+%%\r
+%% IEEEtran.cls 2012/12/27 version V1.8\r
+%% \r
+%% This is the IEEEtran LaTeX class for authors of the Institute of \r
+%% Electrical and Electronics Engineers (IEEE) Transactions journals and\r
+%% conferences.\r
+%% \r
+%% Support sites:\r
+%% http://www.michaelshell.org/tex/ieeetran/\r
+%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/\r
+%% and\r
+%% http://www.ieee.org/\r
+%%\r
+%% Based on the original 1993 IEEEtran.cls, but with many bug fixes\r
+%% and enhancements (from both JVH and MDS) over the 1996/7 version.\r
+%%\r
+%%\r
+%% Contributors:\r
+%% Gerry Murray (1993), Silvano Balemi (1993),\r
+%% Jon Dixon (1996), Peter N"uchter (1996),\r
+%% Juergen von Hagen (2000), and Michael Shell (2001-2012)\r
+%% \r
+%% \r
+%% Copyright (c) 1993-2000 by Gerry Murray, Silvano Balemi, \r
+%% Jon Dixon, Peter N"uchter,\r
+%% Juergen von Hagen\r
+%% and\r
+%% Copyright (c) 2001-2012 by Michael Shell\r
+%%\r
+%% Current maintainer (V1.3 to V1.8): Michael Shell\r
+%% See:\r
+%% http://www.michaelshell.org/\r
+%% for current contact information.\r
+%%\r
+%% Special thanks to Peter Wilson (CUA) and Donald Arseneau\r
+%% for allowing the inclusion of the \@ifmtarg command \r
+%% from their ifmtarg LaTeX package. \r
+%% \r
+%%*************************************************************************\r
+%% Legal Notice:\r
+%% This code is offered as-is without any warranty either expressed or\r
+%% implied; without even the implied warranty of MERCHANTABILITY or\r
+%% FITNESS FOR A PARTICULAR PURPOSE! \r
+%% User assumes all risk.\r
+%% In no event shall IEEE or any contributor to this code be liable for\r
+%% any damages or losses, including, but not limited to, incidental,\r
+%% consequential, or any other damages, resulting from the use or misuse\r
+%% of any information contained here.\r
+%%\r
+%% All comments are the opinions of their respective authors and are not\r
+%% necessarily endorsed by the IEEE.\r
+%%\r
+%% This work is distributed under the LaTeX Project Public License (LPPL)\r
+%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,\r
+%% distributed and modified. A copy of the LPPL, version 1.3, is included\r
+%% in the base LaTeX documentation of all distributions of LaTeX released\r
+%% 2003/12/01 or later.\r
+%% Retain all contribution notices and credits.\r
+%% ** Modified files should be clearly indicated as such, including **\r
+%% ** renaming them and changing author support contact information. **\r
+%%\r
+%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,\r
+%% bare_conf.tex, bare_jrnl.tex, bare_jrnl_compsoc.tex\r
+%% \r
+%% Major changes to the user interface should be indicated by an \r
+%% increase in the version numbers. If a version is a beta, it will \r
+%% be indicated with a BETA suffix, i.e., 1.4 BETA.\r
+%% Small changes can be indicated by appending letters to the version\r
+%% such as "IEEEtran_v14a.cls".\r
+%% In all cases, \Providesclass, any \typeout messages to the user,\r
+%% \IEEEtransversionmajor and \IEEEtransversionminor must reflect the\r
+%% correct version information.\r
+%% The changes should also be documented via source comments.\r
+%%*************************************************************************\r
+%%\r
+%\r
+% Available class options \r
+% e.g., \documentclass[10pt,conference]{IEEEtran} \r
+% \r
+% *** choose only one from each category ***\r
+%\r
+% 9pt, 10pt, 11pt, 12pt\r
+% Sets normal font size. The default is 10pt.\r
+% \r
+% conference, journal, technote, peerreview, peerreviewca\r
+% determines format mode - conference papers, journal papers,\r
+% correspondence papers (technotes), or peer review papers. The user\r
+% should also select 9pt when using technote. peerreview is like\r
+% journal mode, but provides for a single-column "cover" title page for\r
+% anonymous peer review. The paper title (without the author names) is\r
+% repeated at the top of the page after the cover page. For peer review\r
+% papers, the \IEEEpeerreviewmaketitle command must be executed (will\r
+% automatically be ignored for non-peerreview modes) at the place the\r
+% cover page is to end, usually just after the abstract (keywords are\r
+% not normally used with peer review papers). peerreviewca is like\r
+% peerreview, but allows the author names to be entered and formatted\r
+% as with conference mode so that author affiliation and contact\r
+% information can be easily seen on the cover page.\r
+% The default is journal.\r
+%\r
+% draft, draftcls, draftclsnofoot, final\r
+% determines if paper is formatted as a widely spaced draft (for\r
+% handwritten editor comments) or as a properly typeset final version.\r
+% draftcls restricts draft mode to the class file while all other LaTeX\r
+% packages (i.e., \usepackage{graphicx}) will behave as final - allows\r
+% for a draft paper with visible figures, etc. draftclsnofoot is like\r
+% draftcls, but does not display the date and the word "DRAFT" at the foot\r
+% of the pages. If using one of the draft modes, the user will probably\r
+% also want to select onecolumn.\r
+% The default is final.\r
+%\r
+% letterpaper, a4paper\r
+% determines paper size: 8.5in X 11in or 210mm X 297mm. CHANGING THE PAPER\r
+% SIZE WILL NOT ALTER THE TYPESETTING OF THE DOCUMENT - ONLY THE MARGINS\r
+% WILL BE AFFECTED. In particular, documents using the a4paper option will\r
+% have reduced side margins (A4 is narrower than US letter) and a longer\r
+% bottom margin (A4 is longer than US letter). For both cases, the top\r
+% margins will be the same and the text will be horizontally centered. \r
+% For final submission to IEEE, authors should use US letter (8.5 X 11in)\r
+% paper. Note that authors should ensure that all post-processing \r
+% (ps, pdf, etc.) uses the same paper specificiation as the .tex document.\r
+% Problems here are by far the number one reason for incorrect margins.\r
+% IEEEtran will automatically set the default paper size under pdflatex \r
+% (without requiring a change to pdftex.cfg), so this issue is more\r
+% important to dvips users. Fix config.ps, config.pdf, or ~/.dvipsrc for\r
+% dvips, or use the dvips -t papersize option instead as needed. See the\r
+% testflow documentation\r
+% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/testflow\r
+% for more details on dvips paper size configuration.\r
+% The default is letterpaper.\r
+%\r
+% oneside, twoside\r
+% determines if layout follows single sided or two sided (duplex)\r
+% printing. The only notable change is with the headings at the top of\r
+% the pages.\r
+% The default is oneside.\r
+%\r
+% onecolumn, twocolumn\r
+% determines if text is organized into one or two columns per page. One\r
+% column mode is usually used only with draft papers.\r
+% The default is twocolumn.\r
+%\r
+% compsoc, transmag\r
+% Use the format of the IEEE Computer Society or IEEE Transactions on Magnetics\r
+%\r
+% romanappendices\r
+% Use the "Appendix I" convention when numbering appendices. IEEEtran.cls\r
+% now defaults to Alpha "Appendix A" convention - the opposite of what\r
+% v1.6b and earlier did.\r
+%\r
+% captionsoff\r
+% disables the display of the figure/table captions. Some IEEE journals\r
+% request that captions be removed and figures/tables be put on pages\r
+% of their own at the end of an initial paper submission. The endfloat\r
+% package can be used with this class option to achieve this format.\r
+%\r
+% nofonttune\r
+% turns off tuning of the font interword spacing. Maybe useful to those\r
+% not using the standard Times fonts or for those who have already "tuned"\r
+% their fonts.\r
+% The default is to enable IEEEtran to tune font parameters.\r
+%\r
+%\r
+%----------\r
+% Available CLASSINPUTs provided (all are macros unless otherwise noted):\r
+% \CLASSINPUTbaselinestretch\r
+% \CLASSINPUTinnersidemargin\r
+% \CLASSINPUToutersidemargin\r
+% \CLASSINPUTtoptextmargin\r
+% \CLASSINPUTbottomtextmargin\r
+%\r
+% Available CLASSINFOs provided:\r
+% \ifCLASSINFOpdf (TeX if conditional)\r
+% \CLASSINFOpaperwidth (macro)\r
+% \CLASSINFOpaperheight (macro)\r
+% \CLASSINFOnormalsizebaselineskip (length)\r
+% \CLASSINFOnormalsizeunitybaselineskip (length)\r
+%\r
+% Available CLASSOPTIONs provided:\r
+% all class option flags (TeX if conditionals) unless otherwise noted,\r
+% e.g., \ifCLASSOPTIONcaptionsoff\r
+% point size options provided as a single macro:\r
+% \CLASSOPTIONpt\r
+% which will be defined as 9, 10, 11, or 12 depending on the document's\r
+% normalsize point size.\r
+% also, class option peerreviewca implies the use of class option peerreview\r
+% and classoption draft implies the use of class option draftcls\r
+\r
+\r
+\r
+\r
+\r
+\ProvidesClass{IEEEtran}[2012/12/27 V1.8 by Michael Shell]\r
+\typeout{-- See the "IEEEtran_HOWTO" manual for usage information.}\r
+\typeout{-- http://www.michaelshell.org/tex/ieeetran/}\r
+\NeedsTeXFormat{LaTeX2e}\r
+\r
+% IEEEtran.cls version numbers, provided as of V1.3\r
+% These values serve as a way a .tex file can\r
+% determine if the new features are provided.\r
+% The version number of this IEEEtrans.cls can be obtained from \r
+% these values. i.e., V1.4\r
+% KEEP THESE AS INTEGERS! i.e., NO {4a} or anything like that-\r
+% (no need to enumerate "a" minor changes here)\r
+\def\IEEEtransversionmajor{1}\r
+\def\IEEEtransversionminor{8}\r
+\r
+% These do nothing, but provide them like in article.cls\r
+\newif\if@restonecol\r
+\newif\if@titlepage\r
+\r
+\r
+% class option conditionals\r
+\newif\ifCLASSOPTIONonecolumn \CLASSOPTIONonecolumnfalse\r
+\newif\ifCLASSOPTIONtwocolumn \CLASSOPTIONtwocolumntrue\r
+\r
+\newif\ifCLASSOPTIONoneside \CLASSOPTIONonesidetrue\r
+\newif\ifCLASSOPTIONtwoside \CLASSOPTIONtwosidefalse\r
+\r
+\newif\ifCLASSOPTIONfinal \CLASSOPTIONfinaltrue\r
+\newif\ifCLASSOPTIONdraft \CLASSOPTIONdraftfalse\r
+\newif\ifCLASSOPTIONdraftcls \CLASSOPTIONdraftclsfalse\r
+\newif\ifCLASSOPTIONdraftclsnofoot \CLASSOPTIONdraftclsnofootfalse\r
+\r
+\newif\ifCLASSOPTIONpeerreview \CLASSOPTIONpeerreviewfalse\r
+\newif\ifCLASSOPTIONpeerreviewca \CLASSOPTIONpeerreviewcafalse\r
+\r
+\newif\ifCLASSOPTIONjournal \CLASSOPTIONjournaltrue\r
+\newif\ifCLASSOPTIONconference \CLASSOPTIONconferencefalse\r
+\newif\ifCLASSOPTIONtechnote \CLASSOPTIONtechnotefalse\r
+\r
+\newif\ifCLASSOPTIONnofonttune \CLASSOPTIONnofonttunefalse\r
+\r
+\newif\ifCLASSOPTIONcaptionsoff \CLASSOPTIONcaptionsofffalse\r
+\r
+\newif\ifCLASSOPTIONcompsoc \CLASSOPTIONcompsocfalse\r
+\newif\ifCLASSOPTIONtransmag \CLASSOPTIONtransmagfalse\r
+\r
+\newif\ifCLASSOPTIONromanappendices \CLASSOPTIONromanappendicesfalse\r
+\r
+\r
+% class info conditionals\r
+\r
+% indicates if pdf (via pdflatex) output\r
+\newif\ifCLASSINFOpdf \CLASSINFOpdffalse\r
+\r
+\r
+% V1.6b internal flag to show if using a4paper\r
+\newif\if@IEEEusingAfourpaper \@IEEEusingAfourpaperfalse\r
+\r
+\r
+\r
+% IEEEtran class scratch pad registers\r
+% dimen\r
+\newdimen\@IEEEtrantmpdimenA\r
+\newdimen\@IEEEtrantmpdimenB\r
+% count\r
+\newcount\@IEEEtrantmpcountA\r
+\newcount\@IEEEtrantmpcountB\r
+% token list\r
+\newtoks\@IEEEtrantmptoksA\r
+\r
+% we use \CLASSOPTIONpt so that we can ID the point size (even for 9pt docs)\r
+% as well as LaTeX's \@ptsize to retain some compatability with some\r
+% external packages\r
+\def\@ptsize{0}\r
+% LaTeX does not support 9pt, so we set \@ptsize to 0 - same as that of 10pt\r
+\DeclareOption{9pt}{\def\CLASSOPTIONpt{9}\def\@ptsize{0}}\r
+\DeclareOption{10pt}{\def\CLASSOPTIONpt{10}\def\@ptsize{0}}\r
+\DeclareOption{11pt}{\def\CLASSOPTIONpt{11}\def\@ptsize{1}}\r
+\DeclareOption{12pt}{\def\CLASSOPTIONpt{12}\def\@ptsize{2}}\r
+\r
+\r
+\r
+\DeclareOption{letterpaper}{\setlength{\paperheight}{11in}%\r
+ \setlength{\paperwidth}{8.5in}%\r
+ \@IEEEusingAfourpaperfalse\r
+ \def\CLASSOPTIONpaper{letter}%\r
+ \def\CLASSINFOpaperwidth{8.5in}%\r
+ \def\CLASSINFOpaperheight{11in}}\r
+\r
+\r
+\DeclareOption{a4paper}{\setlength{\paperheight}{297mm}%\r
+ \setlength{\paperwidth}{210mm}%\r
+ \@IEEEusingAfourpapertrue\r
+ \def\CLASSOPTIONpaper{a4}%\r
+ \def\CLASSINFOpaperwidth{210mm}%\r
+ \def\CLASSINFOpaperheight{297mm}}\r
+\r
+\DeclareOption{oneside}{\@twosidefalse\@mparswitchfalse\r
+ \CLASSOPTIONonesidetrue\CLASSOPTIONtwosidefalse}\r
+\DeclareOption{twoside}{\@twosidetrue\@mparswitchtrue\r
+ \CLASSOPTIONtwosidetrue\CLASSOPTIONonesidefalse}\r
+\r
+\DeclareOption{onecolumn}{\CLASSOPTIONonecolumntrue\CLASSOPTIONtwocolumnfalse}\r
+\DeclareOption{twocolumn}{\CLASSOPTIONtwocolumntrue\CLASSOPTIONonecolumnfalse}\r
+\r
+% If the user selects draft, then this class AND any packages\r
+% will go into draft mode.\r
+\DeclareOption{draft}{\CLASSOPTIONdrafttrue\CLASSOPTIONdraftclstrue\r
+ \CLASSOPTIONdraftclsnofootfalse} \r
+% draftcls is for a draft mode which will not affect any packages\r
+% used by the document.\r
+\DeclareOption{draftcls}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue\r
+ \CLASSOPTIONdraftclsnofootfalse} \r
+% draftclsnofoot is like draftcls, but without the footer.\r
+\DeclareOption{draftclsnofoot}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclstrue\r
+ \CLASSOPTIONdraftclsnofoottrue} \r
+\DeclareOption{final}{\CLASSOPTIONdraftfalse\CLASSOPTIONdraftclsfalse\r
+ \CLASSOPTIONdraftclsnofootfalse}\r
+\r
+\DeclareOption{journal}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse\r
+ \CLASSOPTIONjournaltrue\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}\r
+\r
+\DeclareOption{conference}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse\r
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencetrue\CLASSOPTIONtechnotefalse}\r
+\r
+\DeclareOption{technote}{\CLASSOPTIONpeerreviewfalse\CLASSOPTIONpeerreviewcafalse\r
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotetrue}\r
+\r
+\DeclareOption{peerreview}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcafalse\r
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}\r
+\r
+\DeclareOption{peerreviewca}{\CLASSOPTIONpeerreviewtrue\CLASSOPTIONpeerreviewcatrue\r
+ \CLASSOPTIONjournalfalse\CLASSOPTIONconferencefalse\CLASSOPTIONtechnotefalse}\r
+\r
+\DeclareOption{nofonttune}{\CLASSOPTIONnofonttunetrue}\r
+\r
+\DeclareOption{captionsoff}{\CLASSOPTIONcaptionsofftrue}\r
+\r
+\DeclareOption{compsoc}{\CLASSOPTIONcompsoctrue\CLASSOPTIONtransmagfalse}\r
+\r
+\DeclareOption{transmag}{\CLASSOPTIONtransmagtrue\CLASSOPTIONcompsocfalse}\r
+\r
+\DeclareOption{romanappendices}{\CLASSOPTIONromanappendicestrue}\r
+\r
+\r
+% default to US letter paper, 10pt, twocolumn, one sided, final, journal\r
+\ExecuteOptions{letterpaper,10pt,twocolumn,oneside,final,journal}\r
+% overrride these defaults per user requests\r
+\ProcessOptions\r
+\r
+\r
+\r
+% Computer Society conditional execution command\r
+\long\def\@IEEEcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\relax#1\relax\fi\relax}\r
+% inverse\r
+\long\def\@IEEEnotcompsoconly#1{\relax\ifCLASSOPTIONcompsoc\else\relax#1\relax\fi\relax}\r
+% compsoc conference\r
+\long\def\@IEEEcompsocconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\relax#1\relax\fi\fi\relax}\r
+% compsoc not conference\r
+\long\def\@IEEEcompsocnotconfonly#1{\relax\ifCLASSOPTIONcompsoc\ifCLASSOPTIONconference\else\relax#1\relax\fi\fi\relax}\r
+\r
+\r
+% IEEE uses Times Roman font, so we'll default to Times.\r
+% These three commands make up the entire times.sty package.\r
+\renewcommand{\sfdefault}{phv}\r
+\renewcommand{\rmdefault}{ptm}\r
+\renewcommand{\ttdefault}{pcr}\r
+\r
+\@IEEEcompsoconly{\typeout{-- Using IEEE Computer Society mode.}}\r
+\r
+% V1.7 compsoc nonconference papers, use Palatino/Palladio as the main text font,\r
+% not Times Roman.\r
+\@IEEEcompsocnotconfonly{\renewcommand{\rmdefault}{ppl}}\r
+\r
+% enable Times/Palatino main text font\r
+\normalfont\selectfont\r
+\r
+\r
+\r
+\r
+\r
+% V1.7 conference notice message hook\r
+\def\@IEEEconsolenoticeconference{\typeout{}%\r
+\typeout{** Conference Paper **}%\r
+\typeout{Before submitting the final camera ready copy, remember to:}%\r
+\typeout{}%\r
+\typeout{ 1. Manually equalize the lengths of two columns on the last page}%\r
+\typeout{ of your paper;}%\r
+\typeout{}%\r
+\typeout{ 2. Ensure that any PostScript and/or PDF output post-processing}%\r
+\typeout{ uses only Type 1 fonts and that every step in the generation}%\r
+\typeout{ process uses the appropriate paper size.}%\r
+\typeout{}}\r
+\r
+\r
+% we can send console reminder messages to the user here\r
+\AtEndDocument{\ifCLASSOPTIONconference\@IEEEconsolenoticeconference\fi}\r
+\r
+\r
+% warn about the use of single column other than for draft mode\r
+\ifCLASSOPTIONtwocolumn\else%\r
+ \ifCLASSOPTIONdraftcls\else%\r
+ \typeout{** ATTENTION: Single column mode is not typically used with IEEE publications.}%\r
+ \fi%\r
+\fi\r
+\r
+\r
+% V1.7 improved paper size setting code.\r
+% Set pdfpage and dvips paper sizes. Conditional tests are similar to that\r
+% of ifpdf.sty. Retain within {} to ensure tested macros are never altered,\r
+% even if only effect is to set them to \relax.\r
+% if \pdfoutput is undefined or equal to relax, output a dvips special\r
+{\@ifundefined{pdfoutput}{\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}}{%\r
+% pdfoutput is defined and not equal to \relax\r
+% check for pdfpageheight existence just in case someone sets pdfoutput\r
+% under non-pdflatex. If exists, set them regardless of value of \pdfoutput.\r
+\@ifundefined{pdfpageheight}{\relax}{\global\pdfpagewidth\paperwidth\r
+\global\pdfpageheight\paperheight}%\r
+% if using \pdfoutput=0 under pdflatex, send dvips papersize special\r
+\ifcase\pdfoutput\r
+\AtBeginDvi{\special{papersize=\CLASSINFOpaperwidth,\CLASSINFOpaperheight}}%\r
+\else\r
+% we are using pdf output, set CLASSINFOpdf flag\r
+\global\CLASSINFOpdftrue\r
+\fi}}\r
+\r
+% let the user know the selected papersize\r
+\typeout{-- Using \CLASSINFOpaperwidth\space x \CLASSINFOpaperheight\space\r
+(\CLASSOPTIONpaper)\space paper.}\r
+\r
+\ifCLASSINFOpdf\r
+\typeout{-- Using PDF output.}\r
+\else\r
+\typeout{-- Using DVI output.}\r
+\fi\r
+\r
+\r
+% The idea hinted here is for LaTeX to generate markleft{} and markright{}\r
+% automatically for you after you enter \author{}, \journal{},\r
+% \journaldate{}, journalvol{}, \journalnum{}, etc.\r
+% However, there may be some backward compatibility issues here as\r
+% well as some special applications for IEEEtran.cls and special issues\r
+% that may require the flexible \markleft{}, \markright{} and/or \markboth{}.\r
+% We'll leave this as an open future suggestion.\r
+%\newcommand{\journal}[1]{\def\@journal{#1}}\r
+%\def\@journal{}\r
+\r
+\r
+\r
+% pointsize values\r
+% used with ifx to determine the document's normal size\r
+\def\@IEEEptsizenine{9}\r
+\def\@IEEEptsizeten{10}\r
+\def\@IEEEptsizeeleven{11}\r
+\def\@IEEEptsizetwelve{12}\r
+\r
+\r
+\r
+% FONT DEFINITIONS (No sizexx.clo file needed) \r
+% V1.6 revised font sizes, displayskip values and\r
+% revised normalsize baselineskip to reduce underfull vbox problems\r
+% on the 58pc = 696pt = 9.5in text height we want\r
+% normalsize #lines/column baselineskip (aka leading)\r
+% 9pt 63 11.0476pt (truncated down)\r
+% 10pt 58 12pt (exact)\r
+% 11pt 52 13.3846pt (truncated down)\r
+% 12pt 50 13.92pt (exact)\r
+%\r
+\r
+% we need to store the nominal baselineskip for the given font size\r
+% in case baselinestretch ever changes.\r
+% this is a dimen, so it will not hold stretch or shrink\r
+\newdimen\@IEEEnormalsizeunitybaselineskip\r
+\@IEEEnormalsizeunitybaselineskip\baselineskip\r
+\r
+\ifx\CLASSOPTIONpt\@IEEEptsizenine\r
+\typeout{-- This is a 9 point document.}\r
+\def\normalsize{\@setfontsize{\normalsize}{9}{11.0476pt}}%\r
+\setlength{\@IEEEnormalsizeunitybaselineskip}{11.0476pt}%\r
+\normalsize\r
+\abovedisplayskip 1.5ex plus3pt minus1pt%\r
+\belowdisplayskip \abovedisplayskip%\r
+\abovedisplayshortskip 0pt plus3pt%\r
+\belowdisplayshortskip 1.5ex plus3pt minus1pt\r
+\def\small{\@setfontsize{\small}{8.5}{10pt}}\r
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}\r
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}\r
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}\r
+% sublargesize is the same as large - 10pt\r
+\def\sublargesize{\@setfontsize{\sublargesize}{10}{12pt}}\r
+\def\large{\@setfontsize{\large}{10}{12pt}}\r
+\def\Large{\@setfontsize{\Large}{12}{14pt}}\r
+\def\LARGE{\@setfontsize{\LARGE}{14}{17pt}}\r
+\def\huge{\@setfontsize{\huge}{17}{20pt}}\r
+\def\Huge{\@setfontsize{\Huge}{20}{24pt}}\r
+\fi\r
+\r
+\r
+% Check if we have selected 10 points\r
+\ifx\CLASSOPTIONpt\@IEEEptsizeten\r
+\typeout{-- This is a 10 point document.}\r
+\def\normalsize{\@setfontsize{\normalsize}{10}{12.00pt}}%\r
+\setlength{\@IEEEnormalsizeunitybaselineskip}{12pt}%\r
+\normalsize\r
+\abovedisplayskip 1.5ex plus4pt minus2pt%\r
+\belowdisplayskip \abovedisplayskip%\r
+\abovedisplayshortskip 0pt plus4pt%\r
+\belowdisplayshortskip 1.5ex plus4pt minus2pt\r
+\def\small{\@setfontsize{\small}{9}{10pt}}\r
+\def\footnotesize{\@setfontsize{\footnotesize}{8}{9pt}}\r
+\def\scriptsize{\@setfontsize{\scriptsize}{7}{8pt}}\r
+\def\tiny{\@setfontsize{\tiny}{5}{6pt}}\r
+% sublargesize is a tad smaller than large - 11pt\r
+\def\sublargesize{\@setfontsize{\sublargesize}{11}{13.4pt}}\r
+\def\large{\@setfontsize{\large}{12}{14pt}}\r
+\def\Large{\@setfontsize{\Large}{14}{17pt}}\r
+\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}\r
+\def\huge{\@setfontsize{\huge}{20}{24pt}}\r
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}\r
+\fi\r
+\r
+\r
+% Check if we have selected 11 points\r
+\ifx\CLASSOPTIONpt\@IEEEptsizeeleven\r
+\typeout{-- This is an 11 point document.}\r
+\def\normalsize{\@setfontsize{\normalsize}{11}{13.3846pt}}%\r
+\setlength{\@IEEEnormalsizeunitybaselineskip}{13.3846pt}%\r
+\normalsize\r
+\abovedisplayskip 1.5ex plus5pt minus3pt%\r
+\belowdisplayskip \abovedisplayskip%\r
+\abovedisplayshortskip 0pt plus5pt%\r
+\belowdisplayshortskip 1.5ex plus5pt minus3pt\r
+\def\small{\@setfontsize{\small}{10}{12pt}}\r
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}\r
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}\r
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}\r
+% sublargesize is the same as large - 12pt\r
+\def\sublargesize{\@setfontsize{\sublargesize}{12}{14pt}}\r
+\def\large{\@setfontsize{\large}{12}{14pt}}\r
+\def\Large{\@setfontsize{\Large}{14}{17pt}}\r
+\def\LARGE{\@setfontsize{\LARGE}{17}{20pt}}\r
+\def\huge{\@setfontsize{\huge}{20}{24pt}}\r
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}\r
+\fi\r
+\r
+\r
+% Check if we have selected 12 points\r
+\ifx\CLASSOPTIONpt\@IEEEptsizetwelve\r
+\typeout{-- This is a 12 point document.}\r
+\def\normalsize{\@setfontsize{\normalsize}{12}{13.92pt}}%\r
+\setlength{\@IEEEnormalsizeunitybaselineskip}{13.92pt}%\r
+\normalsize\r
+\abovedisplayskip 1.5ex plus6pt minus4pt%\r
+\belowdisplayskip \abovedisplayskip%\r
+\abovedisplayshortskip 0pt plus6pt%\r
+\belowdisplayshortskip 1.5ex plus6pt minus4pt\r
+\def\small{\@setfontsize{\small}{10}{12pt}}\r
+\def\footnotesize{\@setfontsize{\footnotesize}{9}{10.5pt}}\r
+\def\scriptsize{\@setfontsize{\scriptsize}{8}{9pt}}\r
+\def\tiny{\@setfontsize{\tiny}{6}{7pt}}\r
+% sublargesize is the same as large - 14pt\r
+\def\sublargesize{\@setfontsize{\sublargesize}{14}{17pt}}\r
+\def\large{\@setfontsize{\large}{14}{17pt}}\r
+\def\Large{\@setfontsize{\Large}{17}{20pt}}\r
+\def\LARGE{\@setfontsize{\LARGE}{20}{24pt}}\r
+\def\huge{\@setfontsize{\huge}{22}{26pt}}\r
+\def\Huge{\@setfontsize{\Huge}{24}{28pt}}\r
+\fi\r
+\r
+\r
+% V1.6 The Computer Modern Fonts will issue a substitution warning for\r
+% 24pt titles (24.88pt is used instead) increase the substitution\r
+% tolerance to turn off this warning\r
+\def\fontsubfuzz{.9pt}\r
+% However, the default (and correct) Times font will scale exactly as needed.\r
+\r
+\r
+% warn the user in case they forget to use the 9pt option with\r
+% technote\r
+\ifCLASSOPTIONtechnote%\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\else%\r
+ \typeout{** ATTENTION: Technotes are normally 9pt documents.}%\r
+ \fi%\r
+\fi\r
+\r
+\r
+% V1.7\r
+% Improved \textunderscore to provide a much better fake _ when used with\r
+% OT1 encoding. Under OT1, detect use of pcr or cmtt \ttfamily and use\r
+% available true _ glyph for those two typewriter fonts.\r
+\def\@IEEEstringptm{ptm} % Times Roman family\r
+\def\@IEEEstringppl{ppl} % Palatino Roman family\r
+\def\@IEEEstringphv{phv} % Helvetica Sans Serif family\r
+\def\@IEEEstringpcr{pcr} % Courier typewriter family\r
+\def\@IEEEstringcmtt{cmtt} % Computer Modern typewriter family\r
+\DeclareTextCommandDefault{\textunderscore}{\leavevmode\r
+\ifx\f@family\@IEEEstringpcr\string_\else\r
+\ifx\f@family\@IEEEstringcmtt\string_\else\r
+\ifx\f@family\@IEEEstringptm\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else\r
+\ifx\f@family\@IEEEstringppl\kern 0em\vbox{\hrule\@width 0.5em\@height 0.5pt\kern -0.3ex}\else\r
+\ifx\f@family\@IEEEstringphv\kern -0.03em\vbox{\hrule\@width 0.62em\@height 0.52pt\kern -0.33ex}\kern -0.03em\else\r
+\kern 0.09em\vbox{\hrule\@width 0.6em\@height 0.44pt\kern -0.63pt\kern -0.42ex}\kern 0.09em\fi\fi\fi\fi\fi\relax}\r
+\r
+\r
+\r
+\r
+% set the default \baselinestretch\r
+\def\baselinestretch{1}\r
+\ifCLASSOPTIONdraftcls\r
+ \def\baselinestretch{1.5}% default baselinestretch for draft modes\r
+\fi \r
+\r
+\r
+% process CLASSINPUT baselinestretch\r
+\ifx\CLASSINPUTbaselinestretch\@IEEEundefined\r
+\else\r
+ \edef\baselinestretch{\CLASSINPUTbaselinestretch} % user CLASSINPUT override\r
+ \typeout{** ATTENTION: Overriding \string\baselinestretch\space to\r
+ \baselinestretch\space via \string\CLASSINPUT.}\r
+\fi\r
+\r
+\normalsize % make \baselinestretch take affect\r
+\r
+\r
+\r
+\r
+% store the normalsize baselineskip\r
+\newdimen\CLASSINFOnormalsizebaselineskip\r
+\CLASSINFOnormalsizebaselineskip=\baselineskip\relax\r
+% and the normalsize unity (baselinestretch=1) baselineskip\r
+% we could save a register by giving the user access to\r
+% \@IEEEnormalsizeunitybaselineskip. However, let's protect\r
+% its read only internal status\r
+\newdimen\CLASSINFOnormalsizeunitybaselineskip\r
+\CLASSINFOnormalsizeunitybaselineskip=\@IEEEnormalsizeunitybaselineskip\relax\r
+% store the nominal value of jot\r
+\newdimen\IEEEnormaljot\r
+\IEEEnormaljot=0.25\baselineskip\relax\r
+\r
+% set \jot\r
+\jot=\IEEEnormaljot\relax\r
+\r
+\r
+\r
+\r
+% V1.6, we are now going to fine tune the interword spacing\r
+% The default interword glue for Times under TeX appears to use a\r
+% nominal interword spacing of 25% (relative to the font size, i.e., 1em)\r
+% a maximum of 40% and a minimum of 19%.\r
+% For example, 10pt text uses an interword glue of:\r
+% \r
+% 2.5pt plus 1.49998pt minus 0.59998pt\r
+% \r
+% However, IEEE allows for a more generous range which reduces the need\r
+% for hyphenation, especially for two column text. Furthermore, IEEE\r
+% tends to use a little bit more nominal space between the words.\r
+% IEEE's interword spacing percentages appear to be:\r
+% 35% nominal\r
+% 23% minimum\r
+% 50% maximum\r
+% (They may even be using a tad more for the largest fonts such as 24pt.)\r
+% \r
+% for bold text, IEEE increases the spacing a little more:\r
+% 37.5% nominal\r
+% 23% minimum\r
+% 55% maximum\r
+\r
+% here are the interword spacing ratios we'll use\r
+% for medium (normal weight)\r
+\def\@IEEEinterspaceratioM{0.35}\r
+\def\@IEEEinterspaceMINratioM{0.23}\r
