GÓ0DÔEÓEÐEr*   c                 ó6   — t        t        j                  | «      S r4   )r   r>   r  )rd  s    r+   r  r  û  s   € Ü”%—)‘)˜RÓ Ð r*   Ú	num_stepsc                 óŠ   — | dk  rt        j                  d||¬«      S |s| dz
  | z  nd}t        j                  | || ||¬«      S )Nr!   r   r‘  )Ústepsr�  ræ   )r>   rw  Úlinspace)rk  rö  ræ   r�  rù  s        r+   Ú_linspace_from_neg_onero  ÿ  sI   € ð �A‚~Ü�|‰|˜A f°EÔ:Ð:á-:ˆ)�a‰-˜9Ò	$À€AÜ�>‰>˜1˜"˜a y¸ÀuÔMÐMr*   ÚthetaÚhrL  c                 óü  — | j                   }| j                  }t        ||||«      j                  d|d«      }t        ||||«      j                  |dd«      }t	        j
                  d||¬«      }t        j                  j                  j                  |ddd¬«      }t        j                  j                  j                  |ddd¬«      }t        j                  j                  j                  |d	dd¬«      }||z   |z   S )
Nr!   )r!   r!   r!   rµ  )r   r"   Úconstantr   ©rì  r›  r{   ©r!   r!   )r"   r   ©	ræ   r�  ro  r˜  r>   r•  r¯  r  rì  )	rp  rq  rL  rö  ræ   r�  Úgrid_xÚgrid_yÚgrid_ones	            r+   Ú_make_base_grid_4drz  	  så   € Ø�K‰K€EØ�\‰\€Fô $ A }°e¸VÓD×IÑIÈ!ÈQÐPQÓR€FÜ# A }°e¸VÓD×IÑIÈ!ÈQÐPQÓR€FÜ�z‰z˜)¨5¸Ô@€Hô �X‰X× Ñ ×$Ñ$ V°¸jÐPQÐ$ÓR€FÜ�X‰X× Ñ ×$Ñ$ V°¸jÐPQÐ$ÓR€FÜ�x‰x×"Ñ"×&Ñ& x°VÀ*ÐTUÐ&ÓV€HØ�F‰?˜XÑ%Ð%r*   rä  c                 ó   — | j                   }| j                  }t        ||||«      j                  dd|d«      }t        ||||«      j                  d|dd«      }t        ||||«      j                  |ddd«      }	t	        j
                  d||¬«      }
t        j                  j                  j                  |ddd¬«      }t        j                  j                  j                  |ddd¬«      }t        j                  j                  j                  |	d	dd¬«      }	t        j                  j                  j                  |
d
dd¬«      }
||z   |	z   |
z   S )Nr!   )r!   r!   r!   r!   rµ  )r   r‡   rs  r   rt  )r!   r"   )r"   r!   )r‡   r   rv  )rp  rä  rq  rL  rö  ræ   r�  rw  rx  Úgrid_zry  s              r+   Ú_make_base_grid_5dr}    s5  € Ø�K‰K€EØ�\‰\€Fä# A }°e¸VÓD×IÑIÈ!ÈQÐPQÐSTÓU€FÜ# A }°e¸VÓD×IÑIÈ!ÈQÐPQÐSTÓU€FÜ# A }°e¸VÓD×IÑIÈ!ÈQÐPQÐSTÓU€FÜ�z‰z˜,¨e¸FÔC€Hô �X‰X× Ñ ×$Ñ$ V°¸jÐPQÐ$ÓR€FÜ�X‰X× Ñ ×$Ñ$ V°¸jÐPQÐ$ÓR€FÜ�X‰X× Ñ ×$Ñ$ V°¸jÐPQÐ$ÓR€FÜ�x‰x×"Ñ"×&Ñ& x°VÀ*ÐTUÐ&ÓV€HØ�F‰?˜VÑ# hÑ.Ð.r*   c                 óÒ   — |\  }}}}t        | |||¬«      }|j                  ddd«      | j                  j                  d«      z  j	                  d«      }|j                  |||d«      S )N©rö  rR   r‡   r!   rZ  r"   )rz  r˜  r^  rT   ró   )	rp  r.  rö  r#  rU   rq  rL  Ú	base_gridÚgrids	            r+   Ú_affine_grid_generator_4dr‚  +  sg   € Ø�J€A€qˆ!ˆQÜ" 5¨!¨Q¸mÔL€Ið �N‰N˜2˜q !Ó$ u§x¡x×'9Ñ'9¸!Ó'<Ñ<×AÑAÀ"ÓE€DØ�9‰9�Q˜˜1˜aÓ Ð r*   c                 óØ   — |\  }}}}}t        | ||||¬«      }|j                  ddd«      | j                  j                  d«      z  j	                  d«      }	|	j                  ||||d«      S )Nr  rR   rD  r!   rZ  r‡   )r}  r˜  r^  rT   ró   )
rp  r.  rö  r#  rU   rä  rq  rL  r€  r�  s
             r+   Ú_affine_grid_generator_5dr„  5  sm   € Ø�M€A€qˆ!ˆQ�Ü" 5¨!¨Q°ÀÔO€Ið �N‰N˜2˜q !Ó$ u§x¡x×'9Ñ'9¸!Ó'<Ñ<×AÑAÀ"ÓE€DØ�9‰9�Q˜˜1˜a Ó#Ð#r*   c                 óš   — t        j                  t        |«      dv d„ «       t        |«      dk(  rt        | ||¬«      S t	        | ||¬«      S )NrÛ  c                   ó   — y)NzCaffine_grid_generator needs 4d (spatial) or 5d (volumetric) inputs.r)   r)   r*   r+   r€   z'affine_grid_generator.<locals>.<lambda>E  rÆ  r*   rD  r  )r>   r�   r‚  r‚  r„  )rp  r.  rö  s      r+   Úaffine_grid_generatorr‡  ?  sJ   € ô 
‡L�LÜˆD‹	�VÐÙUôô ˆ4ƒy�A‚~Ü(¨°ÀMÔRÐRä(¨°ÀMÔRÐRr*   r�  Úinterpolation_modeÚpadding_modeÚ_expand_gridc           	      óà  ‡ ‡‡‡‡‡‡‡‡‡‡ ‡!‡"‡#‡$‡%‡&‡'‡(‡)‡*‡+‡,‡-— t        j                  ‰dv ˆfd„«       t        j                  ‰dv ˆfd„«       dt        dt        dt        fˆfd„Š-dt        dt        d	t        dt        fd
„Š+dt        dt        dt        fˆˆˆ+fd„Š dt        dt        dt        fˆ ˆ-fd„}‰ j                  \  ŠŠŠ$Š%|j                  \  }Š)Š*}|dk7  rt        d|› �«      ‚‰r(|j                  ‰d‰)‰*|«      j                  ‰‰‰)‰*d«      }dt        dt        dt        fˆ$ˆ%fd„Š&t        j                  ‰‰ j                  ¬«      j                  ‰ddd«      Št        j                  ‰‰ j                  ¬«      j                  d‰dd«      Šdt        dt        dt        dt        fˆˆˆˆ&ˆ)ˆ*fd„Šdt        dt        dt        fˆˆˆ ˆfd„Š"|d   }	|d   }
‰dk(  r• ||	‰%«      } ||
‰$«      }|j                  «       |j                  «       cŠ'Š(‰'dz   ‰(}}‰'‰(dz   }}||}}||z
  ||z
  z  }||z
  ||z
  z  }||z
  ||z
  z  }|‰'z
  |‰(z
  z  }t        ˆ"fd„‰'‰(|f|||f|||f|||ffD «       «      S ‰dk(  r< ||	‰%«      } ||
‰$«      }|j                  «       }|j                  «       } ‰"||d«      S  ‰-|	‰%«      } ‰-|
‰$«      }|j                  «       Š'|j                  «       Š(|‰'z
  Š,|‰(z
  }‰s"‰,j                  d«      Š,|j                  d«      }dt        dt        dt        fˆ ˆ"ˆ$ˆ%fd„Š#dt        dt        fˆ#ˆ'ˆ(ˆ,fd„Š!t        ˆ!fd „t!        d!«      D «       «      }t#        ||«      S )"N)r   r!   r"   c                  ó   •— d‰ › �S )NzInvalid interpolation mode r)   )rˆ  s   €r+   r€   z"_grid_sampler_2d.<locals>.<lambda>^  s   ø€ Ð-Ð.@Ð-AÐB€ r*   c                  ó   •— d‰ › �S )NzInvalid padding mode r)   )r‰  s   €r+   r€   z"_grid_sampler_2d.<locals>.<lambda>a  s   ø€ Ð-BÀ<À.Ð+Q€ r*   Úcoordsr.  rO   c                 óB   •— ‰r|dz  dz
  n|dz  }|dz  dz
  }| |z  |z   S r  r)   )rŽ  r.  rØ   Úofsrö  s       €r+   Úunnormalizez%_grid_sampler_2d.<locals>.unnormalized  s8   ø€ ñ %2ˆt�c‰z˜CÒ¸¸s¹
ˆØ�S‰j˜3ÑˆØ˜‰|˜cÑ!Ð!r*   Ú	twice_lowÚ
twice_highc                 óP  — ||k(  rt        j                  | «      S |dz  }||z
  dz  }| |z
  j                  «       }t        j                  ||«      }||z  j	                  «       j                  t         j                  ¬«      }t        j                  |dz  dk(  ||z   ||z   |z
  «      S )Nr"   rå   r!   r   )r>   r	  rÝ   ÚfmodÚfloorr7   Úint8rh   )rŽ  r’  r“  Ú
coords_minÚcoords_spanÚcoords2ÚextraÚflipss           r+   Úreflect_coordinatesz-_grid_sampler_2d.<locals>.reflect_coordinateso  sª   € Ø˜
Ò"Ü×#Ñ# FÓ+Ð+Ø ‘]ˆ
Ø! IÑ-°Ñ2ˆØ˜JÑ&×+Ñ+Ó-ˆÜ—
‘
˜7 KÓ0ˆØ˜;Ñ&×-Ñ-Ó/×2Ñ2¼¿¹Ð2ÓDˆÜ�{‰{Ø�A‰I˜‰N˜E JÑ.°¸jÑ0HÈ5Ñ0Pó
ð 	
r*   c                 óÊ   •— ‰dk(  r| S ‰dk(  rt        j                  | d|dz
  «      S ‰r ‰| dd|dz
  z  «      }n ‰| dd|z  dz
  «      }t        j                  |d|dz
  «      S )Nr   r!   r"   rR   r�   )rŽ  r.  Úcoords_reflectedrö  r‰  r�  s      €€€r+   Úcompute_coordinatesz-_grid_sampler_2d.<locals>.compute_coordinates{  sx   ø€ Ø˜1ÒØˆMØ˜QÒÜ—;‘;˜v q¨$°©(Ó3Ð3áÙ#6°v¸qÀ!ÀtÈaÁxÁ.Ó#QÑ á#6°v¸rÀ1ÀtÁ8ÈaÁ<Ó#PÐ Ü—;‘;Ð/°°D¸1±HÓ=Ð=r*   c                 ó(   •—  ‰| |«      } ‰||«      S r4   r)   )rŽ  r.  Ú	coords_unr   r‘  s      €€r+   Úcompute_source_indexz._grid_sampler_2d.<locals>.compute_source_index‡  s   ø€ Ù ¨Ó-ˆ	Ù" 9¨dÓ3Ð3r*   r"   z4grid last dimension must be 2 (for x,y coords), got r!   r.  Úysc                 ó˜   •— t        j                  d| k  t        j                  | ‰k  t        j                  d|k  |‰k  «      «      «      S rr   ©r>   r—  )r.  r¤  ÚiHÚiWs     €€r+   Úin_bounds_condz(_grid_sampler_2d.<locals>.in_bounds_condš  sF   ø€ Ü× Ñ Ø�‰G”U×&Ñ& r¨B¡w´×0AÑ0AÀ!ÀrÁ'È2ÐPRÉ7Ó0SÓTó
ð 	
r*   r�  Úwsc                 óÔ   •‡‡—  ‰| |«      Š‰r‰ndŠt        ˆˆˆˆ	ˆ
fd„| j                  t        j                  ¬«      |j                  t        j                  ¬«      |fD «       «      S )Nr!   c              3   óp   •K  — | ]-  }t        j                  ‰|d «      j                  ‰‰‰‰«      –— Œ/ y­wrÌ  )r>   rh   r˜  )rÎ  rÚ  rÂ  rñ  rÝ  ÚoHÚoWs     €€€€€r+   rÏ  z1_grid_sampler_2d.<locals>.clip.<locals>.<genexpr>©  s7   øè ø€ ò 
àô �K‰K˜˜a Ó#×(Ñ(¨¨A¨r°2×6ñ
ùs   ƒ36rå   )rè  r7   r>   r¶  )r.  r¤  rª  rñ  rÝ  rÃ  rÂ  rŠ  r©  r­  r®  s      @@€€€€€€r+   Úclipz_grid_sampler_2d.<locals>.clip¢  sY   ú€ Ù˜b "Ó%ˆñ
 ‰A 1ˆÜ÷ 
à—e‘e¤%§+¡+�eÓ.°·±¼E¿K¹K°Ó0HÈ"ÐMô
ó 
ð 	
r*   ÚixÚiyc                 ó8   •—  ‰	| ||«      \  }}}‰‰‰||f   |z  S r4   r)   )
r°  r±  rL  Úidx_xÚidx_yÚw_ÚC_idxÚN_idxrù  r¯  s
         €€€€r+   Úget_summandz%_grid_sampler_2d.<locals>.get_summand®  s0   ø€ á  B¨›?Ñˆˆu�bØ�˜˜u eÐ+Ñ,¨rÑ1Ð1r*   ).r   ).r!   r   c              3   ó:   •K  — | ]  \  }}} ‰|||«      –— Œ y ­wr4   r)   )rÎ  r°  r±  rL  r¸  s       €r+   rÏ  z#_grid_sampler_2d.<locals>.<genexpr>Ä  s(   øè ø€ ò 
á��R˜ñ ˜˜B ×"ñ
ùs   ƒc                 ó<   •—  ‰| ‰«      } ‰|‰«      } ‰||d«      S r[   r)   )r°  r±  r8   rY   r   r¸  r§  r¨  s       €€€€r+   Úget_value_boundedz+_grid_sampler_2d.<locals>.get_value_boundedã  s*   ø€ Ù# B¨Ó+ˆAÙ# B¨Ó+ˆAÙ˜q ! QÓ'Ð'r*   r�  c                 ó‚   •— ‰| dz
  z   } ‰‰dz
  |«       ‰‰|«       ‰‰dz   |«       ‰‰dz   |«      f}t        |‰«      S )Nr!   r"   )ri  )r�  Úiy_ofsÚcsr»  Úix_nwÚiy_nwÚtxs      €€€€r+   Ú	get_coeffz#_grid_sampler_2d.<locals>.get_coeffè  s[   ø€ Ø˜c A™gÑ&ˆFá! %¨!¡)¨VÓ4Ù! %¨Ó0Ù! %¨!¡)¨VÓ4Ù! %¨!¡)¨VÓ4ð	ˆBô ,¨B°Ó3Ð3r*   c              3   ó.   •K  — | ]  } ‰|«      –— Œ y ­wr4   r)   )rÎ  r�  rÂ  s     €r+   rÏ  z#_grid_sampler_2d.<locals>.<genexpr>ò  s   øè ø€ Ò:¨#‘y —~Ñ:ùó   ƒrD  )r>   r�   r   r‹  r  r,  r˜  r’  r”  r�  r   r–  r  r*  rT   rè  rS   ri  ).rù  r�  rˆ  r‰  rö  rŠ  r£  rU   Útwor8   rY   r°  r±  Úix_neÚiy_neÚix_swÚiy_swÚix_seÚiy_seÚw_nwÚw_neÚw_swÚw_seÚ
ix_nearestÚ
iy_nearestÚtyrc  rÃ  r¶  rÂ  r·  r¯  r   rÂ  r¸  r»  r§  r¨  r©  r¿  rÀ  r­  r®  r�  rÁ  r‘  s.   ` ````                     @@@@@@@@@@@@@@@@@@@r+   Ú_grid_sampler_2drÓ  M  s¿  ÿÿÿ€ ô 
‡L�LØ˜iÐ'ÛBôô 
‡L�LØ˜	Ð!Ó#Qôð"œFð "¬#ð "´&õ "ð