+\def\@IEEEinterspaceMAXratioM{0.50}\r
+\r
+% for bold\r
+\def\@IEEEinterspaceratioB{0.375}\r
+\def\@IEEEinterspaceMINratioB{0.23}\r
+\def\@IEEEinterspaceMAXratioB{0.55}\r
+\r
+\r
+% command to revise the interword spacing for the current font under TeX:\r
+% \fontdimen2 = nominal interword space\r
+% \fontdimen3 = interword stretch\r
+% \fontdimen4 = interword shrink\r
+% since all changes to the \fontdimen are global, we can enclose these commands\r
+% in braces to confine any font attribute or length changes\r
+\def\@@@IEEEsetfontdimens#1#2#3{{%\r
+\setlength{\@IEEEtrantmpdimenB}{\f@size pt}% grab the font size in pt, could use 1em instead.\r
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%\r
+\fontdimen2\font=\@IEEEtrantmpdimenA\relax\r
+\addtolength{\@IEEEtrantmpdimenA}{-#2\@IEEEtrantmpdimenB}%\r
+\fontdimen3\font=-\@IEEEtrantmpdimenA\relax\r
+\setlength{\@IEEEtrantmpdimenA}{#1\@IEEEtrantmpdimenB}%\r
+\addtolength{\@IEEEtrantmpdimenA}{-#3\@IEEEtrantmpdimenB}%\r
+\fontdimen4\font=\@IEEEtrantmpdimenA\relax}}\r
+\r
+% revise the interword spacing for each font weight\r
+\def\@@IEEEsetfontdimens{{%\r
+\mdseries\r
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioM}{\@IEEEinterspaceMAXratioM}{\@IEEEinterspaceMINratioM}%\r
+\bfseries\r
+\@@@IEEEsetfontdimens{\@IEEEinterspaceratioB}{\@IEEEinterspaceMAXratioB}{\@IEEEinterspaceMINratioB}%\r
+}}\r
+\r
+% revise the interword spacing for each font shape\r
+% \slshape is not often used for IEEE work and is not altered here. The \scshape caps are\r
+% already a tad too large in the free LaTeX fonts (as compared to what IEEE uses) so we\r
+% won't alter these either.\r
+\def\@IEEEsetfontdimens{{%\r
+\normalfont\r
+\@@IEEEsetfontdimens\r
+\normalfont\itshape\r
+\@@IEEEsetfontdimens\r
+}}\r
+\r
+% command to revise the interword spacing for each font size (and shape\r
+% and weight). Only the \rmfamily is done here as \ttfamily uses a \r
+% fixed spacing and \sffamily is not used as the main text of IEEE papers.\r
+\def\@IEEEtunefonts{{\selectfont\rmfamily\r
+\tiny\@IEEEsetfontdimens\r
+\scriptsize\@IEEEsetfontdimens\r
+\footnotesize\@IEEEsetfontdimens\r
+\small\@IEEEsetfontdimens\r
+\normalsize\@IEEEsetfontdimens\r
+\sublargesize\@IEEEsetfontdimens\r
+\large\@IEEEsetfontdimens\r
+\LARGE\@IEEEsetfontdimens\r
+\huge\@IEEEsetfontdimens\r
+\Huge\@IEEEsetfontdimens}}\r
+\r
+% if the nofonttune class option is not given, revise the interword spacing\r
+% now - in case IEEEtran makes any default length measurements, and make\r
+% sure all the default fonts are loaded\r
+\ifCLASSOPTIONnofonttune\else\r
+\@IEEEtunefonts\r
+\fi\r
+\r
+% and again at the start of the document in case the user loaded different fonts\r
+\AtBeginDocument{\ifCLASSOPTIONnofonttune\else\@IEEEtunefonts\fi}\r
+\r
+\r
+\r
+% V1.6 \r
+% LaTeX is a little to quick to use hyphenations\r
+% So, we increase the penalty for their use and raise\r
+% the badness level that triggers an underfull hbox\r
+% warning. The author may still have to tweak things,\r
+% but the appearance will be much better "right out\r
+% of the box" than that under V1.5 and prior.\r
+% TeX default is 50\r
+\hyphenpenalty=750\r
+% If we didn't adjust the interword spacing, 2200 might be better.\r
+% The TeX default is 1000\r
+\hbadness=1350\r
+% IEEE does not use extra spacing after punctuation\r
+\frenchspacing\r
+\r
+% V1.7 increase this a tad to discourage equation breaks\r
+\binoppenalty=1000 % default 700\r
+\relpenalty=800 % default 500\r
+\r
+\r
+% margin note stuff\r
+\marginparsep 10pt\r
+\marginparwidth 20pt\r
+\marginparpush 25pt\r
+\r
+\r
+% if things get too close, go ahead and let them touch\r
+\lineskip 0pt\r
+\normallineskip 0pt\r
+\lineskiplimit 0pt\r
+\normallineskiplimit 0pt\r
+\r
+% The distance from the lower edge of the text body to the\r
+% footline\r
+\footskip 0.4in\r
+\r
+% normally zero, should be relative to font height.\r
+% put in a little rubber to help stop some bad breaks (underfull vboxes)\r
+\parskip 0ex plus 0.2ex minus 0.1ex\r
+\r
+\parindent 1.0em\r
+\r
+\topmargin -49.0pt\r
+\headheight 12pt\r
+\headsep 0.25in\r
+\r
+% use the normal font baselineskip\r
+% so that \topskip is unaffected by changes in \baselinestretch\r
+\topskip=\@IEEEnormalsizeunitybaselineskip\r
+% V1.8 \maxdepth defaults to 4pt, but should be font size dependent\r
+\maxdepth=0.5\@IEEEnormalsizeunitybaselineskip\r
+\textheight 58pc % 9.63in, 696pt\r
+% Tweak textheight to a perfect integer number of lines/page.\r
+% The normal baselineskip for each document point size is used \r
+% to determine these values.\r
+\ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=63\@IEEEnormalsizeunitybaselineskip\fi % 63 lines/page\r
+\ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page\r
+\ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=52\@IEEEnormalsizeunitybaselineskip\fi % 52 lines/page\r
+\ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page\r
+\r
+\r
+\columnsep 1pc\r
+\textwidth 43pc % 2 x 21pc + 1pc = 43pc\r
+ \r
+\r
+% the default side margins are equal\r
+\if@IEEEusingAfourpaper \r
+\oddsidemargin 14.32mm\r
+\evensidemargin 14.32mm\r
+\else\r
+\oddsidemargin 0.680in\r
+\evensidemargin 0.680in\r
+\fi\r
+% compensate for LaTeX's 1in offset\r
+\addtolength{\oddsidemargin}{-1in}\r
+\addtolength{\evensidemargin}{-1in}\r
+\r
+\r
+\r
+% adjust margins for conference mode\r
+\ifCLASSOPTIONconference\r
+ \topmargin -0.25in\r
+ % we retain the reserved, but unused space for headers\r
+ \addtolength{\topmargin}{-\headheight}\r
+ \addtolength{\topmargin}{-\headsep}\r
+ \textheight 9.25in % The standard for conferences (668.4975pt)\r
+ % Tweak textheight to a perfect integer number of lines/page.\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=61\@IEEEnormalsizeunitybaselineskip\fi % 61 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=56\@IEEEnormalsizeunitybaselineskip\fi % 56 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=50\@IEEEnormalsizeunitybaselineskip\fi % 50 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page\r
+\fi\r
+\r
+\r
+% compsoc conference\r
+\ifCLASSOPTIONcompsoc\r
+\ifCLASSOPTIONconference\r
+ % compsoc conference use a larger value for columnsep\r
+ \columnsep 0.375in\r
+ % compsoc conferences want 1in top margin, 1.125in bottom margin\r
+ \topmargin 0in\r
+ \addtolength{\topmargin}{-6pt}% we tweak this a tad to better comply with top of line stuff\r
+ % we retain the reserved, but unused space for headers\r
+ \addtolength{\topmargin}{-\headheight}\r
+ \addtolength{\topmargin}{-\headsep}\r
+ \textheight 8.875in % (641.39625pt)\r
+ % Tweak textheight to a perfect integer number of lines/page.\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizenine\textheight=58\@IEEEnormalsizeunitybaselineskip\fi % 58 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizeten\textheight=53\@IEEEnormalsizeunitybaselineskip\fi % 53 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizeeleven\textheight=48\@IEEEnormalsizeunitybaselineskip\fi % 48 lines/page\r
+ \ifx\CLASSOPTIONpt\@IEEEptsizetwelve\textheight=46\@IEEEnormalsizeunitybaselineskip\fi % 46 lines/page \r
+ \textwidth 6.5in\r
+ % the default side margins are equal\r
+ \if@IEEEusingAfourpaper \r
+ \oddsidemargin 22.45mm\r
+ \evensidemargin 22.45mm\r
+ \else\r
+ \oddsidemargin 1in\r
+ \evensidemargin 1in\r
+ \fi\r
+ % compensate for LaTeX's 1in offset\r
+ \addtolength{\oddsidemargin}{-1in}\r
+ \addtolength{\evensidemargin}{-1in}\r
+\fi\fi\r
+\r
+\r
+\r
+% draft mode settings override that of all other modes\r
+% provides a nice 1in margin all around the paper and extra\r
+% space between the lines for editor's comments\r
+\ifCLASSOPTIONdraftcls \r
+ % want 1in from top of paper to text\r
+ \setlength{\topmargin}{-\headsep}%\r
+ \addtolength{\topmargin}{-\headheight}%\r
+ % we want 1in side margins regardless of paper type\r
+ \oddsidemargin 0in\r
+ \evensidemargin 0in\r
+ % set the text width\r
+ \setlength{\textwidth}{\paperwidth}%\r
+ \addtolength{\textwidth}{-2.0in}%\r
+ \setlength{\textheight}{\paperheight}%\r
+ \addtolength{\textheight}{-2.0in}%\r
+ % digitize textheight to be an integer number of lines.\r
+ % this may cause the bottom margin to be off a tad\r
+ \addtolength{\textheight}{-1\topskip}%\r
+ \divide\textheight by \baselineskip%\r
+ \multiply\textheight by \baselineskip%\r
+ \addtolength{\textheight}{\topskip}%\r
+\fi\r
+\r
+\r
+\r
+% process CLASSINPUT inner/outer margin\r
+% if inner margin defined, but outer margin not, set outer to inner.\r
+\ifx\CLASSINPUTinnersidemargin\@IEEEundefined\r
+\else\r
+ \ifx\CLASSINPUToutersidemargin\@IEEEundefined\r
+ \edef\CLASSINPUToutersidemargin{\CLASSINPUTinnersidemargin}\r
+ \fi\r
+\fi\r
+\r
+\ifx\CLASSINPUToutersidemargin\@IEEEundefined\r
+\else\r
+ % if outer margin defined, but inner margin not, set inner to outer.\r
+ \ifx\CLASSINPUTinnersidemargin\@IEEEundefined\r
+ \edef\CLASSINPUTinnersidemargin{\CLASSINPUToutersidemargin}\r
+ \fi\r
+ \setlength{\oddsidemargin}{\CLASSINPUTinnersidemargin}\r
+ \ifCLASSOPTIONtwoside\r
+ \setlength{\evensidemargin}{\CLASSINPUToutersidemargin}\r
+ \else\r
+ \setlength{\evensidemargin}{\CLASSINPUTinnersidemargin}\r
+ \fi\r
+ \addtolength{\oddsidemargin}{-1in}\r
+ \addtolength{\evensidemargin}{-1in}\r
+ \setlength{\textwidth}{\paperwidth}\r
+ \addtolength{\textwidth}{-\CLASSINPUTinnersidemargin}\r
+ \addtolength{\textwidth}{-\CLASSINPUToutersidemargin}\r
+ \typeout{** ATTENTION: Overriding inner side margin to \CLASSINPUTinnersidemargin\space and \r
+ outer side margin to \CLASSINPUToutersidemargin\space via \string\CLASSINPUT.}\r
+\fi\r
+\r
+\r
+\r
+% process CLASSINPUT top/bottom text margin\r
+% if toptext margin defined, but bottomtext margin not, set bottomtext to toptext margin\r
+\ifx\CLASSINPUTtoptextmargin\@IEEEundefined\r
+\else\r
+ \ifx\CLASSINPUTbottomtextmargin\@IEEEundefined\r
+ \edef\CLASSINPUTbottomtextmargin{\CLASSINPUTtoptextmargin}\r
+ \fi\r
+\fi\r
+\r
+\ifx\CLASSINPUTbottomtextmargin\@IEEEundefined\r
+\else\r
+ % if bottomtext margin defined, but toptext margin not, set toptext to bottomtext margin\r
+ \ifx\CLASSINPUTtoptextmargin\@IEEEundefined\r
+ \edef\CLASSINPUTtoptextmargin{\CLASSINPUTbottomtextmargin}\r
+ \fi\r
+ \setlength{\topmargin}{\CLASSINPUTtoptextmargin}\r
+ \addtolength{\topmargin}{-1in}\r
+ \addtolength{\topmargin}{-\headheight}\r
+ \addtolength{\topmargin}{-\headsep}\r
+ \setlength{\textheight}{\paperheight}\r
+ \addtolength{\textheight}{-\CLASSINPUTtoptextmargin}\r
+ \addtolength{\textheight}{-\CLASSINPUTbottomtextmargin}\r
+ % in the default format we use the normal baselineskip as topskip\r
+ % we only need 0.7 of this to clear typical top text and we need\r
+ % an extra 0.3 spacing at the bottom for descenders. This will\r
+ % correct for both.\r
+ \addtolength{\topmargin}{-0.3\@IEEEnormalsizeunitybaselineskip}\r
+ \typeout{** ATTENTION: Overriding top text margin to \CLASSINPUTtoptextmargin\space and \r
+ bottom text margin to \CLASSINPUTbottomtextmargin\space via \string\CLASSINPUT.}\r
+\fi\r
+\r
+\r
+\r
+\r
+\r
+\r
+\r
+% LIST SPACING CONTROLS\r
+\r
+% Controls the amount of EXTRA spacing\r
+% above and below \trivlist \r
+% Both \list and IED lists override this.\r
+% However, \trivlist will use this as will most\r
+% things built from \trivlist like the \center\r
+% environment.\r
+\topsep 0.5\baselineskip\r
+\r
+% Controls the additional spacing around lists preceded\r
+% or followed by blank lines. IEEE does not increase\r
+% spacing before or after paragraphs so it is set to zero.\r
+% \z@ is the same as zero, but faster.\r
+\partopsep \z@\r
+\r
+% Controls the spacing between paragraphs in lists. \r
+% IEEE does not increase spacing before or after paragraphs\r
+% so this is also zero. \r
+% With IEEEtran.cls, global changes to\r
+% this value DO affect lists (but not IED lists).\r
+\parsep \z@\r
+\r
+% Controls the extra spacing between list items. \r
+% IEEE does not put extra spacing between items.\r
+% With IEEEtran.cls, global changes to this value DO affect\r
+% lists (but not IED lists).\r
+\itemsep \z@\r
+\r
+% \itemindent is the amount to indent the FIRST line of a list\r
+% item. It is auto set to zero within the \list environment. To alter\r
+% it, you have to do so when you call the \list.\r
+% However, IEEE uses this for the theorem environment\r
+% There is an alternative value for this near \leftmargini below\r
+\itemindent -1em\r
+\r
+% \leftmargin, the spacing from the left margin of the main text to\r
+% the left of the main body of a list item is set by \list.\r
+% Hence this statement does nothing for lists.\r
+% But, quote and verse do use it for indention.\r
+\leftmargin 2em\r
+\r
+% we retain this stuff from the older IEEEtran.cls so that \list\r
+% will work the same way as before. However, itemize, enumerate and\r
+% description (IED) could care less about what these are as they\r
+% all are overridden.\r
+\leftmargini 2em\r
+%\itemindent 2em % Alternative values: sometimes used.\r
+%\leftmargini 0em\r
+\leftmarginii 1em\r
+\leftmarginiii 1.5em\r
+\leftmarginiv 1.5em\r
+\leftmarginv 1.0em\r
+\leftmarginvi 1.0em\r
+\labelsep 0.5em \r
+\labelwidth \z@\r
+\r
+\r
+% The old IEEEtran.cls behavior of \list is retained.\r
+% However, the new V1.3 IED list environments override all the\r
+% @list stuff (\@listX is called within \list for the\r
+% appropriate level just before the user's list_decl is called). \r
+% \topsep is now 2pt as IEEE puts a little extra space around\r
+% lists - used by those non-IED macros that depend on \list.\r
+% Note that \parsep and \itemsep are not redefined as in \r
+% the sizexx.clo \@listX (which article.cls uses) so global changes\r
+% of these values DO affect \list\r
+% \r
+\def\@listi{\leftmargin\leftmargini \topsep 2pt plus 1pt minus 1pt}\r
+\let\@listI\@listi\r
+\def\@listii{\leftmargin\leftmarginii\labelwidth\leftmarginii%\r
+ \advance\labelwidth-\labelsep \topsep 2pt}\r
+\def\@listiii{\leftmargin\leftmarginiii\labelwidth\leftmarginiii%\r
+ \advance\labelwidth-\labelsep \topsep 2pt}\r
+\def\@listiv{\leftmargin\leftmarginiv\labelwidth\leftmarginiv%\r
+ \advance\labelwidth-\labelsep \topsep 2pt}\r
+\def\@listv{\leftmargin\leftmarginv\labelwidth\leftmarginv%\r
+ \advance\labelwidth-\labelsep \topsep 2pt}\r
+\def\@listvi{\leftmargin\leftmarginvi\labelwidth\leftmarginvi%\r
+ \advance\labelwidth-\labelsep \topsep 2pt}\r
+\r
+\r
+% IEEE uses 5) not 5.\r
+\def\labelenumi{\theenumi)} \def\theenumi{\arabic{enumi}}\r
+\r
+% IEEE uses a) not (a)\r
+\def\labelenumii{\theenumii)} \def\theenumii{\alph{enumii}}\r
+\r
+% IEEE uses iii) not iii.\r
+\def\labelenumiii{\theenumiii)} \def\theenumiii{\roman{enumiii}}\r
+\r
+% IEEE uses A) not A.\r
+\def\labelenumiv{\theenumiv)} \def\theenumiv{\Alph{enumiv}}\r
+\r
+% exactly the same as in article.cls\r
+\def\p@enumii{\theenumi}\r
+\def\p@enumiii{\theenumi(\theenumii)}\r
+\def\p@enumiv{\p@enumiii\theenumiii}\r
+\r
+% itemized list label styles\r
+\def\labelitemi{$\scriptstyle\bullet$}\r
+\def\labelitemii{\textbf{--}}\r
+\def\labelitemiii{$\ast$}\r
+\def\labelitemiv{$\cdot$}\r
+\r
+\r
+\r
+% **** V1.3 ENHANCEMENTS ****\r
+% Itemize, Enumerate and Description (IED) List Controls\r
+% ***************************\r
+% \r
+% \r
+% IEEE seems to use at least two different values by\r
+% which ITEMIZED list labels are indented to the right\r
+% For The Journal of Lightwave Technology (JLT) and The Journal\r
+% on Selected Areas in Communications (JSAC), they tend to use\r
+% an indention equal to \parindent. For Transactions on Communications\r
+% they tend to indent ITEMIZED lists a little more--- 1.3\parindent.\r
+% We'll provide both values here for you so that you can choose \r
+% which one you like in your document using a command such as:\r
+% setlength{\IEEEilabelindent}{\IEEEilabelindentB}\r
+\newdimen\IEEEilabelindentA\r
+\IEEEilabelindentA \parindent\r
+\r
+\newdimen\IEEEilabelindentB\r
+\IEEEilabelindentB 1.3\parindent\r
+% However, we'll default to using \parindent\r
+% which makes more sense to me\r
+\newdimen\IEEEilabelindent\r
+\IEEEilabelindent \IEEEilabelindentA\r
+\r
+\r
+% This controls the default amount the enumerated list labels\r
+% are indented to the right.\r
+% Normally, this is the same as the paragraph indention\r
+\newdimen\IEEEelabelindent\r
+\IEEEelabelindent \parindent\r
+\r
+% This controls the default amount the description list labels\r
+% are indented to the right.\r
+% Normally, this is the same as the paragraph indention\r
+\newdimen\IEEEdlabelindent\r
+\IEEEdlabelindent \parindent\r
+\r
+% This is the value actually used within the IED lists.\r
+% The IED environments automatically set its value to\r
+% one of the three values above, so global changes do \r
+% not have any effect\r
+\newdimen\IEEElabelindent\r
+\IEEElabelindent \parindent\r
+\r
+% The actual amount labels will be indented is\r
+% \IEEElabelindent multiplied by the factor below\r
+% corresponding to the level of nesting depth\r
+% This provides a means by which the user can\r
+% alter the effective \IEEElabelindent for deeper\r
+% levels\r
+% There may not be such a thing as correct "standard IEEE"\r
+% values. What IEEE actually does may depend on the specific\r
+% circumstances.\r
+% The first list level almost always has full indention.\r
+% The second levels I've seen have only 75% of the normal indentation\r
+% Three level or greater nestings are very rare. I am guessing\r
+% that they don't use any indentation.\r
+\def\IEEElabelindentfactori{1.0} % almost always one\r
+\def\IEEElabelindentfactorii{0.75} % 0.0 or 1.0 may be used in some cases\r
+\def\IEEElabelindentfactoriii{0.0} % 0.75? 0.5? 0.0?\r
+\def\IEEElabelindentfactoriv{0.0}\r
+\def\IEEElabelindentfactorv{0.0}\r
+\def\IEEElabelindentfactorvi{0.0}\r
+\r
+% value actually used within IED lists, it is auto\r
+% set to one of the 6 values above\r
+% global changes here have no effect\r
+\def\IEEElabelindentfactor{1.0}\r
+\r
+% This controls the default spacing between the end of the IED\r
+% list labels and the list text, when normal text is used for\r
+% the labels.\r
+\newdimen\IEEEiednormlabelsep\r
+\IEEEiednormlabelsep 0.6em\r
+\r
+% This controls the default spacing between the end of the IED\r
+% list labels and the list text, when math symbols are used for\r
+% the labels (nomenclature lists). IEEE usually increases the \r
+% spacing in these cases\r
+\newdimen\IEEEiedmathlabelsep\r
+\IEEEiedmathlabelsep 1.2em\r
+\r
+% This controls the extra vertical separation put above and\r
+% below each IED list. IEEE usually puts a little extra spacing\r
+% around each list. However, this spacing is barely noticeable.\r
+\newskip\IEEEiedtopsep\r
+\IEEEiedtopsep 2pt plus 1pt minus 1pt\r
+\r
+\r
+% This command is executed within each IED list environment\r
+% at the beginning of the list. You can use this to set the \r
+% parameters for some/all your IED list(s) without disturbing \r
+% global parameters that affect things other than lists.\r
+% i.e., renewcommand{\IEEEiedlistdecl}{\setlength{\labelsep}{5em}}\r
+% will alter the \labelsep for the next list(s) until \r
+% \IEEEiedlistdecl is redefined. \r
+\def\IEEEiedlistdecl{\relax}\r
+\r
+% This command provides an easy way to set \leftmargin based\r
+% on the \labelwidth, \labelsep and the argument \IEEElabelindent\r
+% Usage: \IEEEcalcleftmargin{width-to-indent-the-label}\r
+% output is in the \leftmargin variable, i.e., effectively:\r
+% \leftmargin = argument + \labelwidth + \labelsep\r
+% Note controlled spacing here, shield end of lines with %\r
+\def\IEEEcalcleftmargin#1{\setlength{\leftmargin}{#1}%\r
+\addtolength{\leftmargin}{\labelwidth}%\r
+\addtolength{\leftmargin}{\labelsep}}\r
+\r
+% This command provides an easy way to set \labelwidth to the\r
+% width of the given text. It is the same as\r
+% \settowidth{\labelwidth}{label-text}\r
+% and useful as a shorter alternative.\r
+% Typically used to set \labelwidth to be the width\r
+% of the longest label in the list\r
+\def\IEEEsetlabelwidth#1{\settowidth{\labelwidth}{#1}}\r
+\r
+% When this command is executed, IED lists will use the \r
+% IEEEiedmathlabelsep label separation rather than the normal\r
+% spacing. To have an effect, this command must be executed via\r
+% the \IEEEiedlistdecl or within the option of the IED list\r
+% environments.\r
+\def\IEEEusemathlabelsep{\setlength{\labelsep}{\IEEEiedmathlabelsep}}\r
+\r
+% A flag which controls whether the IED lists automatically\r
+% calculate \leftmargin from \IEEElabelindent, \labelwidth and \labelsep\r
+% Useful if you want to specify your own \leftmargin\r
+% This flag must be set (\IEEEnocalcleftmargintrue or \IEEEnocalcleftmarginfalse) \r
+% via the \IEEEiedlistdecl or within the option of the IED list\r
+% environments to have an effect.\r
+\newif\ifIEEEnocalcleftmargin\r
+\IEEEnocalcleftmarginfalse\r
+\r
+% A flag which controls whether \IEEElabelindent is multiplied by\r
+% the \IEEElabelindentfactor for each list level.\r
+% This flag must be set via the \IEEEiedlistdecl or within the option \r
+% of the IED list environments to have an effect.\r
+\newif\ifIEEEnolabelindentfactor\r
+\IEEEnolabelindentfactorfalse\r
+\r
+\r
+% internal variable to indicate type of IED label\r
+% justification\r
+% 0 - left; 1 - center; 2 - right\r
+\def\@IEEEiedjustify{0}\r
+\r
+\r
+% commands to allow the user to control IED\r
+% label justifications. Use these commands within\r
+% the IED environment option or in the \IEEEiedlistdecl\r
+% Note that changing the normal list justifications\r
+% is nonstandard and IEEE may not like it if you do so!\r
+% I include these commands as they may be helpful to\r
+% those who are using these enhanced list controls for\r
+% other non-IEEE related LaTeX work.\r
+% itemize and enumerate automatically default to right\r
+% justification, description defaults to left.\r
+\def\IEEEiedlabeljustifyl{\def\@IEEEiedjustify{0}}%left\r
+\def\IEEEiedlabeljustifyc{\def\@IEEEiedjustify{1}}%center\r
+\def\IEEEiedlabeljustifyr{\def\@IEEEiedjustify{2}}%right\r
+\r
+\r
+\r
+\r
+% commands to save to and restore from the list parameter copies\r
+% this allows us to set all the list parameters within\r
+% the list_decl and prevent \list (and its \@list) \r
+% from overriding any of our parameters\r
+% V1.6 use \edefs instead of dimen's to conserve dimen registers\r
+% Note controlled spacing here, shield end of lines with %\r
+\def\@IEEEsavelistparams{\edef\@IEEEiedtopsep{\the\topsep}%\r
+\edef\@IEEEiedlabelwidth{\the\labelwidth}%\r
+\edef\@IEEEiedlabelsep{\the\labelsep}%\r
+\edef\@IEEEiedleftmargin{\the\leftmargin}%\r
+\edef\@IEEEiedpartopsep{\the\partopsep}%\r
+\edef\@IEEEiedparsep{\the\parsep}%\r
+\edef\@IEEEieditemsep{\the\itemsep}%\r
+\edef\@IEEEiedrightmargin{\the\rightmargin}%\r
+\edef\@IEEEiedlistparindent{\the\listparindent}%\r
+\edef\@IEEEieditemindent{\the\itemindent}}\r
+\r
+% Note controlled spacing here\r
+\def\@IEEErestorelistparams{\topsep\@IEEEiedtopsep\relax%\r
+\labelwidth\@IEEEiedlabelwidth\relax%\r
+\labelsep\@IEEEiedlabelsep\relax%\r
+\leftmargin\@IEEEiedleftmargin\relax%\r
+\partopsep\@IEEEiedpartopsep\relax%\r
+\parsep\@IEEEiedparsep\relax%\r
+\itemsep\@IEEEieditemsep\relax%\r
+\rightmargin\@IEEEiedrightmargin\relax%\r
+\listparindent\@IEEEiedlistparindent\relax%\r
+\itemindent\@IEEEieditemindent\relax}\r
+\r
+\r
+% v1.6b provide original LaTeX IED list environments\r
+% note that latex.ltx defines \itemize and \enumerate, but not \description\r
+% which must be created by the base classes\r
+% save original LaTeX itemize and enumerate\r
+\let\LaTeXitemize\itemize\r
+\let\endLaTeXitemize\enditemize\r
+\let\LaTeXenumerate\enumerate\r
+\let\endLaTeXenumerate\endenumerate\r
+\r
+% provide original LaTeX description environment from article.cls\r
+\newenvironment{LaTeXdescription}\r
+ {\list{}{\labelwidth\z@ \itemindent-\leftmargin\r
+ \let\makelabel\descriptionlabel}}\r
+ {\endlist}\r
+\newcommand*\descriptionlabel[1]{\hspace\labelsep\r
+ \normalfont\bfseries #1}\r
+\r
+\r
+% override LaTeX's default IED lists\r
+\def\itemize{\@IEEEitemize}\r
+\def\enditemize{\@endIEEEitemize}\r
+\def\enumerate{\@IEEEenumerate}\r
+\def\endenumerate{\@endIEEEenumerate}\r
+\def\description{\@IEEEdescription}\r
+\def\enddescription{\@endIEEEdescription}\r
+\r
+% provide the user with aliases - may help those using packages that\r
+% override itemize, enumerate, or description\r
+\def\IEEEitemize{\@IEEEitemize}\r
+\def\endIEEEitemize{\@endIEEEitemize}\r
+\def\IEEEenumerate{\@IEEEenumerate}\r
+\def\endIEEEenumerate{\@endIEEEenumerate}\r
+\def\IEEEdescription{\@IEEEdescription}\r
+\def\endIEEEdescription{\@endIEEEdescription}\r
+\r
+\r
+% V1.6 we want to keep the IEEEtran IED list definitions as our own internal\r
+% commands so they are protected against redefinition\r
+\def\@IEEEitemize{\@ifnextchar[{\@@IEEEitemize}{\@@IEEEitemize[\relax]}}\r
+\def\@IEEEenumerate{\@ifnextchar[{\@@IEEEenumerate}{\@@IEEEenumerate[\relax]}}\r
+\def\@IEEEdescription{\@ifnextchar[{\@@IEEEdescription}{\@@IEEEdescription[\relax]}}\r
+\def\@endIEEEitemize{\endlist}\r
+\def\@endIEEEenumerate{\endlist}\r
+\def\@endIEEEdescription{\endlist}\r
+\r
+\r
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS\r
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS\r
+% IEEEtran itemized list MDS 1/2001\r
+% Note controlled spacing here, shield end of lines with %\r
+\def\@@IEEEitemize[#1]{%\r
+ \ifnum\@itemdepth>3\relax\@toodeep\else%\r
+ \ifnum\@listdepth>5\relax\@toodeep\else%\r
+ \advance\@itemdepth\@ne%\r
+ \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%\r
+ % get the IEEElabelindentfactor for this level\r
+ \advance\@listdepth\@ne% we need to know what the level WILL be\r
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%\r
+ \advance\@listdepth-\@ne% undo our increment\r
+ \def\@IEEEiedjustify{2}% right justified labels are default\r
+ % set other defaults\r
+ \IEEEnocalcleftmarginfalse%\r
+ \IEEEnolabelindentfactorfalse%\r
+ \topsep\IEEEiedtopsep%\r
+ \IEEElabelindent\IEEEilabelindent%\r
+ \labelsep\IEEEiednormlabelsep%\r
+ \partopsep 0ex%\r
+ \parsep 0ex%\r
+ \itemsep 0ex%\r
+ \rightmargin 0em%\r
+ \listparindent 0em%\r
+ \itemindent 0em%\r
+ % calculate the label width\r
+ % the user can override this later if\r
+ % they specified a \labelwidth\r
+ \settowidth{\labelwidth}{\csname labelitem\romannumeral\the\@itemdepth\endcsname}%\r
+ \@IEEEsavelistparams% save our list parameters\r
+ \list{\csname\@itemitem\endcsname}{%\r
+ \@IEEErestorelistparams% override any list{} changes\r
+ % to our globals\r
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel\r
+ \IEEEiedlistdecl% let user alter parameters\r
+ #1\relax%\r
+ % If the user has requested not to use the\r
+ % IEEElabelindent factor, don't revise \IEEElabelindent\r
+ \ifIEEEnolabelindentfactor\relax%\r
+ \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%\r
+ \fi%\r
+ % Unless the user has requested otherwise,\r
+ % calculate our left margin based\r
+ % on \IEEElabelindent, \labelwidth and\r
+ % \labelsep\r
+ \ifIEEEnocalcleftmargin\relax%\r
+ \else\IEEEcalcleftmargin{\IEEElabelindent}%\r
+ \fi}\fi\fi}%\r
+\r
+\r
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS\r
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS\r
+% IEEEtran enumerate list MDS 1/2001\r
+% Note controlled spacing here, shield end of lines with %\r
+\def\@@IEEEenumerate[#1]{%\r
+ \ifnum\@enumdepth>3\relax\@toodeep\else%\r
+ \ifnum\@listdepth>5\relax\@toodeep\else%\r
+ \advance\@enumdepth\@ne%\r
+ \edef\@enumctr{enum\romannumeral\the\@enumdepth}%\r
+ % get the IEEElabelindentfactor for this level\r
+ \advance\@listdepth\@ne% we need to know what the level WILL be\r
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%\r
+ \advance\@listdepth-\@ne% undo our increment\r
+ \def\@IEEEiedjustify{2}% right justified labels are default\r
+ % set other defaults\r
+ \IEEEnocalcleftmarginfalse%\r
+ \IEEEnolabelindentfactorfalse%\r
+ \topsep\IEEEiedtopsep%\r
+ \IEEElabelindent\IEEEelabelindent%\r
+ \labelsep\IEEEiednormlabelsep%\r
+ \partopsep 0ex%\r
+ \parsep 0ex%\r
+ \itemsep 0ex%\r
+ \rightmargin 0em%\r
+ \listparindent 0em%\r
+ \itemindent 0em%\r
+ % calculate the label width\r
+ % We'll set it to the width suitable for all labels using\r
+ % normalfont 1) to 9)\r
+ % The user can override this later\r
+ \settowidth{\labelwidth}{9)}%\r
+ \@IEEEsavelistparams% save our list parameters\r
+ \list{\csname label\@enumctr\endcsname}{\usecounter{\@enumctr}%\r
+ \@IEEErestorelistparams% override any list{} changes\r
+ % to our globals\r
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel\r
+ \IEEEiedlistdecl% let user alter parameters \r
+ #1\relax%\r
+ % If the user has requested not to use the\r
+ % IEEElabelindent factor, don't revise \IEEElabelindent\r
+ \ifIEEEnolabelindentfactor\relax%\r
+ \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%\r
+ \fi%\r
+ % Unless the user has requested otherwise,\r
+ % calculate our left margin based\r
+ % on \IEEElabelindent, \labelwidth and\r
+ % \labelsep\r
+ \ifIEEEnocalcleftmargin\relax%\r
+ \else\IEEEcalcleftmargin{\IEEElabelindent}%\r
+ \fi}\fi\fi}%\r
+\r
+\r
+% DO NOT ALLOW BLANK LINES TO BE IN THESE IED ENVIRONMENTS\r
+% AS THIS WILL FORCE NEW PARAGRAPHS AFTER THE IED LISTS\r
+% IEEEtran description list MDS 1/2001\r
+% Note controlled spacing here, shield end of lines with %\r
+\def\@@IEEEdescription[#1]{%\r
+ \ifnum\@listdepth>5\relax\@toodeep\else%\r
+ % get the IEEElabelindentfactor for this level\r
+ \advance\@listdepth\@ne% we need to know what the level WILL be\r
+ \edef\IEEElabelindentfactor{\csname IEEElabelindentfactor\romannumeral\the\@listdepth\endcsname}%\r
+ \advance\@listdepth-\@ne% undo our increment\r
+ \def\@IEEEiedjustify{0}% left justified labels are default\r
+ % set other defaults\r
+ \IEEEnocalcleftmarginfalse%\r
+ \IEEEnolabelindentfactorfalse%\r
+ \topsep\IEEEiedtopsep% \r
+ \IEEElabelindent\IEEEdlabelindent%\r
+ % assume normal labelsep\r
+ \labelsep\IEEEiednormlabelsep%\r
+ \partopsep 0ex%\r
+ \parsep 0ex%\r
+ \itemsep 0ex%\r
+ \rightmargin 0em%\r
+ \listparindent 0em%\r
+ \itemindent 0em%\r
+ % Bogus label width in case the user forgets\r
+ % to set it.\r
+ % TIP: If you want to see what a variable's width is you\r
+ % can use the TeX command \showthe\width-variable to \r
+ % display it on the screen during compilation \r
+ % (This might be helpful to know when you need to find out\r
+ % which label is the widest)\r
+ \settowidth{\labelwidth}{Hello}%\r
+ \@IEEEsavelistparams% save our list parameters\r
+ \list{}{\@IEEErestorelistparams% override any list{} changes\r
+ % to our globals\r
+ \let\makelabel\@IEEEiedmakelabel% v1.6b setup \makelabel\r
+ \IEEEiedlistdecl% let user alter parameters \r
+ #1\relax%\r
+ % If the user has requested not to use the\r
+ % labelindent factor, don't revise \IEEElabelindent\r
+ \ifIEEEnolabelindentfactor\relax%\r
+ \else\IEEElabelindent=\IEEElabelindentfactor\IEEElabelindent%\r
+ \fi%\r
+ % Unless the user has requested otherwise,\r
+ % calculate our left margin based\r
+ % on \IEEElabelindent, \labelwidth and\r
+ % \labelsep\r
+ \ifIEEEnocalcleftmargin\relax%\r
+ \else\IEEEcalcleftmargin{\IEEElabelindent}\relax%\r
+ \fi}\fi}\r
+\r
+% v1.6b we use one makelabel that does justification as needed.\r
+\def\@IEEEiedmakelabel#1{\relax\if\@IEEEiedjustify 0\relax\r
+\makebox[\labelwidth][l]{\normalfont #1}\else\r
+\if\@IEEEiedjustify 1\relax\r
+\makebox[\labelwidth][c]{\normalfont #1}\else\r
+\makebox[\labelwidth][r]{\normalfont #1}\fi\fi}\r
+\r
+\r
+% VERSE and QUOTE\r
+% V1.7 define environments with newenvironment\r
+\newenvironment{verse}{\let\\=\@centercr\r
+ \list{}{\itemsep\z@ \itemindent -1.5em \listparindent \itemindent\r
+ \rightmargin\leftmargin\advance\leftmargin 1.5em}\item\relax}\r
+ {\endlist}\r
+\newenvironment{quotation}{\list{}{\listparindent 1.5em \itemindent\listparindent\r
+ \rightmargin\leftmargin \parsep 0pt plus 1pt}\item\relax}\r
+ {\endlist}\r
+\newenvironment{quote}{\list{}{\rightmargin\leftmargin}\item\relax}\r
+ {\endlist}\r
+\r
+\r
+% \titlepage\r
+% provided only for backward compatibility. \maketitle is the correct\r
+% way to create the title page. \r
+\newif\if@restonecol\r
+\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn\r
+ \else \newpage \fi \thispagestyle{empty}\c@page\z@}\r
+\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}\r
+\r
+% standard values from article.cls\r
+\arraycolsep 5pt\r
+\arrayrulewidth .4pt\r
+\doublerulesep 2pt\r
+\r
+\tabcolsep 6pt\r
+\tabbingsep 0.5em\r
+\r
+\r
+%% FOOTNOTES\r
+%\r
+%\skip\footins 10pt plus 4pt minus 2pt\r
+% V1.6 respond to changes in font size\r
+% space added above the footnotes (if present)\r
+\skip\footins 0.9\baselineskip plus 0.4\baselineskip minus 0.2\baselineskip\r
+\r
+% V1.6, we need to make \footnotesep responsive to changes\r
+% in \baselineskip or strange spacings will result when in\r
+% draft mode. Here is a little LaTeX secret - \footnotesep\r
+% determines the height of an invisible strut that is placed\r
+% *above* the baseline of footnotes after the first. Since\r
+% LaTeX considers the space for characters to be 0.7\baselineskip\r
+% above the baseline and 0.3\baselineskip below it, we need to\r
+% use 0.7\baselineskip as a \footnotesep to maintain equal spacing\r
+% between all the lines of the footnotes. IEEE often uses a tad\r
+% more, so use 0.8\baselineskip. This slightly larger value also helps\r
+% the text to clear the footnote marks. Note that \thanks in IEEEtran\r
+% uses its own value of \footnotesep which is set in \maketitle.\r
+{\footnotesize\r
+\global\footnotesep 0.8\baselineskip}\r
+\r
+\r
+\skip\@mpfootins = \skip\footins\r
+\fboxsep = 3pt\r
+\fboxrule = .4pt\r
+% V1.6 use 1em, then use LaTeX2e's \@makefnmark\r
+% Note that IEEE normally *left* aligns the footnote marks, so we don't need\r
+% box resizing tricks here.\r
+\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@makefnmark}#1}% V1.6 use 1em\r
+% V1.7 compsoc does not use superscipts for footnote marks\r
+\ifCLASSOPTIONcompsoc\r
+\def\@IEEEcompsocmakefnmark{\hbox{\normalfont\@thefnmark.\ }}\r
+\long\def\@makefntext#1{\parindent 1em\indent\hbox{\@IEEEcompsocmakefnmark}#1}\r
+\fi\r
+\r
+% IEEE does not use footnote rules\r
+\def\footnoterule{}\r
+\r
+% V1.7 for compsoc, IEEE uses a footnote rule only for \thanks. We devise a "one-shot"\r
+% system to implement this.\r
+\newif\if@IEEEenableoneshotfootnoterule\r
+\@IEEEenableoneshotfootnoterulefalse\r
+\ifCLASSOPTIONcompsoc\r
+\def\footnoterule{\relax\if@IEEEenableoneshotfootnoterule\r
+\kern-5pt\r
+\hbox to \columnwidth{\hfill\vrule width 0.5\columnwidth height 0.4pt\hfill}\r
+\kern4.6pt\r
+\global\@IEEEenableoneshotfootnoterulefalse\r
+\else\r
+\relax\r
+\fi}\r
+\fi\r
+\r
+% V1.6 do not allow LaTeX to break a footnote across multiple pages\r
+\interfootnotelinepenalty=10000\r
+\r
+% V1.6 discourage breaks within equations\r
+% Note that amsmath normally sets this to 10000,\r
+% but LaTeX2e normally uses 100.\r
+\interdisplaylinepenalty=2500\r
+\r
+% default allows section depth up to /paragraph\r
+\setcounter{secnumdepth}{4}\r
+\r
+% technotes do not allow /paragraph\r
+\ifCLASSOPTIONtechnote\r
+ \setcounter{secnumdepth}{3}\r
+\fi\r
+% neither do compsoc conferences\r
+\@IEEEcompsocconfonly{\setcounter{secnumdepth}{3}}\r
+\r
+\r
+\newcounter{section}\r
+\newcounter{subsection}[section]\r
+\newcounter{subsubsection}[subsection]\r
+\newcounter{paragraph}[subsubsection]\r
+\r
+% used only by IEEEtran's IEEEeqnarray as other packages may\r
+% have their own, different, implementations\r
+\newcounter{IEEEsubequation}[equation]\r
+\r
+% as shown when called by user from \ref, \label and in table of contents\r
+\def\theequation{\arabic{equation}} % 1\r
+\def\theIEEEsubequation{\theequation\alph{IEEEsubequation}} % 1a (used only by IEEEtran's IEEEeqnarray)\r
+\ifCLASSOPTIONcompsoc\r
+% compsoc is all arabic\r
+\def\thesection{\arabic{section}} \r
+\def\thesubsection{\thesection.\arabic{subsection}}\r
+\def\thesubsubsection{\thesubsection.\arabic{subsubsection}}\r
+\def\theparagraph{\thesubsubsection.\arabic{paragraph}}\r
+\else\r
+\def\thesection{\Roman{section}} % I\r
+% V1.7, \mbox prevents breaks around - \r
+\def\thesubsection{\mbox{\thesection-\Alph{subsection}}} % I-A\r
+% V1.7 use I-A1 format used by IEEE rather than I-A.1\r
+\def\thesubsubsection{\thesubsection\arabic{subsubsection}} % I-A1\r
+\def\theparagraph{\thesubsubsection\alph{paragraph}} % I-A1a\r
+\fi\r
+\r
+% From Heiko Oberdiek. Because of the \mbox in \thesubsection, we need to\r
+% tell hyperref to disable the \mbox command when making PDF bookmarks.\r
+% This done already with hyperref.sty version 6.74o and later, but\r
+% it will not hurt to do it here again for users of older versions.\r
+\@ifundefined{pdfstringdefPreHook}{\let\pdfstringdefPreHook\@empty}{}%\r
+\g@addto@macro\pdfstringdefPreHook{\let\mbox\relax}\r
+\r
+\r
+% Main text forms (how shown in main text headings)\r
+% V1.6, using \thesection in \thesectiondis allows changes\r
+% in the former to automatically appear in the latter\r
+\ifCLASSOPTIONcompsoc\r
+ \ifCLASSOPTIONconference% compsoc conference\r
+ \def\thesectiondis{\thesection.}\r
+ \def\thesubsectiondis{\thesectiondis\arabic{subsection}.}\r
+ \def\thesubsubsectiondis{\thesubsectiondis\arabic{subsubsection}.}\r
+ \def\theparagraphdis{\thesubsubsectiondis\arabic{paragraph}.}\r
+ \else% compsoc not conferencs\r
+ \def\thesectiondis{\thesection}\r
+ \def\thesubsectiondis{\thesectiondis.\arabic{subsection}}\r
+ \def\thesubsubsectiondis{\thesubsectiondis.\arabic{subsubsection}}\r
+ \def\theparagraphdis{\thesubsubsectiondis.\arabic{paragraph}}\r
+ \fi\r
+\else% not compsoc\r
+ \def\thesectiondis{\thesection.} % I.\r
+ \def\thesubsectiondis{\Alph{subsection}.} % B.\r
+ \def\thesubsubsectiondis{\arabic{subsubsection})} % 3)\r
+ \def\theparagraphdis{\alph{paragraph})} % d)\r
+\fi\r
+\r
+% just like LaTeX2e's \@eqnnum\r
+\def\theequationdis{{\normalfont \normalcolor (\theequation)}}% (1)\r
+% IEEEsubequation used only by IEEEtran's IEEEeqnarray\r
+\def\theIEEEsubequationdis{{\normalfont \normalcolor (\theIEEEsubequation)}}% (1a)\r
+% redirect LaTeX2e's equation number display and all that depend on\r
+% it, through IEEEtran's \theequationdis\r
+\def\@eqnnum{\theequationdis}\r
+\r
+\r
+\r
+% V1.7 provide string macros as article.cls does\r
+\def\contentsname{Contents}\r
+\def\listfigurename{List of Figures}\r
+\def\listtablename{List of Tables}\r
+\def\refname{References}\r
+\def\indexname{Index}\r
+\def\figurename{Fig.}\r
+\def\tablename{TABLE}\r
+\@IEEEcompsocconfonly{\def\figurename{Figure}\def\tablename{Table}}\r
+\def\partname{Part}\r
+\def\appendixname{Appendix}\r
+\def\abstractname{Abstract}\r
+% IEEE specific names\r
+\def\IEEEkeywordsname{Index Terms}\r
+\def\IEEEproofname{Proof}\r
+\r
+\r
+% LIST OF FIGURES AND TABLES AND TABLE OF CONTENTS\r
+%\r
+\def\@pnumwidth{1.55em}\r
+\def\@tocrmarg{2.55em}\r
+\def\@dotsep{4.5}\r
+\setcounter{tocdepth}{3}\r
+\r
+% adjusted some spacings here so that section numbers will not easily \r
+% collide with the section titles. \r
+% VIII; VIII-A; and VIII-A.1 are usually the worst offenders.\r
+% MDS 1/2001\r
+\def\tableofcontents{\section*{\contentsname}\@starttoc{toc}}\r
+\def\l@section#1#2{\addpenalty{\@secpenalty}\addvspace{1.0em plus 1pt}%\r
+ \@tempdima 2.75em \begingroup \parindent \z@ \rightskip \@pnumwidth%\r
+ \parfillskip-\@pnumwidth {\bfseries\leavevmode #1}\hfil\hbox to\@pnumwidth{\hss #2}\par%\r
+ \endgroup}\r
+% argument format #1:level, #2:labelindent,#3:labelsep\r
+\def\l@subsection{\@dottedtocline{2}{2.75em}{3.75em}}\r
+\def\l@subsubsection{\@dottedtocline{3}{6.5em}{4.5em}}\r
+% must provide \l@ defs for ALL sublevels EVEN if tocdepth\r
+% is such as they will not appear in the table of contents\r
+% these defs are how TOC knows what level these things are!\r
+\def\l@paragraph{\@dottedtocline{4}{6.5em}{5.5em}}\r
+\def\l@subparagraph{\@dottedtocline{5}{6.5em}{6.5em}}\r
+\def\listoffigures{\section*{\listfigurename}\@starttoc{lof}}\r
+\def\l@figure{\@dottedtocline{1}{0em}{2.75em}}\r
+\def\listoftables{\section*{\listtablename}\@starttoc{lot}}\r
+\let\l@table\l@figure\r
+\r
+\r
+% Definitions for floats\r
+%\r
+% Normal Floats\r
+% V1.8 floatsep et al. revised down by 0.15\baselineskip\r
+% to account for the sideeffects of \topskip compensation\r
+\floatsep 0.85\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip\r
+\textfloatsep 1.55\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip\r
+\@fptop 0pt plus 1fil\r
+\@fpsep 0.75\baselineskip plus 2fil \r
+\@fpbot 0pt plus 1fil\r
+\def\topfraction{0.9}\r
+\def\bottomfraction{0.4}\r
+\def\floatpagefraction{0.8}\r
+% V1.7, let top floats approach 90% of page\r
+\def\textfraction{0.1}\r
+\r
+% Double Column Floats\r
+\dblfloatsep 0.85\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip\r
+\r
+\dbltextfloatsep 1.55\baselineskip plus 0.2\baselineskip minus 0.4\baselineskip\r
+% Note that it would be nice if the rubber here actually worked in LaTeX2e.\r
+% There is a long standing limitation in LaTeX, first discovered (to the best\r
+% of my knowledge) by Alan Jeffrey in 1992. LaTeX ignores the stretchable\r
+% portion of \dbltextfloatsep, and as a result, double column figures can and\r
+% do result in an non-integer number of lines in the main text columns with\r
+% underfull vbox errors as a consequence. A post to comp.text.tex\r
+% by Donald Arseneau confirms that this had not yet been fixed in 1998.\r
+% IEEEtran V1.6 will fix this problem for you in the titles, but it doesn't\r
+% protect you from other double floats. Happy vspace'ing.\r
+\r
+\@dblfptop 0pt plus 1fil\r
+\@dblfpsep 0.75\baselineskip plus 2fil\r
+\@dblfpbot 0pt plus 1fil\r
+\def\dbltopfraction{0.8}\r
+\def\dblfloatpagefraction{0.8}\r
+\setcounter{dbltopnumber}{4}\r
+\r
+\intextsep 0.85\baselineskip plus 0.2\baselineskip minus 0.2\baselineskip\r
+\setcounter{topnumber}{2}\r
+\setcounter{bottomnumber}{2}\r
+\setcounter{totalnumber}{4}\r
+\r
+\r
+\r
+% article class provides these, we should too.\r
+\newlength\abovecaptionskip\r
+\newlength\belowcaptionskip\r
+% but only \abovecaptionskip is used above figure captions and *below* table\r
+% captions\r
+\setlength\abovecaptionskip{0.5\baselineskip}\r
+\setlength\belowcaptionskip{0pt}\r
+% V1.6 create hooks in case the caption spacing ever needs to be\r
+% overridden by a user\r
+\def\@IEEEfigurecaptionsepspace{\vskip\abovecaptionskip\relax}%\r
+\def\@IEEEtablecaptionsepspace{\vskip\abovecaptionskip\relax}%\r
+\r
+\r
+% 1.6b revise caption system so that \@makecaption uses two arguments\r
+% as with LaTeX2e. Otherwise, there will be problems when using hyperref.\r
+\def\@IEEEtablestring{table}\r
+\r
+\r
+% V1.8 compensate for \topskip so top of top figures align with tops of the first lines of main text\r
+% here we calculate a space equal to the amount \topskip exceeds the main text height\r
+% we hook in at \@floatboxreset\r
+\def\@IEEEfiguretopskipspace{\ifdim\prevdepth=-1000pt\relax\r
+\setlength{\@IEEEtrantmpdimenA}{1\topskip}\relax\r
+\addtolength{\@IEEEtrantmpdimenA}{-0.7\@IEEEnormalsizeunitybaselineskip}\relax\r
+\vspace*{\@IEEEtrantmpdimenA}\fi}\r
+% V1.8 compensate for \topskip at the top of top tables so caption text is on main text baseline\r
+% use a strut set on the caption baseline within \@makecaption\r
+\def\@IEEEtabletopskipstrut{\ifdim\prevdepth=-1000pt\rule{0pt}{\topskip}\fi}\r
+% the \ifdim\prevdepth checks are always expected to be true for IEEE style float caption ordering\r
+% because top of figure content and top of captions in tables is the first thing on the vertical\r
+% list of these floats\r
+% thanks to Donald Arseneau for his 2000/11/11 post "Re: caption hacking" with info on this topic.\r
+\r
+\r
+\ifCLASSOPTIONcompsoc\r
+% V1.7 compsoc \@makecaption\r
+\ifCLASSOPTIONconference% compsoc conference\r
+\long\def\@makecaption#1#2{%\r
+% test if is a for a figure or table\r
+\ifx\@captype\@IEEEtablestring%\r
+% if a table, do table caption\r
+\normalsize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\sffamily\normalsize {#1.}\nobreakspace #2}\par\addvspace{0.5\baselineskip}\egroup%\r
+\@IEEEtablecaptionsepspace\r
+% if not a table, format it as a figure\r
+\else\r
+\@IEEEfigurecaptionsepspace\r
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}\nobreakspace #2}%\r
+\ifdim \wd\@tempboxa >\hsize%\r
+% if caption is longer than a line, let it wrap around\r
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}\nobreakspace}%\r
+\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%\r
+% if caption is shorter than a line, center\r
+\else%\r
+\hbox to\hsize{\normalfont\sffamily\normalsize\hfil\box\@tempboxa\hfil}%\r
+\fi\fi}\r
+%\r
+\else% nonconference compsoc\r
+\long\def\@makecaption#1#2{%\r
+% test if is a for a figure or table\r
+\ifx\@captype\@IEEEtablestring%\r
+% if a table, do table caption\r
+\normalsize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\sffamily\normalsize #1}\\{\normalfont\sffamily\normalsize #2}\par\addvspace{0.5\baselineskip}\egroup%\r
+\@IEEEtablecaptionsepspace\r
+% if not a table, format it as a figure\r
+\else\r
+\@IEEEfigurecaptionsepspace\r
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}\nobreakspace #2}%\r
+\ifdim \wd\@tempboxa >\hsize%\r
+% if caption is longer than a line, let it wrap around\r
+\setbox\@tempboxa\hbox{\normalfont\sffamily\normalsize {#1.}\nobreakspace}%\r
+\parbox[t]{\hsize}{\normalfont\sffamily\normalsize \noindent\unhbox\@tempboxa#2}%\r
+% if caption is shorter than a line, left justify\r
+\else%\r
+\hbox to\hsize{\normalfont\sffamily\normalsize\box\@tempboxa\hfil}%\r
+\fi\fi}\r
+\fi\r
+%\r
+\else% traditional noncompsoc \@makecaption\r
+\long\def\@makecaption#1#2{%\r
+% test if is a for a figure or table\r
+\ifx\@captype\@IEEEtablestring%\r
+% if a table, do table caption\r
+\footnotesize\bgroup\par\centering\@IEEEtabletopskipstrut{\normalfont\footnotesize #1}\\{\normalfont\footnotesize\scshape #2}\par\addvspace{0.5\baselineskip}\egroup%\r
+\@IEEEtablecaptionsepspace\r
+% if not a table, format it as a figure\r
+\else\r
+\@IEEEfigurecaptionsepspace\r
+% 3/2001 use footnotesize, not small; use two nonbreaking spaces, not one\r
+\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace\nobreakspace #2}%\r
+\ifdim \wd\@tempboxa >\hsize%\r
+% if caption is longer than a line, let it wrap around\r
+\setbox\@tempboxa\hbox{\normalfont\footnotesize {#1.}\nobreakspace\nobreakspace}%\r
+\parbox[t]{\hsize}{\normalfont\footnotesize\noindent\unhbox\@tempboxa#2}%\r
+% if caption is shorter than a line, center if conference, left justify otherwise\r
+\else%\r
+\ifCLASSOPTIONconference \hbox to\hsize{\normalfont\footnotesize\hfil\box\@tempboxa\hfil}%\r
+\else \hbox to\hsize{\normalfont\footnotesize\box\@tempboxa\hfil}%\r
+\fi\fi\fi}\r
+\fi\r
+\r
+\r
+\r
+% V1.7 disable captions class option, do so in a way that retains operation of \label\r
+% within \caption\r
+\ifCLASSOPTIONcaptionsoff\r
+\long\def\@makecaption#1#2{\vspace*{2em}\footnotesize\bgroup\par\addvspace{0.5\baselineskip}\centering{\footnotesize #1}\par\addvspace{0.5\baselineskip}\egroup%\r
+\let\@IEEEtemporiglabeldefsave\label\r
+\let\@IEEEtemplabelargsave\relax\r
+\def\label##1{\gdef\@IEEEtemplabelargsave{##1}}%\r
+\setbox\@tempboxa\hbox{#2}%\r
+\let\label\@IEEEtemporiglabeldefsave\r
+\ifx\@IEEEtemplabelargsave\relax\else\label{\@IEEEtemplabelargsave}\fi}\r
+\fi\r
+\r
+\r
+% V1.7 define end environments with \def not \let so as to work OK with\r
+% preview-latex\r
+\newcounter{figure}\r
+\def\thefigure{\@arabic\c@figure}\r
+\def\fps@figure{tbp}\r
+\def\ftype@figure{1}\r
+\def\ext@figure{lof}\r
+\def\fnum@figure{\figurename\nobreakspace\thefigure}\r
+% V1.8 within figures add \@IEEEfiguretopskipspace compensation to LaTeX2e's \@floatboxreset\r
+\def\figure{\def\@floatboxreset{\reset@font\normalsize\@setminipage\@IEEEfiguretopskipspace}\@float{figure}}\r
+\def\endfigure{\end@float}\r
+% V1.8 also add \@IEEEfiguretopskipspace compensation to \figure*\r
+\@namedef{figure*}{\def\@floatboxreset{\reset@font\normalsize\@setminipage\@IEEEfiguretopskipspace}\@dblfloat{figure}}\r
+\@namedef{endfigure*}{\end@dblfloat}\r
+\r
+\newcounter{table}\r
+\ifCLASSOPTIONcompsoc\r
+\def\thetable{\arabic{table}}\r
+\else\r
+\def\thetable{\@Roman\c@table}\r
+\fi\r
+\def\fps@table{tbp}\r
+\def\ftype@table{2}\r
+\def\ext@table{lot}\r
+\def\fnum@table{\tablename\nobreakspace\thetable}\r
+% V1.6 IEEE uses 8pt text for tables\r
+% within tables alter LaTeX2e's \@floatboxreset to use \footnotesize\r
+\def\table{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@float{table}}\r
+\def\endtable{\end@float}\r
+% v1.6b double column tables need to default to footnotesize as well.\r
+\@namedef{table*}{\def\@floatboxreset{\reset@font\footnotesize\@setminipage}\@dblfloat{table}}\r
+\@namedef{endtable*}{\end@dblfloat}\r
+\r
+\r
+\r
+\r
+%%\r
+%% START OF IEEEeqnarray DEFINITIONS\r
+%%\r
+%% Inspired by the concepts, examples, and previous works of LaTeX \r
+%% coders and developers such as Donald Arseneau, Fred Bartlett, \r
+%% David Carlisle, Tony Liu, Frank Mittelbach, Piet van Oostrum, \r
+%% Roland Winkler and Mark Wooding.\r
+%% I don't make the claim that my work here is even near their calibre. ;)\r
+\r
+\r
+% hook to allow easy changeover to IEEEtran.cls/tools.sty error reporting\r
+\def\@IEEEclspkgerror{\ClassError{IEEEtran}}\r
+\r
+\newif\if@IEEEeqnarrayboxnojot% flag to indicate if the environment was called as the star form\r
+\@IEEEeqnarrayboxnojotfalse\r
+\r
+\newif\if@advanceIEEEeqncolcnt% tracks if the environment should advance the col counter\r
+% allows a way to make an \IEEEeqnarraybox that can be used within an \IEEEeqnarray\r
+% used by IEEEeqnarraymulticol so that it can work properly in both\r
+\@advanceIEEEeqncolcnttrue\r
+\r
+\newcount\@IEEEeqnnumcols % tracks how many IEEEeqnarray cols are defined\r
+\newcount\@IEEEeqncolcnt % tracks how many IEEEeqnarray cols the user actually used\r
+\r
+\r
+% The default math style used by the columns\r
+\def\IEEEeqnarraymathstyle{\displaystyle}\r
+% The default text style used by the columns\r
+% default to using the current font\r
+\def\IEEEeqnarraytextstyle{\relax}\r
+\r
+% like the iedlistdecl but for \IEEEeqnarray\r
+\def\IEEEeqnarraydecl{\relax}\r
+\def\IEEEeqnarrayboxdecl{\relax}\r
+\r
+\r
+\r
+% V1.8 flags to indicate that equation numbering is to persist\r
+\newif\if@IEEEeqnumpersist%\r
+\@IEEEeqnumpersistfalse\r
+\newif\if@IEEEsubeqnumpersist%\r
+\@IEEEsubeqnumpersistfalse\r
+%\r
+% V1.8 flags to indicate if (sub)equation number of last line was preadvanced\r
+\newif\if@IEEEeqnumpreadv%\r
+\@IEEEeqnumpreadvfalse\r
+\newif\if@IEEEsubeqnumpreadv%\r
+\@IEEEsubeqnumpreadvfalse\r
+\r
+\newcount\@IEEEsubeqnnumrollback% saves previous value of IEEEsubequation number in case we need to restore it\r
+\r
+% \yesnumber is the opposite of \nonumber\r
+% a novel concept with the same def as the equationarray package\r
+% However, we give IEEE versions too since some LaTeX packages such as \r
+% the MDWtools mathenv.sty redefine \nonumber to something else.\r
+% This command is intended for use in non-IEEEeqnarray math environments\r
+\providecommand{\yesnumber}{\global\@eqnswtrue}\r
+\r
+\r
+% IEEEyes/nonumber \r
+% V1.8 add persistant * forms\r
+% These commands can alter the type of equation an IEEEeqnarray line is.\r
+\def\IEEEyesnumber{\@ifstar{\global\@IEEEeqnumpersisttrue\global\@IEEEsubeqnumpersistfalse\@IEEEyesnumber}{\@IEEEyesnumber}}\r
+\r
+\def\@IEEEyesnumber{\global\@eqnswtrue\r
+\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray\r
+\ifnum\c@IEEEsubequation>0\relax\r
+ \stepcounter{equation}\setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label\r
+\fi\r
+% even if we reached this eqn num via a preadv, it is legit now\r
+\global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse\r
+\fi}\r
+\r
+\def\IEEEnonumber{\@ifstar{\global\@IEEEeqnumpersistfalse\global\@IEEEsubeqnumpersistfalse\global\@eqnswfalse}{\global\@eqnswfalse}}\r
+\r
+\r
+\def\IEEEyessubnumber{\@ifstar{\global\@IEEEsubeqnumpersisttrue\@IEEEyessubnumber}{\@IEEEyessubnumber}}\r
+%\r
+\def\@IEEEyessubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray\r
+ \ifnum\c@IEEEsubequation>0\relax% if it already is a subequation, we are good to go as-is\r
+ \else% if we are a regular equation we have to watch out for two cases\r
+ \if@IEEEeqnumpreadv% if this equation is the result of a preadvance, backout and bump the sub eqnnum\r
+ \global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\addtocounter{IEEEsubequation}{1}\relax\r
+ \else% non-preadvanced equations just need initialization of their sub eqnnum\r
+ \setcounter{IEEEsubequation}{1}\relax\r
+ \fi\r
+ \fi% fi already is subequation\r
+ \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label\r
+ \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore\r
+ \global\@eqnswtrue\r
+\fi}\r
+\r
+\r
+\def\IEEEnosubnumber{\@ifstar{\global\@IEEEsubeqnumpersistfalse\@IEEEnosubnumber}{\@IEEEnosubnumber}}\r
+%\r
+\def\@IEEEnosubnumber{\if@IEEEeqnarrayISinner% alter counters and label only inside an IEEEeqnarray\r
+ \if@eqnsw % we do nothing unless we know we will display because we play with the counters here\r
+ % if it currently is a subequation, bump up to the next equation number and turn off the subequation\r
+ \ifnum\c@IEEEsubequation>0\relax\addtocounter{equation}{1}\setcounter{IEEEsubequation}{0}\relax\r
+ \fi\r
+ \global\@IEEEeqnumpreadvfalse\global\@IEEEsubeqnumpreadvfalse% no longer a preadv anymore\r
+ \gdef\@currentlabel{\p@equation\theequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label\r
+ \fi\r
+\fi}\r
+\r
+\r
+\r
+% allows users to "push away" equations that get too close to the equation numbers\r
+\def\IEEEeqnarraynumspace{\hphantom{\ifnum\c@IEEEsubequation>0\relax\theIEEEsubequationdis\else\theequationdis\fi}}\r
+\r
+% provides a way to span multiple columns within IEEEeqnarray environments\r
+% will consider \if@advanceIEEEeqncolcnt before globally advancing the\r
+% column counter - so as to work within \IEEEeqnarraybox\r
+% usage: \IEEEeqnarraymulticol{number cols. to span}{col type}{cell text}\r
+\long\def\IEEEeqnarraymulticol#1#2#3{\multispan{#1}\relax\r
+% check if column is defined for the precolumn definition\r
+% We have to be careful here because TeX scans for & even within an \iffalse\r
+% where it does not expand macros. So, if we used only one \ifx and a #3\r
+% appeared in the false branch and the user inserted another alignment\r
+% structure that uses & in the \IEEEeqnarraymulticol{}, TeX will not see that\r
+% there is an inner alignment in the false branch yet still will see any &\r
+% there and will think that they apply to the outer alignment resulting in an\r