¤Fð 

´sð 

Ìð 

ÔPVó 

ð
>¤Fð 
>´#ð 
>¼&÷ 
>ð4¤Vð 4´3ð 4¼6ö 4ð —7‘7�L€A€qˆ"ˆbØ—Z‘Z�N€A€rˆ2ˆsØ
ˆa‚xÜØBÀ3À%ÐHó
ð 	
ñ ð �y‰y˜˜A˜r 2 sÓ+×2Ñ2°1°a¸¸RÀÓCˆð
œ6ð 
¤vð 
´&ö 
ô
 �L‰L˜ 1§8¡8Ô,×1Ñ1°!°Q¸¸1Ó=€EÜ�L‰L˜ 1§8¡8Ô,×1Ñ1°!°Q¸¸1Ó=€Eð

”ð 

œVð 

¬ð 

Ô4F÷ 

ò 

ð2œð 2¤Fð 2´&÷ 2ð 2ð
 	ˆV‰€AØˆV‰€Aà˜QÒÙ! ! RÓ(ˆÙ! ! RÓ(ˆà—x‘x“z 2§8¡8£:ˆˆˆuØ˜q‘y %ˆuˆØ˜e a™iˆuˆØ˜eˆuˆà˜‘
˜u r™zÑ*ˆØ�U‘
˜u r™zÑ*ˆØ˜‘
˜r E™zÑ*ˆØ�U‘
˜r E™zÑ*ˆäó 
ð ˜˜tÐ$Ø˜˜tÐ$Ø˜˜tÐ$Ø˜˜tÐ$ð	 ô
ó 
ð 	
ð 
˜qÒ	 Ù! ! RÓ(ˆÙ! ! RÓ(ˆà—X‘X“Zˆ
Ø—X‘X“Zˆ
á˜: z°1Ó5Ð5á˜˜BÓˆÙ˜˜BÓˆà—‘“
ˆØ—‘“
ˆà�%‰ZˆØ�%‰ZˆáØ—‘˜a“ˆBØ—‘˜a“ˆBð	(¤&ð 	(¬fð 	(¼÷ 	(ð 	(ð
	4œ3ð 	4¤6÷ 	4ð 	4ô Ó:´°q³Ô:Ó:ˆÜ'¨°Ó3Ð3r*   c                 ó"   — t        | ||||¬«      S )N)r�  rˆ  r‰  rö  )rÓ  )rù  r�  rˆ  r‰  rö  s        r+   Úgrid_sampler_2drÕ  ö  s    € ô Ø	ØØ-Ø!Ø#ôð r*   c                 ó&  ‡ ‡— t        j                  ‰ j                  «       dk(  xr ‰j                  «       dk(  ˆ ˆfd„«       t        j                  ‰ j                  d«      ‰j                  d«      k(  ˆ ˆfd„«       ‰ ‰z  j	                  d¬«      S )Nr"   r!   c                  óL   •— d‰ j                  «       › d‰j                  «       › �S )Nzmatrix @ vector expected, got rË  r   ©rz   r¼  s   €€r+   r€   zmv.<locals>.<lambda>  s!   ø€ Ð0°·±³°¸B¸s¿w¹w»y¸kÐJ€ r*   r   c                  óv   •— d‰ j                  d«      › d‰ j                  d«      › d‰j                  d«      › d�S )Nzsize mismatch, got input (r   r8   r!   z), vec (r?  r  rØ  s   €€r+   r€   zmv.<locals>.<lambda>  s<   ø€ Ð,¨T¯Y©Y°q«\¨N¸!¸D¿I¹IÀa»L¸>ÈÐRU×RZÑRZÐ[\ÓR]ÐQ^Ð^_Ð`€ r*   r   )r>   r�   rN   r.  ró   rØ  s   ``r+   r¾  r¾  	  ss   ù€ ô 
‡L�LØ�‰‹
�a‰Ò*˜CŸG™G›I¨™NÜJôô 
‡L�LØ�	‰	�!‹˜Ÿ™ ›Ñ#Ü`ôð �3‰J×Ñ ÐÓ"Ð"r*   c                 óø   — |�-|dz
  |z  dz   }d|z
  | z  |t        j                  | «      z  z
  }nd|z
  | z  t        j                  | «      z
  }|�||z  }|j                  |j                  «      }t	        ||«      S r[   )rÀ   Ú
logsigmoidr7   ræ   rô   )rz   rü   rË   Ú
pos_weightrð   Ú
log_weightrï   s          r+   Ú binary_cross_entropy_with_logitsrÞ    sŠ   € ð
 ÐØ  1‘n¨Ñ.°Ñ2ˆ
Ø�F‘
˜dÑ" j´1·<±<ÀÓ3EÑ&EÑF‰à�F‘
˜dÑ"¤Q§\¡\°$Ó%7Ñ7ˆàÐØ�f‰}ˆð �7‰7�6—<‘<Ó €DÜ  iÓ0Ð0r*   Útensor1Útensor2Úis_outc                 óü  ‡	— | j                   |j                   k\  r| |fn|| f\  }}ddlmŠ	 |j                   dk\  r|j                   dk  sy|j                  r|sy| j                   dk(  ry ‰	|j	                  «       dk(  «      ry|j
                  }|j                  «       }dg}t        |dd  «      D ]  }|j                  ||d   z  «       Œ t        ˆ	fd	„t        |t        t        |«      «      |«      D «       «      S )
Nr   rR  r‡   r"   FTr!   rR   c              3   óV   •K  — | ]   \  }}} ‰|d k(  «      xs  ‰||k(  «      –— Œ" y­wr“  r)   )rÎ  r´   rµ   r.  rS  s       €r+   rÏ  zshould_fold.<locals>.<genexpr>D  s9   øè ø€ ò áˆD�%˜ñ 	�t˜q‘yÓ!ÒB¡^°D¸E±MÓ%BÓBñùs   ƒ&))r}  rs  rS  rÙ  rÜ   r  rv  r)  ru  r  rú  ru  )
rß  rà  rá  Út1Út2Út1_shapeÚ	t1_strideÚexpected_strider.  rS  s
            @r+   Úshould_foldré  ,  sõ   ø€ ð $+§<¡<°7·<±<Ò#?ˆg�wÑÀgÈwÐEW�F€BˆåDà�G‰G�qŠL˜RŸW™W¨š\ØØ	×Ò¡ØØ‡|�|�qÒØÙ�b—h‘h“j A‘oÔ&Øà�x‰x€HØ—	‘	“€Ið �c€OÜ˜ ! "˜Ó&ò ;ˆØ×Ñ˜t o°bÑ&9Ñ9Õ:ð;äó ä!$Ø”tœH _Ó5Ó6¸ó"
ôó ð r*   )Úpass_is_out)rá  c                óŒ	  — ddl m}m} | j                  «       }|j                  «       }|dk(  s|dk(  rt	        d|› d|› �«      ‚|dk(  r|dk(  rt        j                  | |«      S |dk(  r|dk(  rt        j                  | |«      S |dk(  rC|dk(  r>t        j                  t        j                  t        j                  | d«      |«      d«      S |dk(  r|dk(  rt        j                  | |«      S t        | ||«      �r>||kD  }|r|j                  n| }|s|n|dk(  r| j                  «       n| }	|j                  }
t        |
d d «      }t!        t"        j$                  |«      }|	j                  «       dk(  }|r|j'                  |	j                  d   «       |j)                  ||
d   «      }|rWt
        j*                  j,                  j/                  |j                  |	«      |«      }|r|j                  j1                  «       S |S t
        j*                  j,                  j/                  |j                  |	«      |«      S |dk\  �rp|dk\  �rj|dkD  r| j3                  d«      nd}| j3                  d«      }| j                  d d }|dkD  r|j3                  d«      n|j3                  d«      }|dkD  r|j3                  d«      nd}g }t5        |dz
  «      D ]"  }|j'                  |j3                  |«      «       Œ$ |d	k(  r€|d	k(  r{ ||d   |d   k7  «      rj ||d   dk(  «      r'| j6                  rt9        | j                  d«      |«      S  ||d   dk(  «      r'|j6                  rt9        | |j                  d«      «      S t        t        j:                  ||«      «      }|||gz   }t=        |«      }| j?                  |«      j)                  |||«      }|dk(  }|r7||gz   }|j?                  |«      j)                  ||«      j                  d«      }n)|||gz   }|j?                  |«      j)                  |||«      }|}|dkD  r|j'                  |«       |dkD  r|j'                  |«       |r/|jA                  |«      j                  d«      jC                  |«      S |jA                  |«      jC                  |«      S t        jD                  d
d„ «       y )Nr   )rS  Úguard_or_truez9matmul does not support 0-dimensional tensors, got dims: z and r!   r"   rR   rZ  r‡   Fc                   ó   — y)Nz/both arguments to matmul need to be at least 1Dr)   r)   r*   r+   r€   zmatmul.<locals>.<lambda>È  rÆ  r*   )#rs  rS  rì  rN   r,  r>   Údotr¾  rü  r´  rT   ré  r^  rÚ  r  ru  r   rÃ  rØ   ru  r&  r  r‚   Ú_unsafe_viewr¯  r.  rS   rÙ  r]  Úbroadcast_shapesr&  r’  Úbmmr˜  r�   )rß  rà  rá  rS  rì  Údim_tensor1Údim_tensor2r£  rä  rå  Úsizes_1rÄ  Úfolded_dim1Út2_is_matrixÚ	t1_foldedr¬  r#  Úm1Úbatch_tensor1Úm2rR  Úbatch_tensor2ro  Úexpand_batch_portionÚtensor1_expand_sizeÚexpand_batch_productÚtensor1_expandedÚ
vector_rhsÚtensor2_expand_sizeÚtensor2_expandeds                                 r+   r]  r]  L  sŠ  € ÷ Tà—+‘+“-€KØ—+‘+“-€KØ�aÒ˜;¨!Ò+ÜØGÈÀ}ÐTYÐZeÐYfÐgó
ð 	
ð �aÒ˜K¨1Ò,Ü�y‰y˜ 'Ó*Ð*Ø	˜Ò	˜k¨QÒ.Ü�x‰x˜ Ó)Ð)Ø	˜Ò	˜k¨QÒ.Ü�}‰}œUŸX™X¤e§o¡o°g¸qÓ&AÀ7ÓKÈQÓOÐOØ	˜Ò	˜k¨QÒ.Ü�x‰x˜ Ó)Ð)Ü	�W˜g vÕ	.ð   +Ñ-ˆ	Ù$ˆW�ZŠZ¨'ˆá$‰G¸+ÈÒ:J¨7¯9©9¬;ÐPWð 	ð —(‘(ˆÜ˜G C R˜LÓ)ˆÜœXŸ\™\¨<Ó8ˆð —v‘v“x 1‘}ˆÙØ×Ñ §¡¨¡Ô,ð —J‘J˜{¨G°B©KÓ8ˆ	Ùô —Y‘Y—^‘^×0Ñ0°·±¸bÓ1AÀ<ÓPˆFÙ-6�6—9‘9×'Ñ'Ó)ÐB¸FÐBä—9‘9—>‘>×.Ñ.¨y¯|©|¸BÓ/?ÀÓNÐNà	˜Ó	˜k¨QÓ.ð !,¨a¢ˆG�L‰L˜Ô°QˆØ�\‰\˜"ÓˆØŸ™ c rÐ*ˆØ!,¨q¢ˆW�\‰\˜"Ô°g·l±lÀ2Ó6FˆØ +¨a¢ˆG�L‰L˜Ô°Qˆà#%ˆä�{ Q‘Ó'ò 	2ˆAØ× Ñ  §¡¨a£Õ1ð	2ð ˜1ÒØ˜qÒ Ù˜m¨AÑ.°-ÀÑ2BÑBÔCá˜m¨AÑ.°!Ñ3Ô4¸×9NÒ9NÜ˜gŸo™o¨aÓ0°'Ó:Ð:Ù˜m¨AÑ.°!Ñ3Ô4¸×9NÒ9NÜ˜g w§¡°qÓ'9Ó:Ð:ô  $Ü×"Ñ" =°-Ó@ó 
Ðð 3°a¸°WÑ<Ðä#Ð$8Ó9Ðð #Ÿ>™>Ð*=Ó>×FÑFØ  ! Ró
Ðð ! AÑ%ˆ
ÙØ"6¸"¸Ñ"=Ðà—‘Ð2Ó3ß‘Ð-¨rÓ2ß‘˜1“ñ ð #7¸"¸a¸Ñ"@ÐØ&Ÿ~™~Ð.AÓB×JÑJØ$ b¨!ó Ðð ,ˆØ˜Š?Ø×Ñ Ô"à˜Š?Ø×Ñ Ô"áØ#×'Ñ'Ð(8Ó9×AÑAÀ"ÓE×JÑJÈ<ÓXÐXà#×'Ñ'Ð(8Ó9×>Ñ>¸|ÓLÐLä�‰�UÑUÕVr*   r÷  rø  c                 ón  ‡ ‡‡‡‡‡‡‡— ‰ j                   \  }}ŠŠt        ‰|d   ||«      }t        ‰|d   ||«      }t        j                  ‰ t        j                  j
                  ¬«      \  }}t        j                  |d   ‰ j                  ¬«      j                  |¬«      }	t        j                  |d   ‰ j                  ¬«      j                  |¬«      }
t        ||
|«      }t        ||	|«      }|j                  d«      }|j                  «       }|j                  «       }||z
  j                  dd«      }||z
  j                  dd«      }|j                  t        j                  «      }|j                  t        j                  «      }|dz
  ||dz   |d	z   f}|dz
  ||dz   |d	z   fŠt        |«      Št        |«      }d