+% incomplete \ifx error.\r
+% So, here we use separate checks for the pre and post parts in order to keep\r
+% the #3 outside of all conditionals.\r
+\relax\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax\r
+\csname @IEEEeqnarraycolPRE#2\endcsname\r
+\else% if not, error and use default type\r
+\@IEEEclspkgerror{Invalid column type "#2" in \string\IEEEeqnarraymulticol.\MessageBreak\r
+Using a default centering column instead}%\r
+{You must define IEEEeqnarray column types before use.}%\r
+\csname @IEEEeqnarraycolPRE@IEEEdefault\endcsname\r
+\fi\r
+% The ten \relax are to help prevent misleading error messages in case a user\r
+% accidently inserted a macro that tries to acquire additional arguments.\r
+#3\relax\relax\relax\relax\relax\relax\relax\relax\relax\relax\r
+% check if column is defined for the postcolumn definition\r
+\expandafter\ifx\csname @IEEEeqnarraycolDEF#2\endcsname\@IEEEeqnarraycolisdefined\relax\r
+\csname @IEEEeqnarraycolPOST#2\endcsname\r
+\else% if not, use the default type\r
+\csname @IEEEeqnarraycolPOST@IEEEdefault\endcsname\r
+\fi\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by #1\relax\fi}\r
+\r
+% like \omit, but maintains track of the column counter for \IEEEeqnarray\r
+\def\IEEEeqnarrayomit{\omit\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by 1\relax\fi}\r
+\r
+\r
+% provides a way to define a letter referenced column type\r
+% usage: \IEEEeqnarraydefcol{col. type letter/name}{pre insertion text}{post insertion text}\r
+\def\IEEEeqnarraydefcol#1#2#3{\expandafter\def\csname @IEEEeqnarraycolPRE#1\endcsname{#2}%\r
+\expandafter\def\csname @IEEEeqnarraycolPOST#1\endcsname{#3}%\r
+\expandafter\def\csname @IEEEeqnarraycolDEF#1\endcsname{1}}\r
+\r
+\r
+% provides a way to define a numerically referenced inter-column glue types\r
+% usage: \IEEEeqnarraydefcolsep{col. glue number}{glue definition}\r
+\def\IEEEeqnarraydefcolsep#1#2{\expandafter\def\csname @IEEEeqnarraycolSEP\romannumeral #1\endcsname{#2}%\r
+\expandafter\def\csname @IEEEeqnarraycolSEPDEF\romannumeral #1\endcsname{1}}\r
+\r
+\r
+\def\@IEEEeqnarraycolisdefined{1}% just a macro for 1, used for checking undefined column types\r
+\r
+\r
+% expands and appends the given argument to the \@IEEEtrantmptoksA token list\r
+% used to build up the \halign preamble\r
+\def\@IEEEappendtoksA#1{\edef\@@IEEEappendtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA #1}}%\r
+\@@IEEEappendtoksA}\r
+\r
+% also appends to \@IEEEtrantmptoksA, but does not expand the argument\r
+% uses \toks8 as a scratchpad register\r
+\def\@IEEEappendNOEXPANDtoksA#1{\toks8={#1}%\r
+\edef\@@IEEEappendNOEXPANDtoksA{\@IEEEtrantmptoksA={\the\@IEEEtrantmptoksA\the\toks8}}%\r
+\@@IEEEappendNOEXPANDtoksA}\r
+\r
+% define some common column types for the user\r
+% math\r
+\IEEEeqnarraydefcol{l}{$\IEEEeqnarraymathstyle}{$\hfil}\r
+\IEEEeqnarraydefcol{c}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}\r
+\IEEEeqnarraydefcol{r}{\hfil$\IEEEeqnarraymathstyle}{$}\r
+\IEEEeqnarraydefcol{L}{$\IEEEeqnarraymathstyle{}}{{}$\hfil}\r
+\IEEEeqnarraydefcol{C}{\hfil$\IEEEeqnarraymathstyle{}}{{}$\hfil}\r
+\IEEEeqnarraydefcol{R}{\hfil$\IEEEeqnarraymathstyle{}}{{}$}\r
+% text\r
+\IEEEeqnarraydefcol{s}{\IEEEeqnarraytextstyle}{\hfil}\r
+\IEEEeqnarraydefcol{t}{\hfil\IEEEeqnarraytextstyle}{\hfil}\r
+\IEEEeqnarraydefcol{u}{\hfil\IEEEeqnarraytextstyle}{}\r
+\r
+% vertical rules\r
+\IEEEeqnarraydefcol{v}{}{\vrule width\arrayrulewidth}\r
+\IEEEeqnarraydefcol{vv}{\vrule width\arrayrulewidth\hfil}{\hfil\vrule width\arrayrulewidth}\r
+\IEEEeqnarraydefcol{V}{}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}\r
+\IEEEeqnarraydefcol{VV}{\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth\hfil}%\r
+{\hfil\vrule width\arrayrulewidth\hskip\doublerulesep\vrule width\arrayrulewidth}\r
+\r
+% horizontal rules\r
+\IEEEeqnarraydefcol{h}{}{\leaders\hrule height\arrayrulewidth\hfil}\r
+\IEEEeqnarraydefcol{H}{}{\leaders\vbox{\hrule width\arrayrulewidth\vskip\doublerulesep\hrule width\arrayrulewidth}\hfil}\r
+\r
+% plain\r
+\IEEEeqnarraydefcol{x}{}{}\r
+\IEEEeqnarraydefcol{X}{$}{$}\r
+\r
+% the default column type to use in the event a column type is not defined\r
+\IEEEeqnarraydefcol{@IEEEdefault}{\hfil$\IEEEeqnarraymathstyle}{$\hfil}\r
+\r
+\r
+% a zero tabskip (used for "-" col types)\r
+\def\@IEEEeqnarraycolSEPzero{0pt plus 0pt minus 0pt}\r
+% a centering tabskip (used for "+" col types)\r
+\def\@IEEEeqnarraycolSEPcenter{1000pt plus 0pt minus 1000pt}\r
+\r
+% top level default tabskip glues for the start, end, and inter-column\r
+% may be reset within environments not always at the top level, e.g., \IEEEeqnarraybox\r
+\edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPcenter}% default start glue\r
+\edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPcenter}% default end glue\r
+\edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue\r
+\r
+\r
+\r
+% creates a vertical rule that extends from the bottom to the top a a cell\r
+% Provided in case other packages redefine \vline some other way.\r
+% usage: \IEEEeqnarrayvrule[rule thickness]\r
+% If no argument is provided, \arrayrulewidth will be used for the rule thickness. \r
+\newcommand\IEEEeqnarrayvrule[1][\arrayrulewidth]{\vrule\@width#1\relax}\r
+\r
+% creates a blank separator row\r
+% usage: \IEEEeqnarrayseprow[separation length][font size commands]\r
+% default is \IEEEeqnarrayseprow[0.25\normalbaselineskip][\relax]\r
+% blank arguments inherit the default values\r
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers\r
+\def\IEEEeqnarrayseprow{\relax\@ifnextchar[{\@IEEEeqnarrayseprow}{\@IEEEeqnarrayseprow[0.25\normalbaselineskip]}}\r
+\def\@IEEEeqnarrayseprow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprow[#1]}{\@@IEEEeqnarrayseprow[#1][\relax]}}\r
+\def\@@IEEEeqnarrayseprow[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%\r
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%\r
+% get the skip value, based on the font commands\r
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3\r
+% assign within a bogus box to confine the font changes\r
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%\r
+\else%\r
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%\r
+\fi%\r
+\@IEEEeqnarrayhoptolastcolumn\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}\r
+\r
+% creates a blank separator row, but omits all the column templates\r
+% usage: \IEEEeqnarrayseprowcut[separation length][font size commands]\r
+% default is \IEEEeqnarrayseprowcut[0.25\normalbaselineskip][\relax]\r
+% blank arguments inherit the default values\r
+% uses \skip5 as a scratch register - calls \@IEEEeqnarraystrutsize which uses more scratch registers\r
+\def\IEEEeqnarrayseprowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\@ifnextchar[{\@IEEEeqnarrayseprowcut}{\@IEEEeqnarrayseprowcut[0.25\normalbaselineskip]}}\r
+\def\@IEEEeqnarrayseprowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarrayseprowcut[#1]}{\@@IEEEeqnarrayseprowcut[#1][\relax]}}\r
+\def\@@IEEEeqnarrayseprowcut[#1][#2]{\def\@IEEEeqnarrayseprowARGONE{#1}%\r
+\ifx\@IEEEeqnarrayseprowARGONE\@empty%\r
+% get the skip value, based on the font commands\r
+% use skip5 because \IEEEeqnarraystrutsize uses \skip0, \skip2, \skip3\r
+% assign within a bogus box to confine the font changes\r
+{\setbox0=\hbox{#2\relax\global\skip5=0.25\normalbaselineskip}}%\r
+\else%\r
+{\setbox0=\hbox{#2\relax\global\skip5=#1}}%\r
+\fi%\r
+\IEEEeqnarraystrutsize{\skip5}{0pt}[\relax]\relax}\r
+\r
+\r
+\r
+% draws a single rule across all the columns optional\r
+% argument determines the rule width, \arrayrulewidth is the default\r
+% updates column counter as needed and turns off struts\r
+% usage: \IEEEeqnarrayrulerow[rule line thickness]\r
+\def\IEEEeqnarrayrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\@ifnextchar[{\@IEEEeqnarrayrulerow}{\@IEEEeqnarrayrulerow[\arrayrulewidth]}}\r
+\def\@IEEEeqnarrayrulerow[#1]{\leaders\hrule height#1\hfil\relax% put in our rule \r
+% turn off any struts\r
+\IEEEeqnarraystrutsize{0pt}{0pt}[\relax]\relax}\r
+\r
+\r
+% draws a double rule by using a single rule row, a separator row, and then\r
+% another single rule row \r
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default\r
+% second optional argument determines the rule spacing, \doublerulesep is the default\r
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]\r
+\def\IEEEeqnarraydblrulerow{\multispan{\@IEEEeqnnumcols}\relax% span all the cols\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\@ifnextchar[{\@IEEEeqnarraydblrulerow}{\@IEEEeqnarraydblrulerow[\arrayrulewidth]}}\r
+\def\@IEEEeqnarraydblrulerow[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerow[#1]}%\r
+{\@@IEEEeqnarraydblrulerow[#1][\doublerulesep]}}\r
+\def\@@IEEEeqnarraydblrulerow[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%\r
+% we allow the user to say \IEEEeqnarraydblrulerow[][]\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%\r
+\else%\r
+\@IEEEeqnarrayrulerow[#1]\relax%\r
+\fi%\r
+\def\@IEEEeqnarraydblrulerowARG{#2}%\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\\\IEEEeqnarrayseprow[\doublerulesep][\relax]%\r
+\else%\r
+\\\IEEEeqnarrayseprow[#2][\relax]%\r
+\fi%\r
+\\\multispan{\@IEEEeqnnumcols}%\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\def\@IEEEeqnarraydblrulerowARG{#1}%\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%\r
+\else%\r
+\@IEEEeqnarrayrulerow[#1]%\r
+\fi%\r
+}\r
+\r
+% draws a double rule by using a single rule row, a separator (cutting) row, and then\r
+% another single rule row \r
+% first optional argument determines the rule thicknesses, \arrayrulewidth is the default\r
+% second optional argument determines the rule spacing, \doublerulesep is the default\r
+% usage: \IEEEeqnarraydblrulerow[rule line thickness][rule spacing]\r
+\def\IEEEeqnarraydblrulerowcut{\multispan{\@IEEEeqnnumcols}\relax% span all the cols\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\@ifnextchar[{\@IEEEeqnarraydblrulerowcut}{\@IEEEeqnarraydblrulerowcut[\arrayrulewidth]}}\r
+\def\@IEEEeqnarraydblrulerowcut[#1]{\relax\@ifnextchar[{\@@IEEEeqnarraydblrulerowcut[#1]}%\r
+{\@@IEEEeqnarraydblrulerowcut[#1][\doublerulesep]}}\r
+\def\@@IEEEeqnarraydblrulerowcut[#1][#2]{\def\@IEEEeqnarraydblrulerowARG{#1}%\r
+% we allow the user to say \IEEEeqnarraydblrulerow[][]\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%\r
+\else%\r
+\@IEEEeqnarrayrulerow[#1]%\r
+\fi%\r
+\def\@IEEEeqnarraydblrulerowARG{#2}%\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\\\IEEEeqnarrayseprowcut[\doublerulesep][\relax]%\r
+\else%\r
+\\\IEEEeqnarrayseprowcut[#2][\relax]%\r
+\fi%\r
+\\\multispan{\@IEEEeqnnumcols}%\r
+% advance column counter only if the IEEEeqnarray environment wants it\r
+\if@advanceIEEEeqncolcnt\global\advance\@IEEEeqncolcnt by \@IEEEeqnnumcols\relax\fi%\r
+\def\@IEEEeqnarraydblrulerowARG{#1}%\r
+\ifx\@IEEEeqnarraydblrulerowARG\@empty%\r
+\@IEEEeqnarrayrulerow[\arrayrulewidth]%\r
+\else%\r
+\@IEEEeqnarrayrulerow[#1]%\r
+\fi%\r
+}\r
+\r
+\r
+\r
+% inserts a full row's worth of &'s\r
+% relies on \@IEEEeqnnumcols to provide the correct number of columns\r
+% uses \@IEEEtrantmptoksA, \count0 as scratch registers\r
+\def\@IEEEeqnarrayhoptolastcolumn{\@IEEEtrantmptoksA={}\count0=1\relax%\r
+\loop% add cols if the user did not use them all\r
+\ifnum\count0<\@IEEEeqnnumcols\relax%\r
+\@IEEEappendtoksA{&}%\r
+\advance\count0 by 1\relax% update the col count\r
+\repeat%\r
+\the\@IEEEtrantmptoksA%execute the &'s\r
+}\r
+\r
+\r
+\r
+\newif\if@IEEEeqnarrayISinner % flag to indicate if we are within the lines\r
+\@IEEEeqnarrayISinnerfalse % of an IEEEeqnarray - after the IEEEeqnarraydecl\r
+\r
+\edef\@IEEEeqnarrayTHEstrutheight{0pt} % height and depth of IEEEeqnarray struts\r
+\edef\@IEEEeqnarrayTHEstrutdepth{0pt}\r
+\r
+\edef\@IEEEeqnarrayTHEmasterstrutheight{0pt} % default height and depth of\r
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{0pt} % struts within an IEEEeqnarray\r
+\r
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{0pt} % saved master strut height\r
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{0pt} % and depth\r
+\r
+\newif\if@IEEEeqnarrayusemasterstrut % flag to indicate that the master strut value\r
+\@IEEEeqnarrayusemasterstruttrue % is to be used\r
+\r
+\r
+\r
+% saves the strut height and depth of the master strut\r
+\def\@IEEEeqnarraymasterstrutsave{\relax%\r
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%\r
+% remove stretchability\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% save values\r
+\edef\@IEEEeqnarrayTHEmasterstrutHSAVE{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEmasterstrutDSAVE{\the\dimen2}}\r
+\r
+% restores the strut height and depth of the master strut\r
+\def\@IEEEeqnarraymasterstrutrestore{\relax%\r
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutHSAVE\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutDSAVE\relax%\r
+% remove stretchability\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% restore values\r
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}}\r
+\r
+\r
+% globally restores the strut height and depth to the \r
+% master values and sets the master strut flag to true\r
+\def\@IEEEeqnarraystrutreset{\relax%\r
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%\r
+% remove stretchability\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% restore values\r
+\xdef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%\r
+\xdef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%\r
+\global\@IEEEeqnarrayusemasterstruttrue}\r
+\r
+\r
+% if the master strut is not to be used, make the current\r
+% values of \@IEEEeqnarrayTHEstrutheight, \@IEEEeqnarrayTHEstrutdepth\r
+% and the use master strut flag, global\r
+% this allows user strut commands issued in the last column to be carried\r
+% into the isolation/strut column\r
+\def\@IEEEeqnarrayglobalizestrutstatus{\relax%\r
+\if@IEEEeqnarrayusemasterstrut\else%\r
+\xdef\@IEEEeqnarrayTHEstrutheight{\@IEEEeqnarrayTHEstrutheight}%\r
+\xdef\@IEEEeqnarrayTHEstrutdepth{\@IEEEeqnarrayTHEstrutdepth}%\r
+\global\@IEEEeqnarrayusemasterstrutfalse%\r
+\fi}\r
+\r
+\r
+\r
+% usage: \IEEEeqnarraystrutsize{height}{depth}[font size commands]\r
+% If called outside the lines of an IEEEeqnarray, sets the height\r
+% and depth of both the master and local struts. If called inside\r
+% an IEEEeqnarray line, sets the height and depth of the local strut\r
+% only and sets the flag to indicate the use of the local strut\r
+% values. If the height or depth is left blank, 0.7\normalbaselineskip\r
+% and 0.3\normalbaselineskip will be used, respectively.\r
+% The optional argument can be used to evaluate the lengths under\r
+% a different font size and styles. If none is specified, the current\r
+% font is used.\r
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2\r
+\def\IEEEeqnarraystrutsize#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsize{#1}{#2}}{\@IEEEeqnarraystrutsize{#1}{#2}[\relax]}}\r
+\def\@IEEEeqnarraystrutsize#1#2[#3]{\def\@IEEEeqnarraystrutsizeARG{#1}%\r
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%\r
+{\setbox0=\hbox{#3\relax\global\skip3=0.7\normalbaselineskip}}%\r
+\skip0=\skip3\relax%\r
+\else% arg one present\r
+{\setbox0=\hbox{#3\relax\global\skip3=#1\relax}}%\r
+\skip0=\skip3\relax%\r
+\fi% if null arg\r
+\def\@IEEEeqnarraystrutsizeARG{#2}%\r
+\ifx\@IEEEeqnarraystrutsizeARG\@empty%\r
+{\setbox0=\hbox{#3\relax\global\skip3=0.3\normalbaselineskip}}%\r
+\skip2=\skip3\relax%\r
+\else% arg two present\r
+{\setbox0=\hbox{#3\relax\global\skip3=#2\relax}}%\r
+\skip2=\skip3\relax%\r
+\fi% if null arg\r
+% remove stretchability, just to be safe\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% dimen0 = height, dimen2 = depth\r
+\if@IEEEeqnarrayISinner% inner does not touch master strut size\r
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%\r
+\@IEEEeqnarrayusemasterstrutfalse% do not use master\r
+\else% outer, have to set master strut too\r
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%\r
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%\r
+\@IEEEeqnarrayusemasterstruttrue% use master strut\r
+\fi}\r
+\r
+\r
+% usage: \IEEEeqnarraystrutsizeadd{added height}{added depth}[font size commands]\r
+% If called outside the lines of an IEEEeqnarray, adds the given height\r
+% and depth to both the master and local struts.\r
+% If called inside an IEEEeqnarray line, adds the given height and depth\r
+% to the local strut only and sets the flag to indicate the use \r
+% of the local strut values.\r
+% In both cases, if a height or depth is left blank, 0pt is used instead.\r
+% The optional argument can be used to evaluate the lengths under\r
+% a different font size and styles. If none is specified, the current\r
+% font is used.\r
+% uses scratch registers \skip0, \skip2, \skip3, \dimen0, \dimen2\r
+\def\IEEEeqnarraystrutsizeadd#1#2{\relax\@ifnextchar[{\@IEEEeqnarraystrutsizeadd{#1}{#2}}{\@IEEEeqnarraystrutsizeadd{#1}{#2}[\relax]}}\r
+\def\@IEEEeqnarraystrutsizeadd#1#2[#3]{\def\@IEEEeqnarraystrutsizearg{#1}%\r
+\ifx\@IEEEeqnarraystrutsizearg\@empty%\r
+\skip0=0pt\relax%\r
+\else% arg one present\r
+{\setbox0=\hbox{#3\relax\global\skip3=#1}}%\r
+\skip0=\skip3\relax%\r
+\fi% if null arg\r
+\def\@IEEEeqnarraystrutsizearg{#2}%\r
+\ifx\@IEEEeqnarraystrutsizearg\@empty%\r
+\skip2=0pt\relax%\r
+\else% arg two present\r
+{\setbox0=\hbox{#3\relax\global\skip3=#2}}%\r
+\skip2=\skip3\relax%\r
+\fi% if null arg\r
+% remove stretchability, just to be safe\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% dimen0 = height, dimen2 = depth\r
+\if@IEEEeqnarrayISinner% inner does not touch master strut size\r
+% get local strut size\r
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%\r
+% add it to the user supplied values\r
+\advance\dimen0 by \skip0\relax%\r
+\advance\dimen2 by \skip2\relax%\r
+% update the local strut size\r
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%\r
+\@IEEEeqnarrayusemasterstrutfalse% do not use master\r
+\else% outer, have to set master strut too\r
+% get master strut size\r
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%\r
+% add it to the user supplied values\r
+\advance\dimen0 by \skip0\relax%\r
+\advance\dimen2 by \skip2\relax%\r
+% update the local and master strut sizes\r
+\edef\@IEEEeqnarrayTHEmasterstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEmasterstrutdepth{\the\dimen2}%\r
+\edef\@IEEEeqnarrayTHEstrutheight{\the\dimen0}%\r
+\edef\@IEEEeqnarrayTHEstrutdepth{\the\dimen2}%\r
+\@IEEEeqnarrayusemasterstruttrue% use master strut\r
+\fi}\r
+\r
+\r
+% allow user a way to see the struts\r
+\newif\ifIEEEvisiblestruts\r
+\IEEEvisiblestrutsfalse\r
+\r
+% inserts an invisible strut using the master or local strut values\r
+% uses scratch registers \skip0, \skip2, \dimen0, \dimen2\r
+\def\@IEEEeqnarrayinsertstrut{\relax%\r
+\if@IEEEeqnarrayusemasterstrut\r
+% get master strut size\r
+\expandafter\skip0=\@IEEEeqnarrayTHEmasterstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEmasterstrutdepth\relax%\r
+\else%\r
+% get local strut size\r
+\expandafter\skip0=\@IEEEeqnarrayTHEstrutheight\relax%\r
+\expandafter\skip2=\@IEEEeqnarrayTHEstrutdepth\relax%\r
+\fi%\r
+% remove stretchability, probably not needed\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+% dimen0 = height, dimen2 = depth\r
+% allow user to see struts if desired\r
+\ifIEEEvisiblestruts%\r
+\vrule width0.2pt height\dimen0 depth\dimen2\relax%\r
+\else%\r
+\vrule width0pt height\dimen0 depth\dimen2\relax\fi}\r
+\r
+\r
+% creates an invisible strut, useable even outside \IEEEeqnarray\r
+% if \IEEEvisiblestrutstrue, the strut will be visible and 0.2pt wide. \r
+% usage: \IEEEstrut[height][depth][font size commands]\r
+% default is \IEEEstrut[0.7\normalbaselineskip][0.3\normalbaselineskip][\relax]\r
+% blank arguments inherit the default values\r
+% uses \dimen0, \dimen2, \skip0, \skip2\r
+\def\IEEEstrut{\relax\@ifnextchar[{\@IEEEstrut}{\@IEEEstrut[0.7\normalbaselineskip]}}\r
+\def\@IEEEstrut[#1]{\relax\@ifnextchar[{\@@IEEEstrut[#1]}{\@@IEEEstrut[#1][0.3\normalbaselineskip]}}\r
+\def\@@IEEEstrut[#1][#2]{\relax\@ifnextchar[{\@@@IEEEstrut[#1][#2]}{\@@@IEEEstrut[#1][#2][\relax]}}\r
+\def\@@@IEEEstrut[#1][#2][#3]{\mbox{#3\relax%\r
+\def\@IEEEstrutARG{#1}%\r
+\ifx\@IEEEstrutARG\@empty%\r
+\skip0=0.7\normalbaselineskip\relax%\r
+\else%\r
+\skip0=#1\relax%\r
+\fi%\r
+\def\@IEEEstrutARG{#2}%\r
+\ifx\@IEEEstrutARG\@empty%\r
+\skip2=0.3\normalbaselineskip\relax%\r
+\else%\r
+\skip2=#2\relax%\r
+\fi%\r
+% remove stretchability, probably not needed\r
+\dimen0\skip0\relax%\r
+\dimen2\skip2\relax%\r
+\ifIEEEvisiblestruts%\r
+\vrule width0.2pt height\dimen0 depth\dimen2\relax%\r
+\else%\r
+\vrule width0.0pt height\dimen0 depth\dimen2\relax\fi}}\r
+\r
+\r
+% enables strut mode by setting a default strut size and then zeroing the\r
+% \baselineskip, \lineskip, \lineskiplimit and \jot\r
+\def\IEEEeqnarraystrutmode{\IEEEeqnarraystrutsize{0.7\normalbaselineskip}{0.3\normalbaselineskip}[\relax]%\r
+\baselineskip=0pt\lineskip=0pt\lineskiplimit=0pt\jot=0pt}\r
+\r
+\r
+% equation and subequation forms to use to setup hyperref's \@currentHref\r
+\def\@IEEEtheHrefequation{equation.\theHequation}\r
+\def\@IEEEtheHrefsubequation{equation.\theHequation\alph{IEEEsubequation}}\r
+\r
+\r
+\def\IEEEeqnarray{\@IEEEeqnumpersisttrue\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}\r
+\def\endIEEEeqnarray{\end@IEEEeqnarray}\r
+\r
+\@namedef{IEEEeqnarray*}{\@IEEEeqnumpersistfalse\@IEEEsubeqnumpersistfalse\@IEEEeqnarray}\r
+\@namedef{endIEEEeqnarray*}{\end@IEEEeqnarray}\r
+\r
+\r
+% \IEEEeqnarray is an enhanced \eqnarray. \r
+% The star form defaults to not putting equation numbers at the end of each row.\r
+% usage: \IEEEeqnarray[decl]{cols}\r
+\def\@IEEEeqnarray{\relax\@ifnextchar[{\@@IEEEeqnarray}{\@@IEEEeqnarray[\relax]}}\r
+\def\@@IEEEeqnarray[#1]#2{%\r
+ % default to showing the equation number or not based on whether or not\r
+ % the star form was involked\r
+ \if@IEEEeqnumpersist\global\@eqnswtrue\r
+ \else% not the star form\r
+ \global\@eqnswfalse\r
+ \fi% if star form\r
+ % provide a basic hyperref \theHequation if this has not already been setup (hyperref not loaded, or no section counter)\r
+ \@ifundefined{theHequation}{\def\theHequation{\arabic{equation}}}{}\relax\r
+ % provide dummy hyperref commands in case hyperref is not loaded\r
+ \providecommand{\Hy@raisedlink}[1]{}\relax\r
+ \providecommand{\hyper@anchorstart}[1]{}\relax\r
+ \providecommand{\hyper@anchorend}{}\relax\r
+ \providecommand{\@currentHref}{}\relax\r
+ \@IEEEeqnumpreadvfalse% reset eqnpreadv flag\r
+ \@IEEEsubeqnumpreadvfalse% reset subeqnpreadv flag\r
+ \@IEEEeqnarrayISinnerfalse% not yet within the lines of the halign\r
+ \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default\r
+ \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise\r
+ \IEEEvisiblestrutsfalse% diagnostic mode defaults to off\r
+ % no extra space unless the user specifically requests it\r
+ \lineskip=0pt\relax\r
+ \lineskiplimit=0pt\relax\r
+ \baselineskip=\normalbaselineskip\relax%\r
+ \jot=\IEEEnormaljot\relax%\r
+ \mathsurround\z@\relax% no extra spacing around math\r
+ \@advanceIEEEeqncolcnttrue% advance the col counter for each col the user uses, \r
+ % used in \IEEEeqnarraymulticol and in the preamble build\r
+ %V1.8 Here we preadvance to the next equation number.\r
+ % If the user later wants a continued subequation, we can roll back.\r
+ \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation%\r
+ \stepcounter{equation}\@IEEEeqnumpreadvtrue% advance equation counter before first line\r
+ \setcounter{IEEEsubequation}{0}% no subequation yet\r
+ \let\@IEEEcurrentlabelsave\@currentlabel% save current label as we later change it globally\r
+ \let\@IEEEcurrentHrefsave\@currentHref% save current href label as we later change it globally\r
+ \def\@currentlabel{\p@equation\theequation}% redefine the ref label\r
+ \def\@currentHref{\@IEEEtheHrefequation}% setup hyperref label\r
+ \IEEEeqnarraydecl\relax% allow a way for the user to make global overrides\r
+ #1\relax% allow user to override defaults\r
+ \let\\\@IEEEeqnarraycr% replace newline with one that can put in eqn. numbers\r
+ \global\@IEEEeqncolcnt\z@% col. count = 0 for first line\r
+ \@IEEEbuildpreamble #2\end\relax% build the preamble and put it into \@IEEEtrantmptoksA \r
+ % put in the column for the equation number\r
+ \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first\r
+ \toks0={##}%\r
+ % advance the \@IEEEeqncolcnt for the isolation col, this helps with error checking\r
+ \@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}%\r
+ % add the isolation column\r
+ \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}%\r
+ % advance the \@IEEEeqncolcnt for the equation number col, this helps with error checking\r
+ \@IEEEappendtoksA{&\global\advance\@IEEEeqncolcnt by 1\relax}%\r
+ % add the equation number col to the preamble\r
+ \@IEEEappendtoksA{\tabskip\z@skip\hb@xt@\z@\bgroup\hss\the\toks0\egroup}%\r
+ % note \@IEEEeqnnumcols does not count the equation col or isolation col\r
+ % set the starting tabskip glue as determined by the preamble build\r
+ \tabskip=\@IEEEBPstartglue\relax\r
+ % begin the display alignment\r
+ \@IEEEeqnarrayISinnertrue% commands are now within the lines\r
+ $$\everycr{}\halign to\displaywidth\bgroup\r
+ % "exspand" the preamble\r
+ \span\the\@IEEEtrantmptoksA\cr}\r
+\r
+% enter isolation/strut column (or the next column if the user did not use\r
+% every column), record the strut status, complete the columns, do the strut if needed,\r
+% restore counters (to backout any equation setup for a next line that was never used)\r
+% to their correct values and exit\r
+\def\end@IEEEeqnarray{\@IEEEeqnarrayglobalizestrutstatus&\@@IEEEeqnarraycr\egroup\r
+\if@IEEEsubeqnumpreadv\global\advance\c@IEEEsubequation\m@ne\fi\r
+\if@IEEEeqnumpreadv\global\advance\c@equation\m@ne\global\c@IEEEsubequation=\@IEEEsubeqnnumrollback\fi\r
+\global\let\@currentlabel\@IEEEcurrentlabelsave% restore current label\r
+\global\let\@currentHref\@IEEEcurrentHrefsave% restore current href label\r
+$$\@ignoretrue}\r
+\r
+\r
+% IEEEeqnarray uses a modifed \\ instead of the plain \cr to\r
+% end rows. This allows for things like \\*[vskip amount]\r
+% These "cr" macros are modified versions of those for LaTeX2e's eqnarray\r
+% the {\ifnum0=`} braces must be kept away from the last column to avoid\r
+% altering spacing of its math, so we use & to advance to the next column\r
+% as there is an isolation/strut column after the user's columns\r
+\def\@IEEEeqnarraycr{\@IEEEeqnarrayglobalizestrutstatus&% save strut status and advance to next column\r
+ {\ifnum0=`}\fi\r
+ \@ifstar{%\r
+ \global\@eqpen\@M\@IEEEeqnarrayYCR\r
+ }{%\r
+ \global\@eqpen\interdisplaylinepenalty \@IEEEeqnarrayYCR\r
+ }%\r
+}\r
+\r
+\def\@IEEEeqnarrayYCR{\@testopt\@IEEEeqnarrayXCR\z@skip}\r
+\r
+\def\@IEEEeqnarrayXCR[#1]{%\r
+ \ifnum0=`{\fi}%\r
+ \@@IEEEeqnarraycr\r
+ \noalign{\penalty\@eqpen\vskip\jot\vskip #1\relax}}%\r
+\r
+\def\@@IEEEeqnarraycr{\@IEEEtrantmptoksA={}% clear token register\r
+ \advance\@IEEEeqncolcnt by -1\relax% adjust col count because of the isolation column\r
+ \ifnum\@IEEEeqncolcnt>\@IEEEeqnnumcols\relax\r
+ \@IEEEclspkgerror{Too many columns within the IEEEeqnarray\MessageBreak\r
+ environment}%\r
+ {Use fewer \string &'s or put more columns in the IEEEeqnarray column\MessageBreak \r
+ specifications.}\relax%\r
+ \else\r
+ \loop% add cols if the user did not use them all\r
+ \ifnum\@IEEEeqncolcnt<\@IEEEeqnnumcols\relax\r
+ \@IEEEappendtoksA{&}%\r
+ \advance\@IEEEeqncolcnt by 1\relax% update the col count\r
+ \repeat\r
+ % this number of &'s will take us the the isolation column\r
+ \fi\r
+ % execute the &'s\r
+ \the\@IEEEtrantmptoksA%\r
+ % handle the strut/isolation column\r
+ \@IEEEeqnarrayinsertstrut% do the strut if needed\r
+ \@IEEEeqnarraystrutreset% reset the strut system for next line or IEEEeqnarray\r
+ &% and enter the equation number column\r
+ \if@eqnsw% only if we display something\r
+ \Hy@raisedlink{\hyper@anchorstart{\@currentHref}}% start a hyperref anchor\r
+ \global\@IEEEeqnumpreadvfalse\relax% displaying an equation number means\r
+ \global\@IEEEsubeqnumpreadvfalse\relax% the equation counters point to valid equations\r
+ % V1.8 Here we setup the counters, currentlabel and status for what would be the *next*\r
+ % equation line as would be the case under the current settings. However, there are two problems.\r
+ % One problem is that there might not ever be a next line. The second problem is that the user\r
+ % may later alter the meaning of a line with commands such as \IEEEyessubnumber. So, to handle\r
+ % these cases we have to record the current values of the (sub)equation counters and revert back\r
+ % to them if the next line is changed or never comes. The \if@IEEEeqnumpreadv, \if@IEEEsubeqnumpreadv\r
+ % and \@IEEEsubeqnnumrollback stuff tracks this.\r
+ % The logic to handle all this is surprisingly complex, but a nice feature of the approach here is\r
+ % that the equation counters and labels remain valid for what the line would be unless a\r
+ % \IEEEyessubnumber et al. later changes it. So, any hyperref links are always correct.\r
+ \ifnum\c@IEEEsubequation>0\relax% handle subequation\r
+ \theIEEEsubequationdis\relax\r
+ \if@IEEEsubeqnumpersist% setup for default type of next line\r
+ \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax\r
+ \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label\r
+ \else\r
+ % if no subeqnum persist, go ahead and setup for a new equation number\r
+ \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation\r
+ \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax\r
+ \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label\r
+ \fi\r
+ \else% display a standard equation number\r
+ \theequationdis\relax\r
+ \setcounter{IEEEsubequation}{0}\relax% not really needed\r
+ \if@IEEEsubeqnumpersist% setup for default type of next line\r
+ % subequations that follow plain equations carry the same equation number e.g, 5, 5a rather than 5, 6a\r
+ \stepcounter{IEEEsubequation}\global\@IEEEsubeqnumpreadvtrue\relax\r
+ \gdef\@currentlabel{\p@IEEEsubequation\theIEEEsubequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefsubequation}% setup hyperref label\r
+ \else\r
+ % if no subeqnum persist, go ahead and setup for a new equation number\r
+ \global\@IEEEsubeqnnumrollback=\c@IEEEsubequation\r
+ \stepcounter{equation}\global\@IEEEeqnumpreadvtrue\relax\r
+ \setcounter{IEEEsubequation}{0}\gdef\@currentlabel{\p@equation\theequation}\relax\r
+ \gdef\@currentHref{\@IEEEtheHrefequation}% setup hyperref label\r
+ \fi\r
+ \fi%\r
+ \Hy@raisedlink{\hyper@anchorend}% end hyperref anchor\r
+ \fi% fi only if we display something\r
+ % reset the flags to indicate the default preferences of the display of equation numbers\r
+ \if@IEEEeqnumpersist\global\@eqnswtrue\else\global\@eqnswfalse\fi\r
+ \if@IEEEsubeqnumpersist\global\@eqnswtrue\fi% ditto for the subequation flag\r
+ % reset the number of columns the user actually used\r
+ \global\@IEEEeqncolcnt\z@\relax\r
+ % the real end of the line\r
+ \cr}\r
+\r
+\r
+\r
+\r
+\r
+% \IEEEeqnarraybox is like \IEEEeqnarray except the box form puts everything\r
+% inside a vtop, vbox, or vcenter box depending on the letter in the second\r
+% optional argument (t,b,c). Vbox is the default. Unlike \IEEEeqnarray,\r
+% equation numbers are not displayed and \IEEEeqnarraybox can be nested.\r
+% \IEEEeqnarrayboxm is for math mode (like \array) and does not put the vbox\r
+% within an hbox.\r
+% \IEEEeqnarrayboxt is for text mode (like \tabular) and puts the vbox within\r
+% a \hbox{$ $} construct.\r
+% \IEEEeqnarraybox will auto detect whether to use \IEEEeqnarrayboxm or \r
+% \IEEEeqnarrayboxt depending on the math mode.\r
+% The third optional argument specifies the width this box is to be set to -\r
+% natural width is the default.\r
+% The * forms do not add \jot line spacing\r
+% usage: \IEEEeqnarraybox[decl][pos][width]{cols}\r
+\def\IEEEeqnarrayboxm{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}\r
+\def\endIEEEeqnarrayboxm{\end@IEEEeqnarraybox}\r
+\@namedef{IEEEeqnarrayboxm*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWfalse\@IEEEeqnarraybox}\r
+\@namedef{endIEEEeqnarrayboxm*}{\end@IEEEeqnarraybox}\r
+\r
+\def\IEEEeqnarrayboxt{\@IEEEeqnarrayboxnojotfalse\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}\r
+\def\endIEEEeqnarrayboxt{\end@IEEEeqnarraybox}\r
+\@namedef{IEEEeqnarrayboxt*}{\@IEEEeqnarrayboxnojottrue\@IEEEeqnarrayboxHBOXSWtrue\@IEEEeqnarraybox}\r
+\@namedef{endIEEEeqnarrayboxt*}{\end@IEEEeqnarraybox}\r
+\r
+\def\IEEEeqnarraybox{\@IEEEeqnarrayboxnojotfalse\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%\r
+\@IEEEeqnarraybox}\r
+\def\endIEEEeqnarraybox{\end@IEEEeqnarraybox}\r
+\r
+\@namedef{IEEEeqnarraybox*}{\@IEEEeqnarrayboxnojottrue\ifmmode\@IEEEeqnarrayboxHBOXSWfalse\else\@IEEEeqnarrayboxHBOXSWtrue\fi%\r
+\@IEEEeqnarraybox}\r
+\@namedef{endIEEEeqnarraybox*}{\end@IEEEeqnarraybox}\r
+\r
+% flag to indicate if the \IEEEeqnarraybox needs to put things into an hbox{$ $} \r
+% for \vcenter in non-math mode\r
+\newif\if@IEEEeqnarrayboxHBOXSW%\r
+\@IEEEeqnarrayboxHBOXSWfalse\r
+\r
+\def\@IEEEeqnarraybox{\relax\@ifnextchar[{\@@IEEEeqnarraybox}{\@@IEEEeqnarraybox[\relax]}}\r
+\def\@@IEEEeqnarraybox[#1]{\relax\@ifnextchar[{\@@@IEEEeqnarraybox[#1]}{\@@@IEEEeqnarraybox[#1][b]}}\r
+\def\@@@IEEEeqnarraybox[#1][#2]{\relax\@ifnextchar[{\@@@@IEEEeqnarraybox[#1][#2]}{\@@@@IEEEeqnarraybox[#1][#2][\relax]}}\r
+\r
+% #1 = decl; #2 = t,b,c; #3 = width, #4 = col specs\r
+\def\@@@@IEEEeqnarraybox[#1][#2][#3]#4{\@IEEEeqnarrayISinnerfalse % not yet within the lines of the halign\r
+ \@IEEEeqnarraymasterstrutsave% save current master strut values\r
+ \@IEEEeqnarraystrutsize{0pt}{0pt}[\relax]% turn off struts by default\r
+ \@IEEEeqnarrayusemasterstruttrue% use master strut till user asks otherwise\r
+ \IEEEvisiblestrutsfalse% diagnostic mode defaults to off\r
+ % no extra space unless the user specifically requests it\r
+ \lineskip=0pt\relax%\r
+ \lineskiplimit=0pt\relax%\r
+ \baselineskip=\normalbaselineskip\relax%\r
+ \jot=\IEEEnormaljot\relax%\r
+ \mathsurround\z@\relax% no extra spacing around math\r
+ % the default end glues are zero for an \IEEEeqnarraybox\r
+ \edef\@IEEEeqnarraycolSEPdefaultstart{\@IEEEeqnarraycolSEPzero}% default start glue\r
+ \edef\@IEEEeqnarraycolSEPdefaultend{\@IEEEeqnarraycolSEPzero}% default end glue\r
+ \edef\@IEEEeqnarraycolSEPdefaultmid{\@IEEEeqnarraycolSEPzero}% default inter-column glue\r
+ \@advanceIEEEeqncolcntfalse% do not advance the col counter for each col the user uses, \r
+ % used in \IEEEeqnarraymulticol and in the preamble build\r
+ \IEEEeqnarrayboxdecl\relax% allow a way for the user to make global overrides\r
+ #1\relax% allow user to override defaults\r
+ \let\\\@IEEEeqnarrayboxcr% replace newline with one that allows optional spacing\r
+ \@IEEEbuildpreamble #4\end\relax% build the preamble and put it into \@IEEEtrantmptoksA\r
+ % add an isolation column to the preamble to stop \\'s {} from getting into the last col\r
+ \ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi% col separator for those after the first\r
+ \toks0={##}%\r
+ % add the isolation column to the preamble\r
+ \@IEEEappendtoksA{\tabskip\z@skip\bgroup\the\toks0\egroup}% \r
+ % set the starting tabskip glue as determined by the preamble build\r
+ \tabskip=\@IEEEBPstartglue\relax\r
+ % begin the alignment\r
+ \everycr{}%\r
+ % use only the very first token to determine the positioning\r
+ % this stops some problems when the user uses more than one letter,\r
+ % but is probably not worth the effort\r
+ % \noindent is used as a delimiter\r
+ \def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%\r
+ \@IEEEgrabfirstoken#2\relax\relax\noindent\r
+ % \@IEEEgrabbedfirstoken has the first token, the rest are discarded\r
+ % if we need to put things into and hbox and go into math mode, do so now\r
+ \if@IEEEeqnarrayboxHBOXSW \leavevmode \hbox \bgroup $\fi%\r
+ % use the appropriate vbox type\r
+ \if\@IEEEgrabbedfirstoken t\relax\vtop\else\if\@IEEEgrabbedfirstoken c\relax%\r
+ \vcenter\else\vbox\fi\fi\bgroup%\r
+ \@IEEEeqnarrayISinnertrue% commands are now within the lines\r
+ \ifx#3\relax\halign\else\halign to #3\relax\fi%\r
+ \bgroup\r
+ % "exspand" the preamble\r
+ \span\the\@IEEEtrantmptoksA\cr}\r
+\r
+% carry strut status and enter the isolation/strut column, \r
+% exit from math mode if needed, and exit\r
+\def\end@IEEEeqnarraybox{\@IEEEeqnarrayglobalizestrutstatus% carry strut status\r
+&% enter isolation/strut column\r
+\@IEEEeqnarrayinsertstrut% do strut if needed\r
+\@IEEEeqnarraymasterstrutrestore% restore the previous master strut values\r
+% reset the strut system for next IEEEeqnarray\r
+% (sets local strut values back to previous master strut values)\r
+\@IEEEeqnarraystrutreset%\r
+% ensure last line, exit from halign, close vbox\r
+\crcr\egroup\egroup%\r
+% exit from math mode and close hbox if needed\r
+\if@IEEEeqnarrayboxHBOXSW $\egroup\fi}\r
+\r
+\r
+\r
+% IEEEeqnarraybox uses a modifed \\ instead of the plain \cr to\r
+% end rows. This allows for things like \\[vskip amount]\r
+% This "cr" macros are modified versions those for LaTeX2e's eqnarray\r
+% For IEEEeqnarraybox, \\* is the same as \\\r
+% the {\ifnum0=`} braces must be kept away from the last column to avoid\r
+% altering spacing of its math, so we use & to advance to the isolation/strut column\r
+% carry strut status into isolation/strut column\r
+\def\@IEEEeqnarrayboxcr{\@IEEEeqnarrayglobalizestrutstatus% carry strut status\r
+&% enter isolation/strut column\r
+\@IEEEeqnarrayinsertstrut% do strut if needed\r
+% reset the strut system for next line or IEEEeqnarray\r
+\@IEEEeqnarraystrutreset%\r
+{\ifnum0=`}\fi%\r
+\@ifstar{\@IEEEeqnarrayboxYCR}{\@IEEEeqnarrayboxYCR}}\r
+\r
+% test and setup the optional argument to \\[]\r
+\def\@IEEEeqnarrayboxYCR{\@testopt\@IEEEeqnarrayboxXCR\z@skip}\r
+\r
+% IEEEeqnarraybox does not automatically increase line spacing by \jot\r
+\def\@IEEEeqnarrayboxXCR[#1]{\ifnum0=`{\fi}%\r
+\cr\noalign{\if@IEEEeqnarrayboxnojot\else\vskip\jot\fi\vskip#1\relax}}\r
+\r
+\r
+\r
+% starts the halign preamble build\r
+\def\@IEEEbuildpreamble{\@IEEEtrantmptoksA={}% clear token register\r
+\let\@IEEEBPcurtype=u%current column type is not yet known\r
+\let\@IEEEBPprevtype=s%the previous column type was the start\r
+\let\@IEEEBPnexttype=u%next column type is not yet known\r
+% ensure these are valid\r
+\def\@IEEEBPcurglue={0pt plus 0pt minus 0pt}%\r
+\def\@IEEEBPcurcolname{@IEEEdefault}% name of current column definition\r
+% currently acquired numerically referenced glue\r
+% use a name that is easier to remember\r
+\let\@IEEEBPcurnum=\@IEEEtrantmpcountA%\r
+\@IEEEBPcurnum=0%\r
+% tracks number of columns in the preamble\r
+\@IEEEeqnnumcols=0%\r
+% record the default end glues\r
+\edef\@IEEEBPstartglue{\@IEEEeqnarraycolSEPdefaultstart}%\r
+\edef\@IEEEBPendglue{\@IEEEeqnarraycolSEPdefaultend}%\r
+% now parse the user's column specifications\r
+\@@IEEEbuildpreamble}\r
+\r
+\r
+% parses and builds the halign preamble\r
+\def\@@IEEEbuildpreamble#1#2{\let\@@nextIEEEbuildpreamble=\@@IEEEbuildpreamble%\r
+% use only the very first token to check the end\r
+% \noindent is used as a delimiter as \end can be present here\r
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%\r
+\@IEEEgrabfirstoken#1\relax\relax\noindent\r
+\ifx\@IEEEgrabbedfirstoken\end\let\@@nextIEEEbuildpreamble=\@@IEEEfinishpreamble\else%\r
+% identify current and next token type\r
+\@IEEEgetcoltype{#1}{\@IEEEBPcurtype}{1}% current, error on invalid\r
+\@IEEEgetcoltype{#2}{\@IEEEBPnexttype}{0}% next, no error on invalid next\r
+% if curtype is a glue, get the glue def\r
+\if\@IEEEBPcurtype g\@IEEEgetcurglue{#1}{\@IEEEBPcurglue}\fi%\r
+% if curtype is a column, get the column def and set the current column name\r
+\if\@IEEEBPcurtype c\@IEEEgetcurcol{#1}\fi%\r
+% if curtype is a numeral, acquire the user defined glue\r
+\if\@IEEEBPcurtype n\@IEEEprocessNcol{#1}\fi%\r
+% process the acquired glue \r
+\if\@IEEEBPcurtype g\@IEEEprocessGcol\fi%\r
+% process the acquired col \r
+\if\@IEEEBPcurtype c\@IEEEprocessCcol\fi%\r
+% ready prevtype for next col spec.\r
+\let\@IEEEBPprevtype=\@IEEEBPcurtype%\r
+% be sure and put back the future token(s) as a group\r
+\fi\@@nextIEEEbuildpreamble{#2}}\r
+\r
+\r
+% executed just after preamble build is completed\r
+% warn about zero cols, and if prevtype type = u, put in end tabskip glue\r
+\def\@@IEEEfinishpreamble#1{\ifnum\@IEEEeqnnumcols<1\relax\r
+\@IEEEclspkgerror{No column specifiers declared for IEEEeqnarray}%\r
+{At least one column type must be declared for each IEEEeqnarray.}%\r
+\fi%num cols less than 1\r
+%if last type undefined, set default end tabskip glue\r
+\if\@IEEEBPprevtype u\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue}\fi}\r
+\r
+\r
+% Identify and return the column specifier's type code\r
+\def\@IEEEgetcoltype#1#2#3{%\r
+% use only the very first token to determine the type\r
+% \noindent is used as a delimiter as \end can be present here\r
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%\r
+\@IEEEgrabfirstoken#1\relax\relax\noindent\r
+% \@IEEEgrabfirstoken has the first token, the rest are discarded\r
+% n = number\r
+% g = glue (any other char in catagory 12)\r
+% c = letter\r
+% e = \end\r
+% u = undefined\r
+% third argument: 0 = no error message, 1 = error on invalid char\r
+\let#2=u\relax% assume invalid until know otherwise\r
+\ifx\@IEEEgrabbedfirstoken\end\let#2=e\else\r
+\ifcat\@IEEEgrabbedfirstoken\relax\else% screen out control sequences\r
+\if0\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if1\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if2\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if3\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if4\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if5\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if6\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if7\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if8\@IEEEgrabbedfirstoken\let#2=n\else\r
+\if9\@IEEEgrabbedfirstoken\let#2=n\else\r
+\ifcat,\@IEEEgrabbedfirstoken\let#2=g\relax\r
+\else\ifcat a\@IEEEgrabbedfirstoken\let#2=c\relax\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\r
+\if#2u\relax\r
+\if0\noexpand#3\relax\else\@IEEEclspkgerror{Invalid character in column specifications}%\r
+{Only letters, numerals and certain other symbols are allowed \MessageBreak\r
+as IEEEeqnarray column specifiers.}\fi\fi}\r
+\r
+\r
+% identify the current letter referenced column\r
+% if invalid, use a default column\r
+\def\@IEEEgetcurcol#1{\expandafter\ifx\csname @IEEEeqnarraycolDEF#1\endcsname\@IEEEeqnarraycolisdefined%\r
+\def\@IEEEBPcurcolname{#1}\else% invalid column name\r
+\@IEEEclspkgerror{Invalid column type "#1" in column specifications.\MessageBreak\r
+Using a default centering column instead}%\r
+{You must define IEEEeqnarray column types before use.}%\r
+\def\@IEEEBPcurcolname{@IEEEdefault}\fi}\r
+\r
+\r
+% identify and return the predefined (punctuation) glue value\r
+\def\@IEEEgetcurglue#1#2{%\r
+% ! = \! (neg small) -0.16667em (-3/18 em)\r
+% , = \, (small) 0.16667em ( 3/18 em)\r
+% : = \: (med) 0.22222em ( 4/18 em)\r
+% ; = \; (large) 0.27778em ( 5/18 em)\r
+% ' = \quad 1em\r
+% " = \qquad 2em\r
+% . = 0.5\arraycolsep\r
+% / = \arraycolsep\r
+% ? = 2\arraycolsep\r
+% * = 1fil\r
+% + = \@IEEEeqnarraycolSEPcenter\r
+% - = \@IEEEeqnarraycolSEPzero\r
+% Note that all em values are referenced to the math font (textfont2) fontdimen6\r
+% value for 1em.\r
+% \r
+% use only the very first token to determine the type\r
+% this prevents errant tokens from getting in the main text\r
+% \noindent is used as a delimiter here\r
+\def\@IEEEgrabfirstoken##1##2\noindent{\let\@IEEEgrabbedfirstoken=##1}%\r
+\@IEEEgrabfirstoken#1\relax\relax\noindent\r
+% get the math font 1em value\r
+% LaTeX2e's NFSS2 does not preload the fonts, but \IEEEeqnarray needs\r
+% to gain access to the math (\textfont2) font's spacing parameters.\r
+% So we create a bogus box here that uses the math font to ensure\r
+% that \textfont2 is loaded and ready. If this is not done,\r
+% the \textfont2 stuff here may not work.\r
+% Thanks to Bernd Raichle for his 1997 post on this topic.\r
+{\setbox0=\hbox{$\displaystyle\relax$}}%\r
+% fontdimen6 has the width of 1em (a quad).\r
+\@IEEEtrantmpdimenA=\fontdimen6\textfont2\relax%\r
+% identify the glue value based on the first token\r
+% we discard anything after the first\r
+\if!\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=-0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if,\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.16667\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if:\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.22222\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if;\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.27778\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if'\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=1\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if"\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\@IEEEtrantmpdimenA\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if.\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=0.5\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if/\@IEEEgrabbedfirstoken\edef#2{\the\arraycolsep}\else\r
+\if?\@IEEEgrabbedfirstoken\@IEEEtrantmpdimenA=2\arraycolsep\edef#2{\the\@IEEEtrantmpdimenA}\else\r
+\if *\@IEEEgrabbedfirstoken\edef#2{0pt plus 1fil minus 0pt}\else\r
+\if+\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPcenter}\else\r
+\if-\@IEEEgrabbedfirstoken\edef#2{\@IEEEeqnarraycolSEPzero}\else\r
+\edef#2{\@IEEEeqnarraycolSEPzero}%\r
+\@IEEEclspkgerror{Invalid predefined inter-column glue type "#1" in\MessageBreak\r
+column specifications. Using a default value of\MessageBreak\r
+0pt instead}%\r
+{Only !,:;'"./?*+ and - are valid predefined glue types in the\MessageBreak \r
+IEEEeqnarray column specifications.}\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi}\r
+\r
+\r
+\r
+% process a numerical digit from the column specification\r
+% and look up the corresponding user defined glue value\r
+% can transform current type from n to g or a as the user defined glue is acquired\r
+\def\@IEEEprocessNcol#1{\if\@IEEEBPprevtype g%\r
+\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak\r
+specifications. Ignoring consecutive glue specifiers\MessageBreak\r
+after the first}%\r
+{You cannot have two or more glue types next to each other\MessageBreak \r
+in the IEEEeqnarray column specifications.}%\r
+\let\@IEEEBPcurtype=a% abort this glue, future digits will be discarded\r
+\@IEEEBPcurnum=0\relax%\r
+\else% if we previously aborted a glue\r
+\if\@IEEEBPprevtype a\@IEEEBPcurnum=0\let\@IEEEBPcurtype=a%maintain digit abortion\r
+\else%acquire this number\r
+% save the previous type before the numerical digits started\r
+\if\@IEEEBPprevtype n\else\let\@IEEEBPprevsavedtype=\@IEEEBPprevtype\fi%\r
+\multiply\@IEEEBPcurnum by 10\relax%\r
+\advance\@IEEEBPcurnum by #1\relax% add in number, \relax is needed to stop TeX's number scan\r
+\if\@IEEEBPnexttype n\else%close acquisition\r
+\expandafter\ifx\csname @IEEEeqnarraycolSEPDEF\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname\@IEEEeqnarraycolisdefined%\r
+\edef\@IEEEBPcurglue{\csname @IEEEeqnarraycolSEP\expandafter\romannumeral\number\@IEEEBPcurnum\endcsname}%\r
+\else%user glue not defined\r
+\@IEEEclspkgerror{Invalid user defined inter-column glue type "\number\@IEEEBPcurnum" in\MessageBreak\r
+column specifications. Using a default value of\MessageBreak\r
+0pt instead}%\r
+{You must define all IEEEeqnarray numerical inter-column glue types via\MessageBreak\r
+\string\IEEEeqnarraydefcolsep \space before they are used in column specifications.}%\r
+\edef\@IEEEBPcurglue{\@IEEEeqnarraycolSEPzero}%\r
+\fi% glue defined or not\r
+\let\@IEEEBPcurtype=g% change the type to reflect the acquired glue\r
+\let\@IEEEBPprevtype=\@IEEEBPprevsavedtype% restore the prev type before this number glue\r
+\@IEEEBPcurnum=0\relax%ready for next acquisition\r
+\fi%close acquisition, get glue\r
+\fi%discard or acquire number\r
+\fi%prevtype glue or not\r
+}\r
+\r
+\r
+% process an acquired glue\r
+% add any acquired column/glue pair to the preamble\r
+\def\@IEEEprocessGcol{\if\@IEEEBPprevtype a\let\@IEEEBPcurtype=a%maintain previous glue abortions\r
+\else\r
+% if this is the start glue, save it, but do nothing else \r
+% as this is not used in the preamble, but before\r
+\if\@IEEEBPprevtype s\edef\@IEEEBPstartglue{\@IEEEBPcurglue}%\r
+\else%not the start glue\r
+\if\@IEEEBPprevtype g%ignore if back to back glues\r
+\@IEEEclspkgerror{Back-to-back inter-column glue specifiers in column\MessageBreak\r
+specifications. Ignoring consecutive glue specifiers\MessageBreak\r
+after the first}%\r
+{You cannot have two or more glue types next to each other\MessageBreak \r
+in the IEEEeqnarray column specifications.}%\r
+\let\@IEEEBPcurtype=a% abort this glue\r
+\else% not a back to back glue\r
+\if\@IEEEBPprevtype c\relax% if the previoustype was a col, add column/glue pair to preamble\r
+\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi\r
+\toks0={##}%\r
+% make preamble advance col counter if this environment needs this\r
+\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi\r
+% insert the column defintion into the preamble, being careful not to expand\r
+% the column definition\r
+\@IEEEappendtoksA{\tabskip=\@IEEEBPcurglue}%\r
+\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%\r
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%\r
+\@IEEEappendNOEXPANDtoksA{\endcsname}%\r
+\@IEEEappendtoksA{\the\toks0}%\r
+\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%\r
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%\r
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%\r
+\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%\r
+\relax\relax\relax\relax\relax\endgroup}%\r
+\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble\r
+\else% error: non-start glue with no pending column\r
+\@IEEEclspkgerror{Inter-column glue specifier without a prior column\MessageBreak\r
+type in the column specifications. Ignoring this glue\MessageBreak \r
+specifier}%\r
+{Except for the first and last positions, glue can be placed only\MessageBreak\r
+between column types.}%\r
+\let\@IEEEBPcurtype=a% abort this glue\r
+\fi% previous was a column\r
+\fi% back-to-back glues\r
+\fi% is start column glue\r
+\fi% prev type not a\r
+}\r
+\r
+\r
+% process an acquired letter referenced column and, if necessary, add it to the preamble\r
+\def\@IEEEprocessCcol{\if\@IEEEBPnexttype g\else\r
+\if\@IEEEBPnexttype n\else\r
+% we have a column followed by something other than a glue (or numeral glue)\r
+% so we must add this column to the preamble now\r
+\ifnum\@IEEEeqnnumcols>0\relax\@IEEEappendtoksA{&}\fi%col separator for those after the first\r
+\if\@IEEEBPnexttype e\@IEEEappendtoksA{\tabskip=\@IEEEBPendglue\relax}\else%put in end glue\r
+\@IEEEappendtoksA{\tabskip=\@IEEEeqnarraycolSEPdefaultmid\relax}\fi% or default mid glue\r
+\toks0={##}%\r
+% make preamble advance col counter if this environment needs this\r
+\if@advanceIEEEeqncolcnt\@IEEEappendtoksA{\global\advance\@IEEEeqncolcnt by 1\relax}\fi\r
+% insert the column definition into the preamble, being careful not to expand\r
+% the column definition\r
+\@IEEEappendNOEXPANDtoksA{\begingroup\csname @IEEEeqnarraycolPRE}%\r
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%\r
+\@IEEEappendNOEXPANDtoksA{\endcsname}%\r
+\@IEEEappendtoksA{\the\toks0}%\r
+\@IEEEappendNOEXPANDtoksA{\relax\relax\relax\relax\relax%\r
+\relax\relax\relax\relax\relax\csname @IEEEeqnarraycolPOST}%\r
+\@IEEEappendtoksA{\@IEEEBPcurcolname}%\r
+\@IEEEappendNOEXPANDtoksA{\endcsname\relax\relax\relax\relax\relax%\r
+\relax\relax\relax\relax\relax\endgroup}%\r
+\advance\@IEEEeqnnumcols by 1\relax%one more column in the preamble\r
+\fi%next type not numeral\r
+\fi%next type not glue\r
+}\r
+\r
+\r
+%%\r
+%% END OF IEEEeqnarray DEFINITIONS\r
+%%\r
+\r
+\r
+\r
+\r
+% set up the running headings, this complex because of all the different\r
+% modes IEEEtran supports\r
+\if@twoside\r
+ \ifCLASSOPTIONtechnote\r
+ \def\ps@headings{%\r
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}\r
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}\r
+ \ifCLASSOPTIONdraftcls\r
+ \ifCLASSOPTIONdraftclsnofoot\r
+ \def\@oddfoot{}\def\@evenfoot{}%\r
+ \else\r
+ \def\@oddfoot{\scriptsize\@date\hfil DRAFT}\r
+ \def\@evenfoot{\scriptsize DRAFT\hfil\@date}\r
+ \fi\r
+ \else\r
+ \def\@oddfoot{}\def\@evenfoot{}\r
+ \fi}\r
+ \else % not a technote\r
+ \def\ps@headings{%\r
+ \ifCLASSOPTIONconference\r
+ \def\@oddhead{}\r
+ \def\@evenhead{}\r
+ \else\r
+ \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}\r
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}\r
+ \fi\r
+ \ifCLASSOPTIONdraftcls\r
+ \def\@oddhead{\hbox{}\scriptsize\rightmark \hfil \thepage}\r
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}\r
+ \ifCLASSOPTIONdraftclsnofoot\r
+ \def\@oddfoot{}\def\@evenfoot{}%\r
+ \else\r
+ \def\@oddfoot{\scriptsize\@date\hfil DRAFT}\r
+ \def\@evenfoot{\scriptsize DRAFT\hfil\@date}\r
+ \fi\r
+ \else\r
+ \def\@oddfoot{}\def\@evenfoot{}%\r
+ \fi}\r
+ \fi\r
+\else % single side\r
+\def\ps@headings{%\r
+ \ifCLASSOPTIONconference\r
+ \def\@oddhead{}\r
+ \def\@evenhead{}\r
+ \else\r
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}\r
+ \def\@evenhead{}\r
+ \fi\r
+ \ifCLASSOPTIONdraftcls\r
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}\r
+ \def\@evenhead{}\r
+ \ifCLASSOPTIONdraftclsnofoot\r
+ \def\@oddfoot{}\r
+ \else\r
+ \def\@oddfoot{\scriptsize \@date \hfil DRAFT}\r
+ \fi\r
+ \else\r
+ \def\@oddfoot{}\r
+ \fi\r
+ \def\@evenfoot{}}\r
+\fi\r
+\r
+\r
+% title page style\r
+\def\ps@IEEEtitlepagestyle{\def\@oddfoot{}\def\@evenfoot{}%\r
+\ifCLASSOPTIONconference\r
+ \def\@oddhead{}%\r
+ \def\@evenhead{}%\r
+\else\r
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%\r
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%\r
+\fi\r
+\ifCLASSOPTIONdraftcls\r
+ \def\@oddhead{\hbox{}\scriptsize\leftmark \hfil \thepage}%\r
+ \def\@evenhead{\scriptsize\thepage \hfil \leftmark\hbox{}}%\r
+ \ifCLASSOPTIONdraftclsnofoot\else\r
+ \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%\r
+ \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%\r
+ \fi\r
+\else\r
+ % all non-draft mode footers\r
+ \if@IEEEusingpubid\r
+ % for title pages that are using a pubid\r