\  Š}‰ j                   t        j"                  k(  r­t%        ‰«      Št%        |«      }‰D �cg c]@  }|d‰z  z  t        j&                  |«      dz  z   j                  t        j(                  «      ‘ŒB c}Š|D �cg c]@  }|d|z  z  t        j&                  |«      dz  z   j                  t        j(                  «      ‘ŒB }}ˆˆˆ fd„Šˆ ˆˆˆˆfd„Št+        ˆfd„|D «       «      }‰ j                   t        j"                  k(  r|€t-        d«      ‚t/        |||«      }nt1        d„ t3        ||«      D «       «      }t        j4                  ‰ «      }|j7                  |¬«      }|S c c}w c c}w )Nr   r!   rT  r�  rå   rR   r’   rf   r"   re  rž   c                 ó¤   •— t        j                  | d‰dz
  «      }t        j                  |d‰dz
  «      }t        j                  ‰d d ||g«      }|S ró  )r>   rŽ   r‚   r[  )r¤  r.  Úy_idxÚx_idxr2  Úin_hÚin_wr¾   s        €€€r+   Úload_boundedz0upsample_bicubic2d_default.<locals>.load_bounded  sO   ø€ Ü—‘˜B  4¨!¡8Ó,ˆÜ—‘˜B  4¨!¡8Ó,ˆÜ×Ñ˜u t¨T°5¸%Ð&@ÓAˆØˆr*   c                 óÖ   •‡ — t        ˆˆ fd„‰D «       «      }‰j                  t        j                  k(  r‰€t	        d«      ‚t        |‰‰«      S t        d„ t        |‰«      D «       «      S )Nc              3   ó0   •K  — | ]  } ‰‰|«      –— Œ y ­wr4   r)   )rÎ  Úx_ofsr	  rY   s     €€r+   rÏ  zCupsample_bicubic2d_default.<locals>.get_x_interp.<locals>.<genexpr>  s   øè ø€ ÒB°‘l 1 e×,ÑBùs   ƒz4weights_precision_x must not be None for uint8 inputc              3   ó,   K  — | ]  \  }}||z  –— Œ y ­wr4   r)   rg  s      r+   rÏ  zCupsample_bicubic2d_default.<locals>.get_x_interp.<locals>.<genexpr>  s   è ø€ ÒJ©¨¨R˜B �GÑJùr‘  )rè  ræ   r>   rE  r,  r  r  rú  )rY   Úsrc_xr¾   Úixs_ofsr	  Úweights_precision_xÚ	weights_xs   ` €€€€€r+   Úget_x_interpz0upsample_bicubic2d_default.<locals>.get_x_interp  sc   ù€ ÜÔB¸'ÔBÓBˆØ�;‰;œ%Ÿ+™+Ò%Ø"Ð*Ü$ØJóð ô & e¨YÐ8KÓLÐLÜÑJ´C¸¸yÓ4IÔJÓJÐJr*   c              3   ó.   •K  — | ]  } ‰|«      –— Œ y ­wr4   r)   )rÎ  Úy_ofsr  s     €r+   rÏ  z-upsample_bicubic2d_default.<locals>.<genexpr>  s   øè ø€ Ò;¨%‘,˜u×%Ñ;ùrÄ  z4weights_precision_y must not be None for uint8 inputc              3   ó,   K  — | ]  \  }}||z  –— Œ y ­wr4   r)   rg  s      r+   rÏ  z-upsample_bicubic2d_default.<locals>.<genexpr>  s   è ø€ ÒL©(¨2¨r˜b 2�gÑLùr‘  rX  )r  r  rC   rD   rV  r(  r>   r”  r�  r7   r  rT   r–  rŽ   r¶  rb  ræ   rE  r  rà   Úint16rè  r,  r  r  rú  r   r¯  )r¾   r÷  rö  r÷  rø  rU   Úh_scale_factorÚw_scale_factorræ   ro  r»  Úx_floatÚy_floatr8   rY   Úyscaler3  Úiys_ofsÚ	weights_yÚweights_precision_yrL  Úsrc_yr  rY  r  r  r  r  r	  r  r  s   `                       @@@@@@@r+   Úupsample_bicubic2d_defaultr   Ë  só  ÿ€ ð —{‘{Ñ€A€qˆ$�ô $ D¨+°a©.¸-ÈÓQ€NÜ# D¨+°a©.¸-ÈÓQ€Nä×'Ñ'Ø¤5×#HÑ#H×#UÑ#Uô�H€A€uô 	�‰�[ ‘^¨E¯L©LÔ9×<Ñ<À5Ð<ÓI€AÜ�‰�[ ‘^¨E¯L©LÔ9×<Ñ<À5Ð<ÓI€Aä# N°A°}ÓE€GÜ# N°A°}ÓE€GØ×Ñ Ó#€Gà�‰‹€AØ�‰‹€Að ˜‰k× Ñ   cÓ*€FØ˜‰k× Ñ   cÓ*€FØ	�‰ŒU�[‰[Ó€AØ	�‰ŒU�[‰[Ó€Aà�1‰u�a˜˜Q™  A¡Ð&€GØ�1‰u�a˜˜Q™  A¡Ð&€Gä0°Ó8€IÜ0°Ó8€Ià/9Ñ,ÐÐ,Ø‡{�{”e—k‘kÒ!Ü7¸	ÓBÐÜ7¸	ÓBÐð ö
àð �!Ð*Ñ*Ñ+¬e¯j©j¸«m¸cÑ.AÑA×EÑEÄeÇkÁkÕRò
ˆ	ð ö
àð �!Ð*Ñ*Ñ+¬e¯j©j¸«m¸cÑ.AÑA×EÑEÄeÇkÁkÕRð
ˆ	ð 
ö
÷Kð Kô Ó;°7Ô;Ó;€EØ‡{�{”e—k‘kÒ!ØÐ&Ü Ð!WÓXÐXÜ# E¨9Ð6IÓJ‰äÑL´c¸%ÀÓ6KÔLÓLˆô ×/Ñ/°Ó6€MØ×Ñ¨]ÐÓ;€FØ€MùòI
ùò
s   Ç9AL-ÉAL2c                 ó6  — t        j                  t        |«      t        |«      z   dk(  d„ «       |€Q|€t        d«      ‚t	        t
        t        t        f   t        d„ t        | j                  dd  |«      D «       «      «      }|r|nd\  }}t        | ||||«      S )Nr!   c                   ó   — y)Nz:Must specify exactly one of output_size and scale_factors.r)   r)   r*   r+   r€   z(upsample_bicubic2d_vec.<locals>.<lambda>3  rÆ  r*   z7scale_factors must not be None when output_size is Nonec              3   óP   K  — | ]  \  }}t        t        |«      |z  «      –— Œ  y ­wr4   )r   r   )rÎ  rL  rm   s      r+   rÏ  z)upsample_bicubic2d_vec.<locals>.<genexpr><  s*   è ø€ ò á�A�uô œ	 !› uÑ,×-ñùs   ‚$&r"   re  )
r>   r�   r–  r,  r   rè  r‹  rú  r  r   )rù  r÷  rö  r.  r÷  rø  s         r+   Úupsample_bicubic2d_vecr$  &  s¨   € ô 
‡L�LÜˆ[ÓœD Ó/Ñ/°1Ñ4ÙLôð ÐØÐ Ü ØIóð ô Ü”#”s�(‰OÜñ ä # A§G¡G¨A¨B K°Ó ?ôó ó
ˆñ )6‘}¸<Ñ€GˆWÜ% a¨°mÀWÈgÓVÐVr*   c                 ó(   ‡ — ˆ fd„}t        ‰ ||«      S )Nc                 ó¤   •— t        j                  |  ||z   ‰j                  ¬«      }|dz
  |dz
  |j                  «       z
  j                  «       z
  S )Nr�  r!   )r>   r”  r�  rÝ   ©r´   Úmiddlerµ   Údim_idxrù  s       €r+   rœ  z_reflection_pad.<locals>.idxK  sF   ø€ Ü—,‘, ˜u f¨u¡n¸Q¿X¹XÔFˆØ˜‰z˜V a™Z¨'¯+©+«-Ñ7×<Ñ<Ó>Ñ>Ð>r*   ©Ú_reflection_or_replication_pad©rù  rÃ  rœ  s   `  r+   Ú_reflection_padr-  E  s    ø€ ô?ô *Ø	ØØóð r*   c                 ó(   ‡ — ˆ fd„}t        ‰ ||«      S )Nc                 ó„   •— t        j                  |  ||z   ‰j                  ¬«      }t        j                  |d|dz
  «      S )Nr�  r   r!   )r>   r”  r�  rŽ   r'  s       €r+   rœ  z_replication_pad.<locals>.idx\  s6   ø€ Ü—,‘, ˜u f¨u¡n¸Q¿X¹XÔFˆÜ�{‰{˜7 A v°¡zÓ2Ð2r*   r*  r,  s   `  r+   Ú_replication_padr0  V  s    ø€ ô3ô *Ø	ØØóð r*   Úidx_fnc                 ón  ‡— t        |«      dz  Št        j                  | j                  «       ‰dz   ‰dz   fv ˆfd„«       | j                  ‰ d  }| j                  «       ‰z
  }t        ‰«      D �cg c]  }|d‰dz
  |z
  z     ‘Œ }}t        ‰«      D �cg c]  }|d‰dz
  |z
  z  dz      ‘Œ }}| }t        ‰«      D ]E  }d g|j                  «       z  }	 |||   ||   ||   «      |	||z   <   t        j                  ||	«      }ŒG t        j                  |«      }
|j                  |
¬«      }|S c c}w c c}w )Nr"   r!   c                  ó(   •— d‰ › d‰ dz   › d‰ dz   › d�S )NÚreflection_padzd requires r!   zD or r"   zD inputr)   r   s   €r+   r€   z0_reflection_or_replication_pad.<locals>.<lambda>o  s$   ø€ �.   [°°q±°	¸¸sÀQ¹w¸iÀwÐO€ r*   rX  )r‚  r>   r�   rN   r  rS   r‚   r[  rC   r   r¯  )rù  rÃ  r1  Ú	inp_shapeÚnc_dimro  Úpadding_leftÚpadding_rightr  rœ  rY  rN   s              @r+   r+  r+  g  sH  ø€ ô
 ˆg‹,˜!Ñ
€CÜ	‡L�LØ	�‰‹�C˜!‘G˜S 1™WÐ%Ð%ÛOôð —‘˜˜˜�€IØ�U‰U‹W�s‰]€Fä8=¸c»
ÖC°1�G˜A  q¡¨1¡Ñ-Ó.ÐC€LÐCÜ=BÀ3»ZÖH¸�W˜Q #¨¡'¨A¡+Ñ.°Ñ2Ó3ÐH€MÐHà€FÜ�3‹Zò 1ˆØ˜ &§*¡*£,Ñ.ˆÙ  ¨a¡°)¸A±,ÀÈaÑ@PÓQˆˆA�‰J‰Ü×#Ñ# F¨CÓ0‰ð1ô ×/Ñ/°Ó7€MØ×Ñ¨]ÐÓ;€FØ€Mùò DùÚHs   Á1D-ÂD2c           
      ó  ‡ ‡‡‡— t        |«      dz  Š|j                  ‰ d  D �cg c]  }|dz
  ‘Œ	 }}t        ‰«      D �cg c]  }|d‰dz
  |z
  z     ‘Œ }}t        ‰«      D �cg c]  }|d‰dz
  |z
  z  dz      ‘Œ }}g }t        |j                  «      D ]c  }dg|j                  z  }	d|	|<   |j	                  t        j                  |j                  |   |j                  ¬«      j                  |	«      «       Œe |d ‰  Š|‰ d  }
d„ Št        ‰«      D �cg c]  }|
|   ||   z   ‘Œ }}t        ‰«      D �cg c]  }||   |
|   z
  ‘Œ }}t        ‰«      D �cg c]  }d||   z  ||   z   |
|   z
  ‘Œ }}t        ‰«      D �cg c]  }||   d||   ||   z   ||   z   f‘Œ }}t        j                  t        j                  t        ‰«      D �cg c]  } ‰||   «      ‘Œ c}«      }t        j                  ‰ |‰|z   d«      }ˆˆˆ ˆfd„}t        j                  t        ‰«      D �cg c]  }g d	¢‘Œ c}Ž D ]¥  }|t!        dg‰z  «      k(  rŒg }g }t        ‰«      D ]t  }||   dk(  r||   }||   }n=||   dk(  r||   }|
|   d||   f}n$||   dk(  r||   }|
|   ||   ||   z
  ||   dz
  f}|j	                  «       |j	                  «       Œv  ||||«      }Œ§ |S c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w c c}w )
Nr"   r!   rR   r�  c                 óF   — | \  }}}t        j                  ||k\  ||k  «      S r4   r¦  )Úindex_rangero  ÚlbÚubs       r+   Úindex_range_conditionz7_reflection_pad_backward.<locals>.index_range_condition˜  s(   € Ø‰	ˆˆ2ˆrÜ× Ñ   b¡¨!¨r©'Ó2Ð2r*   r   r’   c           	      ó.  •— t        ‰	«      D ]*  }||   d   ||   d   k  }t        |t        «      sŒ%|sŒ(| c S  t        j                  t
        j                  |D �cg c]
  } ‰|«      ‘Œ c}«      }t
        j                  ‰
|‰|z   d«      }| |z   S c c}w )Nr"   r!   r’   )rS   r6   r–  rK   r   r‚   r—  r™  )r¦   rÅ   Úindex_rangesro  Úupper_less_than_lowerr;  rÝ  Úgrú  rN   rk   r>  s           €€€€r+   r%  z,_reflection_pad_backward.<locals>.accumulate´  s¢   ø€ ô �s“ò 	ˆAØ$0°¡O°AÑ$6¸Àa¹ÈÑ9KÑ$KÐ!ÜÐ/´Õ6Ò;PØ’ð	ô
 ×ÑÜ×ÑØCOÖP°KÑ" ;Õ/ÒPó