+ % do not repeat pubid if using peer review option\r
+ \ifCLASSOPTIONpeerreview\r
+ \else\r
+ \footskip 0pt%\r
+ \ifCLASSOPTIONcompsoc\r
+ \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%\r
+ \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%\r
+ \else\r
+ \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%\r
+ \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%\r
+ \fi\r
+ \fi\r
+ \fi\r
+\fi}\r
+\r
+\r
+% peer review cover page style\r
+\def\ps@IEEEpeerreviewcoverpagestyle{%\r
+\def\@oddhead{}\def\@evenhead{}%\r
+\def\@oddfoot{}\def\@evenfoot{}%\r
+\ifCLASSOPTIONdraftcls\r
+ \ifCLASSOPTIONdraftclsnofoot\else\r
+ \def\@oddfoot{\scriptsize \@date\hfil DRAFT}%\r
+ \def\@evenfoot{\scriptsize DRAFT\hfil \@date}%\r
+ \fi\r
+\else\r
+ % non-draft mode footers\r
+ \if@IEEEusingpubid\r
+ \footskip 0pt%\r
+ \ifCLASSOPTIONcompsoc\r
+ \def\@oddfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%\r
+ \def\@evenfoot{\hss\normalfont\scriptsize\raisebox{-1.5\@IEEEnormalsizeunitybaselineskip}[0ex][0ex]{\@IEEEpubid}\hss}%\r
+ \else\r
+ \def\@oddfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%\r
+ \def\@evenfoot{\hss\normalfont\footnotesize\raisebox{1.5ex}[1.5ex]{\@IEEEpubid}\hss}%\r
+ \fi\r
+ \fi\r
+\fi}\r
+\r
+\r
+% start with empty headings\r
+\def\rightmark{}\def\leftmark{}\r
+\r
+\r
+%% Defines the command for putting the header. \footernote{TEXT} is the same\r
+%% as \markboth{TEXT}{TEXT}. \r
+%% Note that all the text is forced into uppercase, if you have some text\r
+%% that needs to be in lower case, for instance et. al., then either manually\r
+%% set \leftmark and \rightmark or use \MakeLowercase{et. al.} within the\r
+%% arguments to \markboth.\r
+%% V1.7b add \protect to work with Babel\r
+\def\markboth#1#2{\def\leftmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{\protect#1}}%\r
+\def\rightmark{\@IEEEcompsoconly{\sffamily}\MakeUppercase{\protect#2}}}\r
+\def\footernote#1{\markboth{#1}{#1}}\r
+\r
+\def\today{\ifcase\month\or\r
+ January\or February\or March\or April\or May\or June\or\r
+ July\or August\or September\or October\or November\or December\fi\r
+ \space\number\day, \number\year}\r
+\r
+\r
+\r
+\r
+%% CITATION AND BIBLIOGRAPHY COMMANDS\r
+%% \r
+%% V1.6 no longer supports the older, nonstandard \shortcite and \citename setup stuff\r
+% \r
+% \r
+% Modify Latex2e \@citex to separate citations with "], ["\r
+\def\@citex[#1]#2{%\r
+ \let\@citea\@empty\r
+ \@cite{\@for\@citeb:=#2\do\r
+ {\@citea\def\@citea{], [}%\r
+ \edef\@citeb{\expandafter\@firstofone\@citeb\@empty}%\r
+ \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi\r
+ \@ifundefined{b@\@citeb}{\mbox{\reset@font\bfseries ?}%\r
+ \G@refundefinedtrue\r
+ \@latex@warning\r
+ {Citation `\@citeb' on page \thepage \space undefined}}%\r
+ {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}\r
+\r
+% V1.6 we create hooks for the optional use of Donald Arseneau's\r
+% cite.sty package. cite.sty is "smart" and will notice that the\r
+% following format controls are already defined and will not\r
+% redefine them. The result will be the proper sorting of the\r
+% citation numbers and auto detection of 3 or more entry "ranges" -\r
+% all in IEEE style: [1], [2], [5]--[7], [12]\r
+% This also allows for an optional note, i.e., \cite[mynote]{..}.\r
+% If the \cite with note has more than one reference, the note will\r
+% be applied to the last of the listed references. It is generally\r
+% desired that if a note is given, only one reference is listed in\r
+% that \cite.\r
+% Thanks to Mr. Arseneau for providing the required format arguments\r
+% to produce the IEEE style.\r
+\def\citepunct{], [}\r
+\def\citedash{]--[}\r
+\r
+% V1.7 default to using same font for urls made by url.sty\r
+\AtBeginDocument{\csname url@samestyle\endcsname}\r
+\r
+% V1.6 class files should always provide these\r
+\def\newblock{\hskip .11em\@plus.33em\@minus.07em}\r
+\let\@openbib@code\@empty\r
+\r
+\r
+% Provide support for the control entries of IEEEtran.bst V1.00 and later.\r
+% V1.7 optional argument allows for a different aux file to be specified in\r
+% order to handle multiple bibliographies. For example, with multibib.sty:\r
+% \newcites{sec}{Secondary Literature}\r
+% \bstctlcite[@auxoutsec]{BSTcontrolhak}\r
+\def\bstctlcite{\@ifnextchar[{\@bstctlcite}{\@bstctlcite[@auxout]}}\r
+\def\@bstctlcite[#1]#2{\@bsphack\r
+ \@for\@citeb:=#2\do{%\r
+ \edef\@citeb{\expandafter\@firstofone\@citeb}%\r
+ \if@filesw\immediate\write\csname #1\endcsname{\string\citation{\@citeb}}\fi}%\r
+ \@esphack}\r
+\r
+% V1.6 provide a way for a user to execute a command just before \r
+% a given reference number - used to insert a \newpage to balance\r
+% the columns on the last page\r
+\edef\@IEEEtriggerrefnum{0} % the default of zero means that\r
+ % the command is not executed\r
+\def\@IEEEtriggercmd{\newpage}\r
+\r
+% allow the user to alter the triggered command\r
+\long\def\IEEEtriggercmd#1{\long\def\@IEEEtriggercmd{#1}}\r
+\r
+% allow user a way to specify the reference number just before the\r
+% command is executed\r
+\def\IEEEtriggeratref#1{\@IEEEtrantmpcountA=#1%\r
+\edef\@IEEEtriggerrefnum{\the\@IEEEtrantmpcountA}}%\r
+\r
+% trigger command at the given reference\r
+\def\@IEEEbibitemprefix{\@IEEEtrantmpcountA=\@IEEEtriggerrefnum\relax%\r
+\advance\@IEEEtrantmpcountA by -1\relax%\r
+\ifnum\c@enumiv=\@IEEEtrantmpcountA\relax\@IEEEtriggercmd\relax\fi}\r
+\r
+\r
+\def\@biblabel#1{[#1]}\r
+\r
+% compsoc journals left align the reference numbers\r
+\@IEEEcompsocnotconfonly{\def\@biblabel#1{[#1]\hfill}}\r
+\r
+% controls bib item spacing\r
+\def\IEEEbibitemsep{0pt plus .5pt}\r
+\r
+\@IEEEcompsocconfonly{\def\IEEEbibitemsep{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}}\r
+\r
+\r
+\def\thebibliography#1{\section*{\refname}%\r
+ \addcontentsline{toc}{section}{\refname}%\r
+ % V1.6 add some rubber space here and provide a command trigger\r
+ \footnotesize\@IEEEcompsocconfonly{\small}\vskip 0.3\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip%\r
+ \list{\@biblabel{\@arabic\c@enumiv}}%\r
+ {\settowidth\labelwidth{\@biblabel{#1}}%\r
+ \leftmargin\labelwidth\r
+ \advance\leftmargin\labelsep\relax\r
+ \itemsep \IEEEbibitemsep\relax\r
+ \usecounter{enumiv}%\r
+ \let\p@enumiv\@empty\r
+ \renewcommand\theenumiv{\@arabic\c@enumiv}}%\r
+ \let\@IEEElatexbibitem\bibitem%\r
+ \def\bibitem{\@IEEEbibitemprefix\@IEEElatexbibitem}%\r
+\def\newblock{\hskip .11em plus .33em minus .07em}%\r
+% originally:\r
+% \sloppy\clubpenalty4000\widowpenalty4000%\r
+% by adding the \interlinepenalty here, we make it more\r
+% difficult, but not impossible, for LaTeX to break within a reference.\r
+% IEEE almost never breaks a reference (but they do it more often with\r
+% technotes). You may get an underfull vbox warning around the bibliography, \r
+% but the final result will be much more like what IEEE will publish. \r
+% MDS 11/2000\r
+\ifCLASSOPTIONtechnote\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty100%\r
+\else\sloppy\clubpenalty4000\widowpenalty4000\interlinepenalty500\fi%\r
+ \sfcode`\.=1000\relax}\r
+\let\endthebibliography=\endlist\r
+\r
+\r
+\r
+\r
+% TITLE PAGE COMMANDS\r
+% \r
+% \r
+% \IEEEmembership is used to produce the sublargesize italic font used to indicate author \r
+% IEEE membership. compsoc uses a large size sans slant font\r
+\def\IEEEmembership#1{{\@IEEEnotcompsoconly{\sublargesize}\normalfont\@IEEEcompsoconly{\sffamily}\textit{#1}}}\r
+ \r
+\r
+% \IEEEauthorrefmark{} produces a footnote type symbol to indicate author affiliation.\r
+% When given an argument of 1 to 9, \IEEEauthorrefmark{} follows the standard LaTeX footnote\r
+% symbol sequence convention. However, for arguments 10 and above, \IEEEauthorrefmark{} \r
+% reverts to using lower case roman numerals, so it cannot overflow. Do note that you \r
+% cannot use \footnotemark[] in place of \IEEEauthorrefmark{} within \author as the footnote\r
+% symbols will have been turned off to prevent \thanks from creating footnote marks.\r
+% \IEEEauthorrefmark{} produces a symbol that appears to LaTeX as having zero vertical\r
+% height - this allows for a more compact line packing, but the user must ensure that\r
+% the interline spacing is large enough to prevent \IEEEauthorrefmark{} from colliding\r
+% with the text above.\r
+% V1.7 make this a robust command\r
+% V1.8 transmag uses an arabic author affiliation symbol\r
+\ifCLASSOPTIONtransmag\r
+\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize #1}}}\r
+\else\r
+\DeclareRobustCommand*{\IEEEauthorrefmark}[1]{\raisebox{0pt}[0pt][0pt]{\textsuperscript{\footnotesize\ensuremath{\ifcase#1\or *\or \dagger\or \ddagger\or%\r
+ \mathsection\or \mathparagraph\or \|\or **\or \dagger\dagger%\r
+ \or \ddagger\ddagger \else\textsuperscript{\expandafter\romannumeral#1}\fi}}}}\r
+\fi\r
+\r
+\r
+% FONT CONTROLS AND SPACINGS FOR CONFERENCE MODE AUTHOR NAME AND AFFILIATION BLOCKS\r
+% \r
+% The default font styles for the author name and affiliation blocks (confmode)\r
+\def\@IEEEauthorblockNstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize\@IEEEcompsocconfonly{\large}}\r
+\def\@IEEEauthorblockAstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\@IEEEcompsocconfonly{\itshape}\normalsize\@IEEEcompsocconfonly{\large}}\r
+% The default if the user does not use an author block\r
+\def\@IEEEauthordefaulttextstyle{\normalfont\@IEEEcompsocnotconfonly{\sffamily}\sublargesize}\r
+\r
+% adjustment spacing from title (or special paper notice) to author name blocks (confmode)\r
+% can be negative\r
+\def\@IEEEauthorblockconfadjspace{-0.25em}\r
+% compsoc conferences need more space here\r
+\@IEEEcompsocconfonly{\def\@IEEEauthorblockconfadjspace{0.75\@IEEEnormalsizeunitybaselineskip}}\r
+\r
+% spacing between name and affiliation blocks (confmode)\r
+% This can be negative.\r
+% IEEE doesn't want any added spacing here, but I will leave these\r
+% controls in place in case they ever change their mind.\r
+% Personally, I like 0.75ex.\r
+%\def\@IEEEauthorblockNtopspace{0.75ex}\r
+%\def\@IEEEauthorblockAtopspace{0.75ex}\r
+\def\@IEEEauthorblockNtopspace{0.0ex}\r
+\def\@IEEEauthorblockAtopspace{0.0ex}\r
+\ifCLASSOPTIONtransmag\r
+% transmag uses one line of space above first affiliation block\r
+\def\@IEEEauthorblockAtopspace{1\@IEEEnormalsizeunitybaselineskip}\r
+\fi\r
+\r
+% baseline spacing within name and affiliation blocks (confmode)\r
+% must be positive, spacings below certain values will make \r
+% the position of line of text sensitive to the contents of the\r
+% line above it i.e., whether or not the prior line has descenders, \r
+% subscripts, etc. For this reason it is a good idea to keep\r
+% these above 2.6ex\r
+\def\@IEEEauthorblockNinterlinespace{2.6ex}\r
+\def\@IEEEauthorblockAinterlinespace{2.75ex}\r
+\r
+% This tracks the required strut size.\r
+% See the \@IEEEauthorhalign command for the actual default value used.\r
+\def\@IEEEauthorblockXinterlinespace{2.7ex}\r
+\r
+% variables to retain font size and style across groups\r
+% values given here have no effect as they will be overwritten later\r
+\gdef\@IEEESAVESTATEfontsize{10}\r
+\gdef\@IEEESAVESTATEfontbaselineskip{12}\r
+\gdef\@IEEESAVESTATEfontencoding{OT1}\r
+\gdef\@IEEESAVESTATEfontfamily{ptm}\r
+\gdef\@IEEESAVESTATEfontseries{m}\r
+\gdef\@IEEESAVESTATEfontshape{n}\r
+\r
+% saves the current font attributes\r
+\def\@IEEEcurfontSAVE{\global\let\@IEEESAVESTATEfontsize\f@size%\r
+\global\let\@IEEESAVESTATEfontbaselineskip\f@baselineskip%\r
+\global\let\@IEEESAVESTATEfontencoding\f@encoding%\r
+\global\let\@IEEESAVESTATEfontfamily\f@family%\r
+\global\let\@IEEESAVESTATEfontseries\f@series%\r
+\global\let\@IEEESAVESTATEfontshape\f@shape}\r
+\r
+% restores the saved font attributes\r
+\def\@IEEEcurfontRESTORE{\fontsize{\@IEEESAVESTATEfontsize}{\@IEEESAVESTATEfontbaselineskip}%\r
+\fontencoding{\@IEEESAVESTATEfontencoding}%\r
+\fontfamily{\@IEEESAVESTATEfontfamily}%\r
+\fontseries{\@IEEESAVESTATEfontseries}%\r
+\fontshape{\@IEEESAVESTATEfontshape}%\r
+\selectfont}\r
+\r
+\r
+% variable to indicate if the current block is the first block in the column\r
+\newif\if@IEEEprevauthorblockincol \@IEEEprevauthorblockincolfalse\r
+\r
+\r
+% the command places a strut with height and depth = \@IEEEauthorblockXinterlinespace\r
+% we use this technique to have complete manual control over the spacing of the lines\r
+% within the halign environment.\r
+% We set the below baseline portion at 30%, the above\r
+% baseline portion at 70% of the total length.\r
+% Responds to changes in the document's \baselinestretch\r
+\def\@IEEEauthorstrutrule{\@IEEEtrantmpdimenA\@IEEEauthorblockXinterlinespace%\r
+\@IEEEtrantmpdimenA=\baselinestretch\@IEEEtrantmpdimenA%\r
+\rule[-0.3\@IEEEtrantmpdimenA]{0pt}{\@IEEEtrantmpdimenA}}\r
+\r
+\r
+% blocks to hold the authors' names and affilations. \r
+% Makes formatting easy for conferences\r
+%\r
+% use real definitions in conference mode\r
+% name block\r
+\def\IEEEauthorblockN#1{\relax\@IEEEauthorblockNstyle% set the default text style\r
+\gdef\@IEEEauthorblockXinterlinespace{0pt}% disable strut for spacer row\r
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs\r
+% for details, probably not needed here as the \cr is in a macro\r
+% do a spacer row if needed\r
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockNtopspaceline\fi\r
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column\r
+%restore the correct strut value\r
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockNinterlinespace}%\r
+% input the author names\r
+#1%\r
+% end the row if the user did not already\r
+\crcr}\r
+% spacer row for names\r
+\def\@IEEEauthorblockNtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockNtopspace}}\r
+%\r
+% affiliation block\r
+\def\IEEEauthorblockA#1{\relax\@IEEEauthorblockAstyle% set the default text style\r
+\gdef\@IEEEauthorblockXinterlinespace{0pt}%disable strut for spacer row\r
+% the \expandafter hides the \cr in conditional tex, see the array.sty docs\r
+% for details, probably not needed here as the \cr is in a macro\r
+% do a spacer row if needed\r
+\if@IEEEprevauthorblockincol\expandafter\@IEEEauthorblockAtopspaceline\fi\r
+\global\@IEEEprevauthorblockincoltrue% we now have a block in this column\r
+%restore the correct strut value\r
+\gdef\@IEEEauthorblockXinterlinespace{\@IEEEauthorblockAinterlinespace}%\r
+% input the author affiliations\r
+#1%\r
+% end the row if the user did not already\r
+\crcr\r
+% V1.8 transmag does not use any additional affiliation spacing after the first author\r
+\ifCLASSOPTIONtransmag\gdef\@IEEEauthorblockAtopspace{0pt}\fi}\r
+\r
+% spacer row for affiliations\r
+\def\@IEEEauthorblockAtopspaceline{\cr\noalign{\vskip\@IEEEauthorblockAtopspace}}\r
+\r
+\r
+% allow papers to compile even if author blocks are used in modes other\r
+% than conference or peerreviewca. For such cases, we provide dummy blocks.\r
+\ifCLASSOPTIONconference\r
+\else\r
+ \ifCLASSOPTIONpeerreviewca\else\r
+ % not conference, peerreviewca or transmag mode\r
+ \ifCLASSOPTIONtransmag\else\r
+ \def\IEEEauthorblockN#1{#1}%\r
+ \def\IEEEauthorblockA#1{#1}%\r
+ \fi\r
+ \fi\r
+\fi\r
+\r
+\r
+\r
+% we provide our own halign so as not to have to depend on tabular\r
+\def\@IEEEauthorhalign{\@IEEEauthordefaulttextstyle% default text style\r
+ \lineskip=0pt\relax% disable line spacing\r
+ \lineskiplimit=0pt\relax%\r
+ \baselineskip=0pt\relax%\r
+ \@IEEEcurfontSAVE% save the current font\r
+ \mathsurround\z@\relax% no extra spacing around math\r
+ \let\\\@IEEEauthorhaligncr% replace newline with halign friendly one\r
+ \tabskip=0pt\relax% no column spacing\r
+ \everycr{}% ensure no problems here\r
+ \@IEEEprevauthorblockincolfalse% no author blocks yet\r
+ \def\@IEEEauthorblockXinterlinespace{2.7ex}% default interline space\r
+ \vtop\bgroup%vtop box\r
+ \halign\bgroup&\relax\hfil\@IEEEcurfontRESTORE\relax ##\relax\r
+ \hfil\@IEEEcurfontSAVE\@IEEEauthorstrutrule\cr}\r
+\r
+% ensure last line, exit from halign, close vbox\r
+\def\end@IEEEauthorhalign{\crcr\egroup\egroup}\r
+\r
+% handle bogus star form\r
+\def\@IEEEauthorhaligncr{{\ifnum0=`}\fi\@ifstar{\@@IEEEauthorhaligncr}{\@@IEEEauthorhaligncr}}\r
+\r
+% test and setup the optional argument to \\[]\r
+\def\@@IEEEauthorhaligncr{\@testopt\@@@IEEEauthorhaligncr\z@skip}\r
+\r
+% end the line and do the optional spacer\r
+\def\@@@IEEEauthorhaligncr[#1]{\ifnum0=`{\fi}\cr\noalign{\vskip#1\relax}}\r
+\r
+\r
+\r
+% flag to prevent multiple \and warning messages\r
+\newif\if@IEEEWARNand\r
+\@IEEEWARNandtrue\r
+\r
+% if in conference or peerreviewca modes, we support the use of \and as \author is a\r
+% tabular environment, otherwise we warn the user that \and is invalid\r
+% outside of conference or peerreviewca modes.\r
+\def\and{\relax} % provide a bogus \and that we will then override\r
+\r
+\renewcommand{\and}[1][\relax]{\if@IEEEWARNand\typeout{** WARNING: \noexpand\and is valid only\r
+ when in conference or peerreviewca}\typeout{modes (line \the\inputlineno).}\fi\global\@IEEEWARNandfalse}\r
+\r
+\ifCLASSOPTIONconference%\r
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%\r
+\fi\r
+\ifCLASSOPTIONpeerreviewca\r
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%\r
+\fi\r
+% V1.8 transmag uses conference author format\r
+\ifCLASSOPTIONtransmag\r
+\renewcommand{\and}[1][\hfill]{\end{@IEEEauthorhalign}#1\begin{@IEEEauthorhalign}}%\r
+\fi\r
+\r
+% page clearing command\r
+% based on LaTeX2e's \cleardoublepage, but allows different page styles\r
+% for the inserted blank pages\r
+\def\@IEEEcleardoublepage#1{\clearpage\if@twoside\ifodd\c@page\else\r
+\hbox{}\thispagestyle{#1}\newpage\if@twocolumn\hbox{}\thispagestyle{#1}\newpage\fi\fi\fi}\r
+\r
+\r
+% user command to invoke the title page\r
+\def\maketitle{\par%\r
+ \begingroup%\r
+ \normalfont%\r
+ \def\thefootnote{}% the \thanks{} mark type is empty\r
+ \def\footnotemark{}% and kill space from \thanks within author\r
+ \let\@makefnmark\relax% V1.7, must *really* kill footnotemark to remove all \textsuperscript spacing as well.\r
+ \footnotesize% equal spacing between thanks lines\r
+ \footnotesep 0.7\baselineskip%see global setting of \footnotesep for more info\r
+ % V1.7 disable \thanks note indention for compsoc\r
+ \@IEEEcompsoconly{\long\def\@makefntext##1{\parindent 1em\noindent\hbox{\@makefnmark}##1}}%\r
+ \normalsize%\r
+ \ifCLASSOPTIONpeerreview\r
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%\r
+ \thispagestyle{IEEEpeerreviewcoverpagestyle}\@thanks%\r
+ \else\r
+ \if@twocolumn%\r
+ \ifCLASSOPTIONtechnote%\r
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%\r
+ \else\r
+ \twocolumn[\@maketitle\@IEEEdynamictitlevspace\@IEEEaftertitletext]%\r
+ \fi\r
+ \else\r
+ \newpage\global\@topnum\z@ \@maketitle\@IEEEstatictitlevskip\@IEEEaftertitletext%\r
+ \fi\r
+ \thispagestyle{IEEEtitlepagestyle}\@thanks%\r
+ \fi\r
+ % pullup page for pubid if used.\r
+ \if@IEEEusingpubid\r
+ \enlargethispage{-\@IEEEpubidpullup}%\r
+ \fi \r
+ \endgroup\r
+ \setcounter{footnote}{0}\let\maketitle\relax\let\@maketitle\relax\r
+ \gdef\@thanks{}%\r
+ % v1.6b do not clear these as we will need the title again for peer review papers\r
+ % \gdef\@author{}\gdef\@title{}%\r
+ \let\thanks\relax}\r
+\r
+\r
+\r
+% V1.8 parbox to format \@IEEEtitleabstractindextext\r
+\long\def\@IEEEtitleabstractindextextbox#1{\parbox{1\textwidth}{#1}}\r
+% V1.8 compsoc is partial width\r
+\ifCLASSOPTIONcompsoc\r
+\long\def\@IEEEtitleabstractindextextbox#1{\parbox{0.915\textwidth}{#1}}\r
+\fi\r
+\r
+% formats the Title, authors names, affiliations and special paper notice\r
+% THIS IS A CONTROLLED SPACING COMMAND! Do not allow blank lines or unintentional\r
+% spaces to enter the definition - use % at the end of each line\r
+\def\@maketitle{\newpage\r
+\bgroup\par\addvspace{0.5\baselineskip}\centering%\r
+\ifCLASSOPTIONtechnote% technotes\r
+ {\bfseries\large\@IEEEcompsoconly{\sffamily}\@title\par}\vskip 1.3em{\lineskip .5em\@IEEEcompsoconly{\sffamily}\@author\r
+ \@IEEEspecialpapernotice\par{\@IEEEcompsoconly{\vskip 1.5em\relax\r
+ \@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\par\r
+ \hfill\@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax\r
+\else% not a technote\r
+ \vskip0.2em{\Huge\ifCLASSOPTIONtransmag\bfseries\LARGE\fi\@IEEEcompsoconly{\sffamily}\@IEEEcompsocconfonly{\normalfont\normalsize\vskip 2\@IEEEnormalsizeunitybaselineskip\r
+ \bfseries\Large}\@title\par}\vskip1.0em\par%\r
+ % V1.6 handle \author differently if in conference mode\r
+ \ifCLASSOPTIONconference%\r
+ {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%\r
+ \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par}\relax\r
+ \else% peerreviewca, peerreview or journal\r
+ \ifCLASSOPTIONpeerreviewca\r
+ % peerreviewca handles author names just like conference mode\r
+ {\@IEEEcompsoconly{\sffamily}\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%\r
+ \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par\r
+ {\@IEEEcompsoconly{\vskip 1.5em\relax\r
+ \@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\par\hfill\r
+ \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax\r
+ \else% journal, peerreview or transmag\r
+ \ifCLASSOPTIONtransmag\r
+ % transmag also handles author names just like conference mode\r
+ % it also uses \@IEEEtitleabstractindextex, but with one line less\r
+ % space above, and one more below\r
+ {\@IEEEspecialpapernotice\mbox{}\vskip\@IEEEauthorblockconfadjspace%\r
+ \mbox{}\hfill\begin{@IEEEauthorhalign}\@author\end{@IEEEauthorhalign}\hfill\mbox{}\par\r
+ {\vspace{0.5\baselineskip}\relax\@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\vspace{-1\baselineskip}\par}}\relax\r
+ \else% journal or peerreview\r
+ {\lineskip.5em\@IEEEcompsoconly{\sffamily}\sublargesize\@author\@IEEEspecialpapernotice\par\r
+ {\@IEEEcompsoconly{\vskip 1.5em\relax\r
+ \@IEEEtitleabstractindextextbox{\@IEEEtitleabstractindextext}\par\hfill\r
+ \@IEEEcompsocdiamondline\hfill\hbox{}\par}}}\relax\r
+ \fi\r
+ \fi\r
+ \fi\r
+\fi\par\addvspace{0.5\baselineskip}\egroup}\r
+\r
+\r
+\r
+% V1.7 Computer Society "diamond line" which follows index terms for nonconference papers\r
+\def\@IEEEcompsocdiamondline{\vrule depth 0pt height 0.5pt width 4cm\hspace{7.5pt}%\r
+\raisebox{-3.5pt}{\fontfamily{pzd}\fontencoding{U}\fontseries{m}\fontshape{n}\fontsize{11}{12}\selectfont\char70}%\r
+\hspace{7.5pt}\vrule depth 0pt height 0.5pt width 4cm\relax}\r
+\r
+% V1.7 standard LateX2e \thanks, but with \itshape under compsoc. Also make it a \long\def\r
+% We also need to trigger the one-shot footnote rule\r
+\def\@IEEEtriggeroneshotfootnoterule{\global\@IEEEenableoneshotfootnoteruletrue}\r
+\r
+\r
+\long\def\thanks#1{\footnotemark\r
+ \protected@xdef\@thanks{\@thanks\r
+ \protect\footnotetext[\the\c@footnote]{\@IEEEcompsoconly{\itshape\r
+ \protect\@IEEEtriggeroneshotfootnoterule\relax}\ignorespaces#1}}}\r
+\let\@thanks\@empty\r
+\r
+% V1.7 allow \author to contain \par's. This is needed to allow \thanks to contain \par.\r
+\long\def\author#1{\gdef\@author{#1}}\r
+\r
+\r
+% in addition to setting up IEEEitemize, we need to remove a baselineskip space above and\r
+% below it because \list's \pars introduce blank lines because of the footnote struts.\r
+\def\@IEEEsetupcompsocitemizelist{\def\labelitemi{$\bullet$}%\r
+\setlength{\IEEElabelindent}{0pt}\setlength{\parskip}{0pt}%\r
+\setlength{\partopsep}{0pt}\setlength{\topsep}{0.5\baselineskip}\vspace{-1\baselineskip}\relax}\r
+\r
+\r
+% flag for fake non-compsoc \IEEEcompsocthanksitem - prevents line break on very first item\r
+\newif\if@IEEEbreakcompsocthanksitem \@IEEEbreakcompsocthanksitemfalse\r
+\r
+\ifCLASSOPTIONcompsoc\r
+% V1.7 compsoc bullet item \thanks\r
+% also, we need to redefine this to destroy the argument in \@IEEEdynamictitlevspace\r
+\long\def\IEEEcompsocitemizethanks#1{\relax\@IEEEbreakcompsocthanksitemfalse\footnotemark\r
+ \protected@xdef\@thanks{\@thanks\r
+ \protect\footnotetext[\the\c@footnote]{\itshape\protect\@IEEEtriggeroneshotfootnoterule\r
+ {\let\IEEEiedlistdecl\relax\protect\begin{IEEEitemize}[\protect\@IEEEsetupcompsocitemizelist]\ignorespaces#1\relax\r
+ \protect\end{IEEEitemize}}\protect\vspace{-1\baselineskip}}}}\r
+\DeclareRobustCommand*{\IEEEcompsocthanksitem}{\item}\r
+\else\r
+% non-compsoc, allow for dual compilation via rerouting to normal \thanks\r
+\long\def\IEEEcompsocitemizethanks#1{\thanks{#1}}\r
+% redirect to "pseudo-par" \hfil\break\indent after swallowing [] from \IEEEcompsocthanksitem[]\r
+\DeclareRobustCommand{\IEEEcompsocthanksitem}{\@ifnextchar [{\@IEEEthanksswallowoptionalarg}%\r
+{\@IEEEthanksswallowoptionalarg[\relax]}}\r
+% be sure and break only after first item, be sure and ignore spaces after optional argument\r
+\def\@IEEEthanksswallowoptionalarg[#1]{\relax\if@IEEEbreakcompsocthanksitem\hfil\break\r
+\indent\fi\@IEEEbreakcompsocthanksitemtrue\ignorespaces}\r
+\fi\r
+\r
+\r
+% V1.6b define the \IEEEpeerreviewmaketitle as needed\r
+\ifCLASSOPTIONpeerreview\r
+\def\IEEEpeerreviewmaketitle{\@IEEEcleardoublepage{empty}%\r
+\ifCLASSOPTIONtwocolumn\r
+\twocolumn[\@IEEEpeerreviewmaketitle\@IEEEdynamictitlevspace]\r
+\else\r
+\newpage\@IEEEpeerreviewmaketitle\@IEEEstatictitlevskip\r
+\fi\r
+\thispagestyle{IEEEtitlepagestyle}}\r
+\else\r
+% \IEEEpeerreviewmaketitle does nothing if peer review option has not been selected\r
+\def\IEEEpeerreviewmaketitle{\relax}\r
+\fi\r
+\r
+% peerreview formats the repeated title like the title in journal papers.\r
+\def\@IEEEpeerreviewmaketitle{\bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEcompsoconly{\sffamily}%\r
+\normalfont\normalsize\vskip0.2em{\Huge\@title\par}\vskip1.0em\par\r
+\par\addvspace{0.5\baselineskip}\egroup}\r
+\r
+\r
+\r
+% V1.6 \r
+% this is a static rubber spacer between the title/authors and the main text\r
+% used for single column text, or when the title appears in the first column\r
+% of two column text (technotes). \r
+\def\@IEEEstatictitlevskip{{\normalfont\normalsize\r
+% adjust spacing to next text\r
+% v1.6b handle peer review papers\r
+\ifCLASSOPTIONpeerreview\r
+% for peer review papers, the same value is used for both title pages\r
+% regardless of the other paper modes\r
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip\r
+\else\r
+ \ifCLASSOPTIONconference% conference\r
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%\r
+ \else%\r
+ \ifCLASSOPTIONtechnote% technote\r
+ \vskip 1\baselineskip plus 0.375\baselineskip minus 0.1875\baselineskip%\r
+ \else% journal uses more space\r
+ \vskip 2.5\baselineskip plus 0.75\baselineskip minus 0.375\baselineskip%\r
+ \fi\r
+ \fi\r
+\fi}}\r
+\r
+\r
+% V1.6\r
+% This is a dynamically determined rigid spacer between the title/authors \r
+% and the main text. This is used only for single column titles over two \r
+% column text (most common)\r
+% This is bit tricky because we have to ensure that the textheight of the\r
+% main text is an integer multiple of \baselineskip\r
+% otherwise underfull vbox problems may develop in the second column of the\r
+% text on the titlepage\r
+% The possible use of \IEEEpubid must also be taken into account.\r
+\def\@IEEEdynamictitlevspace{{%\r
+ % we run within a group so that all the macros can be forgotten when we are done\r
+ \long\def\thanks##1{\relax}%don't allow \thanks to run when we evaluate the vbox height\r
+ \long\def\IEEEcompsocitemizethanks##1{\relax}%don't allow \IEEEcompsocitemizethanks to run when we evaluate the vbox height\r