ˆô ×%Ñ% k°4¸¸S¹À#ÓFˆØ�a‰xˆùò Qs   ÁB
)rR   r   r!   )r‚  r  rS   r}  ru  r>   r”  r�  r˜  rK   r   r‚   r—  r™  Ú	itertoolsr
   rè  )rk   r8   rÃ  rq  Údhwro  r7  r8  r›  Ú
view_shapeÚxyzÚcenterÚleft_reflectÚright_reflectÚrange_crÝ  r¦   r%  rU   ÚareaÚoutsr@  rÅ   r;  rú  rN   r>  s   `                       @@@r+   Ú_reflection_pad_backwardrM  ƒ  s`  û€ ô
 ˆg‹,˜!Ñ
€CàŸ'™' 3 $ %˜.Ö
)�Qˆ1ˆq‹5Ð
)€CÐ
)ä8=¸c»
ÖC°1�G˜A  q¡¨1¡Ñ-Ó.ÐC€LÐCÜ=BÀ3»ZÖH¸�W˜Q #¨¡'¨A¡+Ñ.°Ñ2Ó3ÐH€MÐHà€GÜ�1—6‘6‹]ò SˆØ�S˜1Ÿ6™6‘\ˆ
Øˆ
�1‰Ø�‰”u—|‘| A§G¡G¨A¡J°q·x±xÔ@×EÑEÀjÓQÕRðSð
 	��#�ˆ€AØ
�3�$�%ˆ.€Cò3ô 16°c³
Ö;¨1ˆc�!‰f�| A‘Ó&Ð;€FÐ;Ü6;¸C³jÖA°�L ‘O c¨!¡fÓ,ÐA€LÐAÜDIÈ#ÃJÖO¸q�Q˜˜Q™‘Z ,¨q¡/Ñ1°C¸±FÓ:ÐO€MÐOô
 NSÐSVËZöØHIˆ�‰�A�s˜1‘v ¨Q¡Ñ/°-ÀÑ2BÑBÒCð€Gð ô ×ÑÜ×ÑÄeÈCÃjÖQÀÑ0°¸±Õ<ÒQó€Dô ×$Ñ$ [°$¸¸F¹
ÀCÓH€D÷ô ×!Ñ!¼¸c»
Ö#C°1¤JÒ#CÐDò 4ˆØ”5˜!˜˜s™Ó#Ò#ààˆØˆä�s“ò 	-ˆAØ�A‰w˜!Š|Ø˜Q‘i�Ø% a™j‘Ø�a‘˜B’Ø" 1‘o�Ø" 1™v q¨,°q©/Ð:‘Ø�a‘˜A’Ø# AÑ&�Ø" 1™v s¨1¡v°¸aÑ0@Ñ'@À#ÀaÁ&È1Á*ÐM�à�K‰K˜ÔØ×Ñ Õ,ð	-ñ ˜$  lÓ3‰ð-4ð0 €Kùòc *ùâCùÚHùò2 <ùÚAùÚOùòùò Rùò& $Ds5   ¥KÁ K$Á$K)ÄK.Ä8K3ÅK8ÆK=ÇL
È&Lr‰   rŒ   r  c                ój   — t        j                  | ||¬«      }t        j                  | ||¬«      }||fS )Nr  )r>   ÚaminrX  )rz   rN   r  rO  rX  s        r+   ÚaminmaxrP  Þ  s2   € ô �:‰:�d ¨WÔ5€Dä�:‰:�d ¨WÔ5€DØ�ˆ:Ðr*   rå   c                ó„   — t         j                  t        j                  t        j                  | «      d| «      |||¬«      S )Nr   rå   )r‚   ró   r>   rh   Úisnan)rz   rN   r  ræ   s       r+   ÚnansumrS  è  s2   € ô �8‰8”E—K‘K¤§¡¨DÓ 1°1°dÓ;¸SÀ'ÐQVˆ8ÓWÐWr*   ©ræ   r>  r�  rX  r>  c          	      óN   — t         j                  j                  d| d||||¬«      S )Nr   r!   rT  ©r‚   r”  Ú
start_step)rj  ræ   r>  r�  rX  s        r+   Úarange_defaultrX  î  s/   € ô �;‰;×!Ñ!Ø	ˆ3�˜ v°fÈð "ó ð r*   c          	      óN   — t         j                  j                  | |d||||¬«      S )Nr!   rT  rV  )ri  rj  ræ   r>  r�  rX  s         r+   Úarange_startrZ  ý  s/   € ô �;‰;×!Ñ!Øˆs�A˜U¨6¸&ÈZð "ó ð r*   c                  ó   — ddl m}  || i |¤ŽS )Nr   )Úout_dtype_dense)Ú!torch._higher_order_ops.out_dtyper\  )rE   rF   r\  s      r+   Úout_dtype_decompr^    s   € åAá˜DÐ+ FÑ+Ð+r*   Úmarginc                 ót  ‡ ‡‡‡	‡
— t        j                  ‰ «      Š t        j                  ‰«      Š‰ j                  d   Š
‰ j                  d   Š	t        j                  |dk(  xs |dk(  d„ «       t        j                  ‰ j
                  dk(  xr ‰	dk7  ˆ fd„«       t        j                  ‰j
                  dk(  xr ‰j                  «       ‰
k(  ˆ
ˆfd„«       ‰�Qt        j                  ‰«      Št        j                  ‰j
                  dk(  xr ‰j                  «       ‰	k(  ˆ	ˆfd„«       ‰j                  d«      Št        j                  ‰ d‰¬«      }||z
  ‰ z   }|j                  d«      }|dk(  r|n||z  }‰�|‰‰   z  }t        j                  ‰	‰ j                  ¬	«      }t        j                  |‰k7  |d«      }|t        j                  j                  k(  r|j!                  «       S |t        j"                  j                  k(  r |j%                  «       |j                  d   z  S |j!                  d¬
«      S )Nr   r!   r"   c                   ó   — y)Nz only p == 1 and p == 2 supportedr)   r)   r*   r+   r€   z#multi_margin_loss.<locals>.<lambda>"  rÆ  r*   c                  ó"   •— d‰ j                   › �S ©NzMExpected non-empty vector or matrix with optional 0-dim batch size, but got: ré  rÝ  s   €r+   r€   z#multi_margin_loss.<locals>.<lambda>%  s   ø€ Ð_Ð`e×`kÑ`kÐ_lÐm€ r*   c                  ó(   •— d‰ › d‰j                   › �S )Nz#inconsistent target size, expected r  ré  )Únframerü   s   €€r+   r€   z#multi_margin_loss.<locals>.<lambda>)  s   ø€ Ð5°f°X¸YÀvÇ|Á|ÀnÐU€ r*   c                  ó(   •— d‰ › d‰j                   › �S )Nz#inconsistent weight size, expected r  ré  )rN   rË   s   €€r+   r€   z#multi_margin_loss.<locals>.<lambda>/  s   ø€ Ð9¸#¸¸iÈÏÉÀ~ÐV€ r*   r  r�  r   )r>   Ú
atleast_2dÚ
atleast_1dr  r�   r}  rÜ   rT   rK  r_  r”  r�  rh   r    r'   r{   rò   r(   ró   )r¾   rü   rR  r_  rË   rð   Úuri   rœ  rN   re  s   ``  `    @@r+   Úmulti_margin_lossrj    sÔ  ü€ ô ×Ñ˜UÓ#€EÜ×Ñ˜fÓ%€FØ�[‰[˜‰^€FØ
�+‰+�a‰.€CÜ	‡L�L��a‘Ò!˜1 ™6Ñ#MÔNÜ	‡L�LØ�
‰
�a‰Ò$˜C 1™HÛmôô 
‡L�LØ�‰�qÑÒ5˜VŸ\™\›^¨vÑ5ÜUôð ÐÜ×!Ñ! &Ó)ˆÜ�‰Ø�K‰K˜1ÑÒ6 §¡£°3Ñ!6ÜVô	
ð ×Ñ˜aÓ €FÜ�‰�U ¨Ô0€AØ�‰
�UÑ€AØ	�‰�A‹€AØ�!ŠV‰˜˜Q™€AØÐØ��v‘ÑˆÜ
�,‰,�s 5§<¡<Ô
0€CÜ�‰�C˜6‘M 1 aÓ(€AØ”I—N‘N×(Ñ(Ò(Ø�v‰v‹xˆØ	”i—m‘m×)Ñ)Ò	)Ø�u‰u‹w˜Ÿ™ ™Ñ#Ð#à�v‰v˜!ˆv‹}Ðr*   Ú	is_targetc                 óà  ‡‡— | j                   Š|j                   Št        j                  | «      } t        j                  |«      }| j                   d   }t        j                  t	        ‰«      dk  xr |dk7  ˆfd„«       t        j                  t	        ‰«      dk  xr ‰‰k(  ˆˆfd„«       t        j
                  ||j                  ¬«      }|dk(  }t        j                  t        j                  |||«      dd¬	«      }||k  }t        j                  ||d«      }t        j                  | d|¬
«      }	t        j                  ||d«      }
t        j                  ||
j                  d¬«      k(  d¬«      }d|	j                  j                  d¬«      z
  | z   }|j                  d«      }||z  }t        j                  |d|«      }|t        j                  j                   k(  r!|j#                  d¬«      j%                  «       }n@|t        j&                  j                   k(  r|j#                  «       }n|j#                  d¬«      }|j)                  | j*                  «      j-                  ‰«      }||fS )Nr!   r"   r   c                  ó   •— d‰ › �S rc  r)   )Úorig_input_shapes   €r+   r€   z0multilabel_margin_loss_forward.<locals>.<lambda>Q  s   ø€ Ð_Ð`pÐ_qÐr€ r*   c                  ó   •— d‰› d‰ › �S )Nzinconsistent target size: z for input of size: r)   )rn  Úorig_target_shapes   €€r+   r€   z0multilabel_margin_loss_forward.<locals>.<lambda>U  s   ø€ Ð,Ð->Ð,?Ð?SÐTdÐSeÐf€ r*   r�  rR   Tr  r  r   rf   )r   rR   )r  r>   rg  r�   r‚  r”  r�  rO  rh   rK  rÂ  rT   ÚTr_  r    r'   r{   ró   rò   r(   r7   ræ   r&  )r¾   rü   rð   rN   rœ  Úis_endÚend_idxÚtarget_maskÚtidx0ri  Útidx1rk  ri   rn  rp  s                @@r+   Úmultilabel_margin_loss_forwardrw  B  sú  ù€ ð —{‘{ÐØŸ™ÐÜ×Ñ˜UÓ#€EÜ×Ñ˜fÓ%€FØ
�+‰+�a‰.€CÜ	‡L�LÜÐÓ Ñ"Ò/ s¨a¡xÛrôô 
‡L�LÜÐÓ !Ñ#ÒMÐ(9Ð=MÑ(MÜfôô
 �,‰,�s 6§=¡=Ô
1€CØ�r‰\€FÜ�j‰jœŸ™ V¨S°#Ó6¸BÈÔM€Gà˜‘-€Kä�K‰K˜ V¨QÓ/€EÜ�‰�U ¨%Ô0€Aä�K‰K˜ V¨RÓ0€EÜ—	‘	˜# §¡°R Ó!8Ñ8¸aÔ@€Iàˆa�c‰c�m‰m ˆmÓ#Ñ# eÑ+€AØ	�‰�A‹€AØ	ˆC‰€Aä�‰�I˜q !Ó$€Aà”I—N‘N×(Ñ(Ò(Ø�E‰E�gˆEÓ×#Ñ#Ó%‰Ø	”i—m‘m×)Ñ)Ò	)Ø�E‰E‹G‰à�E‰E�gˆEÓˆà—‘˜UŸ[™[Ó)×1Ñ1Ð2CÓD€IØˆiˆ<Ðr*   )Ú	attn_maskrm   ÚqueryÚkeyÚ	dropout_pÚ	is_causalrx  c                ó  ‡ ‡‡‡— t        j                  t        j                  ‰ «      ˆ fd„«       t        j                  ‰ j                  «       dk(  xr( ‰j                  «       dk(  xr ‰j                  «       dk(  ˆˆ ˆfd„«       t        j                  ‰dk(  ˆfd„«       t        j                  ‰ j                  d   ‰j                  d   k(  xr ‰j                  d   ‰j                  d   k(  d„ «       t
        j                  j                  ‰ ‰‰|‰|d |‰ j                  d«      ‰j                  d«      k7  ¬	«	      \  }}|j                  d
ddd«      j                  t         j                  ¬«      j                  dd
dd«      }||fS )Nc                  ó"   •— d‰ j                   › �S )Nz-query must be FP32, FP64, BF16, FP16 but got rå   )ry  s   €r+   r€   z<scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>Ž  s   ø€ Ð?ÀÇÁ¸}ÐM€ r*   rD  c                  ón   •— d‰j                  «       › d‰ j                  «       › d‰j                  «       › �S )Nz,q, k, v must be a 4 dimensional tensor, got rË  r   )rz  ry  r{   s   €€€r+   r€   z<scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>’  s3   ø€ Ð>¸u¿y¹y»{¸mÈ2ÈcÏgÉgËiÈ[ÐXZÐ[`×[dÑ[dÓ[fÐZgÐh€ r*   r’   c                  ó   •— d‰ › �S )Nz&dropout probability must be zero, got r)   )r{  s   €r+   r€   z<scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>•  s   ø€ Ð$JÈ9È+Ð"V€ r*   r‡   c                   ó   — y)Nz&q, k, v should have the same head sizer)   r)   r*   r+   r€   z<scaled_dot_product_flash_attention_for_cpu.<locals>.<lambda>™  rÆ  r*   r!   )rx  r{  r|  Údropout_maskrm   Ú
enable_gqar"   r   rX  )r>   r�   rK  rN   r  r‚   Ú"_scaled_dot_product_attention_mathrˆ  r.  rû  r¯  r\  )	ry  rz  r{   r{  r|  rx  rm   r¬  Úattns	   ````     r+   Ú*scaled_dot_product_flash_attention_for_cpur†  �  sV  û€ ô 
‡L�LÜ×Ñ Ó&ÛMôô 
‡L�LØ�	‰	‹�qÑÒ@˜SŸW™W›Y¨!™^Ò@°·	±	³¸qÑ0@Ýhôô 
‡L�LØ�SÑÓVôô 
‡L�LØ�‰�A‰˜%Ÿ+™+ a™.Ñ(ÒK¨S¯Y©Y°q©\¸U¿[¹[È¹^Ñ-KÙ8ôô
 ×:Ñ:×BÑBØØØØØØØØØ—:‘:˜a“= C§H¡H¨Q£KÑ/ð Có 
�L€FˆDðF 	�‰�q˜!˜Q Ó"ß	‰¤%×"9Ñ"9ˆÓ	:ß	‰��A�q˜!Ó	ð ð
 �4ˆ<Ðr*   c                 ó.   ‡— t        | «      ˆfd„«       }|S )Nc                  ó<   •—  ‰| i |¤Ž}| d   j                  |«      S rr   )r  )rE   rF   rÅ   Úoutplace_ops      €r+   Ú
inplace_opz$register_inplace.<locals>.inplace_opÇ  s%   ø€ á˜4Ð* 6Ñ*ˆØ�A‰w�}‰}˜SÓ!Ð!r*   r   )Úaten_opr‰  rŠ  s    ` r+   Úregister_inplacerŒ  Æ  s"   ø€ Ü˜GÓ$ó"ó %ð"ð Ðr*   c                 óB  — | j                  «       s&| j                  «       st        |«      }t        |«      }t        j                  ||«      }t        |t        j                  «      r|dk7  r||z  }|dk(  r|S t        |t        j                  «      r|dk7  r| |z  } | |z   S r3  )rK  r³  r‹  r>   rñ  r6   ÚnumbersÚNumber)rz   Úbatch1Úbatch2rb   rl   r  s         r+   Úbaddbmmr’  Ï  s‹   € ð ×!Ñ!Ô#¨D¯O©OÔ,=Ü�4‹yˆÜ�E“
ˆÜ�Y‰Y�v˜vÓ&€FÜ�eœWŸ^™^Ô,°¸²
Ø˜%‘ˆØˆq‚yØˆÜ�dœGŸN™NÔ+¨t°qªyØ�d‰{ˆØ�&‰=Ðr*   c                 ó2   — t        j                  | |d¬«      S )Nr–  r–  r˜  )rz   râ   s     r+   Úfloor_divider”  à  s   € ô �9‰9�T˜5°Ô8Ð8r*   c                 ó`   — t        j                  t        j                  | j                  d«      S r[   )rK   r   rÃ  rØ   r  )rÚ  s    r+   Ú	sym_numelr–  æ  s   € ä×ÑœHŸL™L¨!¯'©'°1Ó5Ð5r*   ©ræ   rÅ   c                ó�   — |€"t         j                  j                  | g |¬«      S t         j                  j                  | g ||¬«      S )Nrå   r—  )r‚   ró   Údim_IntListÚIntList_out)rz   ræ   rÅ   s      r+   Úsum_defaultr›  ë  sC   € ð €{Ü�x‰x×#Ñ# D¨"°EÐ#Ó:Ð:ä�x‰x×#Ñ# D¨"°E¸sÐ#ÓCÐCr*   c           	      ó   — t        | t        j                  «      s| S |€@t        j                  j                  | t        t        | j                  «       «      «      «      S t        j                  j                  | |g«      S r4   )	r6   r>   r   r‚   rü  Údimsru  rS   rN   )rz   rN   s     r+   Úsqueeze_defaultrž  ø  s\   € ô �dœEŸL™LÔ)Øˆà
€{Ü�|‰|× Ñ  ¤t¬E°$·(±(³*Ó,=Ó'>Ó?Ð?ä�|‰|× Ñ  ¨ uÓ-Ð-r*   c                 ó2  ‡— t        ˆfd„t        t        | j                  «      «      D «       «      }|j                  t
        j                  k(  rt
        j                  nd }| j                  d|d|¬«      }| ||j                  |j                  «      z  z  |fS )Nc              3   ó.   •K  — | ]  }|‰k7  sŒ	|–— Œ y ­wr4   r)   )rÎ  ro  rN   s     €r+   rÏ  z)_weight_norm_interface.<locals>.<genexpr>  s   øè ø€ Ò@˜1°q¸C³x”QÑ@ùs   ƒ
Žr"   T)r  ræ   )
rè  rS   r‚  r  ræ   r>   rØ  r  r   r7   )r2  rB  rN   Úkeep_dimÚ
norm_dtyper   s     `   r+   Ú_weight_norm_interfacer£    st   ø€ ô Ó@¤¤c¨!¯'©'£lÓ 3Ô@Ó@€Hà !§¡¬5¯>©>Ò 9”—’¸t€JØ�6‰6�!�X t°:ˆ6Ó>€DØ��D—G‘G˜AŸG™GÓ$Ñ$Ñ% tÐ+Ð+r*   ©Úassume_uniqueÚinvertc                ó¶  — t        | t        j                  «      s!t        j                  | |j                  ¬«      } t        |t        j                  «      s.|rt        j
                  | |«      S t        j                  | |«      S ddlm}  ||j                  «       dt        | j                  «       d«      z  k  «      rt        | ||¬«      S t        | |||¬«      S )Nr�  r   rR  g      $@g�Âõ(\�Â?©r¦  r¤  )r6   r>   r   r]  r�  Úner  rs  rS  rÜ   rë   Úisin_defaultÚisin_sorting)ÚelementsÚtest_elementsr¥  r¦  rS  s        r+   Úisinr®    s®   € ô �h¤§¡Ô-Ü×&Ñ& x¸×8LÑ8LÔMˆÜ�m¤U§\¡\Ô2ÙÜ—8‘8˜H mÓ4Ð4ä—8‘8˜H mÓ4Ð4åDá�m×)Ñ)Ó+¨d´S¸¿¹Ó9IÈ5Ó5QÑ.QÑQÔRÜ˜H m¸FÔCÐCäØ�m°=Èô
ð 	
r*   )rV  c                óB  — |€?t        j                  | j                  «       t         j                  | j                  ¬«      }n?t        j                  | j                  «       |t         j                  | j                  ¬«      }|| k  j                  | j                  «      }|S )Nrµ  )rV  ræ   r�  )r>   Úrandr.  ré   r�  r7   ræ   )rz   rV  Úraw_prR  s       r+   Ú	bernoullir²  $  sq   € ð ÐÜ—
‘
˜4Ÿ9™9›;¬e¯m©mÀDÇKÁKÔP‰ä—
‘
Ø�I‰I‹KØÜ—-‘-Ø—;‘;ô	
ˆð 
�‰×Ñ˜$Ÿ*™*Ó%€AØ€Hr*   r¨  c                ó‚  — | j                  «       dk(  r%t        j                  | t        j                  ¬«      S |j                  dk(  r| |k(  }|r| S |S | j
                  d|j                  z  z   }| j                  |«      }t        t        d|j                   dz
  d«      «      }||k(  j                  |¬«      }|r| S |S )Nr   rå   ©r!   rR   r!   r   )
rÜ   r>   Ú
empty_liker–  r}  r  r˜  rè  rS   rÂ  )r¬  r­  r¦  rN  Úexpanded_elem_shaper8   rN   s          r+   rª  rª  7  sÀ   € Ø‡~�~Ó˜1ÒÜ×Ñ ´·
±
Ô;Ð;Ø×Ñ˜QÒØ˜-Ñ'ˆÙ�ˆtÐ& 3Ð&Ø"Ÿ.™.¨4°-×2DÑ2DÑ+DÑDÐØ�‰Ð)Ó*€AÜ
”�b˜=×-Ñ-Ð-°Ñ1°2Ó6Ó
7€CØ�Ñ×
"Ñ
" sÐ
"Ó
+€CÙˆCˆ4Ð"˜sÐ"r*   c                óÖ  — | j                  «       }|j                  «       }|r»t        j                  ||g«      }t        j                  |d¬«      \  }}|dd  |d d k(  }	t        j                  |	ddgd«      }	|r|	j                  «       }	t        j                  |	«      }
|
j                  d||	«      }
|
d| j                  «        j                  | j                  «      S t        j                  |«      \  }}t        j                  ||«      }t        j                  ||j                  «       k  |d«      }||   |k(  }|r|j                  «       n|}|j                  | j                  «      S )NT)Ústabler!   rR   r   F)r;  r>   r0  Úsortrs  Úlogical_notrµ  r  rÜ   r&  r  Úsearchsortedrh   )r¬  r­  r¥  r¦  Úelements_flatÚtest_elements_flatÚall_elementsÚsorted_elementsÚsorted_orderÚduplicate_maskr�  Úsorted_test_elementsrU   rœ  Útest_idxÚcmps                   r+   r«  r«  D  sN  € Ø×$Ñ$Ó&€MØ&×.Ñ.Ó0ÐÙô —y‘y -Ð1CÐ!DÓEˆÜ(-¯
©
°<ÈÔ(MÑ%ˆ˜à(¨¨Ð,°ÀÀÐ0DÑDˆÜ×.Ñ.¨~ÀÀ1¸vÀuÓMˆáØ+×7Ñ7Ó9ˆNä×Ñ Ó/ˆØ�‰˜q ,°Ó?ˆà�A˜Ÿ™Ó(Ð)×1Ñ1°(·.±.ÓAÐAä"'§*¡*Ð-?Ó"@ÑÐ˜aÜ× Ñ Ð!5°}ÓEˆÜ—;‘;˜sÐ%9×%?Ñ%?Ó%AÑAÀ3ÈÓJˆØ" 8Ñ,°Ñ=ˆÙ#)ˆc�o‰oÔ¨sˆØ�{‰{˜8Ÿ>™>Ó*Ð*r*   c                 ó.   — | j                  d«      }||   S rQ   )r&  )rz   rŸ  Ú	flatteneds      r+   ÚtakerÇ  a  s   € ð —‘˜RÓ €IØ�UÑÐr*   c                 ó¦   — |€t         j                  }|t         j                  k(  rt        |«      }t        j                  | |j                  |¬«      S r2  )r>   r\  Úpreserve_formatr   r‚   Úresizer  )rz   râ   rY  s      r+   Ú	resize_asrË  h  sD   € àÐÜ×/Ñ/ˆØœ×-Ñ-Ò-Ü-¨eÓ4ˆÜ�;‰;�t˜UŸ[™[¸ˆ;ÓFÐFr*   Ú	ceil_modec                 óX  — t        j                  «       rt        S | j                  j                  dk(  rt        S |j                  d«      }|j                  d«      }	| j                  d«      }
| j                  d«      }|j                  «       dk(  }|s3|j                  d«      }| j                  d«      } |j                  d«      }|j                  d«      }|j                  d«      }| j                  t         j                  t         j                  fv }|rt         j                  n| j                  }t        j                  ||z  ||	z  || j                  ¬«      }| j                  ||z  |
|z  «      }|j                  ||z  |
|z  «      }|r|j                  t         j                  «      }|j                  d||«      }|j                  ||||	«      }|r|j                  | j                  «      }t!        j"                  |«      }|j%                  |¬«      }|s|j'                  d«      }|S )	uæ  
    Decomposition of max_pool2d_with_indices_backward using scatter_add.