+ \normalfont\normalsize% we declare more descriptive variable names\r
+ \let\@IEEEmaintextheight=\@IEEEtrantmpdimenA%height of the main text columns\r
+ \let\@IEEEINTmaintextheight=\@IEEEtrantmpdimenB%height of the main text columns with integer # lines\r
+ % set the nominal and minimum values for the title spacer\r
+ % the dynamic algorithm will not allow the spacer size to\r
+ % become less than \@IEEEMINtitlevspace - instead it will be\r
+ % lengthened\r
+ % default to journal values\r
+ \def\@IEEENORMtitlevspace{2.5\baselineskip}%\r
+ \def\@IEEEMINtitlevspace{2\baselineskip}%\r
+ % conferences and technotes need tighter spacing\r
+ \ifCLASSOPTIONconference%conference\r
+ \def\@IEEENORMtitlevspace{1\baselineskip}%\r
+ \def\@IEEEMINtitlevspace{0.75\baselineskip}%\r
+ \fi\r
+ \ifCLASSOPTIONtechnote%technote\r
+ \def\@IEEENORMtitlevspace{1\baselineskip}%\r
+ \def\@IEEEMINtitlevspace{0.75\baselineskip}%\r
+ \fi%\r
+ % get the height that the title will take up\r
+ \ifCLASSOPTIONpeerreview\r
+ \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@IEEEpeerreviewmaketitle}}%\r
+ \else\r
+ \settoheight{\@IEEEmaintextheight}{\vbox{\hsize\textwidth \@maketitle}}%\r
+ \fi\r
+ \@IEEEmaintextheight=-\@IEEEmaintextheight% title takes away from maintext, so reverse sign\r
+ % add the height of the page textheight\r
+ \advance\@IEEEmaintextheight by \textheight%\r
+ % correct for title pages using pubid\r
+ \ifCLASSOPTIONpeerreview\else\r
+ % peerreview papers use the pubid on the cover page only.\r
+ % And the cover page uses a static spacer.\r
+ \if@IEEEusingpubid\advance\@IEEEmaintextheight by -\@IEEEpubidpullup\fi\r
+ \fi%\r
+ % subtract off the nominal value of the title bottom spacer\r
+ \advance\@IEEEmaintextheight by -\@IEEENORMtitlevspace%\r
+ % \topskip takes away some too\r
+ \advance\@IEEEmaintextheight by -\topskip%\r
+ % calculate the column height of the main text for lines\r
+ % now we calculate the main text height as if holding\r
+ % an integer number of \normalsize lines after the first\r
+ % and discard any excess fractional remainder\r
+ % we subtracted the first line, because the first line\r
+ % is placed \topskip into the maintext, not \baselineskip like the\r
+ % rest of the lines.\r
+ \@IEEEINTmaintextheight=\@IEEEmaintextheight%\r
+ \divide\@IEEEINTmaintextheight by \baselineskip%\r
+ \multiply\@IEEEINTmaintextheight by \baselineskip%\r
+ % now we calculate how much the title spacer height will\r
+ % have to be reduced from nominal (\@IEEEREDUCEmaintextheight is always\r
+ % a positive value) so that the maintext area will contain an integer\r
+ % number of normal size lines\r
+ % we change variable names here (to avoid confusion) as we no longer\r
+ % need \@IEEEINTmaintextheight and can reuse its dimen register\r
+ \let\@IEEEREDUCEmaintextheight=\@IEEEINTmaintextheight%\r
+ \advance\@IEEEREDUCEmaintextheight by -\@IEEEmaintextheight%\r
+ \advance\@IEEEREDUCEmaintextheight by \baselineskip%\r
+ % this is the calculated height of the spacer\r
+ % we change variable names here (to avoid confusion) as we no longer\r
+ % need \@IEEEmaintextheight and can reuse its dimen register\r
+ \let\@IEEECOMPENSATElen=\@IEEEmaintextheight%\r
+ \@IEEECOMPENSATElen=\@IEEENORMtitlevspace% set the nominal value\r
+ % we go with the reduced length if it is smaller than an increase\r
+ \ifdim\@IEEEREDUCEmaintextheight < 0.5\baselineskip\relax%\r
+ \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%\r
+ % if the resulting spacer is too small back out and go with an increase instead\r
+ \ifdim\@IEEECOMPENSATElen<\@IEEEMINtitlevspace\relax%\r
+ \advance\@IEEECOMPENSATElen by \baselineskip%\r
+ \fi%\r
+ \else%\r
+ % go with an increase because it is closer to the nominal than a decrease\r
+ \advance\@IEEECOMPENSATElen by -\@IEEEREDUCEmaintextheight%\r
+ \advance\@IEEECOMPENSATElen by \baselineskip%\r
+ \fi%\r
+ % set the calculated rigid spacer\r
+ \vspace{\@IEEECOMPENSATElen}}}\r
+\r
+\r
+\r
+% V1.6\r
+% we allow the user access to the last part of the title area\r
+% useful in emergencies such as when a different spacing is needed\r
+% This text is NOT compensated for in the dynamic sizer.\r
+\let\@IEEEaftertitletext=\relax\r
+\long\def\IEEEaftertitletext#1{\def\@IEEEaftertitletext{#1}}\r
+\r
+\r
+% V1.7 provide a way for users to enter abstract and keywords\r
+% into the onecolumn title are. This text is compensated for\r
+% in the dynamic sizer.\r
+\let\@IEEEtitleabstractindextext=\relax\r
+\long\def\IEEEtitleabstractindextext#1{\def\@IEEEtitleabstractindextext{#1}}\r
+% V1.7 provide a way for users to get the \@IEEEtitleabstractindextext if\r
+% not in compsoc or transmag journal mode - this way abstract and keywords\r
+% can still be placed in their conventional position if not in those modes.\r
+\def\IEEEdisplaynontitleabstractindextext{%\r
+% display for all conference formats\r
+\ifCLASSOPTIONconference\@IEEEtitleabstractindextext\relax\r
+\else% non-conferences\r
+ \ifCLASSOPTIONcompsoc% display if not compsoc and not transmag\r
+ \else\r
+ \ifCLASSOPTIONtransmag\r
+ \else% not compsoc journal nor transmag journal\r
+ \@IEEEtitleabstractindextext\relax\r
+ \fi\r
+ \fi\r
+\fi}\r
+\r
+\r
+% command to allow alteration of baselinestretch, but only if the current\r
+% baselineskip is unity. Used to tweak the compsoc abstract and keywords line spacing.\r
+\def\@IEEEtweakunitybaselinestretch#1{{\def\baselinestretch{1}\selectfont\r
+\global\@tempskipa\baselineskip}\ifnum\@tempskipa=\baselineskip%\r
+\def\baselinestretch{#1}\selectfont\fi\relax}\r
+\r
+\r
+% abstract and keywords are in \small, except \r
+% for 9pt docs in which they are in \footnotesize\r
+% Because 9pt docs use an 8pt footnotesize, \small\r
+% becomes a rather awkward 8.5pt\r
+\def\@IEEEabskeysecsize{\small}\r
+\ifx\CLASSOPTIONpt\@IEEEptsizenine\r
+ \def\@IEEEabskeysecsize{\footnotesize}\r
+\fi\r
+\r
+% compsoc journals use \footnotesize, compsoc conferences use normalsize\r
+\@IEEEcompsoconly{\def\@IEEEabskeysecsize{\footnotesize}}\r
+\@IEEEcompsocconfonly{\def\@IEEEabskeysecsize{\normalsize}}\r
+\r
+\r
+\r
+\r
+% V1.6 have abstract and keywords strip leading spaces, pars and newlines\r
+% so that spacing is more tightly controlled.\r
+\def\abstract{\normalfont\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\bfseries\textit{\abstractname}---\relax\r
+ \else\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+% V1.6 IEEE wants only 1 pica from end of abstract to introduction heading when in \r
+% conference mode (the heading already has this much above it)\r
+\def\endabstract{\relax\ifCLASSOPTIONconference\vspace{0ex}\else\vspace{1.34ex}\fi\par\if@twocolumn\else\endquotation\fi\r
+ \normalfont\normalsize}\r
+\r
+\def\IEEEkeywords{\normalfont\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\bfseries\textit{\IEEEkeywordsname}---\relax\r
+ \else\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+\def\endIEEEkeywords{\relax\ifCLASSOPTIONtechnote\vspace{1.34ex}\else\vspace{0.67ex}\fi\r
+ \par\if@twocolumn\else\endquotation\fi%\r
+ \normalfont\normalsize}\r
+\r
+% V1.7 compsoc keywords index terms\r
+\ifCLASSOPTIONcompsoc\r
+ \ifCLASSOPTIONconference% compsoc conference\r
+\def\abstract{\normalfont\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\large\abstractname}\par\addvspace{0.5\baselineskip}\egroup\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip\r
+ \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%\r
+ \par\@IEEEgobbleleadPARNLSP}\r
+\def\IEEEkeywords{\normalfont\vskip 1.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\large\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\vskip 0.5\baselineskip plus 0.1\baselineskip minus 0.1\baselineskip\r
+ \if@twocolumn\else\quotation\fi\itshape\@IEEEabskeysecsize%\r
+ \par\@IEEEgobbleleadPARNLSP}\r
+ \else% compsoc not conference\r
+\def\abstract{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\noindent\textbf{\abstractname}---\relax\r
+ \else\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+\def\IEEEkeywords{\normalfont\@IEEEtweakunitybaselinestretch{1.15}\sffamily\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\vskip 0.5\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip\noindent\r
+ \textbf{\IEEEkeywordsname}---\relax\r
+ \else\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\@IEEEabskeysecsize\textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize%\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+ \fi\r
+\fi\r
+\r
+% V1.8 transmag keywords index terms\r
+% no abstract name, use indentation\r
+\ifCLASSOPTIONtransmag\r
+\def\abstract{\normalfont\parindent 1em\relax\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\bfseries\indent\r
+ \else\r
+ \bgroup\par\addvspace{0.5\baselineskip}\centering\vspace{-1.78ex}\@IEEEabskeysecsize\r
+ \textbf{\abstractname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+\r
+\def\IEEEkeywords{\normalfont\parindent 1em\relax\r
+ \if@twocolumn\r
+ \@IEEEabskeysecsize\vspace{1\baselineskip}\bfseries\indent\textit{\IEEEkeywordsname}---\relax\r
+ \else\r
+ \bgroup\par\vspace{1\baselineskip}\centering\@IEEEabskeysecsize\r
+ \textbf{\IEEEkeywordsname}\par\addvspace{0.5\baselineskip}\egroup\quotation\@IEEEabskeysecsize\r
+ \fi\@IEEEgobbleleadPARNLSP}\r
+\fi\r
+\r
+\r
+\r
+% gobbles all leading \, \\ and \par, upon finding first token that\r
+% is not a \ , \\ or a \par, it ceases and returns that token\r
+% \r
+% used to strip leading \, \\ and \par from the input\r
+% so that such things in the beginning of an environment will not\r
+% affect the formatting of the text\r
+\long\def\@IEEEgobbleleadPARNLSP#1{\let\@IEEEswallowthistoken=0%\r
+\let\@IEEEgobbleleadPARNLSPtoken#1%\r
+\let\@IEEEgobbleleadPARtoken=\par%\r
+\let\@IEEEgobbleleadNLtoken=\\%\r
+\let\@IEEEgobbleleadSPtoken=\ %\r
+\def\@IEEEgobbleleadSPMACRO{\ }%\r
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadPARtoken%\r
+\let\@IEEEswallowthistoken=1%\r
+\fi%\r
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadNLtoken%\r
+\let\@IEEEswallowthistoken=1%\r
+\fi%\r
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPtoken%\r
+\let\@IEEEswallowthistoken=1%\r
+\fi%\r
+% a control space will come in as a macro\r
+% when it is the last one on a line\r
+\ifx\@IEEEgobbleleadPARNLSPtoken\@IEEEgobbleleadSPMACRO%\r
+\let\@IEEEswallowthistoken=1%\r
+\fi%\r
+% if we have to swallow this token, do so and taste the next one\r
+% else spit it out and stop gobbling\r
+\ifx\@IEEEswallowthistoken 1\let\@IEEEnextgobbleleadPARNLSP=\@IEEEgobbleleadPARNLSP\else%\r
+\let\@IEEEnextgobbleleadPARNLSP=#1\fi%\r
+\@IEEEnextgobbleleadPARNLSP}%\r
+\r
+\r
+\r
+\r
+% TITLING OF SECTIONS\r
+\def\@IEEEsectpunct{:\ \,} % Punctuation after run-in section heading (headings which are\r
+ % part of the paragraphs), need little bit more than a single space\r
+ % spacing from section number to title\r
+% compsoc conferences use regular period/space punctuation\r
+\ifCLASSOPTIONcompsoc\r
+\ifCLASSOPTIONconference\r
+\def\@IEEEsectpunct{.\ }\r
+\fi\fi\r
+\r
+\r
+\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 0.5em\relax}\r
+\r
+\ifCLASSOPTIONcompsoc\r
+% compsoc journals need extra spacing\r
+\ifCLASSOPTIONconference\else\r
+\def\@seccntformat#1{\csname the#1dis\endcsname\hskip 1em\relax}\r
+\fi\fi\r
+\r
+%v1.7 put {} after #6 to allow for some types of user font control\r
+%and use \@@par rather than \par\r
+\def\@sect#1#2#3#4#5#6[#7]#8{%\r
+ \ifnum #2>\c@secnumdepth\r
+ \let\@svsec\@empty\r
+ \else\r
+ \refstepcounter{#1}%\r
+ % load section label and spacer into \@svsec\r
+ \protected@edef\@svsec{\@seccntformat{#1}\relax}%\r
+ \fi%\r
+ \@tempskipa #5\relax\r
+ \ifdim \@tempskipa>\z@% tempskipa determines whether is treated as a high\r
+ \begingroup #6{\relax% or low level heading\r
+ \noindent % subsections are NOT indented\r
+ % print top level headings. \@svsec is label, #8 is heading title\r
+ % IEEE does not block indent the section title text, it flows like normal\r
+ {\hskip #3\relax\@svsec}{\interlinepenalty \@M #8\@@par}}%\r
+ \endgroup\r
+ \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else\r
+ \protect\numberline{\csname the#1\endcsname}\fi#7}%\r
+ \else % printout low level headings\r
+ % svsechd seems to swallow the trailing space, protect it with \mbox{}\r
+ % got rid of sectionmark stuff\r
+ \def\@svsechd{#6{\hskip #3\relax\@svsec #8\@IEEEsectpunct\mbox{}}%\r
+ \addcontentsline{toc}{#1}{\ifnum #2>\c@secnumdepth\relax\else\r
+ \protect\numberline{\csname the#1\endcsname}\fi#7}}%\r
+ \fi%skip down\r
+ \@xsect{#5}}\r
+\r
+\r
+% section* handler\r
+%v1.7 put {} after #4 to allow for some types of user font control\r
+%and use \@@par rather than \par\r
+\def\@ssect#1#2#3#4#5{\@tempskipa #3\relax\r
+ \ifdim \@tempskipa>\z@\r
+ %\begingroup #4\@hangfrom{\hskip #1}{\interlinepenalty \@M #5\par}\endgroup\r
+ % IEEE does not block indent the section title text, it flows like normal\r
+ \begingroup \noindent #4{\relax{\hskip #1}{\interlinepenalty \@M #5\@@par}}\endgroup\r
+ % svsechd swallows the trailing space, protect it with \mbox{}\r
+ \else \def\@svsechd{#4{\hskip #1\relax #5\@IEEEsectpunct\mbox{}}}\fi\r
+ \@xsect{#3}}\r
+\r
+\r
+%% SECTION heading spacing and font\r
+%%\r
+% arguments are: #1 - sectiontype name\r
+% (for \@sect) #2 - section level\r
+% #3 - section heading indent\r
+% #4 - top separation (absolute value used, neg indicates not to indent main text)\r
+% If negative, make stretch parts negative too!\r
+% #5 - (absolute value used) positive: bottom separation after heading,\r
+% negative: amount to indent main text after heading\r
+% Both #4 and #5 negative means to indent main text and use negative top separation\r
+% #6 - font control\r
+% You've got to have \normalfont\normalsize in the font specs below to prevent\r
+% trouble when you do something like:\r
+% \section{Note}{\ttfamily TT-TEXT} is known to ... \r
+% IEEE sometimes REALLY stretches the area before a section\r
+% heading by up to about 0.5in. However, it may not be a good\r
+% idea to let LaTeX have quite this much rubber.\r
+\ifCLASSOPTIONconference%\r
+% IEEE wants section heading spacing to decrease for conference mode\r
+\def\section{\@startsection{section}{1}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%\r
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%\r
+\def\subsection{\@startsection{subsection}{2}{\z@}{1.5ex plus 1.5ex minus 0.5ex}%\r
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%\r
+\else % for journals\r
+\def\section{\@startsection{section}{1}{\z@}{3.0ex plus 1.5ex minus 1.5ex}% V1.6 3.0ex from 3.5ex\r
+{0.7ex plus 1ex minus 0ex}{\normalfont\normalsize\centering\scshape}}%\r
+\def\subsection{\@startsection{subsection}{2}{\z@}{3.5ex plus 1.5ex minus 1.5ex}%\r
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%\r
+\fi\r
+\r
+% for both journals and conferences\r
+% decided to put in a little rubber above the section, might help somebody\r
+\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{0ex plus 0.1ex minus 0.1ex}%\r
+{0ex}{\normalfont\normalsize\itshape}}%\r
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%\r
+{0ex}{\normalfont\normalsize\itshape}}%\r
+\r
+\r
+% compsoc\r
+\ifCLASSOPTIONcompsoc\r
+\ifCLASSOPTIONconference\r
+% compsoc conference\r
+\def\section{\@startsection{section}{1}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%\r
+{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\large\bfseries}}%\r
+\def\subsection{\@startsection{subsection}{2}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%\r
+{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}{\normalfont\sublargesize\bfseries}}%\r
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{1\baselineskip plus 0.25\baselineskip minus 0.25\baselineskip}%\r
+{0ex}{\normalfont\normalsize\bfseries}}%\r
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{0ex plus 0.1ex minus 0.1ex}%\r
+{0ex}{\normalfont\normalsize}}%\r
+\else% compsoc journals\r
+% use negative top separation as compsoc journals do not indent paragraphs after section titles\r
+\def\section{\@startsection{section}{1}{\z@}{-3ex plus -2ex minus -1.5ex}%\r
+{0.7ex plus 1ex minus 0ex}{\normalfont\large\sffamily\bfseries\scshape}}%\r
+% Note that subsection and smaller may not be correct for the Computer Society,\r
+% I have to look up an example.\r
+\def\subsection{\@startsection{subsection}{2}{\z@}{-3.5ex plus -1.5ex minus -1.5ex}%\r
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\sffamily\bfseries}}%\r
+\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex plus -1ex minus -1ex}%\r
+{0.5ex plus 0.5ex minus 0ex}{\normalfont\normalsize\sffamily\itshape}}%\r
+\def\paragraph{\@startsection{paragraph}{4}{2\parindent}{-0ex plus -0.1ex minus -0.1ex}%\r
+{0ex}{\normalfont\normalsize}}%\r
+\fi\fi\r
+\r
+% transmag\r
+\ifCLASSOPTIONtransmag\r
+\def\subsection{\@startsection{subsection}{2}{0.75\parindent}{3.5ex plus 1.5ex minus 1.5ex}%\r
+{0.7ex plus .5ex minus 0ex}{\normalfont\normalsize\itshape}}%\r
+\def\subsubsection{\@startsection{subsubsection}{3}{1.25\parindent}{0.1ex plus 0.1ex minus 0.1ex}%\r
+{0.1ex}{\normalfont\normalsize\itshape}}%\r
+\fi\r
+\r
+\r
+%% ENVIRONMENTS\r
+% "box" symbols at end of proofs\r
+\def\IEEEQEDclosed{\mbox{\rule[0pt]{1.3ex}{1.3ex}}} % for a filled box\r
+% V1.6 some journals use an open box instead that will just fit around a closed one\r
+\def\IEEEQEDopen{{\setlength{\fboxsep}{0pt}\setlength{\fboxrule}{0.2pt}\fbox{\rule[0pt]{0pt}{1.3ex}\rule[0pt]{1.3ex}{0pt}}}}\r
+\ifCLASSOPTIONcompsoc\r
+\def\IEEEQED{\IEEEQEDopen} % default to open for compsoc\r
+\else\r
+\def\IEEEQED{\IEEEQEDclosed} % otherwise default to closed\r
+\fi\r
+\r
+%V1.8 flag to indicate if QED symbol is to be shown\r
+\newif\if@IEEEQEDshow \@IEEEQEDshowtrue\r
+\def\IEEEproofindentspace{2\parindent}% V1.8 allow user to change indentation amount if desired\r
+% v1.7 name change to avoid namespace collision with amsthm. Also add support\r
+% for an optional argument.\r
+\def\IEEEproof{\@ifnextchar[{\@IEEEproof}{\@IEEEproof[\IEEEproofname]}}\r
+\def\@IEEEproof[#1]{\@IEEEQEDshowtrue\par\noindent\hspace{\IEEEproofindentspace}{\itshape #1: }}\r
+\def\endIEEEproof{\if@IEEEQEDshow\hspace*{\fill}\nobreakspace\IEEEQED\fi\par}\r
+% qedhere for equation environments, similar to AMS \qedhere\r
+\def\IEEEQEDhereeqn{\global\@IEEEQEDshowfalse\eqno\let\eqno\relax\let\leqno\relax\r
+ \let\veqno\relax\hbox{\IEEEQED}}\r
+% IEEE style qedhere for IEEEeqnarray and other environments\r
+\def\IEEEQEDhere{\global\@IEEEQEDshowfalse\IEEEQED}\r
+% command to disable QED at end of IEEEproof\r
+\def\IEEEQEDoff{\global\@IEEEQEDshowfalse}\r
+\r
+\r
+%\itemindent is set to \z@ by list, so define new temporary variable\r
+\newdimen\@IEEEtmpitemindent\r
+\r
+% V1.8 allow long theorem names to break across lines.\r
+% Thanks to Miquel Payaro for reporting this.\r
+\def\@begintheorem#1#2{\@IEEEtmpitemindent\itemindent\relax\topsep 0pt\rmfamily\trivlist%\r
+ \item[]\textit{\indent #1\ #2:} \itemindent\@IEEEtmpitemindent\relax}\r
+\def\@opargbegintheorem#1#2#3{\@IEEEtmpitemindent\itemindent\relax\topsep 0pt\rmfamily \trivlist%\r
+% V1.6 IEEE is back to using () around theorem names which are also in italics\r
+% Thanks to Christian Peel for reporting this.\r
+ \item[]\textit{\indent #1\ #2\ (#3):} \itemindent\@IEEEtmpitemindent\relax}\r
+% V1.7 remove bogus \unskip that caused equations in theorems to collide with\r
+% lines below.\r
+\def\@endtheorem{\endtrivlist}\r
+\r
+% V1.6\r
+% display command for the section the theorem is in - so that \thesection\r
+% is not used as this will be in Roman numerals when we want arabic.\r
+% LaTeX2e uses \def\@thmcounter#1{\noexpand\arabic{#1}} for the theorem number\r
+% (second part) display and \def\@thmcountersep{.} as a separator.\r
+% V1.7 intercept calls to the section counter and reroute to \@IEEEthmcounterinsection\r
+% to allow \appendix(ices} to override as needed.\r
+%\r
+% special handler for sections, allows appendix(ices) to override\r
+\gdef\@IEEEthmcounterinsection#1{\arabic{#1}}\r
+% string macro\r
+\edef\@IEEEstringsection{section}\r
+\r
+% redefine the #1#2[#3] form of newtheorem to use a hook to \@IEEEthmcounterinsection\r
+% if section in_counter is used\r
+\def\@xnthm#1#2[#3]{%\r
+ \expandafter\@ifdefinable\csname #1\endcsname\r
+ {\@definecounter{#1}\@newctr{#1}[#3]%\r
+ \edef\@IEEEstringtmp{#3}\r
+ \ifx\@IEEEstringtmp\@IEEEstringsection\r
+ \expandafter\xdef\csname the#1\endcsname{%\r
+ \noexpand\@IEEEthmcounterinsection{#3}\@thmcountersep\r
+ \@thmcounter{#1}}%\r
+ \else\r
+ \expandafter\xdef\csname the#1\endcsname{%\r
+ \expandafter\noexpand\csname the#3\endcsname \@thmcountersep\r
+ \@thmcounter{#1}}%\r
+ \fi\r
+ \global\@namedef{#1}{\@thm{#1}{#2}}%\r
+ \global\@namedef{end#1}{\@endtheorem}}}\r
+\r
+\r
+\r
+%% SET UP THE DEFAULT PAGESTYLE\r
+\ps@headings\r
+\pagenumbering{arabic}\r
+\r
+% normally the page counter starts at 1\r
+\setcounter{page}{1}\r
+% however, for peerreview the cover sheet is page 0 or page -1\r
+% (for duplex printing)\r
+\ifCLASSOPTIONpeerreview\r
+ \if@twoside\r
+ \setcounter{page}{-1}\r
+ \else\r
+ \setcounter{page}{0}\r
+ \fi\r
+\fi\r
+\r
+% standard book class behavior - let bottom line float up and down as\r
+% needed when single sided\r
+\ifCLASSOPTIONtwoside\else\raggedbottom\fi\r
+% if two column - turn on twocolumn, allow word spacings to stretch more and\r
+% enforce a rigid position for the last lines\r
+\ifCLASSOPTIONtwocolumn\r
+% the peer review option delays invoking twocolumn\r
+ \ifCLASSOPTIONpeerreview\else\r
+ \twocolumn\r
+ \fi\r
+\sloppy \r
+\flushbottom\r
+\fi\r
+\r
+\r
+\r
+\r
+% \APPENDIX and \APPENDICES definitions\r
+\r
+% This is the \@ifmtarg command from the LaTeX ifmtarg package\r
+% by Peter Wilson (CUA) and Donald Arseneau\r
+% \@ifmtarg is used to determine if an argument to a command\r
+% is present or not.\r
+% For instance:\r
+% \@ifmtarg{#1}{\typeout{empty}}{\typeout{has something}}\r
+% \@ifmtarg is used with our redefined \section command if\r
+% \appendices is invoked.\r
+% The command \section will behave slightly differently depending\r
+% on whether the user specifies a title: \r
+% \section{My appendix title}\r
+% or not:\r
+% \section{}\r
+% This way, we can eliminate the blank lines where the title\r
+% would be, and the unneeded : after Appendix in the table of\r
+% contents \r
+\begingroup\r
+\catcode`\Q=3\r
+\long\gdef\@ifmtarg#1{\@xifmtarg#1QQ\@secondoftwo\@firstoftwo\@nil}\r
+\long\gdef\@xifmtarg#1#2Q#3#4#5\@nil{#4}\r
+\endgroup\r
+% end of \@ifmtarg defs\r
+\r
+\r
+% V1.7\r
+% command that allows the one time saving of the original definition\r
+% of section to \@IEEEappendixsavesection for \appendix or \appendices \r
+% we don't save \section here as it may be redefined later by other\r
+% packages (hyperref.sty, etc.)\r
+\def\@IEEEsaveoriginalsectiononce{\let\@IEEEappendixsavesection\section\r
+\let\@IEEEsaveoriginalsectiononce\relax}\r
+\r
+% neat trick to grab and process the argument from \section{argument}\r
+% we process differently if the user invoked \section{} with no\r
+% argument (title)\r
+% note we reroute the call to the old \section*\r
+\def\@IEEEprocessthesectionargument#1{%\r
+\@ifmtarg{#1}{%\r
+\@IEEEappendixsavesection*{\appendixname\nobreakspace\thesectiondis}%\r
+\addcontentsline{toc}{section}{\appendixname\nobreakspace\thesection}}{%\r
+\@IEEEappendixsavesection*{\appendixname\nobreakspace\thesectiondis\\* #1}%\r
+\addcontentsline{toc}{section}{\appendixname\nobreakspace\thesection: #1}}}\r
+\r
+% we use this if the user calls \section{} after\r
+% \appendix-- which has no meaning. So, we ignore the\r
+% command and its argument. Then, warn the user.\r
+\def\@IEEEdestroythesectionargument#1{\typeout{** WARNING: Ignoring useless\r
+\protect\section\space in Appendix (line \the\inputlineno).}}\r
+\r
+\r
+% remember \thesection forms will be displayed in \ref calls\r
+% and in the Table of Contents.\r
+% The \sectiondis form is used in the actual heading itself\r
+\r
+% appendix command for one single appendix\r
+% normally has no heading. However, if you want a \r
+% heading, you can do so via the optional argument:\r
+% \appendix[Optional Heading]\r
+\def\appendix{\relax}\r
+\renewcommand{\appendix}[1][]{\@IEEEsaveoriginalsectiononce\par\r
+ % v1.6 keep hyperref's identifiers unique\r
+ \gdef\theHsection{Appendix.A}%\r
+ % v1.6 adjust hyperref's string name for the section\r
+ \xdef\Hy@chapapp{appendix}%\r
+ \setcounter{section}{0}%\r
+ \setcounter{subsection}{0}%\r
+ \setcounter{subsubsection}{0}%\r
+ \setcounter{paragraph}{0}%\r
+ \gdef\thesection{A}%\r
+ \gdef\thesectiondis{}% \r
+ \gdef\thesubsection{\Alph{subsection}}%\r
+ \gdef\@IEEEthmcounterinsection##1{A}\r
+ \refstepcounter{section}% update the \ref counter\r
+ \@ifmtarg{#1}{\@IEEEappendixsavesection*{\appendixname}%\r
+ \addcontentsline{toc}{section}{\appendixname}}{%\r
+ \@IEEEappendixsavesection*{\appendixname\nobreakspace\\* #1}%\r
+ \addcontentsline{toc}{section}{\appendixname: #1}}%\r
+ % redefine \section command for appendix\r
+ % leave \section* as is\r
+ \def\section{\@ifstar{\@IEEEappendixsavesection*}{%\r
+ \@IEEEdestroythesectionargument}}% throw out the argument\r
+ % of the normal form\r
+}\r
+\r
+\r
+\r
+% appendices command for multiple appendices\r
+% user then calls \section with an argument (possibly empty) to\r
+% declare the individual appendices\r
+\def\appendices{\@IEEEsaveoriginalsectiononce\par\r
+ % v1.6 keep hyperref's identifiers unique\r
+ \gdef\theHsection{Appendix.\Alph{section}}%\r
+ % v1.6 adjust hyperref's string name for the section\r
+ \xdef\Hy@chapapp{appendix}%\r
+ \setcounter{section}{-1}% we want \refstepcounter to use section 0\r
+ \setcounter{subsection}{0}%\r
+ \setcounter{subsubsection}{0}%\r
+ \setcounter{paragraph}{0}%\r
+ \ifCLASSOPTIONromanappendices%\r
+ \gdef\thesection{\Roman{section}}%\r
+ \gdef\thesectiondis{\Roman{section}}%\r
+ \@IEEEcompsocconfonly{\gdef\thesectiondis{\Roman{section}.}}%\r
+ \gdef\@IEEEthmcounterinsection##1{A\arabic{##1}}\r
+ \else%\r
+ \gdef\thesection{\Alph{section}}%\r
+ \gdef\thesectiondis{\Alph{section}}%\r
+ \@IEEEcompsocconfonly{\gdef\thesectiondis{\Alph{section}.}}%\r
+ \gdef\@IEEEthmcounterinsection##1{\Alph{##1}}\r
+ \fi%\r
+ \refstepcounter{section}% update the \ref counter\r
+ \setcounter{section}{0}% NEXT \section will be the FIRST appendix\r
+ % redefine \section command for appendices\r
+ % leave \section* as is\r
+ \def\section{\@ifstar{\@IEEEappendixsavesection*}{% process the *-form\r
+ \refstepcounter{section}% or is a new section so,\r
+ \@IEEEprocessthesectionargument}}% process the argument \r
+ % of the normal form\r
+}\r
+\r
+\r
+\r
+% \IEEEPARstart\r
+% Definition for the big two line drop cap letter at the beginning of the\r
+% first paragraph of journal papers. The first argument is the first letter\r
+% of the first word, the second argument is the remaining letters of the\r
+% first word which will be rendered in upper case.\r
+% In V1.6 this has been completely rewritten to:\r
+% \r
+% 1. no longer have problems when the user begins an environment\r
+% within the paragraph that uses \IEEEPARstart.\r
+% 2. auto-detect and use the current font family\r
+% 3. revise handling of the space at the end of the first word so that\r
+% interword glue will now work as normal.\r