    This replaces the native implementation with a high-level decomposition
    that uses scatter_add for gradient accumulation. The scatter-based approach
    provides automatic optimization opportunities for Inductor and handles all
    pooling configurations without requiring specialized fallback paths.

    Algorithm:
        For each output gradient position, use the corresponding index from the
        forward pass to scatter the gradient to the input position. When multiple
        output positions select the same input position as max, scatter_add
        automatically accumulates their gradients.

    Complexity: O(B * C * H_out * W_out)
        Independent of kernel size, unlike traditional O(B * C * H_in * W_in * KÂ²)
        approaches that iterate over input positions and kernel windows.

    Known Limitations:
        - FP16/BF16: Uses FP32 accumulation internally to preserve precision when
          many gradients accumulate to the same position (overlapping pooling windows).
          This adds slight overhead but ensures numerical stability.
        - Deterministic mode: Falls back to native implementation to ensure
          consistent results across runs

    Args:
        grad_output: Gradient w.r.t. pooling output [B, C, H_out, W_out]
        self: Original input tensor (for shape) [B, C, H_in, W_in]
        kernel_size: Pooling kernel size
        stride: Pooling stride
        padding: Pooling padding
        dilation: Pooling dilation
        ceil_mode: Whether to use ceil for output size calculation
        indices: Indices from forward pass (per-channel linear positions)

    Returns:
        Gradient w.r.t. input [B, C, H_in, W_in]
    ÚmpsrZ  rR   rD  r   r!   rµ  rX  )r>   Ú$are_deterministic_algorithms_enabledÚNotImplementedr�  r¥  r.  rN   rT   ræ   r÷   rØ  ré   r  r&  r7   Úscatter_addrC   r   r¯  rü  )rk   rz   rÁ  rv  rÃ  rÂ  rÌ  r›  Ú	in_heightÚin_widthÚ
out_heightÚ	out_widthÚ
is_batchedrp  ÚchannelsÚuse_fp32_accumÚaccum_dtypeÚgrad_input_flatÚgrad_output_flatrÈ  rW   rY  s                         r+   Ú max_pool2d_with_indices_backwardrÜ  q  s	  € ôd ×1Ñ1Ô3ÜÐð ×Ñ×Ñ %Ò'ÜÐð —	‘	˜"“€IØ�y‰y˜‹}€HØ×!Ñ! "Ó%€JØ× Ñ  Ó$€Ið —‘“˜q‘€JÙØ�~‰~˜aÓ ˆØ!×+Ñ+¨AÓ.ˆØ×#Ñ# AÓ&ˆà—‘˜1“€JØ�y‰y˜‹|€Hð
 !×&Ñ&¬5¯=©=¼%¿.¹.Ð*IÐI€NÙ#1”%—-’-°{×7HÑ7H€Kô —k‘kØ�XÑØ�HÑØØ×!Ñ!ô	€Oð #×*Ñ*Ø�XÑ˜z¨IÑ5óÐð —?‘? :°Ñ#8¸*ÀyÑ:PÓQ€Lñ Ø+×.Ñ.¬u¯}©}Ó=Ðð &×1Ñ1°!°\ÐCSÓT€Oð !×(Ñ(¨°X¸yÈ(ÓS€Jñ Ø—]‘] ;×#4Ñ#4Ó5ˆ
ô ×/Ñ/°Ó5€MØ×&Ñ&°]Ð&ÓC€Jñ Ø×'Ñ'¨Ó*ˆ
àÐr*   Úwindow_lengthc                óL   — t         j                  j                  | d||||¬«      S )aÃ  hann_window(window_length, *, dtype=None, layout=None, device=None, pin_memory=False) -> Tensor

    Returns a Hann window of size :attr:`window_length` with ``periodic=True``.

    Equivalent to :func:`torch.hann_window` with ``periodic=True``.

    Args:
        window_length (int): the size of returned window.

    Keyword args:
        dtype (:class:`torch.dtype`, optional): desired dtype. Default: global default.
        layout (:class:`torch.layout`, optional): desired layout. Default: ``torch.strided``.
        device (:class:`torch.device`, optional): desired device. Default: current device.
        pin_memory (bool, optional): if ``True``, pins the returned tensor. Default: ``False``.
    TrT  )r‚   Úhann_windowÚperiodic)rÝ  ræ   r>  r�  rX  s        r+   rß  rß  è  s4   € ô2 ×Ñ×$Ñ$ØØØØØØð %ó ð r*   rà  c                óà  — |�|nt        j                  «       }| dk(  rt        j                  d||||¬«      S | dk(  rt        j                  d||||¬«      S t	        j
                  |«      }|r| dz   n| }t        j                  |||||¬«      }|dt         j                  z  |dz
  z  z  }t        j                  |«      }|dz  dz   }|r|j                  dd| «      n|}	|	j                  |«      S )	a@  hann_window(window_length, periodic=True, *, dtype=None, layout=None, device=None, pin_memory=False) -> Tensor

    Returns a Hann window of size :attr:`window_length`.

    .. math::
        w[n] = 0.5 - 0.5 \cos\!\left(\frac{2\pi n}{N-1}\right)

    where :math:`N` is ``window_length + 1`` when ``periodic=True`` (for spectral analysis),
    or ``window_length`` when ``periodic=False`` (symmetric window).

    Low-precision dtypes (``bfloat16``, ``float16``) are computed in ``float32`` then cast.

    Args:
        window_length (int): the size of returned window.
        periodic (bool, optional): if ``True``, returns a periodic window for use with STFT.
            Default: ``True``.

    Keyword args:
        dtype (:class:`torch.dtype`, optional): desired dtype. Default: global default.
        layout (:class:`torch.layout`, optional): desired layout. Default: ``torch.strided``.
        device (:class:`torch.device`, optional): desired device. Default: current device.
        pin_memory (bool, optional): if ``True``, pins the returned tensor. Default: ``False``.
    r   r  rT  r!   r´  rä   rª   rž   )r>   Úget_default_dtyperD  r•  rC   rê  r”  ÚpiÚcosr/  r7   )
rÝ  rà  ræ   r>  r�  rX  Úcompute_dtyper#  rÚ  Úwindows
             r+   Úhann_window_periodicrç    sý   € ðD Ð&‰E¬E×,CÑ,CÓ,E€EØ˜ÒÜ�{‰{Ø˜ f°VÈ
ô
ð 	
ð ˜ÒÜ�z‰zØ˜ f°VÈ
ô
ð 	
ô ×/Ñ/°Ó6€MÙ%ˆ˜Ò¨=€AÜ�‰Ø	ØØØØô	€Að 	
ˆS”5—8‘8‰^˜q 1™uÑ%Ñ&€AÜ�	‰	�!‹€AØ	ˆD‰�3‰€AÙ.6ˆQ�X‰X�a˜˜MÔ*¸A€FØ�9‰9�UÓÐr*   Únum_classesc                 óî  — |dk(  r*t        | j                  «       j                  «       «      dz   }t        j                  j                  t        j                  | dk\  «      d«       t        j                  j                  t        j                  | |k  «      d«       | j                  d«      t        j                  || j                  | j                  ¬«      k(  j                  t        j                  «      S )NrR   r!   r   z+one_hot: Class values must be non-negative.z7one_hot: Class values must be smaller than num_classes.rµ  )r‹  rŒ   r¦  r‚   Ú_assert_asyncÚmsgr>   r  rT   r”  ræ   r�  r7   r¶  )rz   rè  s     r+   Úone_hotrì  b  sµ   € à�bÒÜ˜$Ÿ(™(›*Ÿ/™/Ó+Ó,¨qÑ0ˆä×Ñ×ÑÜ�	‰	�$˜!‘)ÓØ5ôô 	×Ñ×ÑÜ�	‰	�$˜Ñ$Ó%ØAôð
 	�‰�rÓÜ�<‰<˜¨4¯:©:¸d¿k¹kÔJñ	Kç�bŒ�‰ƒoðr*   )FF)Únoner4   )r"   )r   NNr!   )rR   FFrÌ  r  ru  )r!   r!   F)Fr’   )r’   rf   N)r   r!   N)Fre  )NNN)r   r   FT)r   r   Fr*  )r’   Frù  )rR   (’  rK   rC  rŽ  rÃ  rw  Úcollections.abcr   r   Ú
contextlibr   Úenumr   r   r   r	   r
   Útypingr   r   r>   Útorch._meta_registrationsÚtorch._primsr^  r   Útorch._prims_commonÚ_prims_commonrC   Útorch.nn.functionalr¯  r  rÀ   r   r   r   Útorch._decompr   r]  r   r   r   r   r   r   Útorch._prims_common.wrappersr   r   r   r   Útorch.utilsr   rA   Útorch.utils._pytreer   r?  ÚDispatchKeyr   ru  ÚstrÚ__annotations__Ú_opsr  r‚   r    rV  r–  rM   rW  Úcompute_only_pw_cast_for_opmathÚpw_cast_for_opmathÚ"pw_cast_for_opmath_non_tensor_argsr(  Úpw_cast_for_int_to_realr‹  rV   r_   ra   rj   r  rv   rC  r  r|   r„   r�   r•   r™   r›   rŸ   r¡   r¥   r½   rÆ   rÈ   rÊ   rÍ   rÑ   rè  rÙ   rá   rî   rô   ræ   rû   rþ   r'   r{   r  Ú_safe_softmaxr  r  r  rˆ  rW   r  r  rÅ   r!  r*  r8  rB  rE  rJ  rM  rO  rQ  rT  rg  ro  Úslicerƒ  rŒ  rn  r¢  r¨  r«  r±  r³  rÀ  r  r0  r4  r=  rC  rG  Úpy_implÚCompositeImplicitAutogradÚAutogradrF  r[  r_  re  rm  r&  r{  r~  r‚  r�  r�  r–  r™  r›  r•  r§  r   r¯  rµ  r»  r¿  rÛ  rß  râ  rü  rþ  r  r  r'  r-  r1  Úunsafe_chunkr4  r0  r/  Úno_statsr8  r<  rH  rN  rR  rT  Ú_fused_dropoutrW  rc  r�  rY  rž  ÚliftÚ
lift_freshrf  rk  rn  rq  rp  r„  r‰  rŒ  Ú_adaptive_avg_pool2dr¼  rÉ  rØ  rå  rì  rî  rê  r  r  r  r  r  r"  Ú	Generatorr$  r0  r3  rI  r¼  rP  rV  r9  Ú_upsample_nearest_exact1drR  rX  r>  rD  rK  r6  rc  rl  rq  ru  rƒ  r‹  rŽ  r’  r¡  rª  Úrnn_tanhr¾   r±  Úrnn_relur´  r¹  rº  r½  rÉ  rÌ  rÒ  rÞ  Úlstmrá  rã  rë  rí  Úgrurï  rñ  rô  rù  rû  rü  rÿ  r   r  r
  r  r  r  r  r  r  r  r7  r9  rï  r[  r'  r™  rI  rO  rS  rU  rY  r\  rb  ri  r  ro  rz  r}  r‚  r„  r‡  rÓ  rÕ  r¾  rÞ  ré  r]  Úupsample_bicubic2dr   r$  Úreflection_pad1dÚreflection_pad2dÚreflection_pad3dr-  Úreplication_pad1dÚreplication_pad2dÚreplication_pad3dr0  r+  Úreflection_pad1d_backwardÚreflection_pad2d_backwardÚreflection_pad3d_backwardrM  rP  rS  r”  r[  r>  rX  ri  rZ  r^  rj  rw  Ú+_scaled_dot_product_flash_attention_for_cpur†  rŒ  r’  r”  r–  ró   r›  rü  rN   rž  r£  r®  r²  rª  r«  rÇ  rË  rÜ  rß  rà  Úperiodic_outrç  Úaddbmm_ÚaddbmmÚaddmm_Úaddmv_Úbaddbmm_Úfill_Úgelu_r¹  Ú
hardswish_Ú	hardtanh_ÚhardtanhÚhardsigmoid_Ú__iand__Ú__and__Ú__ilshift__Ú
__lshift__rü  rý  Úindex_reduce_Úindex_reduceÚ__ior__Ú__or__Ú__irshift__Ú
__rshift__Ú__ixor__Ú__xor__Úldexp_Úleaky_relu_Ú
leaky_reluÚlogit_ÚlogitÚrelu_rº  Úrenorm_ÚrenormÚround_r*  Úscatter_r%  Úscatter_add_rÑ  Úscatter_reduce_Úscatter_reduceÚsilu_rì  r)   r*   r+   ú<module>rE     sP  ðô Û Û Û Û 
ß .Ý "Ý ß %ß $ß ã Û  Ý Ý #ß Ð ß ,Ñ ,Ý 0Ý 7÷õ ÷ó õ *Ý (ð �h‰h×"Ñ"€ð €ˆˆc‰Ó à‡z�z‡~�~×Ñ€ô�ô ð  %Ø$)ò	'Øð'à×9Ñ9ð'ð ð'ð "ó	'ñT #*ØØ×8Ñ8×@Ñ@Øô#Ð ñ
 Ø˜u×DÑD×LÑLôÐ ñ &-ØØ×8Ñ8×@Ñ@Ø ô&Ð "ñ
 "Ø˜u×DÑD×QÑQôÐ ð˜ð  cð ¨fó ñ ˜×*Ñ*Ó+Ùˆ\ÓØð2˜Fð 2 vò 2ó ó ó ,ð2ñ ˜×-Ñ-Ó.Ùˆ\ÓØð4˜vð 4¨&ò 4ó ó ó /ð4ñ ˜×.Ñ.Ó/Ùˆ\ÓØðS ð S¨6ð S¸ð SÈ5ò Só ó ó 0ðSñ
 ˜×)Ñ)Ó*Ùˆ\ÓØð
Øð
àð
ð ð
ð ð	
ð
 ð
ð ò
ó ó ó +ð
ñ2 ˜Ÿ™×)Ñ)Ð*Ó+ñ(ó ,ð(ñ ˜Ÿ™×)Ñ)Ð*Ó+ð"˜Vò "ó ,ð"ñ ˜×(Ñ(Ó)ÙƒØð@�fð @ ò @ó ó ó *ð@ñ ˜×1Ñ1Ó2Ùˆ\ÓØð fð °Fò ó ó ó 3ðñ ˜×.Ñ.Ó/Ùˆ\ÓðPØðPØ%ðPØ05ðPØ@EòPó ó 0ðPñ ˜Ÿ™Ó'ÙƒØðG�Fð G˜vò Gó ó ó (ðGñ ˜×/Ñ/Ó0ÙƒØð Fð °&ð ¸Vò ó ó ó 1ðñ ˜×/Ñ/Ó0Ùˆ\Óð: Fð :°&ð :ÀUò :ó ó 1ð:ñ ˜×0Ñ0Ó1Ùˆ\ÓØðLØðLØ%ðLØ7<ðLØNRòLó ó ó 2ðLñ ˜×*Ñ*Ó+Ùˆ\ÓØò)˜ð ) fð )¸3ò )ó ó ó ,ð)ñ< ˜×*Ñ*Ó+Øð5˜vð 5¨fò 5ó ó ,ð5ñ ˜Ÿ	™	Ó"ÙƒØð&ˆvð &˜&ò &ó ó ó #ð&ñ ˜×*Ñ*Ó+Ùˆ\ÓØð>˜vð >¨Vð >¸ò >ó ó ó ,ð>ñ
 ˜×*Ñ*Ó+ð6˜ð 6¨ð 6°6ò 6ó ,ð6ñ ˜×3Ñ3Ó4ð%Øð%à
ð%ð ð%ð ˆ6�6ˆ>Ñò	%ó 5ð%ñ ˜×6Ñ6Ó7ÙƒØð
Øð
à
ð
ð ð
ð ð	
ð
 ð
ð ð
ð ð
ð ò
ó ó ó 8ð
ñ$ ˜×1Ñ1Ó2Ùˆ\ÓØð< fð <°Fð <ÀFð <Èvò <ó ó ó 3ð<ñ ˜Ÿ
™
Ó#Ùƒð/�ð /˜vð /¨&ò /ó ó $ð/ð˜vð °#ó ð˜Ÿ™ó ñ ˜Ÿ™Ó&ÙƒØà3<·>±>×3GÑ3Gñ1Ø
ð1Ø ð1Ø-0ð1àò1ó ó ó 'ð1ñ ˜×.Ñ.Ó/Ùˆ\ÓØð1Øð1Ø &ð1Ø06ð1ØCFò1ó ó ó 0ð1ñ ˜×*Ñ*Ó+ó0ó ,ð0ñ ˜×+Ñ+Ó,ÙƒØð —^‘^×)Ñ)Øñ		1Ø
ð	1àð	1ð ð	1ð ò		1ó ó ó -ð	1ñ ˜×4Ñ4×<Ñ<Ó=ØðØðØ%ðØ/5ðØBEðØMRòó ó >ðñ ˜×4Ñ4×?Ñ?Ó@Øð
RØð
Rà
ð
Rð ð
Rð ð	
Rð
 ð
Rð ò
Ró ó Að
Rñ ˜×0Ñ0×8Ñ8Ó9Øð	Øð	Ø%ð	Ø/5ð	ØBEð	ØNSò	ó ó :ð	ñ ˜×0Ñ0×4Ñ4Ó5Øð
RØð
Rà
ð
Rð ð
Rð ð	
Rð
 ð
Rð ò
Ró ó 6ð
Rð#$Øð#$à
ð#$ð ð#$ð �T‰Mð	#$ð
 ð#$ð ð#$ð ð#$ð ó#$ñL ˜×)Ñ)Ó*Ùˆ\ÓØðN˜fð N¨Fð N¸ð NÀò Nó ó ó +ðNñ( ˜×.Ñ.Ó/Ùˆ\Óð.Øð.à
ð.ð ð.ð �T‰Mð	.ð
 ð.ð ð.ð ð.ð ò.ó ó 0ð.ñb ˜×0Ñ0Ó1Ùˆ\Óð$Øð$à
ð$ð ð$ð �T‰Mð	$ð
 ð$ð ð$ð ð$ð ò$ó ó 2ð$ñN ˜×1Ñ1Ó2ÙƒØð !Ø—^‘^×)Ñ)ñ	1Ø
ð1àð1ð �T‰Mð1ð ð	1ð
 ò1ó ó ó 3ð1ñ& ˜×:Ñ:Ó;Ùˆ\ÓØð
 !Ø—^‘^×)Ñ)ñØðà
ðð ðð �T‰Mð	ð
 ðð òó ó ó <ðñ  ˜×-Ñ-Ó.ÙƒØð —^‘^×)Ñ)ñ1Øð1àð1ð ð1ð ò	1ó ó ó /ð1ñ ˜×6Ñ6Ó7Ùˆ\ÓØð
 —^‘^×)Ñ)ñ		Øð	à
ð	ð ð	ð ð		ð
 ò	ó ó ó 8ð	ñ ˜Ÿ	™	Ó"Ùƒò)�ð )˜vð )¨%ò )ó ó #ð)ñ ˜×,Ñ,Ó-Ùƒð&˜ð & Fð &¨vò &ó ó .ð&ñ ˜×+Ñ+Ó,Ùƒð	OØð	Oà�c‘ð	Oð 
ð	Oð ð		Oð
 
ð	Oð ò	Oó ó -ð	Oñ ˜Ÿ
š
×)Ñ)Ó*ð ØØØò3?à
ð3?ð 
ð3?ð �‰:ð	3?ð
 
ˆt‰ð3?ð ò3?ó +ð3?ðlØðØðØ # d¡
ðØ14°t±ðà
ˆ3�ˆ8�_óñ. ˜×*Ò*Ó+Ùƒð ØØØò$UØð$Uà	ð$Uð 
ð$Uð �‰:ð	$Uð
 
ˆt‰ð$Uð ò$Uó ó ,ð$UñN ˜×,Ò,Ó-ÙƒðE ð E°d¸3±ið EÀcð EÐRUò Eó ó .ðEñ
 ˜×.Ò.Ó/ÙƒðOØðOØ&*¨3¡iðOØ9<ðOØDGðOØORòOó ó 0ðOðØðØ%+ðØ:?¿+¹+óñ ˜×3Ò3Ó4Ùˆ\ÓØ ðXØðXØ!'ðXØ.1ðXØ@EÇÁòXó !ó ó 5ðXñ ˜×7Ò7Ó8ÙƒØ ðKØðKØ!'ðKØ.1ðKØ@EÇÁòKó !ó ó 9ðKò*ñ& ˜ŸšÓ$ÙƒðMØðMà�c‘ðMð �3‰iðMð �#‰Yð	Mð
 �‰IðMð òMó ó %ðMñ` ˜ŸšÓ$ÙƒØð]Øð]à�c‘ð]ð �c‘ð]ð �3‰ið	]ð
 �#‰Yð]ð �‰Ið]ð ò]ó ó ó %ð]ñ@ ˜×4Ò4Ó5Ùƒð
¨ð 
°vð 
Àeò 
ó ó 6ð
ñ ˜×,Ò,Ó-ÙƒðYØ
ðYØ" 3™iðYØ47ðYØ?BðYØJMðYàòYó ó .ðYñ" ˜×+Ò+×3Ñ3Ó4Øà;?ò
Øð
Ø%ð
Ø,1°D©Lð
àò
ó ó 5ð
ñ& ˜ŸšÓ%Ø‡‚×Ñ×Ò˜k×CÒCÓDØ‡‚×Ñ×Ò˜k×2Ò2Ó3ð�6ð ˜eð ¨D°4©Kò ó 4ó Eó &ðñ ˜×+Ò+Ó,ÙˆV�VÓðA˜&ð A Uð A°4¸$±;ò Aó ó -ðAñ ˜ŸšÓ&Ùƒð�ð ˜Sð °ò ó ó 'ðñ4 ˜×)Ò)Ó*Ù˜Ôð�Fð  ð °Tò ó ó +ðñ6 ˜ŸšÓ'Ùƒð Ø$ØòØðàðð ðð ð	ð
 ðð òó ó (ðñ( ˜×5Ò5Ó6ÙƒðØðàðð ðð ð	ð
 òó ó 7ðð:ˆD�‰Ió ðØ�&‰\ðà	ðð ðð 
ˆ&�\ó	ð*˜T &™\ó ð
 t¨F¡|ð 
¸#ó 
ð"Ø�&‰\ð"à	ð"ð ó"ñJ ˜Ÿš×0Ñ0°$·/²/×2EÑ2EÐFÓGð
 ò	Ø�&‰\ðà	ðð ðð 
�$‰ð	ð
 òó Hðñ  Ø	×Ò×'Ñ'¨×)CÒ)C×)GÑ)GÐHóð Ø#ò	Ø
ðà�c‘ðð 
ðð 
ˆf‰˜Ñ	ð	ð
 