+% 4. produce correctly aligned edges for the (two) indented lines.\r
+% \r
+% We generalize things via control macros - playing with these is fun too.\r
+% \r
+% V1.7 added more control macros to make it easy for IEEEtrantools.sty users\r
+% to change the font style.\r
+% \r
+% the number of lines that are indented to clear it\r
+% may need to increase if using decenders\r
+\def\@IEEEPARstartDROPLINES{2}\r
+% minimum number of lines left on a page to allow a \@IEEEPARstart\r
+% Does not take into consideration rubber shrink, so it tends to\r
+% be overly cautious\r
+\def\@IEEEPARstartMINPAGELINES{2}\r
+% V1.7 the height of the drop cap is adjusted to match the height of this text\r
+% in the current font (when \IEEEPARstart is called).\r
+\def\@IEEEPARstartHEIGHTTEXT{T}\r
+% the depth the letter is lowered below the baseline\r
+% the height (and size) of the letter is determined by the sum\r
+% of this value and the height of the \@IEEEPARstartHEIGHTTEXT in the current\r
+% font. It is a good idea to set this value in terms of the baselineskip\r
+% so that it can respond to changes therein.\r
+\def\@IEEEPARstartDROPDEPTH{1.1\baselineskip}\r
+% V1.7 the font the drop cap will be rendered in,\r
+% can take zero or one argument.\r
+\def\@IEEEPARstartFONTSTYLE{\bfseries}\r
+% V1.7 any additional, non-font related commands needed to modify\r
+% the drop cap letter, can take zero or one argument.\r
+\def\@IEEEPARstartCAPSTYLE{\MakeUppercase}\r
+% V1.7 the font that will be used to render the rest of the word,\r
+% can take zero or one argument.\r
+\def\@IEEEPARstartWORDFONTSTYLE{\relax}\r
+% V1.7 any additional, non-font related commands needed to modify\r
+% the rest of the word, can take zero or one argument.\r
+\def\@IEEEPARstartWORDCAPSTYLE{\MakeUppercase}\r
+% This is the horizontal separation distance from the drop letter to the main text.\r
+% Lengths that depend on the font (e.g., ex, em, etc.) will be referenced\r
+% to the font that is active when \IEEEPARstart is called. \r
+\def\@IEEEPARstartSEP{0.15em}\r
+% V1.7 horizontal offset applied to the left of the drop cap.\r
+\def\@IEEEPARstartHOFFSET{0em}\r
+% V1.7 Italic correction command applied at the end of the drop cap.\r
+\def\@IEEEPARstartITLCORRECT{\/}\r
+\r
+% V1.7 compoc uses nonbold drop cap and small caps word style\r
+\ifCLASSOPTIONcompsoc\r
+\def\@IEEEPARstartFONTSTYLE{\mdseries}\r
+\def\@IEEEPARstartWORDFONTSTYLE{\scshape}\r
+\def\@IEEEPARstartWORDCAPSTYLE{\relax}\r
+\fi\r
+\r
+% definition of \IEEEPARstart\r
+% THIS IS A CONTROLLED SPACING AREA, DO NOT ALLOW SPACES WITHIN THESE LINES\r
+% \r
+% The token \@IEEEPARstartfont will be globally defined after the first use\r
+% of \IEEEPARstart and will be a font command which creates the big letter\r
+% The first argument is the first letter of the first word and the second\r
+% argument is the rest of the first word(s).\r
+\def\IEEEPARstart#1#2{\par{%\r
+% if this page does not have enough space, break it and lets start\r
+% on a new one\r
+\@IEEEtranneedspace{\@IEEEPARstartMINPAGELINES\baselineskip}{\relax}%\r
+% V1.7 move this up here in case user uses \textbf for \@IEEEPARstartFONTSTYLE\r
+% which uses command \leavevmode which causes an unwanted \indent to be issued\r
+\noindent\r
+% calculate the desired height of the big letter\r
+% it extends from the top of \@IEEEPARstartHEIGHTTEXT in the current font\r
+% down to \@IEEEPARstartDROPDEPTH below the current baseline\r
+\settoheight{\@IEEEtrantmpdimenA}{\@IEEEPARstartHEIGHTTEXT}%\r
+\addtolength{\@IEEEtrantmpdimenA}{\@IEEEPARstartDROPDEPTH}%\r
+% extract the name of the current font in bold\r
+% and place it in \@IEEEPARstartFONTNAME\r
+\def\@IEEEPARstartGETFIRSTWORD##1 ##2\relax{##1}%\r
+{\@IEEEPARstartFONTSTYLE{\selectfont\edef\@IEEEPARstartFONTNAMESPACE{\fontname\font\space}%\r
+\xdef\@IEEEPARstartFONTNAME{\expandafter\@IEEEPARstartGETFIRSTWORD\@IEEEPARstartFONTNAMESPACE\relax}}}%\r
+% define a font based on this name with a point size equal to the desired\r
+% height of the drop letter\r
+\font\@IEEEPARstartsubfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenA\relax%\r
+% save this value as a counter (integer) value (sp points)\r
+\@IEEEtrantmpcountA=\@IEEEtrantmpdimenA%\r
+% now get the height of the actual letter produced by this font size\r
+\settoheight{\@IEEEtrantmpdimenB}{\@IEEEPARstartsubfont\@IEEEPARstartCAPSTYLE{#1}}%\r
+% If something bogus happens like the first argument is empty or the\r
+% current font is strange, do not allow a zero height.\r
+\ifdim\@IEEEtrantmpdimenB=0pt\relax%\r
+\typeout{** WARNING: IEEEPARstart drop letter has zero height! (line \the\inputlineno)}%\r
+\typeout{ Forcing the drop letter font size to 10pt.}%\r
+\@IEEEtrantmpdimenB=10pt%\r
+\fi%\r
+% and store it as a counter\r
+\@IEEEtrantmpcountB=\@IEEEtrantmpdimenB%\r
+% Since a font size doesn't exactly correspond to the height of the capital\r
+% letters in that font, the actual height of the letter, \@IEEEtrantmpcountB,\r
+% will be less than that desired, \@IEEEtrantmpcountA\r
+% we need to raise the font size, \@IEEEtrantmpdimenA \r
+% by \@IEEEtrantmpcountA / \@IEEEtrantmpcountB\r
+% But, TeX doesn't have floating point division, so we have to use integer\r
+% division. Hence the use of the counters.\r
+% We need to reduce the denominator so that the loss of the remainder will\r
+% have minimal affect on the accuracy of the result\r
+\divide\@IEEEtrantmpcountB by 200%\r
+\divide\@IEEEtrantmpcountA by \@IEEEtrantmpcountB%\r
+% Then reequalize things when we use TeX's ability to multiply by\r
+% floating point values\r
+\@IEEEtrantmpdimenB=0.005\@IEEEtrantmpdimenA%\r
+\multiply\@IEEEtrantmpdimenB by \@IEEEtrantmpcountA%\r
+% \@IEEEPARstartfont is globaly set to the calculated font of the big letter\r
+% We need to carry this out of the local calculation area to to create the\r
+% big letter.\r
+\global\font\@IEEEPARstartfont\@IEEEPARstartFONTNAME\space at \@IEEEtrantmpdimenB%\r
+% Now set \@IEEEtrantmpdimenA to the width of the big letter\r
+% We need to carry this out of the local calculation area to set the\r
+% hanging indent\r
+\settowidth{\global\@IEEEtrantmpdimenA}{\@IEEEPARstartfont\r
+\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}}}%\r
+% end of the isolated calculation environment\r
+% add in the extra clearance we want\r
+\advance\@IEEEtrantmpdimenA by \@IEEEPARstartSEP\relax%\r
+% add in the optional offset\r
+\advance\@IEEEtrantmpdimenA by \@IEEEPARstartHOFFSET\relax%\r
+% V1.7 don't allow negative offsets to produce negative hanging indents\r
+\@IEEEtrantmpdimenB\@IEEEtrantmpdimenA\r
+\ifnum\@IEEEtrantmpdimenB < 0 \@IEEEtrantmpdimenB 0pt\fi\r
+% \@IEEEtrantmpdimenA has the width of the big letter plus the\r
+% separation space and \@IEEEPARstartfont is the font we need to use\r
+% Now, we make the letter and issue the hanging indent command\r
+% The letter is placed in a box of zero width and height so that other\r
+% text won't be displaced by it.\r
+\hangindent\@IEEEtrantmpdimenB\hangafter=-\@IEEEPARstartDROPLINES%\r
+\makebox[0pt][l]{\hspace{-\@IEEEtrantmpdimenA}%\r
+\raisebox{-\@IEEEPARstartDROPDEPTH}[0pt][0pt]{\hspace{\@IEEEPARstartHOFFSET}%\r
+\@IEEEPARstartfont\@IEEEPARstartCAPSTYLE{#1\@IEEEPARstartITLCORRECT}%\r
+\hspace{\@IEEEPARstartSEP}}}%\r
+{\@IEEEPARstartWORDFONTSTYLE{\@IEEEPARstartWORDCAPSTYLE{\selectfont#2}}}}\r
+\r
+\r
+\r
+\r
+\r
+\r
+% determines if the space remaining on a given page is equal to or greater\r
+% than the specified space of argument one\r
+% if not, execute argument two (only if the remaining space is greater than zero)\r
+% and issue a \newpage\r
+% \r
+% example: \@IEEEtranneedspace{2in}{\vfill}\r
+% \r
+% Does not take into consideration rubber shrinkage, so it tends to\r
+% be overly cautious\r
+% Based on an example posted by Donald Arseneau\r
+% Note this macro uses \@IEEEtrantmpdimenB internally for calculations,\r
+% so DO NOT PASS \@IEEEtrantmpdimenB to this routine\r
+% if you need a dimen register, import with \@IEEEtrantmpdimenA instead\r
+\def\@IEEEtranneedspace#1#2{\penalty-100\begingroup%shield temp variable\r
+\@IEEEtrantmpdimenB\pagegoal\advance\@IEEEtrantmpdimenB-\pagetotal% space left\r
+\ifdim #1>\@IEEEtrantmpdimenB\relax% not enough space left\r
+\ifdim\@IEEEtrantmpdimenB>\z@\relax #2\fi%\r
+\newpage%\r
+\fi\endgroup}\r
+\r
+\r
+\r
+% IEEEbiography ENVIRONMENT\r
+% Allows user to enter biography leaving place for picture (adapts to font size)\r
+% As of V1.5, a new optional argument allows you to have a real graphic!\r
+% V1.5 and later also fixes the "colliding biographies" which could happen when a \r
+% biography's text was shorter than the space for the photo.\r
+% MDS 7/2001\r
+% V1.6 prevent multiple biographies from making multiple TOC entries\r
+\newif\if@IEEEbiographyTOCentrynotmade\r
+\global\@IEEEbiographyTOCentrynotmadetrue\r
+\r
+% biography counter so hyperref can jump directly to the biographies\r
+% and not just the previous section\r
+\newcounter{IEEEbiography}\r
+\setcounter{IEEEbiography}{0}\r
+\r
+% photo area size\r
+\def\@IEEEBIOphotowidth{1.0in} % width of the biography photo area\r
+\def\@IEEEBIOphotodepth{1.25in} % depth (height) of the biography photo area\r
+% area cleared for photo\r
+\def\@IEEEBIOhangwidth{1.14in} % width cleared for the biography photo area\r
+\def\@IEEEBIOhangdepth{1.25in} % depth cleared for the biography photo area\r
+ % actual depth will be a multiple of \r
+ % \baselineskip, rounded up\r
+\def\@IEEEBIOskipN{4\baselineskip}% nominal value of the vskip above the biography\r
+\r
+\newenvironment{IEEEbiography}[2][]{\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize%\r
+\unitlength 1in\parskip=0pt\par\parindent 1em\interlinepenalty500%\r
+% we need enough space to support the hanging indent\r
+% the nominal value of the spacer\r
+% and one extra line for good measure\r
+\@IEEEtrantmpdimenA=\@IEEEBIOhangdepth%\r
+\advance\@IEEEtrantmpdimenA by \@IEEEBIOskipN%\r
+\advance\@IEEEtrantmpdimenA by 1\baselineskip%\r
+% if this page does not have enough space, break it and lets start\r
+% with a new one\r
+\@IEEEtranneedspace{\@IEEEtrantmpdimenA}{\relax}%\r
+% nominal spacer can strech, not shrink use 1fil so user can out stretch with \vfill\r
+\vskip \@IEEEBIOskipN plus 1fil minus 0\baselineskip%\r
+% the default box for where the photo goes\r
+\def\@IEEEtempbiographybox{{\setlength{\fboxsep}{0pt}\framebox{%\r
+\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}\centering PLACE\\ PHOTO\\ HERE \end{minipage}}}}%\r
+%\r
+% detect if the optional argument was supplied, this requires the\r
+% \@ifmtarg command as defined in the appendix section above\r
+% and if so, override the default box with what they want\r
+\@ifmtarg{#1}{\relax}{\def\@IEEEtempbiographybox{\mbox{\begin{minipage}[b][\@IEEEBIOphotodepth][c]{\@IEEEBIOphotowidth}%\r
+\centering%\r
+#1%\r
+\end{minipage}}}}% end if optional argument supplied\r
+% Make an entry into the table of contents only if we have not done so before\r
+\if@IEEEbiographyTOCentrynotmade%\r
+% link labels to the biography counter so hyperref will jump\r
+% to the biography, not the previous section\r
+\setcounter{IEEEbiography}{-1}%\r
+\refstepcounter{IEEEbiography}%\r
+\addcontentsline{toc}{section}{Biographies}%\r
+\global\@IEEEbiographyTOCentrynotmadefalse%\r
+\fi%\r
+% one more biography\r
+\refstepcounter{IEEEbiography}%\r
+% Make an entry for this name into the table of contents \r
+\addcontentsline{toc}{subsection}{#2}%\r
+% V1.6 properly handle if a new paragraph should occur while the\r
+% hanging indent is still active. Do this by redefining \par so\r
+% that it will not start a new paragraph. (But it will appear to the\r
+% user as if it did.) Also, strip any leading pars, newlines, or spaces.\r
+\let\@IEEEBIOORGparCMD=\par% save the original \par command\r
+\edef\par{\hfil\break\indent}% the new \par will not be a "real" \par\r
+\settoheight{\@IEEEtrantmpdimenA}{\@IEEEtempbiographybox}% get height of biography box\r
+\@IEEEtrantmpdimenB=\@IEEEBIOhangdepth%\r
+\@IEEEtrantmpcountA=\@IEEEtrantmpdimenB% countA has the hang depth\r
+\divide\@IEEEtrantmpcountA by \baselineskip% calculates lines needed to produce the hang depth\r
+\advance\@IEEEtrantmpcountA by 1% ensure we overestimate\r
+% set the hanging indent\r
+\hangindent\@IEEEBIOhangwidth%\r
+\hangafter-\@IEEEtrantmpcountA%\r
+% reference the top of the photo area to the top of a capital T\r
+\settoheight{\@IEEEtrantmpdimenB}{\mbox{T}}%\r
+% set the photo box, give it zero width and height so as not to disturb anything\r
+\noindent\makebox[0pt][l]{\hspace{-\@IEEEBIOhangwidth}\raisebox{\@IEEEtrantmpdimenB}[0pt][0pt]{%\r
+\raisebox{-\@IEEEBIOphotodepth}[0pt][0pt]{\@IEEEtempbiographybox}}}%\r
+% now place the author name and begin the bio text\r
+\noindent\textbf{#2\ }\@IEEEgobbleleadPARNLSP}{\relax\let\par=\@IEEEBIOORGparCMD\par%\r
+% 7/2001 V1.5 detect when the biography text is shorter than the photo area\r
+% and pad the unused area - preventing a collision from the next biography entry\r
+% MDS\r
+\ifnum \prevgraf <\@IEEEtrantmpcountA\relax% detect when the biography text is shorter than the photo\r
+ \advance\@IEEEtrantmpcountA by -\prevgraf% calculate how many lines we need to pad\r
+ \advance\@IEEEtrantmpcountA by -1\relax% we compensate for the fact that we indented an extra line\r
+ \@IEEEtrantmpdimenA=\baselineskip% calculate the length of the padding\r
+ \multiply\@IEEEtrantmpdimenA by \@IEEEtrantmpcountA%\r
+ \noindent\rule{0pt}{\@IEEEtrantmpdimenA}% insert an invisible support strut\r
+\fi%\r
+\par\normalfont}\r
+\r
+\r
+\r
+% V1.6\r
+% added biography without a photo environment\r
+\newenvironment{IEEEbiographynophoto}[1]{%\r
+% Make an entry into the table of contents only if we have not done so before\r
+\if@IEEEbiographyTOCentrynotmade%\r
+% link labels to the biography counter so hyperref will jump\r
+% to the biography, not the previous section\r
+\setcounter{IEEEbiography}{-1}%\r
+\refstepcounter{IEEEbiography}%\r
+\addcontentsline{toc}{section}{Biographies}%\r
+\global\@IEEEbiographyTOCentrynotmadefalse%\r
+\fi%\r
+% one more biography\r
+\refstepcounter{IEEEbiography}%\r
+% Make an entry for this name into the table of contents \r
+\addcontentsline{toc}{subsection}{#1}%\r
+\normalfont\@IEEEcompsoconly{\sffamily}\footnotesize\interlinepenalty500%\r
+\vskip 4\baselineskip plus 1fil minus 0\baselineskip%\r
+\parskip=0pt\par%\r
+\noindent\textbf{#1\ }\@IEEEgobbleleadPARNLSP}{\relax\par\normalfont}\r
+\r
+\r
+% provide the user with some old font commands\r
+% got this from article.cls\r
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}\r
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}\r
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}\r
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}\r
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}\r
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}\r
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}\r
+\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}\r
+\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}\r
+\r
+\r
+% SPECIAL PAPER NOTICE COMMANDS\r
+% \r
+% holds the special notice text\r
+\def\@IEEEspecialpapernotice{\relax}\r
+ \r
+% for special papers, like invited papers, the user can do:\r
+% \IEEEspecialpapernotice{(Invited Paper)} before \maketitle\r
+\def\IEEEspecialpapernotice#1{\ifCLASSOPTIONconference%\r
+\def\@IEEEspecialpapernotice{{\sublargesize\textit{#1}\vspace*{1em}}}%\r
+\else%\r
+\def\@IEEEspecialpapernotice{{\\*[1.5ex]\sublargesize\textit{#1}}\vspace*{-2ex}}%\r
+\fi}\r
+\r
+\r
+\r
+\r
+% PUBLISHER ID COMMANDS\r
+% to insert a publisher's ID footer\r
+% V1.6 \IEEEpubid has been changed so that the change in page size and style\r
+% occurs in \maketitle. \IEEEpubid must now be issued prior to \maketitle\r
+% use \IEEEpubidadjcol as before - in the second column of the title page\r
+% These changes allow \maketitle to take the reduced page height into\r
+% consideration when dynamically setting the space between the author \r
+% names and the maintext.\r
+%\r
+% the amount the main text is pulled up to make room for the\r
+% publisher's ID footer\r
+% IEEE uses about 1.3\baselineskip for journals, \r
+% dynamic title spacing will clean up the fraction\r
+\def\@IEEEpubidpullup{1.3\baselineskip}\r
+\ifCLASSOPTIONtechnote\r
+% for technotes it must be an integer of baselineskip as there can be no\r
+% dynamic title spacing for two column mode technotes (the title is in the\r
+% in first column) and we should maintain an integer number of lines in the\r
+% second column\r
+% There are some examples (such as older issues of "Transactions on\r
+% Information Theory") in which IEEE really pulls the text off the ID for\r
+% technotes - about 0.55in (or 4\baselineskip). We'll use 2\baselineskip\r
+% and call it even.\r
+\def\@IEEEpubidpullup{2\baselineskip}\r
+\fi\r
+\r
+% V1.7 compsoc does not use a pullup\r
+\ifCLASSOPTIONcompsoc\r
+\def\@IEEEpubidpullup{0pt}\r
+\fi\r
+\r
+% holds the ID text\r
+\def\@IEEEpubid{\relax}\r
+\r
+% flag so \maketitle can tell if \IEEEpubid was called\r
+\newif\if@IEEEusingpubid\r
+\global\@IEEEusingpubidfalse\r
+% issue this command in the page to have the ID at the bottom\r
+% V1.6 use before \maketitle\r
+\def\IEEEpubid#1{\def\@IEEEpubid{#1}\global\@IEEEusingpubidtrue}\r
+\r
+\r
+% command which will pull up (shorten) the column it is executed in\r
+% to make room for the publisher ID. Place in the second column of\r
+% the title page when using \IEEEpubid\r
+% Is smart enough not to do anything when in single column text or\r
+% if the user hasn't called \IEEEpubid\r
+% currently needed in for the second column of a page with the\r
+% publisher ID. If not needed in future releases, please provide this\r
+% command and define it as \relax for backward compatibility\r
+% v1.6b do not allow command to operate if the peer review option has been \r
+% selected because \IEEEpubidadjcol will not be on the cover page.\r
+% V1.7 do nothing if compsoc\r
+\def\IEEEpubidadjcol{\ifCLASSOPTIONcompsoc\else\ifCLASSOPTIONpeerreview\else\r
+\if@twocolumn\if@IEEEusingpubid\enlargethispage{-\@IEEEpubidpullup}\fi\fi\fi\fi}\r
+\r
+% Special thanks to Peter Wilson, Daniel Luecking, and the other\r
+% gurus at comp.text.tex, for helping me to understand how best to\r
+% implement the IEEEpubid command in LaTeX.\r
+\r
+\r
+\r
+%% Lockout some commands under various conditions\r
+\r
+% general purpose bit bucket\r
+\newsavebox{\@IEEEtranrubishbin}\r
+\r
+% flags to prevent multiple warning messages\r
+\newif\if@IEEEWARNthanks\r
+\newif\if@IEEEWARNIEEEPARstart\r
+\newif\if@IEEEWARNIEEEbiography\r
+\newif\if@IEEEWARNIEEEbiographynophoto\r
+\newif\if@IEEEWARNIEEEpubid\r
+\newif\if@IEEEWARNIEEEpubidadjcol\r
+\newif\if@IEEEWARNIEEEmembership\r
+\newif\if@IEEEWARNIEEEaftertitletext\r
+\@IEEEWARNthankstrue\r
+\@IEEEWARNIEEEPARstarttrue\r
+\@IEEEWARNIEEEbiographytrue\r
+\@IEEEWARNIEEEbiographynophototrue\r
+\@IEEEWARNIEEEpubidtrue\r
+\@IEEEWARNIEEEpubidadjcoltrue\r
+\@IEEEWARNIEEEmembershiptrue\r
+\@IEEEWARNIEEEaftertitletexttrue\r
+\r
+\r
+%% Lockout some commands when in various modes, but allow them to be restored if needed\r
+%%\r
+% save commands which might be locked out\r
+% so that the user can later restore them if needed\r
+\let\@IEEESAVECMDthanks\thanks\r
+\let\@IEEESAVECMDIEEEPARstart\IEEEPARstart\r
+\let\@IEEESAVECMDIEEEbiography\IEEEbiography\r
+\let\@IEEESAVECMDendIEEEbiography\endIEEEbiography\r
+\let\@IEEESAVECMDIEEEbiographynophoto\IEEEbiographynophoto\r
+\let\@IEEESAVECMDendIEEEbiographynophoto\endIEEEbiographynophoto\r
+\let\@IEEESAVECMDIEEEpubid\IEEEpubid\r
+\let\@IEEESAVECMDIEEEpubidadjcol\IEEEpubidadjcol\r
+\let\@IEEESAVECMDIEEEmembership\IEEEmembership\r
+\let\@IEEESAVECMDIEEEaftertitletext\IEEEaftertitletext\r
+\r
+\r
+% disable \IEEEPARstart when in draft mode\r
+% This may have originally been done because the pre-V1.6 drop letter\r
+% algorithm had problems with a non-unity baselinestretch\r
+% At any rate, it seems too formal to have a drop letter in a draft\r
+% paper.\r
+\ifCLASSOPTIONdraftcls\r
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** ATTENTION: \noexpand\IEEEPARstart\r
+ is disabled in draft mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}\r
+\fi\r
+% and for technotes\r
+\ifCLASSOPTIONtechnote\r
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart\r
+ is locked out for technotes (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}\r
+\fi\r
+\r
+\r
+% lockout unneeded commands when in conference mode\r
+\ifCLASSOPTIONconference\r
+% when locked out, \thanks, \IEEEbiography, \IEEEbiographynophoto, \IEEEpubid,\r
+% \IEEEmembership and \IEEEaftertitletext will all swallow their given text. \r
+% \IEEEPARstart will output a normal character instead\r
+% warn the user about these commands only once to prevent the console screen\r
+% from filling up with redundant messages\r
+\def\thanks#1{\if@IEEEWARNthanks\typeout{** WARNING: \noexpand\thanks\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNthanksfalse}\r
+\def\IEEEPARstart#1#2{#1#2\if@IEEEWARNIEEEPARstart\typeout{** WARNING: \noexpand\IEEEPARstart\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEPARstartfalse}\r
+\r
+\r
+% LaTeX treats environments and commands with optional arguments differently.\r
+% the actual ("internal") command is stored as \\commandname \r
+% (accessed via \csname\string\commandname\endcsname )\r
+% the "external" command \commandname is a macro with code to determine\r
+% whether or not the optional argument is presented and to provide the \r
+% default if it is absent. So, in order to save and restore such a command\r
+% we would have to save and restore \\commandname as well. But, if LaTeX\r
+% ever changes the way it names the internal names, the trick would break.\r
+% Instead let us just define a new environment so that the internal\r
+% name can be left undisturbed.\r
+\newenvironment{@IEEEbogusbiography}[2][]{\if@IEEEWARNIEEEbiography\typeout{** WARNING: \noexpand\IEEEbiography\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographyfalse%\r
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}\r
+% and make biography point to our bogus biography\r
+\let\IEEEbiography=\@IEEEbogusbiography\r
+\let\endIEEEbiography=\end@IEEEbogusbiography\r
+\r
+\renewenvironment{IEEEbiographynophoto}[1]{\if@IEEEWARNIEEEbiographynophoto\typeout{** WARNING: \noexpand\IEEEbiographynophoto\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEbiographynophotofalse%\r
+\setbox\@IEEEtranrubishbin\vbox\bgroup}{\egroup\relax}\r
+\r
+\def\IEEEpubid#1{\if@IEEEWARNIEEEpubid\typeout{** WARNING: \noexpand\IEEEpubid \r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidfalse}\r
+\def\IEEEpubidadjcol{\if@IEEEWARNIEEEpubidadjcol\typeout{** WARNING: \noexpand\IEEEpubidadjcol\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEpubidadjcolfalse}\r
+\def\IEEEmembership#1{\if@IEEEWARNIEEEmembership\typeout{** WARNING: \noexpand\IEEEmembership\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEmembershipfalse}\r
+\def\IEEEaftertitletext#1{\if@IEEEWARNIEEEaftertitletext\typeout{** WARNING: \noexpand\IEEEaftertitletext\r
+ is locked out when in conference mode (line \the\inputlineno).}\fi\global\@IEEEWARNIEEEaftertitletextfalse}\r
+\fi\r
+\r
+\r
+% provide a way to restore the commands that are locked out\r
+\def\IEEEoverridecommandlockouts{%\r
+\typeout{** ATTENTION: Overriding command lockouts (line \the\inputlineno).}%\r
+\let\thanks\@IEEESAVECMDthanks%\r
+\let\IEEEPARstart\@IEEESAVECMDIEEEPARstart%\r
+\let\IEEEbiography\@IEEESAVECMDIEEEbiography%\r
+\let\endIEEEbiography\@IEEESAVECMDendIEEEbiography%\r
+\let\IEEEbiographynophoto\@IEEESAVECMDIEEEbiographynophoto%\r
+\let\endIEEEbiographynophoto\@IEEESAVECMDendIEEEbiographynophoto%\r
+\let\IEEEpubid\@IEEESAVECMDIEEEpubid%\r
+\let\IEEEpubidadjcol\@IEEESAVECMDIEEEpubidadjcol%\r
+\let\IEEEmembership\@IEEESAVECMDIEEEmembership%\r
+\let\IEEEaftertitletext\@IEEESAVECMDIEEEaftertitletext}\r
+\r
+\r
+\r
+% need a backslash character for typeout output\r
+{\catcode`\|=0 \catcode`\\=12\r
+|xdef|@IEEEbackslash{\}}\r
+\r
+\r
+% hook to allow easy disabling of all legacy warnings\r
+\def\@IEEElegacywarn#1#2{\typeout{** ATTENTION: \@IEEEbackslash #1 is deprecated (line \the\inputlineno).\r
+Use \@IEEEbackslash #2 instead.}}\r
+\r
+\r
+% provide some legacy IEEEtran commands\r
+\def\authorblockA{\@IEEElegacywarn{authorblockA}{IEEEauthorblockA}\IEEEauthorblockA}\r
+\def\authorblockN{\@IEEElegacywarn{authorblockN}{IEEEauthorblockN}\IEEEauthorblockN}\r
+\def\authorrefmark{\@IEEElegacywarn{authorrefmark}{IEEEauthorrefmark}\IEEEauthorrefmark}\r
+\def\PARstart{\@IEEElegacywarn{PARstart}{IEEEPARstart}\IEEEPARstart}\r
+\def\pubid{\@IEEElegacywarn{pubid}{IEEEpubid}\IEEEpubid}\r
+\def\pubidadjcol{\@IEEElegacywarn{pubidadjcol}{IEEEpubidadjcol}\IEEEpubidadjcol}\r
+\def\specialpapernotice{\@IEEElegacywarn{specialpapernotice}{IEEEspecialpapernotice}\IEEEspecialpapernotice}\r
+\def\IEEEcompsoctitleabstractindextext{\@IEEElegacywarn{IEEEcompsoctitleabstractindextext}{IEEEtitleabstractindextext}\IEEEtitleabstractindextext}\r
+\def\IEEEdisplaynotcompsoctitleabstractindextext{\@IEEElegacywarn{IEEEdisplaynotcompsoctitleabstractindextext}{IEEEdisplaynontitleabstractindextext}\IEEEdisplaynontitleabstractindextext}\r
+% provide some legacy IEEEtran environments\r
+\def\keywords{\@IEEElegacywarn{keywords}{IEEEkeywords}\IEEEkeywords}\r
+\def\endkeywords{\endIEEEkeywords}\r
+\r
+\r
+\r
+% V1.8 no more support for legacy IED list commands\r
+%\let\labelindent\IEEElabelindent\r
+%\def\calcleftmargin{\@IEEElegacywarn{calcleftmargin}{IEEEcalcleftmargin}\IEEEcalcleftmargin}\r
+%\def\setlabelwidth{\@IEEElegacywarn{setlabelwidth}{IEEEsetlabelwidth}\IEEEsetlabelwidth}\r
+%\def\usemathlabelsep{\@IEEElegacywarn{usemathlabelsep}{IEEEusemathlabelsep}\IEEEusemathlabelsep}\r
+%\def\iedlabeljustifyc{\@IEEElegacywarn{iedlabeljustifyc}{IEEEiedlabeljustifyc}\IEEEiedlabeljustifyc}\r
+%\def\iedlabeljustifyl{\@IEEElegacywarn{iedlabeljustifyl}{IEEEiedlabeljustifyl}\IEEEiedlabeljustifyl}\r
+%\def\iedlabeljustifyr{\@IEEElegacywarn{iedlabeljustifyr}{IEEEiedlabeljustifyr}\IEEEiedlabeljustifyr}\r
+% V1.8 no more support for QED and proof stuff\r
+%\def\QED{\@IEEElegacywarn{QED}{IEEEQED}\IEEEQED}\r
+%\def\QEDclosed{\@IEEElegacywarn{QEDclosed}{IEEEQEDclosed}\IEEEQEDclosed}\r
+%\def\QEDopen{\@IEEElegacywarn{QEDopen}{IEEEQEDopen}\IEEEQEDopen}\r
+%\AtBeginDocument{\def\proof{\@IEEElegacywarn{proof}{IEEEproof}\IEEEproof}\def\endproof{\endIEEEproof}}\r
+% V1.8 no longer support biography or biographynophoto\r
+%\def\biography{\@IEEElegacywarn{biography}{IEEEbiography}\IEEEbiography}\r
+%\def\biographynophoto{\@IEEElegacywarn{biographynophoto}{IEEEbiographynophoto}\IEEEbiographynophoto}\r
+%\def\endbiography{\endIEEEbiography}\r
+%\def\endbiographynophoto{\endIEEEbiographynophoto}\r
+% V1.7 and later no longer supports \overrideIEEEmargins\r
+%\def\overrideIEEEmargins{%\r
+%\typeout{** WARNING: \string\overrideIEEEmargins \space no longer supported (line \the\inputlineno).}%\r
+%\typeout{** Use the \string\CLASSINPUTinnersidemargin, \string\CLASSINPUToutersidemargin \space controls instead.}}\r
+\r
+\endinput\r
+\r
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%% End of IEEEtran.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%\r
+% That's all folks!\r
+\r