ˆ&�\�DÑòóðñ  ˜×)Ò)×0Ñ0Ó1ò5˜ð 5¨Cð 5°cð 5À%ÈÐPSÈÑBTò 5ó 2ð5ñ ˜×4Ò4×<Ñ<Ó=à67òBØðBØ $ S¡	ðBØ03ðBà
ˆ6�3ˆ;ÑòBó >ðBñ ˜Ÿ
š
×)Ñ)Ó*ò/�ð / Cð /¨cð /¸%ÀÈÀÑ:Lò /ó +ð/ð( ×Ò×-Ò-×5Ò5Ø×)Ò)óð ò//Ø
ð//à &ð//ð 
ð//ð ˆ6�3ˆ;Ñò	//óð//ñf ˜Ÿ
š
Ó#Ù˜ÔØò�ð ˜fð ¨Fð ¸#ð È#ò ó ó ó $ðñ" ˜×.Ò.Ó/ÙƒØð
 ØØòØ
ðà
ðð ðð ð	ð
 ðð òó ó ó 0ðñ" ˜Ÿ
š
Ó#Ù˜ÔØò	�ð 	˜fð 	¨6ð 	¸ð 	Èò 	ó ó ó $ð	ñ ˜×7Ò7×?Ñ?Ó@ØðS&ØðS&àðS&ð ðS&ð ð	S&ð
 �D‰=ðS&ð ðS&ð ðS&ð 
ðS&ð ðS&ð �d‘ðS&ð ˆ6�D‰=˜& 4™-¨°$©Ð6Ñ7òS&ó ó AðS&ñn ˜×7Ò7×;Ñ;Ó<ðØðàðð ðð ð	ð
 �D‰=ðð ðð ðð 
ðð ðð �d‘ðð �,‰,ðð �,‰,ðð �,‰,ðð ˆ6�D‰=˜& 4™-¨°$©Ð6Ñ7òó =ðð8�6˜D‘=ð ¨F°T©Mó ñ ˜×7Ò7×?Ñ?Ó@ðQØðQàðQð ˜3‘iðQð ð	Qð
 ðQð �T‰MðQð �4‰-ðQð �d‘ðQð ˆ6�D‰=˜& 4™-¨°$©Ð6Ñ7òQó AðQñj ˜×7Ò7×;Ñ;Ó<ðØðàðð ˜3‘iðð ð	ð
 ðð �T‰Mðð �4‰-ðð �d‘ðð �,‰,ðð �,‰,ðð �,‰,ðð ˆ6�D‰=˜& 4™-¨°$©Ð6Ñ7òó =ðñ4 ˜×,Ò,×4Ñ4Ó5ð3Øð3à˜3‘ið3ð �T‰Mð3ð 
�‰ð	3ð
 ˆ6�6ˆ>Ñò3ó 6ð3ñl ˜×5Ò5×=Ñ=Ó>ðHØðHàðHð ˜3‘iðHð ð	Hð
 �T‰MðHð �d‘ðHð ˆ6�D‰=˜& 4™-Ð'Ñ(òHó ?ðHðVRØðRà�T‰MðRð �4‰-ðRð ˜4‘-ð	Rð
 ˜$‘ðRð ðRð ðRð 
ðRð ðRð ˆ6�6˜6 6¨D¡=°&¸4±-Ð?Ñ@óRñj ˜×.Ò.Ó/ÙˆU�K Ó/ð(Øð(à�T‰Mð(ð �4‰-ð(ð ˜4‘-ð	(ð
 ˜$‘ð(ð ð(ð ð(ð 
ð(ð ˆ6�6˜6Ð!Ñ"ò(ó 0ó 0ð(ð4 ×Ò×Ñ×'Ò'¨×(<Ò(<Ó=Ø×Ò×Ñ×'Ò'¨×(MÒ(MÓNð 
Øð 
à�T‰Mð 
ð �4‰-ð 
ð ˜4‘-ð	 
ð
 ˜$‘ð 
ð ð 
ð ð 
ð 
ð 
ð ˆ6�6˜6Ð!Ñ"ò 
ó Oó >ð 
ðF ×Ò×Ñ×"Ò" ;×#HÒ#HÓIòG°4¸±<ò Gó JðGñ ˜×AÒA×IÑIÓJðØðà�T‰Mðð �4‰-ðð ð	ð
 ðð ðð 
ðð ˆ6�6˜6Ð!Ñ"òó Kðñ* ˜×5Ò5×=Ñ=Ó>ð(Øð(à�T‰Mð(ð �4‰-ð(ð ð	(ð
 ð(ð ð(ð ð(ð 
ð(ð ˆ6�6˜6Ð!Ñ"ò(ó ?ð(ñ  ˜×5Ò5×>Ò>Ó?ð(Øð(à�T‰Mð(ð �4‰-ð(ð ð	(ð
 ð(ð 
ð(ð ˆ6�6˜6Ð!Ñ"ò(ó @ð(ñ ˜×@Ò@×HÑHÓIðKØðKà�T‰MðKð �4‰-ðKð ð	Kð
 ðKð ðKð ðKð 
ðKð ˆ6�6˜6 6¨6Ð1Ñ2òKó JðKð4Øðà�T‰Mðð �4‰-ðð ð	ð
 ðð 
ðð ðð óñ: ˜×4Ò4×<Ñ<Ó=ð1Øð1à�T‰Mð1ð �4‰-ð1ð ð	1ð
 ð1ð ð1ð 
ð1ð ˆ6�6˜6 6Ð)Ñ*ò1ó >ð1ñ4 ˜×?Ò?×GÑGÓHðCØðCà�T‰MðCð �4‰-ðCð ð	Cð
 ðCð ðCð 
ðCð ˆ6�6˜6 6¨6°6Ð9Ñ:òCó IðCñ8 ˜×2Ò2×:Ñ:Ó;ð1Øð1à�T‰Mð1ð �4‰-ð1ð ð	1ð
 ð1ð ð1ð 
ð1ð ˆ6�6˜6 6Ð)Ñ*ò1ó <ð1ñ4 ˜×+Ò+Ó,ÙˆV�VÓØóó ó ó -ðñ ˜ŸšÓ&Ùƒð !%ØØ"&ØØØ04ò+Ø�
Ñð+ð �;‰;˜Ñð+ð
 �LŠL˜4Ñð+ð ð+ð ð+ð ×&Ò&¨Ñ-ò+ó ó 'ð+ñb ˜Ÿš d§i¢i°·²ÐAÓBÙƒñó ó Cðð ×Ò×Ñ×&Ò& {×';Ò';Ó<Ù˜×-Ò-Ó.ÙˆV�V˜V VÓ,ðØðàðð �4‰-ðð ˜4‘-ð	ð
 ˜$‘ðð ðð !&ðð òó -ó /ó =ðò>ñ ˜×0Ò0×8Ñ8Ó9ðØðàðð �T‰Mðð ˜4‘-ð	ð
 ˜$‘ðð ˜‰}ðð ˜$‘ðð ðð 
ðð �d‘ðð ðð ˆ6�6˜D‘= &¨4¡-Ð/Ñ0òó :ðñ6 ˜×7Ò7×?Ñ?Ó@ðiØðiàðið �T‰Mðið ˜4‘-ð	ið
 ˜$‘ðið ˜‰}ðið ˜$‘ðið ðið 
ðið �d‘ðið ˆ6�6˜D‘= &¨4¡-Ð/Ñ0òió AðiñZ ˜×7Ò7×;Ñ;Ó<ð"Øð"àð"ð �T‰Mð"ð ˜4‘-ð	"ð
 ˜$‘ð"ð ˜‰}ð"ð ˜$‘ð"ð ð"ð 
ð"ð �d‘ð"ð �,‰,ð"ð �,‰,ð"ð �,‰,ð"ð ˆ6�6˜D‘= &¨4¡-Ð/Ñ0ò"ó =ð"ñJ ˜×7Ò7Ó8ÙˆV�V˜VÓ$ðØðàðð ðð ˜4‘-ð	ð
 ˜$‘ðð ˜‰}ðð �t‰mðð òó %ó 9ðñ0 ˜×6Ò6Ó7ÙˆV�V˜VÓ$ðØðàðð ðð ˜4‘-ð	ð
 ˜$‘ðð ˜‰}ðð �t‰mðð ðð òó %ó 8ðñ2 ˜×1Ò1Ó2ÙƒØðd'˜vð d'°E¸#¸s¸(±Oò d'ó ó ó 3ðd'ðNØ
ðØ)ðØ8<¸S¹	ðØHKóñ6 ˜×)Ò)Ó*Ùƒð*8Ø
ð*8àð*8ð �c‘ò*8ó ó +ð*8ñZ ˜×)Ò)Ó*Ùƒð49Øð49àð49ð �c‘ð49ð �‰Ið	49ð
 �#‰Yò49ó ó +ð49ñn ˜ŸšÓ(ð òHØðHà	ðHð ðHð ð	Hð òHó )ðHñ ˜ŸšÓ'Ùƒð òIØðIà	ðIð ðIð ð	Ið òIó ó (ðIð$ ò%@Øð%@à	ð%@ð ð%@ð ñ	%@ð ð%@ð ô%@ñP ˜×)Ò)×1Ñ1Ó2Ø×Ò×Ñ×"Ò" ;×#HÒ#HÓIôó Jó 3ðñ2 ˜×(Ò(Ó)ð<�:ð < Cð <°
ð <ÀJó <ó *ð<ñ ˜ŸšÓ(Ùƒð=�*ð = 3ð =¨zð =À:ó =ó ó )ð=ð@Øð@Øð@Ø$.ð@Ø8Bñ@ØPTô@ñ, ˜×0Ò0Ó1ÙˆX�xÓ Øð(˜fð (¨¨v°v¨~Ñ)>ó (ó ó !ó 2ð(ñ ˜ŸšÓ%Ùƒð "Ø"Ø(,ò	Øñà	�‰�eÑ	ñð �‰*�uÑ
ñð �Š Ñ%ó	ó ó &ðñ" ˜ŸšÓ&ô;ó 'ð;ó
ó8ñ ˜×/Ò/×3Ò3Ó4Ù˜×/Ò/×3Ò3Ó4Ù˜×/Ò/×3Ò3Ó4Ø×Ò×Ò×$Ò$ [×%JÒ%JÓKØ×Ò×Ò×$Ò$ [×%9Ò%9Ó:Ø×Ò×Ò×$Ò$ [×%JÒ%JÓKØ×Ò×Ò×$Ò$ [×%9Ò%9Ó:Ø×Ò×Ò×$Ò$ [×%JÒ%JÓKØ×Ò×Ò×$Ò$ [×%9Ò%9Ó:ð	3Øð	3à�c‘˜TÑ!ñ	3ð ˜‘; Ñ%ð	3ð ó		3ó ;ó Ló ;ó Ló ;ó Ló 5ó 5ó 5ð	3ñ ˜×6Ò6×:Ò:Ó;Ù˜×6Ò6×:Ò:Ó;Ù˜×6Ò6×:Ò:Ó;Ø×Ò×#Ò#×+Ò+¨K×,QÒ,QÓRØ×Ò×#Ò#×+Ò+¨K×,@Ò,@ÓAØ×Ò×#Ò#×+Ò+¨K×,QÒ,QÓRØ×Ò×#Ò#×+Ò+¨K×,@Ò,@ÓAØ×Ò×#Ò#×+Ò+¨K×,QÒ,QÓRØ×Ò×#Ò#×+Ò+¨K×,@Ò,@ÓAð	?Øð	?à�c‘˜TÑ!ñ	?ð ˜‘; Ñ%ð	?ð ó		?ó Bó Só Bó Só Bó Só <ó <ó <ð	?õ#ñL ˜×0Ò0×8Ñ8¸$×:QÒ:Q×:UÑ:UÐVÓWØ×Ò× Ñ ×(Ò(¨×)NÒ)NÓOØ×Ò× Ñ ×(Ò(¨×)=Ò)=Ó>Ù D°dÕ;ð  ò;Øð;à�c‘ñ;ð �D‰Lð;ð ó	;ó <ó ?ó Pó Xð;ñ Ø	×#Ò#×+Ñ+¨T×-KÒ-K×-OÑ-OÐPóð ×Ò×'Ñ'×/Ò/°×0UÒ0UÓVØ×Ò×'Ñ'×/Ò/°×0DÒ0DÓEÙ D°dÕ;ð  òGØðGà�c‘ñGð �D‰LðGð ó	Gó <ó Fó WóðGñ ˜×0Ò0×8Ñ8¸$×:QÒ:Q×:UÑ:UÐVÓWØ×Ò× Ñ ×(Ò(¨×)NÒ)NÓOØ×Ò× Ñ ×(Ò(¨×)=Ò)=Ó>Ù D°dÕ;ð "Ø!ò	GØðGà�c‘ñGð �d‰lñGð �d‰lð	Gð
 óGó <ó ?ó Pó XðGñ Ø	×#Ò#×+Ñ+¨T×-KÒ-K×-OÑ-OÐPóð ×Ò×'Ñ'×/Ò/°×0UÒ0UÓVØ×Ò×'Ñ'×/Ò/°×0DÒ0DÓEÙ D°dÕ;ð "Ø!ò	SØðSà�c‘ñSð �d‰lñSð �d‰lð	Sð
 óSó <ó Fó WóðSñ ˜×0Ò0×8Ñ8¸$×:QÒ:Q×:UÑ:UÐVÓWØ×Ò× Ñ ×(Ò(¨×)NÒ)NÓOØ×Ò× Ñ ×(Ò(¨×)=Ò)=Ó>Ù D°dÕ;ð "Ø!Ø!òQØðQà�c‘ñQð �d‰lñQð �d‰lñ	Qð
 �d‰lðQð óQó <ó ?ó Pó XðQñ Ø	×#Ò#×+Ñ+¨T×-KÒ-K×-OÑ-OÐPóð ×Ò×'Ñ'×/Ò/°×0UÒ0UÓVØ×Ò×'Ñ'×/Ò/°×0DÒ0DÓEÙ D°dÕ;ð "Ø!Ø!ò	Øð	à�c‘ñ	ð �d‰lñ	ð �d‰lñ		ð
 �d‰lð	ð ó	ó <ó Fó Wóð	ð ð
 ò	Øðà�c‘ñð �˜‘Ññð ð	ð
 óó ðó4ó&>ó/óð$ FKõ+ó\óõ&õ,/-ód& ñR ˜Ÿš×+Ò+Ó,Ø‡‚×Ò×Ò˜[×BÒBÓCØ‡‚×Ò×Ò˜[×1Ò1Ó2ò.ó 3ó Dó -ð.ñ8 ˜Ÿš×+Ò+Ó,Ø‡‚×Ò×Ò˜[×BÒBÓCØ‡‚×Ò×Ò˜[×1Ò1Ó2ò.ó 3ó Dó -ð.ñ8 ˜Ÿš×*Ò*Ó+Ø‡‚×Ò×Ò˜K×AÒAÓBØ‡‚×Ò×Ò˜K×0Ò0Ó1ò.ó 2ó Có ,ð.ñ@ ˜Ÿš×*Ò*Ó+Ø‡‚×Ò×Ò˜K×AÒAÓBØ‡‚×Ò×Ò˜K×0Ò0Ó1ò.ó 2ó Có ,ð.ó@õ/õ6=ô@/ñd ˜Ÿ	š	ŸšÓ(Ø‡‚‡‚×Ò˜×>Ò>Ó?Ø‡‚‡‚×Ò˜×-Ò-Ó.òSó /ó @ó )ñSñ@ ˜Ÿ	š	ŸšÓ'Ø‡‚‡‚×Ò˜×=Ò=Ó>Ø‡‚‡‚×Ò˜×,Ò,Ó-òSó .ó ?ó (ñSô>;ô;ñ ˜ŸšŸšÓ&Ø‡‚‡‚×Ò�{×<Ò<Ó=Ø‡‚‡‚×Ò�{×+Ò+Ó,ò.ó -ó >ó 'ñ.ñ6 ˜ŸšŸšÓ'Ø‡‚‡‚×Ò˜×=Ò=Ó>Ø‡‚‡‚×Ò˜×,Ò,Ó-ò.ó .ó ?ó (ñ.ñ6 ˜×4Ò4×8Ò8Ó9Ø×Ò×!Ò!×)Ò)¨+×*OÒ*OÓPØ×Ò×!Ò!×)Ò)¨+×*>Ò*>Ó?òó @ó Qó :ññ ˜×3Ò3×7Ò7Ó8Ø×Ò× Ò ×(Ò(¨×)NÒ)NÓOØ×Ò× Ò ×(Ò(¨×)=Ò)=Ó>òó ?ó Pó 9ññ ˜×3Ò3×7Ò7Ó8Ø×Ò× Ò ×(Ò(¨×)NÒ)NÓOØ×Ò× Ò ×(Ò(¨×)=Ò)=Ó>òó ?ó Pó 9ññ ˜×0Ò0×4Ò4Ó5Ù˜×1Ò1×5Ò5Ó6Ø×Ò×Ò×#Ò# K×$IÒ$IÓJØ×Ò×Ò×#Ò# K×$8Ò$8Ó9Ø×Ò×Ò×%Ò% k×&KÒ&KÓLØ×Ò×Ò×%Ò% k×&:Ò&:Ó;Ø×Ò×Ò×&Ò& {×'LÒ'LÓMØ×Ò×Ò×&Ò& {×';Ò';Ó<òAó =ó Nó <ó Mó :ó Kó 7ó 6ñAñ ˜×/Ò/×7Ñ7¸×9OÒ9O×9SÑ9SÐTÓUÙƒð
 "ò	KØðKà�c‘ñKð ñKð �d‰lð	Kð
 óKó ó VñKñ Ø	×Ò×%Ñ% t×'?Ò'?×'CÑ'CÐDóð ×Ò×!Ñ!×)Ò)¨+×*>Ò*>Ó?Ùƒð
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ð ñ
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öVô/ð7Ø	�&Ñ	ñ7Ø$,¨VÑ$4ñ7ØIOð7àõ7ñ-Ð'9ð -¸fõ -ð ðIØðIà�c‘ñIð ñIð �˜‘Ñð	Ið
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ð3 àð3 ð �T‰Mð3 ð ð	3 ð
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ñf4ð ñf4ð ñ	f4ð
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ð	Dð �;‰;˜Ñð	Dð 
�$‰ð		Dð
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ó ó #ñ
ñ( ˜Ÿš×.Ñ.Ó/ð )-óØ
�,‰,ñð �Š Ñ%ðð ‡\�\ó	ó 0ñð$ 5:÷ 
#ð <AÈ÷ +ñ: ˜Ÿ	š	Ó"Ùƒòó ó #ññ
 ˜ŸšÓ'ôGó (ñGñ ˜×=Ò=Ó>ðsØðsà
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